{VERSION 5 0 "APPLE_PPC_MAC" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot " -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 107 "This worksheet shows how to use the maple implementation of th e FFT. We examine the effect of zero padding." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name c hangecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "c := x->piecewise(-1<=x and x<= 1, 1-x^2,0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cGf*6#%\"xG6\"6$%)operatorG%&arrow GF(-%*piecewiseG6%31!\"\"9$1F2\"\"\",&F4F4*$)F2\"\"#F4F1\"\"!F(F(F(" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "#By changing the definition of f you can use this worksheet to compute the FFT of other functions." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f := x-> sin(10*Pi*x)*c(x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&a rrowGF(*&-%$sinG6#,$*&%#PiG\"\"\"9$F3\"#5F3-%\"cG6#F4F3F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(f(x),x=-1.2..1.2);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7]\\ l7$$!3%**************>\"!#<$\"\"!F,7$$!3/+++IooZ6F*F+7$$!3*)****\\?%p@ 5\"F*F+7$$!3/+++L.)40\"F*F+7$$!3%******>8;_-\"F*F+7$$!3g******4$>X***! #=$\"3X(ROgWIn)=!#A7$$!3v****\\F=5Q(*F<$\"3ZTr]7$$!3*)*****\\ M%o\"[*F<$\"3')4/JZ]435F<7$$!3C++](Q^AU*F<$\"3lV\"f406))3\"F<7$$!3Y*** ***H%=GO*F<$\"3&)*pfFq\\47\"F<7$$!3?++D^>5L$*F<$\"3=pupfc6;6F<7$$!3\") ****\\saQ.$*F<$\"3#pAEVXJi4\"F<7$$!3U***\\P**oOF*F<$\"3V$zWe<'og5F<7$$ !39+++:D&RC*F<$\"3wb^+gN145F<7$$!3s*******f'3D\"*F<$\"34()pLS)ovS'FE7$ $!3G*****\\o?i+*F<$\"3K8e#>'z,\"p$!#?7$$!3%******\\9j+w)F<$!3!e'Hb:(3? f\"F<7$$!3g+++0c!R^)F<$!3CXcchhr[FF<7$$!3=+++&[h-X)F<$!3mf%yjurW#GF<7$ $!3w*****\\OE(y(yF<$\"3p)>RQRw,U\"F<7$ $!39*****\\f#*4v(F<$\"3E:\">XB.T\"GF<7$$!3)*)*****pD6CwF<$\"3h\"fz>g/I (QF<7$$!3!******\\aKs\\(F<$\"3,4@**3\\)*yVF<7$$!3W+vo>YgkuF<$\"3!RDm$ \\,i+WF<7$$!3')**\\P%pw>V(F<$\"3%**[w^&=uuVF<7$$!3G*\\i!p([$*R(F<$\"35 >UbKF<7$$!3j**\\(=H`4< (F<$\"3v#)G&f[.`[#F<7$$!3e***\\7W(p0rF<$\"33EMs9R%Rh\"F<7$$!3_**\\i!fT //(F<$\"3CTg9N^B!R'FE7$$!3Z******Rd=vpF<$!3'Rf7a1_()*RFE7$$!3>++]i4Bgo F<$!3[/vVx:[]AF<7$$!3\")*****\\=w_u'F<$!3oSSc$o&e5RF<7$$!3V****\\29KIm F<$!3C.3DK/uS^F<7$$!3;+++ImO:lF<$!3C:gSM\\H[dF<7$$!3O**\\(om8I['F<$!3o BTw76!))y&F<7$$!3m***\\Pqg1X'F<$!3:(\\EXi%*)odF<7$$!3)***\\iSxI=kF<$!3 ^b7,K&Hzo&F<7$$!3H++]xZ&fQ'F<$!3kIq&)oU\"fa&F<7$$!3!)***\\7&)[7K'F<$!3 !4ozv>\"3#3&F<7$$!3J*****\\#HaciF<$!3U-C;4Do!R%F<7$$!3#****\\()*p$=>'F <$!3Sk?$*=]C&\\$F<7$$!3W****\\s58FhF<$!3m0\"p$4IvGCF<7$$!3%*)**\\i9DC1 'F<$!3D')Qv8!HCB\"F<7$$!3c******>#>x*fF<$\"3JoNaX=#=C)pF<7$$!3\"4++ +#>s_`F<$\"3k3n&f'=l%Q'F<7$$!35+++Sv\\F_F<$\"3_)[QJ!\\'Hw%F<7$$!3:**** **\\`)[;&F<$\"3=(>Df#[gIOF<7$$!3J******fJF-^F<$\"3Pg+>1$yeL#F<7$$!3Y** ****p4mR]F<$\"3'RQPVH]7F*FE7$$!3h******z([q(\\F<$!3FBQkCcc>aFE7$$!3!** *\\784>?\\F<$!3d]!=!p,Y!)=F<7$$!3=++DYILj[F<$!3dA$)G2lAyJF<7$$!3Y+]Pz^ Z1[F<$!3KEBW&RfCR%F<7$$!3=++]7th\\ZF<$!3NrpqZY\\#[&F<7$$!3?++vy:!fj%F< $!3W6ed5M5YrF<7$$!3w+++Xe=AXF<$!368#4J%*oc$zF<7$$!3[++vQo'pQ%F<$!3(oz# y9qirvF<7$$!3@++]Kyu^UF<$!3I/L(48EX#eF<7$$!32+]PH$QT=%F<$!3H&=/*[SF<$!3l93(H?Z)z 7F<7$$!3n******>)48)RF<$\"3![]I'pD9Q\\FE7$$!3W****\\-d.CRF<$\"3-xy'QZ0 ***>F<7$$!3x*****\\ehn'QF<$\"3J'=[<6.pX$F<7$$!36++]nu[4QF<$\"3)y#yFVf] ;[F<7$$!3*)******\\L@_PF<$\"3)Rl]1RKJ.'F<7$$!3++++:^mPOF<$\"3UU(\\T9Oy (yF<7$$!37+++!)o6BNF<$\"3#*>I9sqnN()F<7$$!3=++D^+()*Q$F<$\"3+j#z\"GjRE $)F<7$$!3D++]AKicKF<$\"3ZQt7\"4)G^kF<7$$!3G+]73)****=$F<$\"3[ue%HqZ)[] F<7$$!3J++v$RwL7$F<$\"3ptgsBj$4T$F<7$$!3M+]PzHvcIF<$\"3e>LInL!yg\"F<7$ $!3O+++l&H,*HF<$!3ir3%)[&*=BGFE7$$!3m+]Pal:JHF<$!3fgm^:]eh>F<7$$!3&4+] Pa$=sGF<$!3%Gp$Rwi+'e$F<7$$!3C,]7L0@8GF<$!3m%fz>b6*)4&F<7$$!3(4++D_PUv #F<$!3[+Yt>$*4ZkF<7$$!3q+](=^k_p#F<$!3hm5C.Es#e(F<7$$!3+,+D,:HOEF<$!3` #QN-\\)*\\Y)F<7$$!3G,]i!\\=td#F<$!3TOPL\\3oh!*F<7$$!3e,++![X$=DF<$!39w _$4#GC]$*F<7$$!3;,+D,+%*)Q#F<$!3'G;vB9e6'))F<7$$!3v++]AX`fAF<$!3aSI`\" *[+3pF<7$$!3a+]7$yJ[>#F<$!3+\"[Wf')R*oaF<7$$!3M++vV!H,8#F<$!3Q0'z&=l#[ z$F<7$$!38+]P/jUl?F<$!30P(4uXF<7$$!3$******\\cB2+#F<$!37\"oF<$\"3C5xzTFuH=F<7$$!3y****\\Z*)\\x=F<$\"3jq'oN ?^=i$F<7$$!3s***\\(Qm)e\"=F<$\"380g<;ql'G&F<7$$!3m******HVFa!)*>`A&*F<7$$!3R*****\\4Dy ]\"F<$\"3gjP[7Npp(*F<7$$!3a**\\P9\"RNW\"F<$\"3^5qvPy)zj*F<7$$!3q***\\P 8`#z8F<$\"3)))\\d\"f:R7\"*F<7$$!3%)**\\7`r'\\J\"F<$\"3]dv=VT*H@)F<7$$! 3******\\s6o]7F<$\"3$R?Zc8T`(pF<7$$!38+](=>&R'=\"F<$\"3wj'f&*4=!\\aF<7 $$!3H++D6#4@7\"F<$\"3u,*z<_Zcp$F<7$$!3W+]iIK#y0\"F<$\"3;F1'4H!Q'y\"F<7 $$!3%f+++]s`$**FE$!3*3bjV$H:5?FE7$$!3y/+v=l-X$*FE$!3h^E*ydF`-#F<7$$!3k .+]P0oa()FE$!3&\\!y(*\\(=Sy$F<7$$!3\\-+DcXLk\")FE$!3@r1eR))=;aF<7$$!3L ,++v&))Rd(FE$!38v_oF:?loF<7$$!3=++v$fUO)pFE$!3w-zg/Zm!3)F<7$$!3/****\\ 7mH$R'FE$!3HQY@&Q'>?!*F<7$$!3)y**\\7j]H!eFE$!3DO/3`O\"4l*F<7$$!3t'**** *\\Yg7_FE$!32f#H*e>f]**F<7$$!3i(*\\7.2A%*[FE$!3FhRge'Q0(**F<7$$!3`)** \\ivOed%FE$!3#)z0b:Wf!*)*F<7$$!3V**\\P4GXdUFE$!3^'oN2U.:r*F<7$$!3K++]i )o!RRFE$!3-JXM`<,N%*F<7$$!37-+vo4I-LFE$!3K[-rkrq,')F<7$$!3#R++]2Lbm#FE $!3UYS$*>kyBuF<7$$!3s0+D\"=l(G?FE$!3\\4Om5>F[fF<7$$!3]2+](G(*>R\"FE$!3 c*=/]Q5UB%F<7$$!3/$4+v$RH_vF]p$!3=3YE?6H]BF<7$$!3+6,++]h%=\"F]p$!3&GiG la82s$FE7$$\"3v%*)\\iS*\\A@F]p$\"3=5;ZC$eIm'FE7$$\"3]+**\\7QhHaF]p$\"3 %*RNFqNX(p\"F<7$$\"3C1*\\(=#Gnt)F]p$\"3yQvflW=5FF<7$$\"3?\"***\\iUQ/7F E$\"3Q'p(\\KD^$p$F<7$$\"3M#**\\P92e'=FE$\"3W*[GSZS(HbF<7$$\"3]$****\\- Is_#FE$\"3:Gm5nNuErF<7$$\"3l%**\\i!Hl)=$FE$\"3Uc:H)GfbT)F<7$$\"3z&*** \\(yv+&QFE$\"3P;E!fU R&e,J#)F<7$$\"3J(******z.gZ(FE$\"3\">zAH3bV3(F<7$$\"36(***\\iVx^!)FE$ \"3jc?ViBC3dF<7$$\"3#p****\\#\\aF')FE$\"3M'z\\)RmA[TF<7$$\"3t'***\\([: L?*FE$\"3))\\-pD+$eX#F<7$$\"3a'*****\\g3z(*FE$\"37f0>N*H$ooFE7$$\"3w** \\7.M4S5F<$!3w?V')=NlU7F<7$$\"3()***\\7?yA5\"F<$!3y%o&pooy>JF<7$$\"3(* **\\P**HYk6F<$!3dhkZ%RTH([F<7$$\"33++](zZmA\"F<$!3UF!o-9YaV'F<7$$\"3<+ ]i&fK))G\"F<$!3%R3LZ1T\"[xF<7$$\"3H++v$R<5N\"F<$!3tz:30bjh()F<7$$\"3S+ ](=>-KT\"F<$!3,iu6s>=Q%*F<7$$\"3]+++!*pQv9F<$!3dsx$=f$4`(*F<7$$\"3a+]i ![3v]\"F<$!30r%*\\iI-q(*F<7$$\"3G++Dr*H'R:F<$!3k*RV&QgQ(o*F<7$$\"3.+]( =Y^F<$!354neA^NXAF<7$$\"3q)*****R3L*)>F<$!3f&*[&ztm&= KFE7$$\"3t)**\\P1!=_?F<$\"3,)['zwTAj:F<7$$\"3u)***\\(GH]6#F<$\"3QA$Q!) )*[uP$F<7$$\"3v)**\\7^yy<#F<$\"31-$)yY**R]]F<7$$\"3x)****\\tF2C#F<$\"3 Z')\\kEH:AHHs(F<7$$\"3\"))***\\#=EkO# F<$\"3ho=N5$o4i)F<7$$\"3#))**\\iSv#HCF<$\"3by%GZkX&y\"*F<7$$\"3%))**** *HY7#\\#F<$\"3Qkutz51w$*F<7$$\"3)))**\\7MWPh#F<$\"3oySuG,IG()F<7$$\"3# *)***\\_SONFF<$\"3Qm*e*GrxNoF<7$$\"3?**\\73R<'z#F<$\"3*)[Ozzf:$F<7$$\"3C**\\i0/;\"=$F<$!3Ug u0]hlV[F<7$$\"3K****\\#Qz'[KF<$!3?2F)F<7$$\"3l*******Gb(=NF<$!3P8f+36jY()F<7$$\"3O***\\P4C%zNF<$ !3it'**z>l([%)F<7$$\"34****\\(*G4SOF<$!3'y@LcPr#[yF<7$$\"3\"))**\\7qh2 q$F<$!3Luh+d0,qpF<7$$\"3`)****\\]I9w$F<$!3fLpV'ok([eF<7$$\"3E)**\\(3$* 4AQF<$!3ikM8o!fy_%F<7$$\"3)z***\\7\"oF)QF<$!3v!p1P\\\"[dIF<7$$\"3q(** \\i\"pVVRF<$!3mc$=HdjF\\\"F<7$$\"3V(*****>d5/SF<$\"3L(e%F<$\"3(yO\"G&px*3[F<7$$\"3.)*****4L@jUF<$\"3s VJ([]E5-'F<7$$\"3M)****\\5nFR%F<$\"3I0lxRPs;wF<7$$\"3k)*******3KAXF<$ \"3S)R45K6`$zF<7$$\"3E)**\\P*erRYF<$\"3Ej**Q))>V.rF<7$$\"3)y***\\()36d ZF<$\"3CfV1jhIZ`F<7$$\"3q(*\\P%Q3e\"[F<$\"3NU\"pi#oh+UF<7$$\"3^(**\\7) e]u[F<$\"3(GY\"GdzZGHF<7$$\"3K(*\\7yL?L\\F<$\"3K&H-\\;ahd\"F<7$$\"37(* ***\\(3!>*\\F<$\"3J%z23Lk,\">FE7$$\"3V(*\\7VF2c]F<$!3[eF0bF<$!3n%fs8dO#opF<7$$\"3u***\\PFPgi&F<$!3#HgzHuZfI'F <7$$\"3w)***\\F()zYdF<$!3Vk6_[l=$y%F<7$$\"3s(*\\Pa%zr!eF<$!3qC)oK+FPx$ F<7$$\"3y(**\\7=gv'eF<$!3S6[L'H<-l#F<7$$\"3&y*\\734%z#fF<$!344))\\'o#y b9F<7$$\"3\"z****\\j@$))fF<$!3kBk&HF$o_BFE7$$\"3Q)***\\#*oV^gF<$\"34HQ Qa:t>5F<7$$\"3&))*****\\@b9hF<$\"3JZHb(zU\\?#F<7$$\"3@)***\\2umxhF<$\" 33<()o-G,vKF<7$$\"3o)****\\m#ySiF<$\"3=Ky1d1F!>%F<7$$\"3\\)*****zJ,njF <$\"3b.yJ'HvYV&F<7$$\"3U*****\\pVK\\'F<$\"3HDN=9eZ#y&F<7$$\"3?)**\\i4d mh'F<$\"3]v$4@iN'[_F<7$$\"34)***\\(\\q+u'F<$\"3CIb/C+ExRF<7$$\"3f)*\\7 )>xMJF<7$$\"3(z**\\()*Q[joF<$\"3]?W!>\"=a*>#F<7$$\"3O( *\\P*f!>DpF<$\"3&HGD(y)f=@\"F<7$$\"3v'******H(*o)pF<$\"3KXU^d&zi5#FE7$ $\"3i(**\\Pp*4;rF<$!3Yw>8*\\L2w\"F<7$$\"3P(***\\(3-`C(F<$!35x!*e![6#4L F<7$$\"3q'*\\P%G.*4tF<$!3$e*4DB7`]QF<7$$\"38(**\\7[/XP(F<$!3c?G&zS4<@% F<7$$\"3N(\\(oz]!oS(F<$!3?s`mAU$=K%F<7$$\"3c(*\\7yc5RuF<$!3hfWxgv\\%Q% F<7$$\"3y(\\ilF19Z(F<$!3aNOqxi***R%F<7$$\"3+)****\\(oq.vF<$!3pv$y1.U\" pVF<7$$\"34***\\i8W\"GwF<$!3L[(RVPyo%QF<7$$\"33****\\(R\"e_xF<$!39A-xf l?)z#F<7$$\"32***\\(e'=q(yF<$!3)=t(=Ol6I9F<7$$\"3<+++?fX,!)F<$\"3T7%** QTNbk\"F]p7$$\"31++]#*4rG\")F<$\"3cu$4$ozmM8F<7$$\"3'******\\1mfD)F<$ \"3ASKS$>eJH#F<7$$\"3O***\\7g$f>$)F<$\"3W`IKm:5(f#F<7$$\"3')****\\P6A$ Q)F<$\"3(*Qrc7^PuFF<7$$\"3O++vt'[oW)F<$\"3[A@)44D_#GF<7$$\"3w******4iZ 5&)F<$\"3d0D1;jobFF<7$$\"3N++]#))yGw)F<$\"3qf.En\"*ft:F<7$$\"3%4++]b\" G:!*F<$!3=,?f4$zf)*)F]p7$$\"3m++DwuCJ\"*F<$!31UA&[#HXgmFE7$$\"3P++](R8 sC*F<$!3soC$G*=_:5F<7$$\"3z+]7ej>0$*F<$!39M+(*Gg)y4\"F<7$$\"33++v=$zJO *F<$!3)GZ_d+>47\"F<7$$\"3R**\\PzA;@%*F<$!3%Q&*G5#e')*3\"F<7$$\"3!)**** **R_9z%*F<$!3n-U.)y.C,\"F<7$$\"3d*****\\Il\\u*F<$!3!HPRH]:mh$FE7$$\"3% ******p`y5+\"F*F+7$$\"3')****\\+Q&[-\"F*F+7$$\"3x*****R1H'[5F*F+7$$\"3 +++]VyK*4\"F*F+7$$\"3#*****\\WI&y9\"F*F+7$$\"3%**************>\"F*F+-% 'COLOURG6&%$RGBG$\"#5!\"\"F+F+-%+AXESLABELSG6$Q\"x6\"Q!Fb`p-%%VIEWG6$; $!#7F]`p$\"#7F]`p%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 134 "#Because of the way maple computes the fft we need to introduce a special type of array, a array of \"hardware floating point\" numbers :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "x1 := hfarray(1..256): y1 := hfarray(1..256):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "#Note \+ that we use ii-1 as the evaluation point." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 108 "for ii from 1 to 256 do x1[ii] := evalf(f(-1+(ii-1 )/128)) od:\nfor iiii from 1 to 256 do y1[iiii] := 0.0 od:\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "#We plot the sequence of samples: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "fl := [seq([jjj,x1[jjj] ],jjj=1..256)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(fl,1..256); " }}{PARA 13 "" 1 "" {GLPLOT2D 348 348 348 {PLOTDATA 2 "6%-%'CURVESG6$ 7\\[l7$$\"\"\"\"\"!$F*F*7$$\"\"#F*$\"39+++x\\t\"y$!#?7$$\"\"$F*$\"3*** ****R41;Y\"!#>7$$\"\"%F*$\"3')*****fwU56$F77$$\"\"&F*$\"3r*****H(o[:^F 77$$\"\"'F*$\"3i+++&yW@@(F77$$\"\"(F*$\"3(******RH)=6\"*F77$$\"\")F*$ \"3%******4GGB0\"!#=7$$\"\"*F*$\"31+++r.w=6FQ7$$\"#5F*$\"3.+++M7!)*3\" FQ7$$\"#6F*$\"3`+++O@>D&*F77$$\"#7F*$\"3m+++xG%G.(F77$$\"#8F*$\"3L+++O uZ'[$F77$$\"#9F*$!3s*****\\;T2Y*F17$$\"#:F*$!3s*****>$Hr-gF77$$\"#;F*$ !3++++RqKM6FQ7$$\"#F*$!3C+++0g:-DFQ7$$\"#?F*$!3r*****>]-^u#FQ7$$\"#@F*$!3#)******pW]DGFQ 7$$\"#AF*$!3%******\\b#*Gs#FQ7$$\"#BF*$!37+++&Ho)GCFQ7$$\"#CF*$!3***** **4Qd%[>FQ7$$\"#DF*$!3))*****zsD0I\"FQ7$$\"#EF*$!3:+++?o#><&F77$$\"#FF *$\"3\"******H!*Hvd$F77$$\"#GF*$\"3(*******yhNr7FQ7$$\"#HF*$\"33+++K2x k@FQ7$$\"#IF*$\"3$******zP+r(HFQ7$$\"#JF*$\"3&)*****z5_&\\OFQ7$$\"#KF* $\"3++++N\">'HTFQ7$$\"#LF*$\"3*************\\P%FQ7$$\"#MF*$\"3<+++5-(p N%FQ7$$\"#NF*$\"3%******4q_H1%FQ7$$\"#OF*$\"3;+++Q;3)\\$FQ7$$\"#PF*$\" 3?+++Eyh&o#FQ7$$\"#QF*$\"31+++w*[hm\"FQ7$$\"#RF*$\"3s******Qf*e&\\F77$ $\"#SF*$!3))*****pmB#zvF77$$\"#TF*$!3,+++kr0=?FQ7$$\"#UF*$!37+++,1,0KF Q7$$\"#VF*$!3\")*****\\a61C%FQ7$$\"#WF*$!3v*****4&**[`]FQ7$$\"#XF*$!3* )*****42jRe&FQ7$$\"#YF*$!3l*****zS2$)y&FQ7$$\"#ZF*$!3M+++$[;@k&FQ7$$\" #[F*$!3A+++Vw\\U^FQ7$$\"#\\F*$!3#)*****p%>$*3VFQ7$$\"#]F*$!3.+++g^q#=$ FQ7$$\"#^F*$!3$******fx4\\#=FQ7$$\"#_F*$!30+++*)*=68$F77$$\"#`F*$\"3&* *****ziLJE\"FQ7$$\"#aF*$\"37+++9ql2GFQ7$$\"#bF*$\"3-+++'e4OA%FQ7$$\"#c F*$\"3W+++M=f>aFQ7$$\"#dF*$\"3#******>u#e:jFQ7$$\"#eF*$\"3W+++%R%G[oFQ 7$$\"#fF*$\"3j*****zvDb(pFQ7$$\"#gF*$\"35+++;IUzmFQ7$$\"#hF*$\"3;+++>! o!ofFQ7$$\"#iF*$\"3$******za1c([FQ7$$\"#jF*$\"3\")*****f\"*o1Y$FQ7$$\" #kF*$\"3!*******=-A.=FQ7$$\"#lF*F+7$$\"#mF*$!3))*****>(e=T=FQ7$$\"#nF* $!34+++'R!)zg$FQ7$$\"#oF*$!3A+++3)*R!>&FQ7$$\"#pF*$!3t*****f_Ox['FQ7$$ \"#qF*$!35+++;V+:uFQ7$$\"#rF*$!3)*******Q9^3zFQ7$$\"#sF*$!3_+++-i>IzFQ 7$$\"#tF*$!3&)*****p:K/Z(FQ7$$\"#uF*$!3q*****fU-\"\\lFQ7$$\"#vF*$!3@++ +$4\\[@&FQ7$$\"#wF*$!3?+++Jt^UNFQ7$$\"#xF*$!3%******>)z#*G;FQ7$$\"#yF* $\"3p*****R71y7%F77$$\"#zF*$\"35+++2v!*fCFQ7$$\"#!)F*$\"3++++nMj(Q%FQ7 $$\"#\")F*$\"3P+++**))pwgFQ7$$\"##)F*$\"3#)*****RER3U(FQ7$$\"#$)F*$\"3 K+++x6^L$)FQ7$$\"#%)F*$\"3z*****zT\"[`()FQ7$$\"#&)F*$\"3r*****>2<*[')F Q7$$\"#')F*$\"3%)******>[q>!)FQ7$$\"#()F*$\"3U+++z\\$y*oFQ7$$\"#))F*$ \"3Y+++x\\!eM&FQ7$$\"#*)F*$\"3>+++N+7`MFQ7$$\"#!*F*$\"34+++$G)3J8FQ7$$ \"#\"*F*$!3t*****\\EUy$*)F77$$\"##*F*$!32+++XIS(3$FQ7$$\"#$*F*$!3]**** *ffPi6&FQ7$$\"#%*F*$!3-+++Dk^boFQ7$$\"#&*F*$!3_*****ziep>)FQ7$$\"#'*F* $!3h*****H4fb0*FQ7$$\"#(*F*$!3*************\\P*FQ7$$\"#)*F*$!3_*****\\ yU88*FQ7$$\"#**F*$!3]+++E)eZL)FQ7$$\"$+\"F*$!3G+++Xo+++W1+>KFQ7$$\"$.\"F*$!3U******4wH(R* F77$$\"$/\"F*$\"3#******4^J8T\"FQ7$$\"$0\"F*$\"3#******4=(H#p$FQ7$$\"$ 1\"F*$\"3#*******\\glkdFQ7$$\"$2\"F*$\"3E+++&R\\<](FQ7$$\"$3\"F*$\"3O+ ++>1d'z)FQ7$$\"$4\"F*$\"3:+++tKSo&*FQ7$$\"$5\"F*$\"3Z+++`I)yw*FQ7$$\"$ 6\"F*$\"3k******pY;!Q*FQ7$$\"$7\"F*$\"3N+++z**)fU)FQ7$$\"$8\"F*$\"3a** ***\\P#egpFQ7$$\"$9\"F*$\"31+++uhUq]FQ7$$\"$:\"F*$\"32+++N.7oGFQ7$$\"$ ;\"F*$\"3n*****\\Tah&[F77$$\"$<\"F*$!37+++6mvL>FQ7$$\"$=\"F*$!3#)***** f!\\(RC%FQ7$$\"$>\"F*$!3.+++]D@0jFQ7$$\"$?\"F*$!3c******efO#*zFQ7$$\"$ @\"F*$!3V+++\"G1F?*FQ7$$\"$A\"F*$!3`*****Hd\"=i)*FQ7$$\"$B\"F*$!3S+++: /)*H**FQ7$$\"$C\"F*$!3b******GQ2,%*FQ7$$\"$D\"F*$!3e*****RIwlI)FQ7$$\" $E\"F*$!3t*****fc+>r'FQ7$$\"$F\"F*$!3!)*****z\\;Gr%FQ7$$\"$G\"F*$!3#** ****f\\`'HCFQ7$$\"$H\"F*F+7$$\"$I\"F*$\"3#******f\\`'HCFQ7$$\"$J\"F*$ \"3!)*****z\\;Gr%FQ7$$\"$K\"F*$\"3t*****fc+>r'FQ7$$\"$L\"F*$\"3e*****R IwlI)FQ7$$\"$M\"F*$\"3b******GQ2,%*FQ7$$\"$N\"F*$\"3S+++:/)*H**FQ7$$\" $O\"F*$\"3`*****Hd\"=i)*FQ7$$\"$P\"F*$\"3V+++\"G1F?*FQ7$$\"$Q\"F*$\"3c ******efO#*zFQ7$$\"$R\"F*$\"3.+++]D@0jFQ7$$\"$S\"F*$\"3#)*****f!\\(RC% FQ7$$\"$T\"F*$\"37+++6mvL>FQ7$$\"$U\"F*$!3n*****\\Tah&[F77$$\"$V\"F*$! 32+++N.7oGFQ7$$\"$W\"F*$!31+++uhUq]FQ7$$\"$X\"F*$!3a*****\\P#egpFQ7$$ \"$Y\"F*$!3N+++z**)fU)FQ7$$\"$Z\"F*$!3k******pY;!Q*FQ7$$\"$[\"F*$!3Z++ +`I)yw*FQ7$$\"$\\\"F*$!3:+++tKSo&*FQ7$$\"$]\"F*$!3O+++>1d'z)FQ7$$\"$^ \"F*$!3E+++&R\\<](FQ7$$\"$_\"F*$!3#*******\\glkdFQ7$$\"$`\"F*$!3#***** *4=(H#p$FQ7$$\"$a\"F*$!3#******4^J8T\"FQ7$$\"$b\"F*$\"3U******4wH(R*F7 7$$\"$c\"F*$\"3>+++W1+>KFQ7$$\"$d\"F*$\"3\")*****RH`)*G&FQ7$$\"$e\"F*$ \"3G+++Xo)FQ7$$\"$k\"F*$\"3-+++Dk^boFQ7$$\"$l\"F*$\"3]***** ffPi6&FQ7$$\"$m\"F*$\"32+++XIS(3$FQ7$$\"$n\"F*$\"3t*****\\EUy$*)F77$$ \"$o\"F*$!34+++$G)3J8FQ7$$\"$p\"F*$!3>+++N+7`MFQ7$$\"$q\"F*$!3Y+++x\\! eM&FQ7$$\"$r\"F*$!3U+++z\\$y*oFQ7$$\"$s\"F*$!3%)******>[q>!)FQ7$$\"$t \"F*$!3r*****>2<*[')FQ7$$\"$u\"F*$!3z*****zT\"[`()FQ7$$\"$v\"F*$!3K+++ x6^L$)FQ7$$\"$w\"F*$!3#)*****RER3U(FQ7$$\"$x\"F*$!3P+++**))pwgFQ7$$\"$ y\"F*$!3++++nMj(Q%FQ7$$\"$z\"F*$!35+++2v!*fCFQ7$$\"$!=F*$!3p*****R71y7 %F77$$\"$\"=F*$\"3%******>)z#*G;FQ7$$\"$#=F*$\"3?+++Jt^UNFQ7$$\"$$=F*$ \"3@+++$4\\[@&FQ7$$\"$%=F*$\"3q*****fU-\"\\lFQ7$$\"$&=F*$\"3&)*****p:K /Z(FQ7$$\"$'=F*$\"3_+++-i>IzFQ7$$\"$(=F*$\"3)*******Q9^3zFQ7$$\"$)=F*$ \"35+++;V+:uFQ7$$\"$*=F*$\"3t*****f_Ox['FQ7$$\"$!>F*$\"3A+++3)*R!>&FQ7 $$\"$\">F*$\"34+++'R!)zg$FQ7$$\"$#>F*$\"3))*****>(e=T=FQ7$$\"$$>F*F+7$ $\"$%>F*$!3!*******=-A.=FQ7$$\"$&>F*$!3\")*****f\"*o1Y$FQ7$$\"$'>F*$!3 $******za1c([FQ7$$\"$(>F*$!3;+++>!o!ofFQ7$$\"$)>F*$!35+++;IUzmFQ7$$\"$ *>F*$!3j*****zvDb(pFQ7$$\"$+#F*$!3W+++%R%G[oFQ7$$\"$,#F*$!3#******>u#e :jFQ7$$\"$-#F*$!3W+++M=f>aFQ7$$\"$.#F*$!3-+++'e4OA%FQ7$$\"$/#F*$!37+++ 9ql2GFQ7$$\"$0#F*$!3&******ziLJE\"FQ7$$\"$1#F*$\"30+++*)*=68$F77$$\"$2 #F*$\"3$******fx4\\#=FQ7$$\"$3#F*$\"3.+++g^q#=$FQ7$$\"$4#F*$\"3#)***** p%>$*3VFQ7$$\"$5#F*$\"3A+++Vw\\U^FQ7$$\"$6#F*$\"3M+++$[;@k&FQ7$$\"$7#F *$\"3l*****zS2$)y&FQ7$$\"$8#F*$\"3*)*****42jRe&FQ7$$\"$9#F*$\"3v*****4 &**[`]FQ7$$\"$:#F*$\"3\")*****\\a61C%FQ7$$\"$;#F*$\"37+++,1,0KFQ7$$\"$ <#F*$\"3,+++kr0=?FQ7$$\"$=#F*$\"3))*****pmB#zvF77$$\"$>#F*$!3s******Qf *e&\\F77$$\"$?#F*$!31+++w*[hm\"FQ7$$\"$@#F*$!3?+++Eyh&o#FQ7$$\"$A#F*$! 3;+++Q;3)\\$FQ7$$\"$B#F*$!3%******4q_H1%FQ7$$\"$C#F*$!3<+++5-(pN%FQ7$$ \"$D#F*$!3*************\\P%FQ7$$\"$E#F*$!3++++N\">'HTFQ7$$\"$F#F*$!3&) *****z5_&\\OFQ7$$\"$G#F*$!3$******zP+r(HFQ7$$\"$H#F*$!33+++K2xk@FQ7$$ \"$I#F*$!3(*******yhNr7FQ7$$\"$J#F*$!3\"******H!*Hvd$F77$$\"$K#F*$\"3: +++?o#><&F77$$\"$L#F*$\"3))*****zsD0I\"FQ7$$\"$M#F*$\"3*******4Qd%[>FQ 7$$\"$N#F*$\"37+++&Ho)GCFQ7$$\"$O#F*$\"3%******\\b#*Gs#FQ7$$\"$P#F*$\" 3#)******pW]DGFQ7$$\"$Q#F*$\"3r*****>]-^u#FQ7$$\"$R#F*$\"3C+++0g:-DFQ7 $$\"$S#F*$\"3&******p\\Xq7#FQ7$$\"$T#F*$\"3,+++=:Gd;FQ7$$\"$U#F*$\"3++ ++RqKM6FQ7$$\"$V#F*$\"3s*****>$Hr-gF77$$\"$W#F*$\"3s*****\\;T2Y*F17$$ \"$X#F*$!3L+++OuZ'[$F77$$\"$Y#F*$!3m+++xG%G.(F77$$\"$Z#F*$!3`+++O@>D&* F77$$\"$[#F*$!3.+++M7!)*3\"FQ7$$\"$\\#F*$!31+++r.w=6FQ7$$\"$]#F*$!3%** ****4GGB0\"FQ7$$\"$^#F*$!3(******RH)=6\"*F77$$\"$_#F*$!3i+++&yW@@(F77$ $\"$`#F*$!3r*****H(o[:^F77$$\"$a#F*$!3')*****fwU56$F77$$\"$b#F*$!3**** ***R41;Y\"F77$$\"$c#F*$!39+++x\\t\"y$F1-%'COLOURG6&%$RGBG$FY!\"\"F+F+- %+AXESLABELSG6$Q!6\"Fg[p-%%VIEWG6$;F(Fjjo%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 255 "#We evaluate the FFT. var(x1) are the real parts \+ of the sampled data and var(y1) the imaginary parts. Maple returns the result of doing the FFT in these same vectors. The first argument to \+ FFT is which power of 2 equals the length of the sample sequence." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "evalhf(FFT(8,var(x1),var(y1 )));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$c#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "#We plot the real and imaginary parts of the F FT. Note the ordering of the frequencies in the output [k_min,....k_ma x, -k_max,....1-k_min]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 " xl :=[seq([(k-256)*Pi,x1[k+1]/128], k=128..255),seq([(k-1)*Pi,x1[k]/12 8], k=1..128)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "yl :=[seq([(k-25 6)*Pi,-y1[k+1]/128], k=128..255),seq([(k-1)*Pi,-y1[k]/128], k=1..128)] :\n" }{TEXT -1 28 "#This is the imaginary part:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "p1 := plot(yl, -50..50,color=blue): display(p1);" }} {PARA 0 "" 0 "" {TEXT -1 425 "#This is the real part. Because the samp le sequence is odd, it should be zero, these very small values are the result of roundoff errors. When testing an implementation of the FFT \+ algorithm it is useful to try it out on sequences with symmetries that should be reflected in symmetries of the transformed sequence. We hav e also graphed the imaginary part. Notice how small the entries are by observing the scale on the y-axis." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot([xl],-50..50); " }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7\\[l7$$!3>N\\f'fQ7-%!#:$\"\"!F,7$$!3OP!f+n A)*)RF*$\"3&******p:pg(=!#C7$$!3`RJ_VnSeRF*$\"30+++^()paPF27$$!39Ts)p \"3*p#RF*$\"3e*****p&egPcF27$$!3KV8X!*[d&*QF*$\"3U+++-`oFvF27$$!3\\Xa \"R'*eT'QF*$\"3`+++v33F%*F27$$!3nZ&zt.VF$QF*$\"33+++;F#Q8\"!#B7$$!3&) \\O%36F8!QF*$\"3'******\\];jK\"FL7$$!3X^xI%=6*pPF*$\"3/+++I7\\?:FL7$$! 3i`=xd_\\QPF*$\"3-+++o5c;FL7$$!3)z 0+ZSjcn$F*$\"3&)*****fTGa6#FL7$$!3;gT;yuCWOF*$\"3#)*****4!)[(=BFL7$$!3 Li#G;bJGh$F*$\"3!)*****fxI]_#FL7$$!3$RO#4DcT\"e$F*$\"3%)******HeaMFFL7 $$!36mkb)p***\\NF*$\"3$******\\#GgZHFL7$$!3Ho0-sPe=NF*$\"3!******\\9oW ;$FL7$$!3YqY[Xy;([$F*$\"3<+++Ds[&Q$FL7$$!3ks([*=>vbMF*$\"3-+++bR*4h$FL 7$$!3CuGT#*fLCMF*$\"3?+++nUDTQFL7$$!3Uwp(e1?HR$F*$\"3j******yVowSFL7$$ !3fy5MRT]hLF*$\"3g*****R$RjL/%eB$F*$\"3#******p0YXM&FL7$$!3\"*)ehm]CW?$F*$\"3Q+++q%y\">cFL 7$$!33\"pD,e3I<$F*$\"3k*****>iW>!fFL7$$!3E$z*e`EfTJF*$\"3o*****zuEL>'F L7$$!3V&*Q0Fn<5JF*$\"3/+++K>(Q\\'FL7$$!3.(*z^+3wyIF*$\"3\")*****psZT!o FL7$$!3@*4#)R([MZIF*$\"3/+++,nxCrFL7$$!3R,iWZ*Gf,$F*$\"3P+++)ezjX(FL7$ $!3c..\"4-8X)HF*$\"3g+++I1m*z(FL7$$!3u0WP%4(4`HF*$\"3X+++19Kb\")FL7$$! 3N2&Qy;\"o@HF*$\"3!)*****p(f8C&)FL7$$!3_4EIT_E!*GF*$\"3T*****4r>p!*)FL 7$$!3q6nw9$\\)eGF*$\"3l+++3&[XI*FL7$$!3)Q\"3B)QLu#GF*$\"3^*****>Jezr*F L7$$!3/;\\phu,'z#F*$\"3)******z85[,\"!#A7$$!3lJi3c=LFF*$\"30+++2,I16F\\x7$$!3,As3#op_2EF*$\"3++++Q&pXJ\"F\\x7$$!39IO%f(f5wDF*$\"3 (******H#Qts8F\\x7$$!3KKxS\\+pWDF*$\"3#******>bqOV\"F\\x7$$!3\\M=(G7uK ^#F*$\"3%******zkev\\\"F\\x7$$!3mOfL'>e=[#F*$\"3')*****p_,Yc\"F\\x7$$! 3cQ+!)pAW]CF*$\"3')******G8-N;F\\x7$$!3tSTEVj->CF*$\"3.+++:?/4!\\%>cBF*$\"3!******p#z% *o=F\\x7$$!3)pWcOcyZK#F*$\"3&)*****>!zSb>F\\x7$$!3')[07PEO$H#F*$\"3*** ****H*>iY?F\\x7$$!3/^Ye5n%>E#F*$\"3%)*****p'4&H9#F\\x7$$!3A`([SyI0B#F* $\"3%)*****zbzZC#F\\x7$$!35bG^d[6*>#F*$\"37+++Q#>DN#F\\x7$$!3Gdp(4$*)p n@F*$\"3*)*****\\%3kmCF\\x7$$!3Yf5W/IGO@F*$\"3()*****>?Lwe#F\\x7$$!3Nh ^!z2n[5#F*$\"3$******H>^gr#F\\x7$$!3_j#p8:^M2#F*$\"3&******z=&\\_GF\\x 7$$!3UlL$[AN?/#F*$\"3/+++_Ri(*HF\\x7$$!3fnuH)H>1,#F*$\"3#)*****fYo@:$F \\x7$$!3wp:wrL?z>F*$\"3s******H\"GpJ$F\\x7$$!3mrcAXuyZ>F*$\"35+++\"*>z #\\$F\\x7$$!3%Qx*o=:P;>F*$\"3G+++`7t!o$F\\x7$$!3svQ:#fb\\)=F*$\"3')*** **pLR=)QF\\x7$$!3!z(zhl'RN&=F*$\"3m*****HU;t4%F\\x7$$!33!3#3RP7A=F*$\" 3)******z$G]GVF\\x7$$!3'>=YD\"yq!z\"F*$\"3\")*****p#4*od%F\\x7$$!39%G5 g)=Hf8F*$\"3++++xe(QA\"F^fl7$$!31: =(z)H0)G\"F*$\"3.+++![(3C8F^fl7$$!3C+!\\8@_A\"F*$\"3&******p_x.c\"F^fl7$$!3I@TO3_!Q>\"F*$\"34+++a(z, q\"F^fl7$$!3[B#G=G*Qi6F*$\"3!******f,7v&=F^fl7$$!3_DBHbL(48\"F*$\"37++ +7(z_.#F^fl7$$!3aFkvGub*4\"F*$\"3*******>o+qB#F^fl7$$!3tH0A-:9o5F*$\"3 !******\\rhpY#F^fl7$$!3wJYovbsO5F*$\"3%)*****z#yUIFF^fl7$$!3!Qt[\"\\'4 `+\"F*$\"35+++P$=R.$F^fl7$$!3Ie$GhAP*Q(*!#;$\"37+++l&ybQ$F^fl7$$!3ky$p 2'zxC%*F^jl$\"3-+++n^o&z$F^fl7$$!3R+/T&p=16*F^jl$\"3?+++tbMxUF^fl7$$!3 s?90I%fkz)F^jl$\"3;+++6AZZ[F^fl7$$!31TCpk,I#[)F^jl$\"3#******>g!=GbF^f l7$$!3\"GYL$**39o\")F^jl$\"3_*****\\o5)[jF^fl7$$!3:$[uRj\")R&yF^jl$\"3 ^+++z5$*[tF^fl7$$!3[.bhoB#)RvF^jl$\"3:+++]d*Ge)F^fl7$$!3\"Q_cK5jcA(F^j l$\"3/+++bbp75!#?7$$!39Wv*y$Q]6pF^jl$\"3\"********Ro!47Fi\\m7$$!3!fcQD dWtf'F^jl$\"3/+++&***fj9Fi\\m7$$!3B'ezrI&=$G'F^jl$\"3/+++\"R95!=Fi\\m7 $$!3d11#=/E!pfF^jl$\"3$)******pacgAFi\\m7$$!3hF;Ywn'[l&F^jl$\"3\"***** *fV*e2HFi\\m7$$!3m[E56vqS`F^jl$\"35+++jJPdQFi\\m7$$!3)*oOuX#[l-&F^jl$ \"37+++]$))*G`Fi\\m7$$!3K*o%Q!)*)Q7ZF^jl$\"3++++m,G\"y(Fi\\m7$$!3O5d-: (H#)R%F^jl$\"3&******pU;8B\"!#>7$$!3TJnm\\/2%3%F^jl$\"35+++M!fK@#Fg_m7 $$!3u^xI%=6*pPF^jl$\"3!******\\/wT-&Fg_m7$$!32s([*=>vbMF^jl$\"3%****** \\CF=-#!#=7$$!37$z*e`EfTJF^jl$!3a+++jRtrmFg`m7$$!3!Q\"3B)QLu#GF^jl$\"3 3+++)>43-#Fg`m7$$FgzF^jl$\"3r******f`].]Fg_m7$$!3=bG^d[6*>#F^jl$\"3*)* ****Hva9=#Fg_m7$$!3(e(Q:#fb\\)=F^jl$\"3.+++?-N(=\"Fg_m7$$!3c'*[zEjzq:F ^jl$\"3q*****4I+]?(Fi\\m7$$!3Ds:]f%Fi\\m7$$!3Mz $p2'zxC%*!#<$\"3!******>Iak$HFi\\m7$$Ff]mF]cm$\"3/+++*oB!fIak$HFi\\m7$$\"3Ds:]f%Fi\\m7$$\"3c'*[zEjz q:F^jl$!3q*****4I+]?(Fi\\m7$$\"3(e(Q:#fb\\)=F^jl$!3.+++?-N(=\"Fg_m7$$ \"3=bG^d[6*>#F^jl$!3*)*****Hva9=#Fg_m7$$\"3\\M=(G7uK^#F^jl$!3r******f` ].]Fg_m7$$\"3!Q\"3B)QLu#GF^jl$!33+++)>43-#Fg`m7$$F[dmF^jl$\"3a+++jRtrm Fg`m7$$\"32s([*=>vbMF^jl$!3%******\\CF=-#Fg`m7$$\"3u^xI%=6*pPF^jl$!3!* *****\\/wT-&Fg_m7$$\"3TJnm\\/2%3%F^jl$!35+++M!fK@#Fg_m7$$\"3O5d-:(H#)R %F^jl$!3&******pU;8B\"Fg_m7$$\"3K*o%Q!)*)Q7ZF^jl$!3++++m,G\"y(Fi\\m7$$ \"3)*oOuX#[l-&F^jl$!37+++]$))*G`Fi\\m7$$\"3m[E56vqS`F^jl$!35+++jJPdQFi \\m7$$\"3hF;Ywn'[l&F^jl$!3\"******fV*e2HFi\\m7$$\"3d11#=/E!pfF^jl$!3$) ******pacgAFi\\m7$$F`dmF^jl$!3/+++\"R95!=Fi\\m7$$\"3!fcQDdWtf'F^jl$!3/ +++&***fj9Fi\\m7$$\"39Wv*y$Q]6pF^jl$!3\"********Ro!47Fi\\m7$$\"3\"Q_cK 5jcA(F^jl$!3/+++bbp75Fi\\m7$$\"3[.bhoB#)RvF^jl$!3:+++]d*Ge)F^fl7$$\"3: $[uRj\")R&yF^jl$!3^+++z5$*[tF^fl7$$\"3\"GYL$**39o\")F^jl$!3_*****\\o5) [jF^fl7$$\"31TCpk,I#[)F^jl$!3#******>g!=GbF^fl7$$\"3s?90I%fkz)F^jl$!3; +++6AZZ[F^fl7$$\"3R+/T&p=16*F^jl$!3?+++tbMxUF^fl7$$\"3ky$p2'zxC%*F^jl$ !3-+++n^o&z$F^fl7$$\"3Ie$GhAP*Q(*F^jl$!37+++l&ybQ$F^fl7$$\"3!Qt[\"\\'4 `+\"F*$!35+++P$=R.$F^fl7$$\"3wJYovbsO5F*$!3%)*****z#yUIFF^fl7$$\"3tH0A -:9o5F*$!3!******\\rhpY#F^fl7$$\"3aFkvGub*4\"F*$!3*******>o+qB#F^fl7$$ \"3_DBHbL(48\"F*$!37+++7(z_.#F^fl7$$\"3[B#G=G*Qi6F*$!3!******f,7v&=F^f l7$$\"3I@TO3_!Q>\"F*$!34+++a(z,q\"F^fl7$$\"3G>+!\\8@_A\"F*$!3&******p_ x.c\"F^fl7$$\"3C8F*$!3++++xe(QA\"F^fl7$$\"3+6O/T[)3N\"F* $!3/+++tAhL6F^fl7$$\"3#)3&zvw+BQ\"F*$!3$*******pL2_5F^fl7$$\"3%pS:Tp;P T\"F*$!30+++LJ8#y*F\\x7$$\"3w/8l?E8X9F*$!3[+++6_N6\"*F\\x7$$\"3(G?(=Z& [lZ\"F*$!3g******)yj1])F\\x7$$\"3q+JstW'z]\"F*$!3o+++nGQVzF\\x7$$\"3_) **e-S!QR:F*$!3E+++0*3PV(F\\x7$$\"3i'*[zEjzq:F*$!3e*****H#*)empF\\x7$$ \"3X%zILD7Ag\"F*$!3!*******)4,w`'F\\x7$$\"3c#pm)z\"GOj\"F*$!3^+++_b(G9 'F\\x7$$\"3Q!f-k5W]m\"F*$!3')*****zH/!zdF\\x7$$\"3?)[QH.gkp\"F*$!3%)** ****p!yHW&F\\x7$$\"3K'Qu%ff(ys\"F*$!3'******H#)[@8&F\\x7$$\"39%G5g)=Hf =YD\"yq!z\"F*$!3\")*****p#4*od%F\\x7$$\"33! 3#3RP7A=F*$!3)******z$G]GVF\\x7$$\"3!z(zhl'RN&=F*$!3m*****HU;t4%F\\x7$ $\"3svQ:#fb\\)=F*$!3')*****pLR=)QF\\x7$$\"3%Qx*o=:P;>F*$!3G+++`7t!o$F \\x7$$\"3mrcAXuyZ>F*$!35+++\"*>z#\\$F\\x7$$\"3wp:wrL?z>F*$!3s******H\" GpJ$F\\x7$$\"3fnuH)H>1,#F*$!3#)*****fYo@:$F\\x7$$\"3UlL$[AN?/#F*$!3/++ +_Ri(*HF\\x7$$\"3_j#p8:^M2#F*$!3&******z=&\\_GF\\x7$$\"3Nh^!z2n[5#F*$! 3$******H>^gr#F\\x7$$\"3Yf5W/IGO@F*$!3()*****>?Lwe#F\\x7$$\"3Gdp(4$*)p n@F*$!3*)*****\\%3kmCF\\x7$$\"35bG^d[6*>#F*$!37+++Q#>DN#F\\x7$$\"3A`([ SyI0B#F*$!3%)*****zbzZC#F\\x7$$\"3/^Ye5n%>E#F*$!3%)*****p'4&H9#F\\x7$$ \"3')[07PEO$H#F*$!3*******H*>iY?F\\x7$$\"3)pWcOcyZK#F*$!3&)*****>!zSb> F\\x7$$\"3![M#>!\\%>cBF*$!3!******p#z%*o=F\\x7$$\"3iU#GnT5wQ#F*$!3')** ***fHFpy\"F\\x7$$\"3tSTEVj->CF*$!3.+++:?/4e=[#F*$!3')*****p_,Yc\"F\\x7$$F^fmF*$!3%*** ***zkev\\\"F\\x7$$\"3KKxS\\+pWDF*$!3#******>bqOV\"F\\x7$$\"39IO%f(f5wD F*$!3(******H#Qts8F\\x7$$\"3aG&zC!>_2EF*$!3++++Q&pXJ\"F\\x7$$\"3OEa,Hy $*QEF*$!3%*******zp**e7F\\x7$$\"3=C8bbPNqEF*$!3(******49he?\"F\\x7$$\" 3,As3#opJi3c=LFF*$!30+++2,I16F\\x7$$\"3l Jezr*FL7$$\"3q6nw9$\\)eGF*$!3l+++3&[XI* FL7$$\"3_4EIT_E!*GF*$!3T*****4r>p!*)FL7$$\"3N2&Qy;\"o@HF*$!3!)*****p(f 8C&)FL7$$\"3u0WP%4(4`HF*$!3X+++19Kb\")FL7$$\"3c..\"4-8X)HF*$!3g+++I1m* z(FL7$$\"3R,iWZ*Gf,$F*$!3P+++)ezjX(FL7$$\"3@*4#)R([MZIF*$!3/+++,nxCrFL 7$$\"3.(*z^+3wyIF*$!3\")*****psZT!oFL7$$\"3V&*Q0Fn<5JF*$!3/+++K>(Q\\'F L7$$\"3E$z*e`EfTJF*$!3o*****zuEL>'FL7$$\"33\"pD,e3I<$F*$!3k*****>iW>!f FL7$$\"3\"*)ehm]CW?$F*$!3Q+++q%y\">cFL7$$\"3t'[(>L/%eB$F*$!3#******p0Y XM&FL7$$\"37&QL(fjDnKF*$!30+++$p6v2&FL7$$\"3%HGpiGs')H$F*$!3')******Q% Rw\"[FL7$$\"3x!=0G@)3ILF*$!3p*****Hu*\\kXFL7$$\"3fy5MRT]hLF*$!3g*****R $RjvbMF*$!3-+++bR*4h$FL7$$\"3YqY[Xy;([$F*$!3<+++Ds[&Q$FL 7$$\"3Ho0-sPe=NF*$!3!******\\9oW;$FL7$$\"36mkb)p***\\NF*$!3$******\\#G gZHFL7$$\"3$RO#4DcT\"e$F*$!3%)******HeaMFFL7$$\"3Li#G;bJGh$F*$!3!)**** *fxI]_#FL7$$\"3;gT;yuCWOF*$!3#)*****4!)[(=BFL7$$\"3)z0+ZSjcn$F*$!3&)** ***fTGa6#FL7$$\"3!e&fBJ$zqq$F*$!33+++J9![\">FL7$$\"3i`=xd_\\QPF*$!3-++ +o5c;N\\f'fQ7-% !#:$\"\"!F,7$$!3OP!f+nA)*)RF*$\"3=+++,EP)G'!#N7$$!3`RJ_VnSeRF*$\"3#*** ****yycO9F27$$!39Ts)p\"3*p#RF*$\"3D*****\\deb,(F27$$!3KV8X!*[d&*QF*$\" 3/+++^OZ!R\"!#O7$$!3\\Xa\"R'*eT'QF*$\"3-+++&R:./\"!#M7$$!3nZ&zt.VF$QF* $\"3m*****>6D>I'FB7$$!3&)\\O%36F8!QF*$\"37+++mbDamF27$$!3X^xI%=6*pPF*$ !3!)*****pzA*>MFB7$$!3i`=xd_\\QPF*$\"3J+++qS!eL)F27$$!3!e&fBJ$zqq$F*$! 3-+++7q?;5FH7$$!3)z0+ZSjcn$F*$\"3o******)y$Q(*))F27$$!3;gT;yuCWOF*$\"3 ,+++my%4_\"F27$$!3Li#G;bJGh$F*$\"3K+++p/CH$)F27$$!3$RO#4DcT\"e$F*$!3/+ ++=&f&**HF27$$!36mkb)p***\\NF*$\"3&******RmL'=)*F27$$!3Ho0-sPe=NF*$\"3 X+++?B@#=*!#P7$$!3YqY[Xy;([$F*$\"3O+++iBm?NF27$$!3ks([*=>vbMF*$!3S+++& >B>6)F27$$!3CuGT#*fLCMF*$\"3%*******Hw(z9#F27$$!3Uwp(e1?HR$F*$\"34+++c 5X-FF27$$!3fy5MRT]hLF*$\"3u+++Rvit')F27$$!3x!=0G@)3ILF*$!3/+++\"*R3&H \"FH7$$!3%HGpiGs')H$F*$\"3(******H7<;l'F27$$!37&QL(fjDnKF*$\"3/+++O#HL \">F27$$!3t'[(>L/%eB$F*$\"3'******>f`N.$F27$$!3\"*)ehm]CW?$F*$!3#***** *4q\\Ji#F27$$!33\"pD,e3I<$F*$!3++++4A:=KF27$$!3E$z*e`EfTJF*$!3y*****Rl 9KZ'FB7$$!3V&*Q0Fn<5JF*$\"3)******Rt(*H9\"FH7$$!3.(*z^+3wyIF*$!3%***** *\\?o#)R\"FH7$$!3@*4#)R([MZIF*$\"3@+++ngr[cF27$$!3R,iWZ*Gf,$F*$!3K+++y 6Q]d!#Q7$$!3c..\"4-8X)HF*$\"33+++)oTu>\"FH7$$!3u0WP%4(4`HF*$!3p******= )*p_lF27$$!3N2&Qy;\"o@HF*$\"3;+++B6PsBF27$$!3_4EIT_E!*GF*$\"3(******>M A[%>F27$$!3q6nw9$\\)eGF*$\"3.+++c6,=))F27$$!3)Q\"3B)QLu#GF*$!36+++/$R6 u\"FH7$$!3/;\\phu,'z#F*$\"3g+++4Jkl')F27$$!3lJi3c=LFF*$\"3^+++B!p?+)F27$$!3,As3#op'H$F2 7$$!3=C8bbPNqEF*$\"3))*****>inlm&F27$$!3OEa,Hy$*QEF*$\"3$******H#)Q,: \"FB7$$!3aG&zC!>_2EF*$\"31+++;k(R>\"FH7$$!39IO%f(f5wDF*$!3!******R=A#y HFH7$$!3KKxS\\+pWDF*$\"3L*****>&3sH$*F27$$!3\\M=(G7uK^#F*$!34+++3yKoLF B7$$!3mOfL'>e=[#F*$\"3v*****p]c5c'F27$$!3cQ+!)pAW]CF*$\"39+++DYR!o\"FH 7$$!3tSTEVj->CF*$\"3g*****pkFih(F27$$!3iU#GnT5wQ#F*$\"34+++E%*e*G\"F27 $$!3![M#>!\\%>cBF*$\"3$******\\PDh%yF27$$!3)pWcOcyZK#F*$\"3*)*****>!*[ ]l\"FH7$$!3')[07PEO$H#F*$\"3^+++*y>`J*F27$$!3/^Ye5n%>E#F*$!3')*****4pR NF#F27$$!3A`([SyI0B#F*$\"3/+++Xu(4H\"FH7$$!35bG^d[6*>#F*$!3t*****>qnO# GFH7$$!3Gdp(4$*)pn@F*$\"3]******Q+0>!*F27$$!3Yf5W/IGO@F*$\"3&******RV; I+\"FB7$$!3Nh^!z2n[5#F*$\"3,+++0A%=\"=FH7$$!3_j#p8:^M2#F*$!3$******>%* >t_#FH7$$!3UlL$[AN?/#F*$\"3()*****R)QdU=FH7$$!3fnuH)H>1,#F*$\"3%****** 4^Y,$>F[v7$$!3wp:wrL?z>F*$\"3-+++GGvf(*F27$$!3mrcAXuyZ>F*$\"3@+++xdfSS F27$$!3%Qx*o=:P;>F*$\"3%******>'*)eI8FH7$$!3svQ:#fb\\)=F*$\"3)******pn q?W\"F27$$!3!z(zhl'RN&=F*$\"3&)*****\\'*e:M#FH7$$!33!3#3RP7A=F*$!3%)** ****Hm%49&FH7$$!3'>=YD\"yq!z\"F*$\"3')*****f)yN+CFH7$$!39%G5g)=HfGGF27$$!3c#pm)z\"G Oj\"F*$!3#******\\C!o(>$FB7$$!3X%zILD7Ag\"F*$\"3C+++YqJ)3$FH7$$!3i'*[z Ejzq:F*$!3=+++.aC$p$FH7$$!3_)**e-S!QR:F*$\"3%)******z-\\)=$FH7$$!3q+Js tW'z]\"F*$!37+++C=eZGFB7$$!3(G?(=Z&[lZ\"F*$\"3&)*****H5Bwq\"FH7$$!3w/8 l?E8X9F*$!39+++pd+9VF27$$!3%pS:Tp;PT\"F*$\"30+++&>\"Ge?FH7$$!3#)3&zvw+ BQ\"F*$\"3#******\\.\"ySWF27$$!3+6O/T[)3N\"F*$\"3%******R3$3J]FH7$$!3= 8x]9*o%>8F*$!3&******z/*yXoFH7$$!31:=(z)H0)G\"F*$\"3*)******H&e6W$FH7$ $!3CF27$$!3G>+!\\8@_A\"F*$\"3#******>]NN(> FH7$$!3I@TO3_!Q>\"F*$\"3.+++4.!>B#FH7$$!3[B#G=G*Qi6F*$\"3.+++iRrt;FH7$ $!3_DBHbL(48\"F*$\"3!******f73\"y@F27$$!3aFkvGub*4\"F*$\"3Z+++RcVYeFH7 $$!3tH0A-:9o5F*$!3g+++d<`lwFH7$$!3wJYovbsO5F*$\"3'*********fi6dFH7$$!3 !Qt[\"\\'4`+\"F*$\"3m*****R:Zx%pFjp7$$!3Ie$GhAP*Q(*!#;$\"3))******f*R \"=VFH7$$!3ky$p2'zxC%*F_jl$\"3S+++bqIb!)F27$$!3R+/T&p=16*F_jl$\"3w**** *z)yq$3%FH7$$!3s?90I%fkz)F_jl$\"3++++x76ohF27$$!31TCpk,I#[)F_jl$\"3n** ****pqWE!*FH7$$!3\"GYL$**39o\")F_jl$!3)******Hi.D/\"!#L7$$!3:$[uRj\")R &yF_jl$\"3Z*****R%=A3$*FH7$$!3[.bhoB#)RvF_jl$\"3*)*****ff71I#F27$$!3\" Q_cK5jcA(F_jl$\"3')*****fo(e-qFH7$$!39Wv*y$Q]6pF_jl$\"35+++.6[ZTFH7$$! 3!fcQDdWtf'F_jl$\"3!)******p]v!*))FH7$$!3B'ezrI&=$G'F_jl$\"3'******f0R LB\"FH7$$!3d11#=/E!pfF_jl$\"3\"******f/lg/#F[\\m7$$!3hF;Ywn'[l&F_jl$!3 1+++kl0,DF[\\m7$$!3m[E56vqS`F_jl$\"3))*****>?#[gBF[\\m7$$!3)*oOuX#[l-& F_jl$\"3N+++f1zK`FB7$$!3K*o%Q!)*)Q7ZF_jl$\"3!)*****fQ&3WEF[\\m7$$!3O5d -:(H#)R%F_jl$\"3i+++4\"3#H()FH7$$!3TJnm\\/2%3%F_jl$\"3)******>(pFFVF[ \\m7$$!3u^xI%=6*pPF_jl$!3,+++r9*Q:\"FH7$$!32s([*=>vbMF_jl$\"32+++FTB\" [#F[\\m7$$!37$z*e`EfTJF_jl$\"3S******>_CruFH7$$!3!Q\"3B)QLu#GF_jl$!3#) *****\\df-?%F[\\m7$$FizF_jl$\"3++++M.99AF27$$!3=bG^d[6*>#F_jl$!3F+++@= <>jF[\\m7$$!3(e(Q:#fb\\)=F_jl$!3<+++,%F[\\m7$$!3Dvf3JFH7$$\"3c'*[zEjzq:F_jl$!3>+++TlmE\\F[\\m7$$\"3 (e(Q:#fb\\)=F_jl$!3r*****4qFkS$FH7$$\"3=bG^d[6*>#F_jl$!3q*****H>4e>'F[ \\m7$$\"3\\M=(G7uK^#F_jl$!3x*****>#zC[\")F27$$\"3!Q\"3B)QLu#GF_jl$!3P+ ++SON[XF[\\m7$$FjcmF_jl$\"3(******HwN9O%FH7$$\"32s([*=>vbMF_jl$\"3%)** ***Hr$oAAF[\\m7$$\"3u^xI%=6*pPF_jl$\"3$******>V2TI\"F27$$\"3TJnm\\/2%3 %F_jl$\"3%******4i\"\\$G%F[\\m7$$\"3O5d-:(H#)R%F_jl$\"3/+++bSY\"z\"F[ \\m7$$\"3K*o%Q!)*)Q7ZF_jl$\"34+++$z\"RA@F[\\m7$$\"3)*oOuX#[l-&F_jl$\"3 ?+++&4K#RjFB7$$\"3m[E56vqS`F_jl$\"3,+++lhX-=F[\\m7$$\"3hF;Ywn'[l&F_jl$ \"30++++0v`**FB7$$\"3d11#=/E!pfF_jl$\"3$******fHa\"z7F[\\m7$$F_dmF_jl$ \"32+++R:b%[\"FH7$$\"3!fcQDdWtf'F_jl$\"3S+++Qa.%>*FH7$$\"39Wv*y$Q]6pF_ jl$\"33+++8*4Qk&FH7$$\"3\"Q_cK5jcA(F_jl$\"3]*****\\$oF;iFH7$$\"3[.bhoB #)RvF_jl$\"3L+++7F0[OF27$$\"3:$[uRj\")R&yF_jl$\"3*)*****pZoo%))FH7$$\" 3\"GYL$**39o\")F_jl$!3;+++0(3Y7$FH7$$\"31TCpk,I#[)F_jl$\"3Q+++I5b!z'FH 7$$\"3s?90I%fkz)F_jl$\"33+++qS:T5FH7$$\"3R+/T&p=16*F_jl$\"3@+++mN\"Gb% FH7$$\"3ky$p2'zxC%*F_jl$\"3#******z;jix%FH7$$\"3Ie$GhAP*Q(*F_jl$\"3q** ***Rn1W%GFH7$$\"3!Qt[\"\\'4`+\"F*$!3w******z*[g*fFjp7$$\"3wJYovbsO5F*$ \"3E+++R(y%>KFH7$$\"3tH0A-:9o5F*$\"3G+++iq'zN*F27$$\"3aFkvGub*4\"F*$\" 3))*****z@zjG#FH7$$\"3_DBHbL(48\"F*$\"39+++_iQ'*QF27$$\"3[B#G=G*Qi6F*$ \"3:+++?GjJAFH7$$\"3I@TO3_!Q>\"F*$\"3#)******p%pRj%FH7$$\"3G>+!\\8@_A \"F*$\"3%******fEYB%=FH7$$\"3C8F*$!3#******RJ<.O&FH7$$\"3+6O/T[) 3N\"F*$\"3J+++))o5COFH7$$\"3#)3&zvw+BQ\"F*$\"3%******Rh0(pfF27$$\"3%pS :Tp;PT\"F*$\"3$******4&o\"3T\"FH7$$\"3w/8l?E8X9F*$\"3))*****z>Hzp%FH7$ $\"3(G?(=Z&[lZ\"F*$\"3L+++A/)G6*F27$$\"3q+JstW'z]\"F*Fjz7$$\"3_)**e-S! QR:F*$\"38+++%37/(=FH7$$\"3i'*[zEjzq:F*$\"3W+++WB0l)*F27$$\"3X%zILD7Ag \"F*$\"3s+++D6&4N*F27$$\"3c#pm)z\"GOj\"F*$!3(******p_d)z@F27$$\"3Q!f-k 5W]m\"F*$!3)******RVi;.'F27$$\"3?)[QH.gkp\"F*Fh\\l7$$\"3K'Qu%ff(ys\"F* $!31+++;!oCc%F27$$\"39%G5g)=Hf=YD\"yq!z\"F*$\"33+++Mo'[ )>FH7$$\"33!3#3RP7A=F*$!3%******zu_\"\\8FH7$$\"3!z(zhl'RN&=F*$\"3(**** ****3RF%>FH7$$\"3svQ:#fb\\)=F*$\"3<+++r?Z/`F27$$\"3%Qx*o=:P;>F*$\"3Y** ***\\K+kF(F27$$\"3mrcAXuyZ>F*$\"3!******z+E$QCFH7$$\"3wp:wrL?z>F*$\"3H *****pZIUE*F27$$\"3fnuH)H>1,#F*$!3%******4^Y,$>F[v7$$\"3UlL$[AN?/#F*$ \"3++++i!HC>\"FH7$$\"3_j#p8:^M2#F*$!3))*****\\\\$=-HF27$$\"3Nh^!z2n[5# F*$\"3v*****\\@O?1&F27$$\"3Yf5W/IGO@F*$\"3.+++$Hvuq&FB7$$\"3Gdp(4$*)pn @F*$\"3E+++.\"f!*z(F27$$\"35bG^d[6*>#F*$\"3%*******z\"Qvz\"FH7$$\"3A`( [SyI0B#F*$\"3l+++30*oQ)F27$$\"3/^Ye5n%>E#F*$\"3e+++Q96p&*FB7$$\"3')[07 PEO$H#F*$\"3#******z$Q^S9FH7$$\"3)pWcOcyZK#F*$!3')*****p3fqz\"FH7$$\"3 ![M#>!\\%>cBF*$\"35+++#zH,n\"FH7$$\"3iU#GnT5wQ#F*$\"34+++BL#[9$F27$$\" 3tSTEVj->CF*$\"3%)*****z=#*>f'F27$$\"3cQ+!)pAW]CF*$\"3++++1)*=]7FH7$$ \"3mOfL'>e=[#F*$\"3N*****z+E1Y)F27$$F]fmF*$\"3&******4x<9V\"FB7$$\"3KK xS\\+pWDF*$\"3E+++0GS$\\%F27$$\"39IO%f(f5wDF*$\"3E+++C:NOTF27$$\"3aG&z C!>_2EF*$\"3A+++Q-\">8(F27$$\"3OEa,Hy$*QEF*$!3))*****z(R-1xFB7$$\"3=C8 bbPNqEF*$\"3n*****Rm(yp')F27$$\"3,As3#op Ji3c=LFF*$\"30+++Q7]_?FH7$$\"3lQ#F 27$$\"3N2&Qy;\"o@HF*$\"3*)*****>V9UQ(F27$$\"3u0WP%4(4`HF*$!3a+++N()34t F27$$\"3c..\"4-8X)HF*$\"3K+++Z&*4P]FB7$$\"3R,iWZ*Gf,$F*$!3;+++c0gmPF[v 7$$\"3@*4#)R([MZIF*$\"3k*****>$QYCjF27$$\"3.(*z^+3wyIF*$\"3)******p6\" fC=F27$$\"3V&*Q0Fn<5JF*$\"3%*******QbNAOF27$$\"3E$z*e`EfTJF*$\"3w***** 4@R$**oFB7$$\"33\"pD,e3I<$F*$\"3-+++_E%>/\"FH7$$\"3\"*)ehm]CW?$F*$\"3V +++><*QX)F27$$\"3t'[(>L/%eB$F*$\"3(******zmf'fqF27$$\"37&QL(fjDnKF*$\" 30+++M+qh9F27$$\"3%HGpiGs')H$F*$\"37+++F:D#G#F27$$\"3x!=0G@)3ILF*$\"3+ +++U!>SH\"FH7$$\"3fy5MRT]hLF*$\"3u+++%[cx&))F27$$\"3Uwp(e1?HR$F*$\"3%* *****fM)y46F27$$\"3CuGT#*fLCMF*$\"3(******\\q6?%eF27$$\"3ks([*=>vbMF*$ !3%******zzR@l#F27$$\"3YqY[Xy;([$F*$\"3))*****zItIW%F27$$\"3Ho0-sPe=NF *$!3O+++F27$$\"3Li#G;bJGh$F*$\"3G+++xa(Hw$F27$$\"3;gT;yuCWOF*$!3 1+++&ROr?%F27$$\"3)z0+ZSjcn$F*$!37+++v=q09FH7$$\"3!e&fBJ$zqq$F*$\"3y** ***4r?Ea%F27$$\"3i`=xd_\\QPF*$\"3r*****Ryl.v%F27$$\"3X^xI%=6*pPF*$!3%* *****zlRWe#F27$$\"3&)\\O%36F8!QF*$\"39+++oi(F27$$\"3`RJ_VnSeRF*$\" 3*)*****4A`B9%F27$$\"3OP!f+nA)*)RF*$\"3k*****\\%\\nsSF2-%'COLOURG6&%$R GBG$\"#5!\"\"F+F+-%+AXESLABELSG6$Q!6\"Fd[p-%%VIEWG6$;$!#]F,$\"#]F,%(DE FAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "#We now compute the FFT of the same sequence with twice as much zero padding:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "x2 := hfarray(1..512): y2 := hfarray(1..5 12):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "for ii from 1 to 256 do x2 [ii] := evalf(f(-1+(ii-1)/128)) od:\nfor iii from 257 to 512 do x2[iii ]:= 0: od:\nfor iiii from 1 to 512 do y2[iiii] := 0 od:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "FFT(9,x2,y2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$7&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 157 "#Because the sequenc e is no longer \"centered\" we need to account for an offset of 128 po ints. This amounts to multiplying the output by exp(-128*Pi*I*k/512). " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "yl2:=[seq([(k-513)*Pi/2,(cos(P i*k/2)*x2[k]-sin(Pi*k/2)*y2[k])/128],k=257..512),seq([(k-1)*Pi/2,(cos( Pi*k/2)*x2[k]-sin(Pi*k/2)*y2[k])/128],k=1..256)]:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 155 "xl2 :=[seq([(k-513)*Pi/2,-(sin(Pi*k/2)*x2[k]+cos(P i*k/2)*y2[k])/128], k=257..512),seq([(k-1)*Pi/2,-(sin(Pi*k/2)*x2[k]+co s(Pi*k/2)*y2[k])/128], k=1..256)]:\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 156 "#We plot the imaginary part of the FFT. Notice that we have s moothly interpolated the previous result. This is a consequence of the additonal zero padding." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "p2 := plot([yl2],-50..50,color=green): display(p2);" }}{PARA 13 "" 1 "" {GLPLOT2D 398 398 398 {PLOTDATA 2 "6%-%'CURVESG6$7\\[m7$$!3>N\\f'fQ 7-%!#:$\"\"!F,7$$!3G')pKL1`0SF*$\"3u*****z$f$e)H!#D7$$!3OP!f+nA)*)RF*$ !3+++++D1w=!#C7$$!3X)3\"z1Z6uRF*$!3%)*****\\(=<')HF27$$!3`RJ_VnSeRF*$ \"3*)*****\\PMZv$F87$$!3i!>b-y)pURF*$\"3;++++](o*HF27$$!39Ts)p\"3*p#RF *$!3I++++]iPcF87$$!3B#H>P&GG6RF*$!35+++](ou+$F27$$!3KV8X!*[d&*QF*$\"3< +++QfeFvF87$$!3S%R$=Fp')zQF*$\"3C+++vV)H-$F27$$!3\\Xa\"R'*eT'QF*$!3A++ +D19F%*F87$$!3e'\\Z1+^%[QF*$!3;+++D\"G)QIF27$$!3nZ&zt.VF$QF*$\"3&***** **=n$Q8\"!#B7$$!3w)f6T2Nq\"QF*$\"3v********\\(=1$F27$$!3&)\\O%36F8!QF* $!3!******\\(oHE8Feo7$$!3$4qvv9>cy$F*$!39+++D\"G84$F27$$!3X^xI%=6*pPF* $\"35+++++]?:Feo7$$!3a-)R5A.Uv$F*$\"30+++++v=JF27$$!3i`=xd_\\QPF*$!3'* *****\\P%[;Feo7$$!3)o+ozOr8p$F*$\"3%)*******\\7`>$F27$$!3)z0+ZSjcn$F*$!3%) ******\\(oa6#Feo7$$!314@VTa&*fOF*$!3r**********\\PKF27$$!3;gT;yuCWOF*$ \"3A+++vVt=BFeo7$$!3C6i*[^R&GOF*$\"32+++]7.#G$F27$$!3Li#G;bJGh$F*$!33+ ++QM-DDFeo7$$!3%GJg$)eBrf$F*$!3F+++vV[LLF27$$!3$RO#4DcT\"e$F*$\"3-+++J q]MFFeo7$$!3-:W#=m2dc$F*$\"3=+++iST!R$F27$$!36mkb)p***\\NF*$!37+++JXfZ HFeo7$$!3?<&)GNEv3e(G]$F*$\"33+++i!Rv^$F27$$!3YqY[Xy;([$F*$!3,++++v[&Q$Feo7 $$!3b@n@#))f9Z$F*$!3H+++i:b%e$F27$$!3ks([*=>vbMF*$\"3)******4G))4h$Feo 7$$!3sB3obR/SMF*$\"34+++DJqmOF27$$!3CuGT#*fLCMF*$!3#)*****>\"yDTQFeo7$ $!3MD\\9H!G'3MF*$!3o*****\\P%[[PF27$$!3Uwp(e1?HR$F*$\"3A+++7`pwSFeo7$$ !3]F!4E57sP$F*$\"3u*****\\ilZ$QF27$$!3fy5MRT]hLF*$!3-++++]iL/%eB$F*$!3)******RfeXM&Feo7$$!3#y`H*pC8 ?KF*$!3***********\\AP%F27$$!3\"*)ehm]CW?$F*$\"3(******zK^\">cFeo7$$!3 **RORVlr)=$F*$\"3I+++1k'y\\%F27$$!33\"pD,e3I<$F*$!3;+++A\\&>!fFeo7$$!3 'Feo7$$!3M W=K!p%)e7$F*$\"3I+++7.#Gy%F27$$!3V&*Q0Fn<5JF*$!3G+++1*oQ\\'Feo7$$!3%f% fyj(oW4$F*$!3G+++](ov$\\F27$$!3.(*z^+3wyIF*$\"33+++Z!3U!oFeo7$$!37[+DP G0jIF*$\"3\")*****4GQW5&F27$$!3@*4#)R([MZIF*$!3A+++cwxCrFeo7$$!3I]Tr5p jJIF*$!37+++]i?w_F27$$!3R,iWZ*Gf,$F*$\"3I+++y]ScuFeo7$$!3[_#yT)4A+IF*$ \"3>+++%[TQY&F27$$!3c..\"4-8X)HF*$!3_+++%[h'*z(Feo7$$!3laBkd]!)oHF*$!3 '*******e3GfcF27$$!3u0WP%4(4`HF*$\"3*******4.F`:)Feo7$$!3#oX168*QPHF*$ \"3K+++f39seF27$$!3N2&Qy;\"o@HF*$!3A+++1R8C&)Feo7$$!3We0d/K(f!HF*$!3%* *****z=(\\\"4'F27$$!3_4EIT_E!*GF*$\"3w+++(zEp!*)Feo7$$!3hgY.ysbuGF*$\" 3)******f^.oK'F27$$!3q6nw9$\\)eGF*$!3S*****Hq]XI*Feo7$$!3yi()\\^89VGF* $!3g*****R4'oulF27$$!3)Q\"3B)QLu#GF*$\"3e*******\\#)zr*Feo7$$!3'\\'G' \\UD<\"GF*$\"3E+++4@b^oF27$$!3/;\\phu,'z#F*$!3%******HQ3[,\"!#A7$$!38n pU)\\4.y#F*$!3W+++paiFrF27$$!3lJi3c=LFF*$!3,+++X**H16F`dl7$$!3# 4)=<1'o#F*$\"3e******\\([L4)F27$$!3=C8bbPNqEF*$!3%******zVge?\"F`dl 7$$!3FvLG#zXYl#F*$!31+++]P)oX)F27$$!3OEa,Hy$*QEF*$\"3#******f,'**e7F`d l7$$!3Wxuul)HKi#F*$\"3h+++v$fM%))F27$$!3aG&zC!>_2EF*$!3/+++t(oXJ\"F`dl 7$$!3/z:@RR\"=f#F*$!3F+++7G)oD*F27$$!39IO%f(f5wDF*$\"3'******>1QFP\"F` dl7$$!3A\"ovE,)RgDF*$\"38+++Q4'4q*F27$$!3KKxS\\+pWDF*$!3)*******H*pOV \"F`dl7$$!3S$yRh3#)*GDF*$!3-+++Zbs;5F87$$!3\\M=(G7uK^#F*$\"3'******4`e v\\\"F`dl7$$!3e&)Qgfhc(\\#F*$\"3-+++\"*G&p1\"F87$$!3mOfL'>e=[#F*$!3()* ****pz,Yc\"F`dl7$$!3Z()z1L-:mCF*$!3*******4`%R?6F87$$!3cQ+!)pAW]CF*$\" 33+++J?-N;F`dl7$$!3k*3KlIMZV#F*$\"3,+++Qf)z<\"F87$$!3tSTEVj->CF*$!34++ +J?/4'**z$=LS#F*$!3+++++]UR7F87$$!3iU#GnT5wQ#F*$\"3)***** *z$f#py\"F`dl7$$!3r$HgMX->P#F*$\"36++++]708F87$$!3![M#>!\\%>cBF*$!33++ +Q%[*o=F`dl7$$!3)eRCp_'[SBF*$!30+++vozw8F87$$!3)pWcOcyZK#F*$\"3-+++7GQ b>F`dl7$$!31)\\)Q+124BF*$\"3#******\\Pf3X\"F87$$!3')[07PEO$H#F*$!3*)** ****=UiY?F`dl7$$!3&**f_QnawF#F*$!3++++vV)H`\"F87$$!3/^Ye5n%>E#F*$\"35+ ++Z0&H9#F`dl7$$!38-nJZ(QiC#F*$\"3))*****R%)*Q?;F87$$!3A`([SyI0B#F*$!3+ +++;5yWAF`dl7$$!3-/3y?G#[@#F*$!3-+++7.([r\"F87$$!35bG^d[6*>#F*$\"3&)** ***pa?DN#F`dl7$$!3>1\\C%*oS$=#F*$\"34+++7.x:=F87$$!3Gdp(4$*)pn@F*$!35+ ++`>kmCF`dl7$$!3P3!4x'4*>:#F*$!3++++(Hz`#>F87$$!3Yf5W/IGO@F*$\"3)***** *>cGwe#F`dl7$$!3E5J1,#F*$\"39+++ Qf;_JF`dl7$$!3o=&H]L6\\*>F*$\"34+++D\"GF*$!38+++.#G pJ$F`dl7$$!3d?O\\3a\\j>F*$!35+++DcE)z#F87$$!3mrcAXuyZ>F*$\"3C+++JXz#\\ $F`dl7$$!3uAx&>[z?$>F*$\"3#)*******\\i0*HF87$$!3%Qx*o=:P;>F*$!3?+++`>t !o$F`dl7$$!3#\\#=UbNm+>F*$!3++++v=x*>$F87$$!3svQ:#fb\\)=F*$\"3$)****** 3'R=)QF`dl7$$!3\"o#f))GwCp=F*$\"3))******\\iXGMF87$$!3!z(zhl'RN&=F*$!3 ))*****f::t4%F`dl7$$!3**G+N-<$y$=F*$!3%)*****>c,\"yOF87$$!33!3#3RP7A=F *$\"3u*****4*y]GVF`dl7$$!3;JT\"ex:k!=F*$\"3%)*****\\7.A&RF87$$!3'>=YD \"yq!z\"F*$!39+++y+*od%F`dl7$$!30L#y#\\)**\\x\"F*$!32+++)=UAD%F87$$!39 %G5g)=Hf+++%)*[@8&F`dl7$$!37Pk?'*z;7+++`W+zdF`dl7$$!3ZTY8VhL\\;F*$!3_+++1k1*y&F87$$!3c#pm)z\" GOj\"F*$\"3Z*****4yuG9'F`dl7$$!3OV()f;-#zh\"F*$\"3$)*****z2g)ziF87$$!3 X%zILD7Ag\"F*$!3e*****z#3gPlF`dl7$$!3`XG1!H/le\"F*$!3k*****R4T[#oF87$$ !3i'*[zEjzq:F*$\"3()*****fe!fmpF`dl7$$!3rZp_j$)3b:F*$\"3')*****4G= \"G`l))F87$$!3(G?(=Z&[lZ\"F*$!33+++`Mm+&)F`dl7$$!3n`#>ReS3Y\"F*$!3h*** **>1/Xr*F87$$!3w/8l?E8X9F*$\"3c+++[^N6\"*F`dl7$$!3&eN$QdYUH9F*$\"3)*** ***z=iq1\"Feo7$$!3%pS:Tp;PT\"F*$!3&******flK@y*F`dl7$$!3-eu%3t3!)R\"F* $!3(******R[@\\<\"Feo7$$!3#)3&zvw+BQ\"F*$\"3*******Hqt?0\"!#@7$$!3\"*f :J/Gfm8F*$\"3#*******o/.(H\"Feo7$$!3+6O/T[)3N\"F*$!3*******pz6O8\"Fc`n 7$$!34icxxo8F*$\"3-+++]i(QA\" Fc`n7$$!3Fk(R7&4w.8F*$\"33+++)oaSf\"Feo7$$!31:=(z)H0)G\"F*$!38+++`p3C8 Fc`n7$$!3:mQqC]Ms7F*$!31+++DJ0vFeo7$$!3G>+!\\8@_A\"F*$!3!******zvx.c\"F c`n7$$!3Pq?jrJ^47F*$!3!******>#**\\BAFeo7$$!3I@TO3_!Q>\"F*$\"3-+++H#z, q\"Fc`n7$$!3Rsh4Xs4y6F*$\"33+++Dm4-DFeo7$$!3[B#G=G*Qi6F*$!3!*******p?^ d=Fc`n7$$!3Vu-c=8oY6F*$!3$)*****4@Zp#GFeo7$$!3_DBHbL(48\"F*$\"3-+++\"z z_.#Fc`n7$$!3hwV-#Rl_6\"F*$\"3=+++-\"Rw?$Feo7$$!3aFkvGub*4\"F*$!39+++] 0+PAFc`n7$$!3ky%)[l%\\Q3\"F*$!3>+++$Q(RcOFeo7$$!3tH0A-:9o5F*$\"35+++BF 'pY#Fc`n7$$!3n!e_*QNV_5F*$\"3;+++U-)*)=%Feo7$$!3wJYovbsO5F*$!37+++xwUI FFc`n7$$!3r#o;Ch<5-\"F*$!3')*****R[L[#[Feo7$$!3!Qt[\"\\'4`+\"F*$\"3'** ****pB=R.$Fc`n7$$!3')[y!)eo,'*)*!#;$\"31+++8F5!f&Feo7$$!3Ie$GhAP*Q(*F_ hn$!3))*****HYybQ$Fc`n7$$!3=p)[Mfd=e*F_hn$!3()*****pP_%=lFeo7$$!3ky$p2 'zxC%*F_hn$\"39+++s_o&z$Fc`n7$$!3_*))*3G$)pn#*F_hn$\"3\"******zR:Zl(Fe o7$$!3R+/T&p=16*F_hn$!3')******oaMxUFc`n7$$!3&)44ti!RN&*)F_hn$!3C+++*G N$f!*Feo7$$!3s?90I%fkz)F_hn$\"30+++u?ZZ[Fc`n7$$!3gJ>P(zz$R')F_hn$\"3++ ++ilX\"3\"F`dl7$$!31TCpk,I#[)F_hn$!3_+++)R!=GbFc`n7$$!3%>&H,K0AD$)F_hn $!3/+++G!zMI\"F`dl7$$!3\"GYL$**39o\")F_hn$\"3`+++02\")[jFc`n7$$!3FsRlm 716!)F_hn$\"35+++)>\">)e\"F`dl7$$!3:$[uRj\")R&yF_hn$!3z*****4)3$*[tFc` n7$$!3g#*\\H,?!pp(F_hn$!38+++#4U*e>F`dl7$$!3[.bhoB#)RvF_hn$\"3B+++1a*G e)Fc`n7$$!3O9g$ftUFQ(F_hn$\"3\"******\\c;.X#F`dl7$$!3\"Q_cK5jcA(F_hn$! 3-+++hbp75!#?7$$!3pMqdqMeoqF_hn$!3%******zmp[6$F`dl7$$!39Wv*y$Q]6pF_hn $\"3-+++G%o!47Fg]o7$$!3-b!=_?CWv'F_hn$\"3K+++7R,NSF`dl7$$!3!fcQDdWtf'F _hn$!30+++\"***fj9Fg]o7$$!3Ov!f)R\\ESkF_hn$!3%******>5#)[M&F`dl7$$!3B' ezrI&=$G'F_hn$\"31+++(Q95!=Fg]o7$$!3S'4+Xn0h7'F_hn$\"3R+++;2FssF`dl7$$ !3d11#=/E!pfF_hn$!3&******4Wl0E#Fg]o7$$!3W<694k%>\"eF_hn$!31+++y5[A5Fc `n7$$!3hF;Ywn'[l&F_hn$\"3%)*****>c*e2HFg]o7$$!3yP@yVry(\\&F_hn$\"3'*** ****pq'z\\\"Fc`n7$$!3m[E56vqS`F_hn$!3))*****z5tt&QFg]o7$$!3#)eJUyyi$=& F_hn$!3,+++Fz79BFc`n7$$!3)*oOuX#[l-&F_hn$\"3l******e$))*G`Fg]o7$$!3:zT 18'o%p[F_hn$\"3/+++9&)3QQFc`n7$$!3K*o%Q!)*)Q7ZF_hn$!3n*****49!G\"y(Fg] o7$$!3?+_qZ$4`b%F_hn$!3v******fXoMqFc`n7$$!3O5d-:(H#)R%F_hn$\"3++++QkJ J7!#>7$$!3`?iM#3]6C%F_hn$\"31+++\"fw%*\\\"Fg]o7$$!3TJnm\\/2%3%F_hn$!3' ******R-fK@#Fbco7$$!3eTs)p\"3*p#RF_hn$!3H+++$\\ND7%Fg]o7$$!3u^xI%=6*pP F_hn$\"39+++[gEG;bJGh$F_hn$\"3'******>?`0\">Fbco7$$!32s( [*=>vbMF_hn$!3-+++Ys#=-#!#=7$$!3'HGpiGs')H$F_hn$!3]*****4jq,;&Faeo7$$! 37$z*e`EfTJF_hn$!3g*****\\'RtrmFaeo7$$!3G..\"4-8X)HF_hn$!3f*****\\XK.; &Faeo7$$!3!Q\"3B)QLu#GF_hn$!3*)******)>43-#Faeo7$$!3LC8bbPNqEF_hn$\"3# ******zb?A\">Fbco7$$FhilF_hn$\"3r******f`].]Fbco7$$!3mWB>!\\%>cBF_hn$! 3f*****H)*H-9%Fg]o7$$!3=bG^d[6*>#F_hn$!3-+++jZX\"=#Fbco7$$!3qlL$[AN?/# F_hn$\"35+++zS+]? (Fg]o7$$!3!pS:Tp;PT\"F_hn$\"3,+++J'H&)3%Fc`n7$$!3Df=Fc`n7$$Fc_oF_jo$\" 31+++HO-fQUu9Fc`n7$$FieoF_jo$!3@+++e 2:q#)Fc`n7$$!3b'*[zEjzq:F_jo$\"37+++*o8&48Fc`n7$F+F+7$$\"3b'*[zEjzq:F_ jo$!33+++?T^48Fc`n7$$\"37$z*e`EfTJF_jo$\"3>+++;&\\,F)Fc`n7$$\"3n*o%Q!) *)Q7ZF_jo$\"3'******4rAWZ\"Fc`n7$$\"3B'ezrI&=$G'F_jo$!32+++WQ-fc)>f=Fc`n7$$\"3Mz$p2'zxC%*F_jo$\"3#)*** **R@ak$HFg]o7$$\"3gFkvGub*4\"F_hn$\"3\"******HV;4h#Fc`n7$$\"3DB]t=\"Fbco7$$\"3qlL$[AN?/#F_hn $!3!******4*>!)=:Fg]o7$$\"3=bG^d[6*>#F_hn$\"3-+++UZX\"=#Fbco7$$\"3mWB> !\\%>cBF_hn$\"3g******p)H-9%Fg]o7$$\"3\\M=(G7uK^#F_hn$!3K+++f`].]Fbco7 $$\"3LC8bbPNqEF_hn$!3%)*****zd?A\">Fbco7$$\"3!Q\"3B)QLu#GF_hn$\"33+++) >43-#Faeo7$$\"3G..\"4-8X)HF_hn$\"3`+++`CLg^Faeo7$$Fa\\pF_hn$\"3H+++gRt rmFaeo7$$\"3'HGpiGs')H$F_hn$\"3G+++F1vbMF_hn$\"3%* *****\\CF=-#Faeo7$$\"3!>EG;bJGh$F_hn$!3'******4=`0\">Fbco7$$\"3u^xI%=6 *pPF_hn$!3J+++]g\"GTJ#Fc`n7$$\"3m[E56vqS`F_hn$\"3,+++ '=tt&QFg]o7$$\"3yP@yVry(\\&F_hn$!3++++Bk'z\\\"Fc`n7$$\"3hF;Ywn'[l&F_hn $!3'******RU*e2HFg]o7$$\"3W<694k%>\"eF_hn$\"3'*******)G\"[A5Fc`n7$$\"3 d11#=/E!pfF_hn$\"3:++++bcgAFg]o7$$\"3S'4+Xn0h7'F_hn$!3u*****>npAF(F`dl 7$$F[]pF_hn$!35+++xV,,=Fg]o7$$\"3Ov!f)R\\ESkF_hn$\"3%******fw%)[M&F`dl 7$$\"3!fcQDdWtf'F_hn$\"3$*******o**fj9Fg]o7$$\"3-b!=_?CWv'F_hn$!3.+++> U-NSF`dl7$$\"39Wv*y$Q]6pF_hn$!3%******\\bo!47Fg]o7$$\"3pMqdqMeoqF_hn$ \"3++++Q4'[6$F`dl7$$\"3\"Q_cK5jcA(F_hn$\"32+++Zbp75Fg]o7$$\"3O9g$ftUFQ (F_hn$!3.+++JXJ]CF`dl7$$\"3[.bhoB#)RvF_hn$!3$)*****zR&*Ge)Fc`n7$$\"3g# *\\H,?!pp(F_hn$\"3++++<;%*e>F`dl7$$\"3:$[uRj\")R&yF_hn$\"3))*****phJ*[ tFc`n7$$\"3FsRlm716!)F_hn$!3%******Rtt\")e\"F`dl7$$\"3\"GYL$**39o\")F_ hn$!3x******[!4)[jFc`n7$$\"3%>&H,K0AD$)F_hn$\"3&********Q\"\\.8F`dl7$$ \"31TCpk,I#[)F_hn$\"3O+++X6=GbFc`n7$$\"3gJ>P(zz$R')F_hn$!32+++rkX\"3\" F`dl7$$\"3s?90I%fkz)F_hn$!35+++s@ZZ[Fc`n7$$\"3&)44ti!RN&*)F_hn$\"3B+++ W$R$f!*Feo7$$\"3R+/T&p=16*F_hn$\"3B+++IdMxUFc`n7$$\"3_*))*3G$)pn#*F_hn $!3S+++;&zYl(Feo7$$\"3ky$p2'zxC%*F_hn$!3-+++iZo&z$Fc`n7$$\"3=p)[Mfd=e* F_hn$\"3S+++'3)\\=lFeo7$$\"3Ie$GhAP*Q(*F_hn$\"3#)*****RpybQ$Fc`n7$$\"3 ')[y!)eo,'*)*F_hn$!3C+++fj3!f&Feo7$$\"3!Qt[\"\\'4`+\"F*$!3'******pB=R. $Fc`n7$$\"3r#o;Ch<5-\"F*$\"3y******fM$[#[Feo7$$\"3wJYovbsO5F*$\"3y**** *f\"yUIFFc`n7$$\"3n!e_*QNV_5F*$!3!)*****4%f#*)=%Feo7$$\"3tH0A-:9o5F*$! 3z*****z)>'pY#Fc`n7$$\"3ky%)[l%\\Q3\"F*$\"3!******zYDkl$Feo7$$\"3aFkvG ub*4\"F*$\"3++++m1+PAFc`n7$$\"3hwV-#Rl_6\"F*$!3++++!yVw?$Feo7$$\"3_DBH bL(48\"F*$!37+++m(z_.#Fc`n7$$\"3Vu-c=8oY6F*$\"3++++7$fp#GFeo7$$\"3[B#G =G*Qi6F*$\"32+++%37v&=Fc`n7$$\"3Rsh4Xs4y6F*$!3#)******z!R?]#Feo7$$\"3I @TO3_!Q>\"F*$!3)******>@z,q\"Fc`n7$$\"3Pq?jrJ^47F*$\"3!******R[MMA#Feo 7$$\"3G>+!\\8@_A\"F*$\"3#******fsx.c\"Fc`n7$$\"3Loz;)4H4C\"F*$!34+++)o pJ)>Feo7$$\"3C8F*$!3.+++PS(QA\"Fc`n7$$\"34icxxoM@y*F`dl7$$\"3&eN$QdYUH9F*$!3-+++DT6n5Feo7$$\"3w/8l?E8X9F*$!3;+ ++MReS3Y\"F*$\"3)*)****zVQ\\r*F87$$\"3(G?(=Z&[lZ\" F*$\"3&******Hxk1])F`dl7$$\"3y^^X5lD#\\\"F*$!3?+++;gbl))F87$$\"3q+JstW 'z]\"F*$!3b*****>\"oQVzF`dl7$$\"3g\\5*pVsO_\"F*$\"3N+++(Hk$3\")F87$$\" 3_)**e-S!QR:F*$\"3%******>n3PV(F`dl7$$\"3rZp_j$)3b:F*$!3i*****f!*y8V(F 87$$\"3i'*[zEjzq:F*$!32+++]iempF`dl7$$\"3`XG1!H/le\"F*$\"3]+++]P4DoF87 $$\"3X%zILD7Ag\"F*$\"3W******o/gPlF`dl7$$\"3OV()f;-#zh\"F*$!3l*****\\( =7!G'F87$$\"3c#pm)z\"GOj\"F*$!3]+++vV(G9'F`dl7$$\"3ZTY8VhL\\;F*$\"3T++ +voH*y&F87$$\"3Q!f-k5W]m\"F*$\"32++++++zdF`dl7$$\"3HR0np?v!o\"F*$!3k** ***\\iSmM&F87$$\"3?)[QH.gkp\"F*$!3()*****>cwHW&F`dl7$$\"37Pk?'*z;7=YD\"yq!z\"F*$\"3#******HX*)od%F`dl7$$ \"3;JT\"ex:k!=F*$!3?++++v$=&RF87$$\"33!3#3RP7A=F*$!3=+++ms\\GVF`dl7$$ \"3**G+N-<$y$=F*$\"3\"*********\\(*yOF87$$\"3!z(zhl'RN&=F*$\"3#)*****z #)=t4%F`dl7$$\"3\"o#f))GwCp=F*$!3=+++G)[&GMF87$$\"3svQ:#fb\\)=F*$!3.++ +c'R=)QF`dl7$$\"3#\\#=UbNm+>F*$\"3?+++QM***>$F87$$\"3%Qx*o=:P;>F*$\"3- +++G=t!o$F`dl7$$\"3uAx&>[z?$>F*$!3(******zKE+*HF87$$\"3mrcAXuyZ>F*$!3u *****Hj$z#\\$F`dl7$$\"3d?O\\3a\\j>F*$\"3!)*****\\il%)z#F87$$\"3wp:wrL? z>F*$\"3A+++9%HpJ$F`dl7$$\"3o=&H]L6\\*>F*$!3u******e3t@EF87$$\"3fnuH)H >1,#F*$!39+++Qf;_JF`dl7$$\"3];achsKE?F*$\"32+++7y:fCF87$$\"3UlL$[AN?/# F*$\"3#)*****R)Ri(*HF`dl7$$\"3h985)=Vx0#F*$!3&******\\(oH4BF87$$\"3_j# p8:^M2#F*$!31+++iS\\_GF`dl7$$\"3V7sj9\"f\"*3#F*$\"3-+++](o9<#F87$$\"3N h^!z2n[5#F*$\"3'******><^gr#F`dl7$$\"3E5J:#F*$\"3(******zV[`#>F87$ $\"3Gdp(4$*)pn@F*$\"3&)*****>cTmY#F`dl7$$\"3>1\\C%*oS$=#F*$!37+++7`W:= F87$$\"35bG^d[6*>#F*$!3%******pz@DN#F`dl7$$\"3-/3y?G#[@#F*$\"3$****** \\i!R9?;F87$$\"3/^Ye5n%>E#F*$!32+++.2&H9#F`dl7$$\"3&**f_QnawF#F*$\"3))**** *R4@G`\"F87$$\"3')[07PEO$H#F*$\"3\"******>UAm/#F`dl7$$\"31)\\)Q+124BF* $!30+++]7G^9F87$$\"3)pWcOcyZK#F*$!3&)******o/Sb>F`dl7$$\"3)eRCp_'[SBF* $\"3/+++D\"GeP\"F87$$\"3![M#>!\\%>cBF*$\"3;+++m(\\*o=F`dl7$$\"3r$HgMX- >P#F*$!3'******R%)*308F87$$\"3iU#GnT5wQ#F*$!3(******RMEpy\"F`dl7$$\"3# =>'**z$=LS#F*$\"3))*****p/$fR7F87$$\"3tSTEVj->CF*$\"3;+++.F/4e=[#F*$\"35+++sEgk:F` dl7$$\"3e&)Qgfhc(\\#F*$!32+++QM&o1\"F87$$Fg`pF*$!3+++++&ev\\\"F`dl7$$ \"3S$yRh3#)*GDF*$\"3'******RMAm,\"F87$$\"3KKxS\\+pWDF*$\"3#******R[qOV \"F`dl7$$\"3A\"ovE,)RgDF*$!3q*****z$f['p*F27$$\"39IO%f(f5wDF*$!3(***** *HQMFP\"F`dl7$$\"3/z:@RR\"=f#F*$\"3:++++]id#*F27$$\"3aG&zC!>_2EF*$\"3- +++++d98F`dl7$$\"3Wxuul)HKi#F*$!3t*****>1kO%))F27$$\"3OEa,Hy$*QEF*$!3- +++1k**e7F`dl7$$\"3FvLG#zXYl#F*$\"3\"******\\(ozc%)F27$$\"3=C8bbPNqEF* $\"3********=<'e?\"F`dl7$$\"34t#>)=<1'o#F*$!3!)*******\\(=#4)F27$$\"3, As3#opJi3c=LFF*$\"30+++>#*H16F`dl7$$\"3uo5*=d$*)[FF*$!3Q++++DJIuF2 7$$\"3ln`XI*Feo7$$\"3hgY.ysbuGF *$!3S+++1*y$GjF27$$\"3_4EIT_E!*GF*$!3]+++D\"Gp!*)Feo7$$\"3We0d/K(f!HF* $\"3s*****f:gC4'F27$$\"3N2&Qy;\"o@HF*$\"3%*******\\P9C&)Feo7$$\"3#oX16 8*QPHF*$!3()*****4y+_'eF27$$\"3u0WP%4(4`HF*$!3<+++J&H`:)Feo7$$\"3laBkd ]!)oHF*$\"3%)*****4G)yhcF27$$\"3c..\"4-8X)HF*$\"3U+++`>m*z(Feo7$$\"3[_ #yT)4A+IF*$!31++++D;iaF27$$\"3R,iWZ*Gf,$F*$!3I+++y]ScuFeo7$$\"3I]Tr5pj JIF*$\"3o*****>nyfF&F27$$\"3@*4#)R([MZIF*$\"3r*****pHzZ7(Feo7$$\"37[+D PG0jIF*$!3D+++mZ2+^F27$$\"3.(*z^+3wyIF*$!3M+++%4YT!oFeo7$$\"3%f%fyj(oW 4$F*$\"3y*****z2&3R\\F27$$\"3V&*Q0Fn<5JF*$\"37+++p/(Q\\'Feo7$$\"3MW=K! p%)e7$F*$!3)******R4'4%y%F27$$\"3E$z*e`EfTJF*$!3E+++GQJ$>'Feo7$$\"3!fFeo7$$ \"3**RORVlr)=$F*$!3o*****f:l&*\\%F27$$\"3\"*)ehm]CW?$F*$!3Q+++A\\8>cFe o7$$\"3#y`H*pC8?KF*$\"3!)*****>c^DP%F27$$\"3t'[(>L/%eB$F*$\"37+++](eXM &Feo7$$\"3kNaY'R[:D$F*$!3$)*****>19.D%F27$$\"37&QL(fjDnKF*$!3s*****zoM v2&Feo7$$\"3.M8+BV'HG$F*$\"3++++cEiNTF27$$\"3%HGpiGs')H$F*$\"3p*****49 \\w\"[Feo7$$\"3'=BP&\\-Q9LF*$!39+++pHkDSF27$$\"3x!=0G@)3ILF*$!33+++f3 \\kXFeo7$$\"3oHJ2whzXLF*$\"3)*******=#*RJRF27$$\"3fy5MRT]hLF*$\"3k**** **\\Pk\"yDTQFeo7$$\"3sB3obR/SMF*$!32+++iSwlOF27$$\"3ks([*=>vbMF*$!3z****** *\\()4h$Feo7$$\"3b@n@#))f9Z$F*$\"3s*****zo/`e$F27$$\"3YqY[Xy;([$F*$\"3 -+++]P\\&Q$Feo7$$\"3Q>Ev3e(G]$F*$!3-+++D\"yg^$F27$$\"3Ho0-sPe=NF*$!3/+ ++\"GjW;$Feo7$$\"3?<&)GNX$F27$$\"36mkb)p***\\NF *$\"3#******fl(fZHFeo7$$\"3-:W#=m2dc$F*$!36+++ilZ*Q$F27$$\"3$RO#4DcT\" e$F*$!33+++v=_MFFeo7$$\"3%GJg$)eBrf$F*$\"3()*******\\7[L$F27$$\"3Li#G; bJGh$F*$\"33+++QM-DDFeo7$$\"3C6i*[^R&GOF*$!3H+++vVt#G$F27$$\"3;gT;yuCW OF*$!3(*******\\(=(=BFeo7$$\"314@VTa&*fOF*$\"35+++]7GQKF27$$\"3)z0+ZSj cn$F*$\"3))*****\\i!R:@Feo7$$\"3)o+ozOr8p$F*$!3x********\\7.KF27$$\"3! e&fBJ$zqq$F*$!3++++Dcw9>Feo7$$\"3s/R]%H(yAPF*$\"3A+++++DcJF27$$\"3i`=x d_\\QPF*$\"3'******\\P%[;cy$F*$\"3A+++]i:!4$F27$$\"3&)\\O% 36F8!QF*$\"3(******zo/jK\"Feo7$$\"3w)f6T2Nq\"QF*$!3x*****\\7yq1$F27$$ \"3nZ&zt.VF$QF*$!3)*******=#\\Q8\"Feo7$$\"3e'\\Z1+^%[QF*$\"3&)******** \\7UIF27$$\"3\\Xa\"R'*eT'QF*$\"3a*****zV)*oU*F87$$\"3S%R$=Fp')zQF*$!31 +++]i:@IF27$$\"3KV8X!*[d&*QF*$!3Q+++v$4w_(F87$$\"3B#H>P&GG6RF*$\"3))** ****\\iS1IF27$$\"39Ts)p\"3*p#RF*$\"3W++++voPcF87$$\"3i!>b-y)pURF*$!3?+ ++QMF&*HF27$$\"3`RJ_VnSeRF*$!3.+++ilsaPF87$$\"3X)3\"z1Z6uRF*$\"3t***** z=#f))HF27$$\"3OP!f+nA)*)RF*$\"35+++%4rh(=F87$$\"3G')pKL1`0SF*$!3v**** *4GQl)HF2-%'COLOURG6&%$RGBGF+$\"*++++\"!\")F+-%+AXESLABELSG6$Q!6\"F\\ \\u-%%VIEWG6$;$!#]F,$\"#]F,%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "#This is the exact Fourier transform of f is" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "g := x->2*((sin(10*Pi-x)-(10*Pi-x) *cos(10*Pi-x))/(10*Pi-x)^3-(sin(10*Pi+x)-(10*Pi+x)*cos(10*Pi+x))/(10*P i+x)^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)oper atorG%&arrowGF(,&*&,&-%$sinG6#,&%#PiG\"#59$!\"\"\"\"\"*&F2F7-%$cosGF1F 7F6F7F2!\"$\"\"#*(F " 0 "" {MPLTEXT 1 0 37 "p3 :=plot([g], -50..50) : display(p3);" }}{PARA 13 "" 1 "" {GLPLOT2D 398 398 398 {PLOTDATA 2 " 6%-%'CURVESG6$7gu7$$!#]\"\"!$\"3.p\"F-7$$!3GLLLe%G?y%F1$!38hMc#=*=p^F-7$$!3'o;/,\\9Yt%F1$!3%*[W eL:iksF-7$$!3X+](=_+so%F1$!3lR7$$!3zK$e9,ZAN%F1$\"3mbcB4)32C\"FW7$$!33 LL3-$4aK%F1$\"3'e9/FC,$=6FW7$$!3OL$3Ffr&)H%F1$\"3!Q,F?n@&***)F-7$$!3$H LLL)QtrUF1$\"3^UyH$QS=#fF-7$$!3\\LLek%e!=UF1$!33b:%zpj(4BF-7$$!3MLL$e/ $QkTF1$!3]u#*f9Icn6FW7$$!3o\\iS\"*GnPTF1$!3U@EPn/^(f\"FW7$$!3sm\"zpti4 6%F1$!3'pYBCrMq&>FW7$$!3x$3_De_U3%F1$!3+UP(obp>@#FW7$$!35+]7GCadSF1$!3 pN8\"Qpd8L#FW7$$!3W;zptA$3.%F1$!3DBH)*Qn!)*G#FW7$$!3[L3F>@7/SF1$!3(4LV @2[(p?FW7$$!3`]P%['>TxRF1$!3![z55\\iMm\"FW7$$!3'om;/\"=q]RF1$!3h#Ge3uS Z2\"FW7$$!37++D\")ok^QF1$\"3^lXKD-#*yAFW7$$!3QLL3_>f_PF1$\"3DhQAS'HnQ& FW7$$!33mmmT0&ps$F1$\"3X_vW2/4$o&FW7$$!3]***\\7848q$F1$\"3k]]0\\x%)GcF W7$$!3\"HLL3sncn$F1$\"3qq#3&pb$z:&FW7$$!3KmmT5j-]OF1$\"3\"4vvseyI@%FW7 $$!39LLe*[V()f$F1$\"3$Q!oT&G>UM(F-7$$!3(****\\(o1YZNF1$!3-!fg(f:8#)\\F W7$$!3kLL3-RU%\\$F1$!3$[(R2>N+78!#=7$$!3hmmTNrQTMF1$!3m['4iXJSI#Feu7$$ !3e***\\(o.N)Q$F1$!3'>!fQykW$R$Feu7$$!3DLL3-OJNLF1$!3*4P/ls;gZ%Feu7$$! 3*******\\#pW#G$F1$!3!4IG(4i1NaFeu7$$!3umm\"zC!eHKF1$!3&)p$3$QLpnhFeu7 $$!3Y+]P4p9.KF1$!3G*p&3NpZ@kFeu7$$!3[LL$3d8n<$F1$!3E_]dsHZ*e'Feu7$$!3* **\\i:!p\\jJF1$!3'*4(3nRG'RmFeu7$$!3\\m;HK-G]JF1$!3x!*z'*zCmmmFeu7$$!3 OL3-jN1PJF1$!3#ouhD3r.n'Feu7$$!3')***\\P*o%Q7$F1$!3(\\7?LFD2l'Feu7$$!3 mm\"H#=qYpIF1$!3F`sF0'*=IjFeu7$$!34L$3F9(3:IF1$!3M]aX`BjgcFeu7$$!3`*\\ (=nsqgHF1$!3k7#y'*\\'>CZFeu7$$!3Kmmm\"RFj!HF1$!3[:9v')[1KOFeu7$$!3DL$3 xcH%eGF1$!3q!G!*f=1*QEFeu7$$!3$)***\\PuJ0\"GF1$!3T7PQXU\\+RjiFF1$!3G=z*z4W\"R))FW7$$!3+LL$e4OZr#F1$!3H_bR'p$*\\O#FW7$$!3r**\\i !\\93m#F1$\"3B)QXYh#*4h#FW7$$!3UmmT&)G*og#F1$\"38PnZ[D\"e;&FW7$$!3x*\\ 7G3K*zDF1$\"3HE>7\"=_Lj&FW7$$!38L$3-GrHb#F1$\"3Ef-mjpAYcFW7$$!3[mTgx/, EDF1$\"3w_?b#\\&R#G&FW7$$!3[*****\\n\\!*\\#F1$\"38\"o]eF_gi%FW7$$!3a** ****\\Ow!R#F1$\"3%>E!f74EVtF-7$$!3$******\\ixCG#F1$!366k()p]A5?FW7$$!3 *)****\\7#*QcAF1$!3gP`;7CKWAFW7$$!3%)*******z+.B#F1$!3Z:\\#y(zn2BFW7$$ !3z****\\(Q7U?#F1$!3=!eCT_Dd@#FW7$$!3v*****\\(R7y@F1$!3O'Q(*Hx`7*>FW7$ $!3m******\\r%f7#F1$!3%fInh7F0E\"FW7$$!3c*****\\KqP2#F1$!3+P^[_%y*pOF- 7$$!3-L3Fp()QE?F1$\"3k#\\;+W;z#QF-7$$!3\\m;a8s+z>F1$\"3?j#)Rdix6$*F-7$ $!3A$3xcV;`&>F1$\"3;Ah>+[Z.6FW7$$!3'**\\7ylD;$>F1$\"3dt=v`&*4-7FW7$$!3 L;z%*z[$z!>F1$\"3!3\"y(RvLyA\"FW7$$!31LL3-TC%)=F1$\"3\"GgWO]c$)oPMF-7$$!3.mmm\"4z)e;F1$!3O\")))[!QK`s&F -7$$!3PmmTg1:6;F1$!3.bm-dB.lsF-7$$!3Omm;HAUj:F1$!3-R`G+`RoqF-7$$!3_mm \"zz$p::F1$!3:XlClV@1aF-7$$!3ommmm`'zY\"F1$!3,)f\")*[\"eu\"GF-7$$!3H#)*!#@7$$!3x(***\\iXg#G'F^el$\"3!38rJ^j(e]F'>(Fael7$$!3:jm;/'=><#F^el$!3zf=7\"fi]5#Fael7 $$!3%G*GLLe*e$\\FW$\"3z;HJC()[3>!#A7$$\"3zrm;zRQb@F^el$\"3C[Y0/IZ\"*>F ael7$$\"310+](=>Y2%F^el$\"3Fz>d&4b6i(Fael7$$\"3Qpmm\"zXu9'F^el$!3&>Pxq $oFx;F-7$$\"3q-+++&y))G)F^el$\"3E:&y'[L4`')Fael7$$\"3I++]i_QQ5F1$\"3K[ E.6VaP@F-7$$\"3C+](=-N(R6F1$!3tl>,!GX?F\"F-7$$\"3>++D\"y%3T7F1$!3e:-@l A*GR%F-7$$\"3#***\\P4kh`8F1$!3f6iL-js%G$F-7$$\"3l****\\P![hY\"F1$\"3i: UGR,Q4FF-7$$\"32L$eRP0n^\"F1$\"3L%\\60T$G`aF-7$$\"3\\mmT5FEn:F1$\"3[E/ h7Z5WrF-7$$\"3#***\\(o/?yh\"F1$\"3a#)o[a*=i:(F-7$$\"3MLLL$Qx$o;F1$\"33 XG^@!zL@&F-7$$\"34nm;z)Qjx\"F1$!3$o>=\"3DP.RF-7$$\"3$3++]P+V)=F1$!3t&Q @i;A`=\"FW7$$\"3+%ek`md(3>F1$!3w[S?HC7G7FW7$$\"3=n\"Hd&\\@L>F1$!3/!)Ga 5Pz(>\"FW7$$\"3N]P4YAnd>F1$!3eZ*RaB>'*3\"FW7$$\"3_L$ek`H@)>F1$!3Ca^PB] *4.*F-7$$\"3')*\\(=rAk6/!*o)F-7$$\"3yKLe9S8&\\ #F1$!3K?!zJ%p`6XFW7$$\"3Hm;aQ?V@DF1$!3*=rTIC)=*=&FW7$$\"3!)****\\i+tZD F1$!3SO0\">IKCg&FW7$$\"3KL$ek3GSd#F1$!3yrQ<+jZscFW7$$\"3%om;/6E.g#F1$! 3wJD]j%HaK&FW7$$\"3(QLL$e@#Hl#F1$!3Ib0#yj]68$FW7$$\"3!4+]i?=bq#F1$\"34 #\\r.U)HP8FW7$$\"3&R$3xc/%pv#F1$\"3_.v#p3(4uzFW7$$\"3*pm\"H2FO3GF1$\"3 ;M8E$)[Wg;Feu7$$\"3/+D\"y&\\yfGF1$\"3_4E8^BhmEFeu7$$\"33LLL3s?6HF1$\"3 k5yH[zBLPFeu7$$\"3(**\\i!R:/lHF1$\"3;P)4u]Mh![Feu7$$\"3%om\"zpe()=IF1$ \"3M\"HAMJyqr&Feu7$$\"3sL3_+-rsIF1$\"3:c1e/yJ/KF1$\"3RR&)eqU+7kFeu7$$\"3GM$e*[ACIKF 1$\"3PZ0M?mHghFeu7$$\"3v+D\"y5\"4#G$F1$\"3;BK?uU'3W&Feu7$$\"3%zmmm'*RR L$F1$\"3B\"p#3SB%H]%Feu7$$\"3Kn;a8H'pQ$F1$\"3&)*\\wm%HMAMFeu7$$\"3TnmT ge)*RMF1$\"3rG9@l/)>L#Feu7$$\"3]n;H2)3I\\$F1$\"3=-iV=:XO8Feu7$$\"3(omm TvJga$F1$\"3lC?n:>1t^FW7$$\"3_L3FWch)f$F1$!391QHK*)oHsF-7$$\"3(3+vV`*> ^OF1$!3uqIaANNnUFW7$$\"3>%3F%z9\\xOF1$!3E0%[>Pqk?&FW7$$\"3Ao\"zWU$y.PF 1$!3$)fAzW%\\7l&FW7$$\"3a^7`p`2IPF1$!3$pV$HQ)RVm&FW7$$\"3'[L$e9tOcPF1$ !3E$*oBQ\"oxJ&FW7$$\"3'zm\"H#e0I&QF1$!3?bpp)R$yEAFW7$$\"32,++]Qk\\RF1$ \"3HskF8B&y/\"FW7$$\"3,oT5SMLxRF1$\"3&HE%[=U*>m\"FW7$$\"3BM$3-.B]+%F1$ \"3$f9se(>>!3#FW7$$\"3Y+DJ?ErKSF1$\"3ijpb:)=%)H#FW7$$\"3SnmT5ASgSF1$\" 31([;82yeK#FW7$$\"3MM3_+=4)3%F1$\"35$Q&zM3*H=#FW7$$\"3d+]i!R\"y:TF1$\" 3ys41T=%*)*=FW7$$\"3!o;H2)4ZVTF1$\"3?*Hef*R&*3:FW7$$\"3uLL$3dg6<%F1$\" 3;H#HSGm90\"FW7$$\"3=n;zpBp?UF1$\"31Q%o#oCtg=F-7$$\"3i++voTAqUF1$!3Q^P FG&eXs&F-7$$\"3)p;H#o+*\\H%F1$!3e/.t1sEQ')F-7$$\"31M$3x'fv>VF1$!39CPld z;!3\"FW7$$\"38,v=n=_WVF1$!3=)G^iC;a@\"FW7$$\"3]nmmmxGpVF1$!3ilW=%**y% o7FW7$$\"3SM$eRA5\\Z%F1$!3*4%\\'*=p3rsF-7$$\"3J,+D\"oK0e%F1$\"3L(os6+m F(HF-7$$\"3q,]il(z5j%F1$\"3m%G=-Dr\"F-7$$\"#]F*$!3. " 0 "" {MPLTEXT 1 0 18 "display(p1,p2,p3);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7\\[ l7$$!3>N\\f'fQ7-%!#:$\"\"!F,7$$!3OP!f+nA)*)RF*$\"3&******p:pg(=!#C7$$! 3`RJ_VnSeRF*$\"30+++^()paPF27$$!39Ts)p\"3*p#RF*$\"3e*****p&egPcF27$$!3 KV8X!*[d&*QF*$\"3U+++-`oFvF27$$!3\\Xa\"R'*eT'QF*$\"3`+++v33F%*F27$$!3n Z&zt.VF$QF*$\"33+++;F#Q8\"!#B7$$!3&)\\O%36F8!QF*$\"3'******\\];jK\"FL7 $$!3X^xI%=6*pPF*$\"3/+++I7\\?:FL7$$!3i`=xd_\\QPF*$\"3-+++o5c;FL7$$!3)z0+ZSjcn$F*$\"3&)*****fTGa6#FL7$$!3 ;gT;yuCWOF*$\"3#)*****4!)[(=BFL7$$!3Li#G;bJGh$F*$\"3!)*****fxI]_#FL7$$ !3$RO#4DcT\"e$F*$\"3%)******HeaMFFL7$$!36mkb)p***\\NF*$\"3$******\\#Gg ZHFL7$$!3Ho0-sPe=NF*$\"3!******\\9oW;$FL7$$!3YqY[Xy;([$F*$\"3<+++Ds[&Q $FL7$$!3ks([*=>vbMF*$\"3-+++bR*4h$FL7$$!3CuGT#*fLCMF*$\"3?+++nUDTQFL7$ $!3Uwp(e1?HR$F*$\"3j******yVowSFL7$$!3fy5MRT]hLF*$\"3g*****R$RjL/%eB$F*$\"3#******p0YXM&FL 7$$!3\"*)ehm]CW?$F*$\"3Q+++q%y\">cFL7$$!33\"pD,e3I<$F*$\"3k*****>iW>!f FL7$$!3E$z*e`EfTJF*$\"3o*****zuEL>'FL7$$!3V&*Q0Fn<5JF*$\"3/+++K>(Q\\'F L7$$!3.(*z^+3wyIF*$\"3\")*****psZT!oFL7$$!3@*4#)R([MZIF*$\"3/+++,nxCrF L7$$!3R,iWZ*Gf,$F*$\"3P+++)ezjX(FL7$$!3c..\"4-8X)HF*$\"3g+++I1m*z(FL7$ $!3u0WP%4(4`HF*$\"3X+++19Kb\")FL7$$!3N2&Qy;\"o@HF*$\"3!)*****p(f8C&)FL 7$$!3_4EIT_E!*GF*$\"3T*****4r>p!*)FL7$$!3q6nw9$\\)eGF*$\"3l+++3&[XI*FL 7$$!3)Q\"3B)QLu#GF*$\"3^*****>Jezr*FL7$$!3/;\\phu,'z#F*$\"3)******z85[ ,\"!#A7$$!3lJi3c=LFF*$\"30+++2 ,I16F\\x7$$!3,As3#op_2EF*$\"3 ++++Q&pXJ\"F\\x7$$!39IO%f(f5wDF*$\"3(******H#Qts8F\\x7$$!3KKxS\\+pWDF* $\"3#******>bqOV\"F\\x7$$!3\\M=(G7uK^#F*$\"3%******zkev\\\"F\\x7$$!3mO fL'>e=[#F*$\"3')*****p_,Yc\"F\\x7$$!3cQ+!)pAW]CF*$\"3')******G8-N;F\\x 7$$!3tSTEVj->CF*$\"3.+++:?/4!\\%>cBF*$\"3!******p#z%*o=F\\x7$$!3)pWcOcyZK#F*$\"3&)*** **>!zSb>F\\x7$$!3')[07PEO$H#F*$\"3*******H*>iY?F\\x7$$!3/^Ye5n%>E#F*$ \"3%)*****p'4&H9#F\\x7$$!3A`([SyI0B#F*$\"3%)*****zbzZC#F\\x7$$!35bG^d[ 6*>#F*$\"37+++Q#>DN#F\\x7$$!3Gdp(4$*)pn@F*$\"3*)*****\\%3kmCF\\x7$$!3Y f5W/IGO@F*$\"3()*****>?Lwe#F\\x7$$!3Nh^!z2n[5#F*$\"3$******H>^gr#F\\x7 $$!3_j#p8:^M2#F*$\"3&******z=&\\_GF\\x7$$!3UlL$[AN?/#F*$\"3/+++_Ri(*HF \\x7$$!3fnuH)H>1,#F*$\"3#)*****fYo@:$F\\x7$$!3wp:wrL?z>F*$\"3s******H \"GpJ$F\\x7$$!3mrcAXuyZ>F*$\"35+++\"*>z#\\$F\\x7$$!3%Qx*o=:P;>F*$\"3G+ ++`7t!o$F\\x7$$!3svQ:#fb\\)=F*$\"3')*****pLR=)QF\\x7$$!3!z(zhl'RN&=F*$ \"3m*****HU;t4%F\\x7$$!33!3#3RP7A=F*$\"3)******z$G]GVF\\x7$$!3'>=YD\"y q!z\"F*$\"3\")*****p#4*od%F\\x7$$!39%G5g)=Hf8F*$\"3++++xe(QA\"F^fl7$$!31:=(z)H0)G\"F*$\"3.+++![(3C8F^fl7 $$!3C+!\\8@_A\"F*$\"3&******p_ x.c\"F^fl7$$!3I@TO3_!Q>\"F*$\"34+++a(z,q\"F^fl7$$!3[B#G=G*Qi6F*$\"3!** ****f,7v&=F^fl7$$!3_DBHbL(48\"F*$\"37+++7(z_.#F^fl7$$!3aFkvGub*4\"F*$ \"3*******>o+qB#F^fl7$$!3tH0A-:9o5F*$\"3!******\\rhpY#F^fl7$$!3wJYovbs O5F*$\"3%)*****z#yUIFF^fl7$$!3!Qt[\"\\'4`+\"F*$\"35+++P$=R.$F^fl7$$!3I e$GhAP*Q(*!#;$\"37+++l&ybQ$F^fl7$$!3ky$p2'zxC%*F^jl$\"3-+++n^o&z$F^fl7 $$!3R+/T&p=16*F^jl$\"3?+++tbMxUF^fl7$$!3s?90I%fkz)F^jl$\"3;+++6AZZ[F^f l7$$!31TCpk,I#[)F^jl$\"3#******>g!=GbF^fl7$$!3\"GYL$**39o\")F^jl$\"3_* ****\\o5)[jF^fl7$$!3:$[uRj\")R&yF^jl$\"3^+++z5$*[tF^fl7$$!3[.bhoB#)RvF ^jl$\"3:+++]d*Ge)F^fl7$$!3\"Q_cK5jcA(F^jl$\"3/+++bbp75!#?7$$!39Wv*y$Q] 6pF^jl$\"3\"********Ro!47Fi\\m7$$!3!fcQDdWtf'F^jl$\"3/+++&***fj9Fi\\m7 $$!3B'ezrI&=$G'F^jl$\"3/+++\"R95!=Fi\\m7$$!3d11#=/E!pfF^jl$\"3$)****** pacgAFi\\m7$$!3hF;Ywn'[l&F^jl$\"3\"******fV*e2HFi\\m7$$!3m[E56vqS`F^jl $\"35+++jJPdQFi\\m7$$!3)*oOuX#[l-&F^jl$\"37+++]$))*G`Fi\\m7$$!3K*o%Q!) *)Q7ZF^jl$\"3++++m,G\"y(Fi\\m7$$!3O5d-:(H#)R%F^jl$\"3&******pU;8B\"!#> 7$$!3TJnm\\/2%3%F^jl$\"35+++M!fK@#Fg_m7$$!3u^xI%=6*pPF^jl$\"3!******\\ /wT-&Fg_m7$$!32s([*=>vbMF^jl$\"3%******\\CF=-#!#=7$$!37$z*e`EfTJF^jl$! 3a+++jRtrmFg`m7$$!3!Q\"3B)QLu#GF^jl$\"33+++)>43-#Fg`m7$$FgzF^jl$\"3r** ****f`].]Fg_m7$$!3=bG^d[6*>#F^jl$\"3*)*****Hva9=#Fg_m7$$!3(e(Q:#fb\\)= F^jl$\"3.+++?-N(=\"Fg_m7$$!3c'*[zEjzq:F^jl$\"3q*****4I+]?(Fi\\m7$$!3D< fVhqjc7F^jl$\"3w*****>s:]f%Fi\\m7$$!3Mz$p2'zxC%*!#<$\"3!******>Iak$HFi \\m7$$Ff]mF]cm$\"3/+++*oB!fIak$HFi\\m7$$\"3Ds:]f%Fi\\m7$$\"3c'*[zEjzq:F^jl$!3q*****4I+]?(Fi\\m7$$\" 3(e(Q:#fb\\)=F^jl$!3.+++?-N(=\"Fg_m7$$\"3=bG^d[6*>#F^jl$!3*)*****Hva9= #Fg_m7$$\"3\\M=(G7uK^#F^jl$!3r******f`].]Fg_m7$$\"3!Q\"3B)QLu#GF^jl$!3 3+++)>43-#Fg`m7$$F[dmF^jl$\"3a+++jRtrmFg`m7$$\"32s([*=>vbMF^jl$!3%**** **\\CF=-#Fg`m7$$\"3u^xI%=6*pPF^jl$!3!******\\/wT-&Fg_m7$$\"3TJnm\\/2%3 %F^jl$!35+++M!fK@#Fg_m7$$\"3O5d-:(H#)R%F^jl$!3&******pU;8B\"Fg_m7$$\"3 K*o%Q!)*)Q7ZF^jl$!3++++m,G\"y(Fi\\m7$$\"3)*oOuX#[l-&F^jl$!37+++]$))*G` Fi\\m7$$\"3m[E56vqS`F^jl$!35+++jJPdQFi\\m7$$\"3hF;Ywn'[l&F^jl$!3\"**** **fV*e2HFi\\m7$$\"3d11#=/E!pfF^jl$!3$)******pacgAFi\\m7$$F`dmF^jl$!3/+ ++\"R95!=Fi\\m7$$\"3!fcQDdWtf'F^jl$!3/+++&***fj9Fi\\m7$$\"39Wv*y$Q]6pF ^jl$!3\"********Ro!47Fi\\m7$$\"3\"Q_cK5jcA(F^jl$!3/+++bbp75Fi\\m7$$\"3 [.bhoB#)RvF^jl$!3:+++]d*Ge)F^fl7$$\"3:$[uRj\")R&yF^jl$!3^+++z5$*[tF^fl 7$$\"3\"GYL$**39o\")F^jl$!3_*****\\o5)[jF^fl7$$\"31TCpk,I#[)F^jl$!3#** ****>g!=GbF^fl7$$\"3s?90I%fkz)F^jl$!3;+++6AZZ[F^fl7$$\"3R+/T&p=16*F^jl $!3?+++tbMxUF^fl7$$\"3ky$p2'zxC%*F^jl$!3-+++n^o&z$F^fl7$$\"3Ie$GhAP*Q( *F^jl$!37+++l&ybQ$F^fl7$$\"3!Qt[\"\\'4`+\"F*$!35+++P$=R.$F^fl7$$\"3wJY ovbsO5F*$!3%)*****z#yUIFF^fl7$$\"3tH0A-:9o5F*$!3!******\\rhpY#F^fl7$$ \"3aFkvGub*4\"F*$!3*******>o+qB#F^fl7$$\"3_DBHbL(48\"F*$!37+++7(z_.#F^ fl7$$\"3[B#G=G*Qi6F*$!3!******f,7v&=F^fl7$$\"3I@TO3_!Q>\"F*$!34+++a(z, q\"F^fl7$$\"3G>+!\\8@_A\"F*$!3&******p_x.c\"F^fl7$$\"3C8 F*$!3++++xe(QA\"F^fl7$$\"3+6O/T[)3N\"F*$!3/+++tAhL6F^fl7$$\"3#)3&zvw+B Q\"F*$!3$*******pL2_5F^fl7$$\"3%pS:Tp;PT\"F*$!30+++LJ8#y*F\\x7$$\"3w/8 l?E8X9F*$!3[+++6_N6\"*F\\x7$$\"3(G?(=Z&[lZ\"F*$!3g******)yj1])F\\x7$$ \"3q+JstW'z]\"F*$!3o+++nGQVzF\\x7$$\"3_)**e-S!QR:F*$!3E+++0*3PV(F\\x7$ $\"3i'*[zEjzq:F*$!3e*****H#*)empF\\x7$$\"3X%zILD7Ag\"F*$!3!*******)4,w `'F\\x7$$\"3c#pm)z\"GOj\"F*$!3^+++_b(G9'F\\x7$$\"3Q!f-k5W]m\"F*$!3')** ***zH/!zdF\\x7$$\"3?)[QH.gkp\"F*$!3%)******p!yHW&F\\x7$$\"3K'Qu%ff(ys \"F*$!3'******H#)[@8&F\\x7$$\"39%G5g)=Hf=YD \"yq!z\"F*$!3\")*****p#4*od%F\\x7$$\"33!3#3RP7A=F*$!3)******z$G]GVF\\x 7$$\"3!z(zhl'RN&=F*$!3m*****HU;t4%F\\x7$$\"3svQ:#fb\\)=F*$!3')*****pLR =)QF\\x7$$\"3%Qx*o=:P;>F*$!3G+++`7t!o$F\\x7$$\"3mrcAXuyZ>F*$!35+++\"*> z#\\$F\\x7$$\"3wp:wrL?z>F*$!3s******H\"GpJ$F\\x7$$\"3fnuH)H>1,#F*$!3#) *****fYo@:$F\\x7$$\"3UlL$[AN?/#F*$!3/+++_Ri(*HF\\x7$$\"3_j#p8:^M2#F*$! 3&******z=&\\_GF\\x7$$\"3Nh^!z2n[5#F*$!3$******H>^gr#F\\x7$$\"3Yf5W/IG O@F*$!3()*****>?Lwe#F\\x7$$\"3Gdp(4$*)pn@F*$!3*)*****\\%3kmCF\\x7$$\"3 5bG^d[6*>#F*$!37+++Q#>DN#F\\x7$$\"3A`([SyI0B#F*$!3%)*****zbzZC#F\\x7$$ \"3/^Ye5n%>E#F*$!3%)*****p'4&H9#F\\x7$$\"3')[07PEO$H#F*$!3*******H*>iY ?F\\x7$$\"3)pWcOcyZK#F*$!3&)*****>!zSb>F\\x7$$\"3![M#>!\\%>cBF*$!3!*** ***p#z%*o=F\\x7$$\"3iU#GnT5wQ#F*$!3')*****fHFpy\"F\\x7$$\"3tSTEVj->CF* $!3.+++:?/4e=[# F*$!3')*****p_,Yc\"F\\x7$$F^fmF*$!3%******zkev\\\"F\\x7$$\"3KKxS\\+pWD F*$!3#******>bqOV\"F\\x7$$\"39IO%f(f5wDF*$!3(******H#Qts8F\\x7$$\"3aG& zC!>_2EF*$!3++++Q&pXJ\"F\\x7$$\"3OEa,Hy$*QEF*$!3%*******zp**e7F\\x7$$ \"3=C8bbPNqEF*$!3(******49he?\"F\\x7$$\"3,As3#opJi3c=LFF*$!30+++2,I16F\\x7$$\"3lJezr*FL7$$\"3q6nw9$\\)eGF*$!3l+++3&[XI*FL7$$\"3_4EIT_E!*GF*$!3T*****4 r>p!*)FL7$$\"3N2&Qy;\"o@HF*$!3!)*****p(f8C&)FL7$$\"3u0WP%4(4`HF*$!3X++ +19Kb\")FL7$$\"3c..\"4-8X)HF*$!3g+++I1m*z(FL7$$\"3R,iWZ*Gf,$F*$!3P+++) ezjX(FL7$$\"3@*4#)R([MZIF*$!3/+++,nxCrFL7$$\"3.(*z^+3wyIF*$!3\")*****p sZT!oFL7$$\"3V&*Q0Fn<5JF*$!3/+++K>(Q\\'FL7$$\"3E$z*e`EfTJF*$!3o*****zu EL>'FL7$$\"33\"pD,e3I<$F*$!3k*****>iW>!fFL7$$\"3\"*)ehm]CW?$F*$!3Q+++q %y\">cFL7$$\"3t'[(>L/%eB$F*$!3#******p0YXM&FL7$$\"37&QL(fjDnKF*$!30+++ $p6v2&FL7$$\"3%HGpiGs')H$F*$!3')******Q%Rw\"[FL7$$\"3x!=0G@)3ILF*$!3p* ****Hu*\\kXFL7$$\"3fy5MRT]hLF*$!3g*****R$RjvbMF*$!3-+++b R*4h$FL7$$\"3YqY[Xy;([$F*$!3<+++Ds[&Q$FL7$$\"3Ho0-sPe=NF*$!3!******\\9 oW;$FL7$$\"36mkb)p***\\NF*$!3$******\\#GgZHFL7$$\"3$RO#4DcT\"e$F*$!3%) ******HeaMFFL7$$\"3Li#G;bJGh$F*$!3!)*****fxI]_#FL7$$\"3;gT;yuCWOF*$!3# )*****4!)[(=BFL7$$\"3)z0+ZSjcn$F*$!3&)*****fTGa6#FL7$$\"3!e&fBJ$zqq$F* $!33+++J9![\">FL7$$\"3i`=xd_\\QPF*$!3-+++o5c;b-y)pURF*$\"3;++++](o*HF`\\p7$F9$!3I++++]iPcF27$$!3B# H>P&GG6RF*$!35+++](ou+$F`\\p7$F>$\"3<+++QfeFvF27$$!3S%R$=Fp')zQF*$\"3C +++vV)H-$F`\\p7$FC$!3A+++D19F%*F27$$!3e'\\Z1+^%[QF*$!3;+++D\"G)QIF`\\p 7$FH$\"3&*******=n$Q8\"FL7$$!3w)f6T2Nq\"QF*$\"3v********\\(=1$F`\\p7$F N$!3!******\\(oHE8FL7$$!3$4qvv9>cy$F*$!39+++D\"G84$F`\\p7$FS$\"35+++++ ]?:FL7$$!3a-)R5A.Uv$F*$\"30+++++v=JF`\\p7$FX$!3'******\\P%[;FL7$$!3)o+ozOr8p$F*$\"3%) *******\\7`>$F`\\p7$F\\o$!3%)******\\(oa6#FL7$$!314@VTa&*fOF*$!3r***** *****\\PKF`\\p7$Fao$\"3A+++vVt=BFL7$$!3C6i*[^R&GOF*$\"32+++]7.#G$F`\\p 7$Ffo$!33+++QM-DDFL7$$!3%GJg$)eBrf$F*$!3F+++vV[LLF`\\p7$F[p$\"3-+++Jq] MFFL7$$!3-:W#=m2dc$F*$\"3=+++iST!R$F`\\p7$F`p$!37+++JXfZHFL7$$!3?<&)GN Ev3e(G]$F*$\"3 3+++i!Rv^$F`\\p7$Fjp$!3,++++v[&Q$FL7$$!3b@n@#))f9Z$F*$!3H+++i:b%e$F`\\ p7$F_q$\"3)******4G))4h$FL7$$!3sB3obR/SMF*$\"34+++DJqmOF`\\p7$Fdq$!3#) *****>\"yDTQFL7$$!3MD\\9H!G'3MF*$!3o*****\\P%[[PF`\\p7$Fiq$\"3A+++7`pw SFL7$$!3]F!4E57sP$F*$\"3u*****\\ilZ$QF`\\p7$F^r$!3-++++]icFL7$$!3**RORVlr)=$F*$\"3I+++1k'y\\%F`\\p7$F\\t$!3;+++A\\&>!fFL7$ $!3'FL7$$!3MW=K!p%) e7$F*$\"3I+++7.#Gy%F`\\p7$Fft$!3G+++1*oQ\\'FL7$$!3%f%fyj(oW4$F*$!3G+++ ](ov$\\F`\\p7$F[u$\"33+++Z!3U!oFL7$$!37[+DPG0jIF*$\"3\")*****4GQW5&F` \\p7$F`u$!3A+++cwxCrFL7$$!3I]Tr5pjJIF*$!37+++]i?w_F`\\p7$Feu$\"3I+++y] ScuFL7$$!3[_#yT)4A+IF*$\"3>+++%[TQY&F`\\p7$Fju$!3_+++%[h'*z(FL7$$!3laB kd]!)oHF*$!3'*******e3GfcF`\\p7$F_v$\"3*******4.F`:)FL7$$!3#oX168*QPHF *$\"3K+++f39seF`\\p7$Fdv$!3A+++1R8C&)FL7$$!3We0d/K(f!HF*$!3%******z=( \\\"4'F`\\p7$Fiv$\"3w+++(zEp!*)FL7$$!3hgY.ysbuGF*$\"3)******f^.oK'F`\\ p7$F^w$!3S*****Hq]XI*FL7$$!3yi()\\^89VGF*$!3g*****R4'oulF`\\p7$Fcw$\"3 e*******\\#)zr*FL7$$!3'\\'G'\\UD<\"GF*$\"3E+++4@b^oF`\\p7$Fhw$!3%***** *HQ3[,\"F\\x7$$!38npU)\\4.y#F*$!3W+++paiFrF`\\p7$F^x$\"3(********\\4'f 5F\\x7$$!3uo5*=d$*)[FF*$\"3i+++D\"30V(F`\\p7$Fcx$!3,+++X**H16F\\x7$$!3 #4)=<1 'o#F*$\"3e******\\([L4)F`\\p7$F]y$!3%******zVge?\"F\\x7$$!3FvLG#zXYl#F *$!31+++]P)oX)F`\\p7$Fby$\"3#******f,'**e7F\\x7$$!3Wxuul)HKi#F*$\"3h++ +v$fM%))F`\\p7$Fgy$!3/+++t(oXJ\"F\\x7$$!3/z:@RR\"=f#F*$!3F+++7G)oD*F` \\p7$F\\z$\"3'******>1QFP\"F\\x7$$!3A\"ovE,)RgDF*$\"38+++Q4'4q*F`\\p7$ Faz$!3)*******H*pOV\"F\\x7$$!3S$yRh3#)*GDF*$!3-+++Zbs;5F27$Ffz$\"3'*** ***4`ev\\\"F\\x7$$!3e&)Qgfhc(\\#F*$\"3-+++\"*G&p1\"F27$F[[l$!3()*****p z,Yc\"F\\x7$$!3Z()z1L-:mCF*$!3*******4`%R?6F27$F`[l$\"33+++J?-N;F\\x7$ $!3k*3KlIMZV#F*$\"3,+++Qf)z<\"F27$Fe[l$!34+++J?/4'**z$=LS #F*$!3+++++]UR7F27$Fj[l$\"3)******z$f#py\"F\\x7$$!3r$HgMX->P#F*$\"36++ ++]708F27$F_\\l$!33+++Q%[*o=F\\x7$$!3)eRCp_'[SBF*$!30+++vozw8F27$Fd\\l $\"3-+++7GQb>F\\x7$$!31)\\)Q+124BF*$\"3#******\\Pf3X\"F27$Fi\\l$!3*)** ****=UiY?F\\x7$$!3&**f_QnawF#F*$!3++++vV)H`\"F27$F^]l$\"35+++Z0&H9#F\\ x7$$!38-nJZ(QiC#F*$\"3))*****R%)*Q?;F27$Fc]l$!3++++;5yWAF\\x7$$!3-/3y? G#[@#F*$!3-+++7.([r\"F27$Fh]l$\"3&)*****pa?DN#F\\x7$$!3>1\\C%*oS$=#F*$ \"34+++7.x:=F27$F]^l$!35+++`>kmCF\\x7$$!3P3!4x'4*>:#F*$!3++++(Hz`#>F27 $Fb^l$\"3)******>cGwe#F\\x7$$!3E5JF*$ \"34+++D\"GF*$!35+++DcE)z# F27$F``l$\"3C+++JXz#\\$F\\x7$$!3uAx&>[z?$>F*$\"3#)*******\\i0*HF27$Fe` l$!3?+++`>t!o$F\\x7$$!3#\\#=UbNm+>F*$!3++++v=x*>$F27$Fj`l$\"3$)******3 'R=)QF\\x7$$!3\"o#f))GwCp=F*$\"3))******\\iXGMF27$F_al$!3))*****f::t4% F\\x7$$!3**G+N-<$y$=F*$!3%)*****>c,\"yOF27$Fdal$\"3u*****4*y]GVF\\x7$$ !3;JT\"ex:k!=F*$\"3%)*****\\7.A&RF27$Fial$!39+++y+*od%F\\x7$$!30L#y#\\ )**\\x\"F*$!32+++)=UAD%F27$F^bl$\"3A+++.2:W[F\\x7$$!3BNBuAReV+++%)*[@8&F\\x7$$!37Pk?'*z;7+++` W+zdF\\x7$$!3ZTY8VhL\\;F*$!3_+++1k1*y&F27$Fbcl$\"3Z*****4yuG9'F\\x7$$! 3OV()f;-#zh\"F*$\"3$)*****z2g)ziF27$Fgcl$!3e*****z#3gPlF\\x7$$!3`XG1!H /le\"F*$!3k*****R4T[#oF27$F\\dl$\"3()*****fe!fmpF\\x7$$!3rZp_j$)3b:F*$ \"3')*****4G=\"G`l))F 27$F[el$!33+++`Mm+&)F\\x7$$!3n`#>ReS3Y\"F*$!3h*****>1/Xr*F27$F`el$\"3c +++[^N6\"*F\\x7$$!3&eN$QdYUH9F*$\"3)******z=iq1\"FL7$Feel$!3&******flK @y*F\\x7$$!3-eu%3t3!)R\"F*$!3(******R[@\\<\"FL7$Fjel$\"3*******Hqt?0\" F^fl7$$!3\"*f:J/Gfm8F*$\"3#*******o/.(H\"FL7$F`fl$!3*******pz6O8\"F^fl 7$$!34icxxoFL7$Fdg l$!3!******zvx.c\"F^fl7$$!3Pq?jrJ^47F*$!3!******>#**\\BAFL7$Figl$\"3-+ ++H#z,q\"F^fl7$$!3Rsh4Xs4y6F*$\"33+++Dm4-DFL7$F^hl$!3!*******p?^d=F^fl 7$$!3Vu-c=8oY6F*$!3$)*****4@Zp#GFL7$Fchl$\"3-+++\"zz_.#F^fl7$$!3hwV-#R l_6\"F*$\"3=+++-\"Rw?$FL7$Fhhl$!39+++]0+PAF^fl7$$!3ky%)[l%\\Q3\"F*$!3> +++$Q(RcOFL7$F]il$\"35+++BF'pY#F^fl7$$!3n!e_*QNV_5F*$\"3;+++U-)*)=%FL7 $Fbil$!37+++xwUIFF^fl7$$!3r#o;Ch<5-\"F*$!3')*****R[L[#[FL7$Fgil$\"3'** ****pB=R.$F^fl7$$!3')[y!)eo,'*)*F^jl$\"31+++8F5!f&FL7$F\\jl$!3))*****H YybQ$F^fl7$$!3=p)[Mfd=e*F^jl$!3()*****pP_%=lFL7$Fbjl$\"39+++s_o&z$F^fl 7$$!3_*))*3G$)pn#*F^jl$\"3\"******zR:Zl(FL7$Fgjl$!3')******oaMxUF^fl7$ $!3&)44ti!RN&*)F^jl$!3C+++*GN$f!*FL7$F\\[m$\"30+++u?ZZ[F^fl7$$!3gJ>P(z z$R')F^jl$\"3++++ilX\"3\"F\\x7$Fa[m$!3_+++)R!=GbF^fl7$$!3%>&H,K0AD$)F^ jl$!3/+++G!zMI\"F\\x7$Ff[m$\"3`+++02\")[jF^fl7$$!3FsRlm716!)F^jl$\"35+ ++)>\">)e\"F\\x7$F[\\m$!3z*****4)3$*[tF^fl7$$!3g#*\\H,?!pp(F^jl$!38+++ #4U*e>F\\x7$F`\\m$\"3B+++1a*Ge)F^fl7$$!3O9g$ftUFQ(F^jl$\"3\"******\\c; .X#F\\x7$Fe\\m$!3-+++hbp75Fi\\m7$$!3pMqdqMeoqF^jl$!3%******zmp[6$F\\x7 $F[]m$\"3-+++G%o!47Fi\\m7$$!3-b!=_?CWv'F^jl$\"3K+++7R,NSF\\x7$F`]m$!30 +++\"***fj9Fi\\m7$$!3Ov!f)R\\ESkF^jl$!3%******>5#)[M&F\\x7$Fe]m$\"31++ +(Q95!=Fi\\m7$$!3S'4+Xn0h7'F^jl$\"3R+++;2FssF\\x7$Fj]m$!3&******4Wl0E# Fi\\m7$$!3W<694k%>\"eF^jl$!31+++y5[A5F^fl7$F_^m$\"3%)*****>c*e2HFi\\m7 $$!3yP@yVry(\\&F^jl$\"3'*******pq'z\\\"F^fl7$Fd^m$!3))*****z5tt&QFi\\m 7$$!3#)eJUyyi$=&F^jl$!3,+++Fz79BF^fl7$Fi^m$\"3l******e$))*G`Fi\\m7$$!3 :zT18'o%p[F^jl$\"3/+++9&)3QQF^fl7$F^_m$!3n*****49!G\"y(Fi\\m7$$!3?+_qZ $4`b%F^jl$!3v******fXoMqF^fl7$Fc_m$\"3++++QkJJ7Fg_m7$$!3`?iM#3]6C%F^jl $\"31+++\"fw%*\\\"Fi\\m7$Fi_m$!3'******R-fK@#Fg_m7$$!3eTs)p\"3*p#RF^jl $!3H+++$\\ND7%Fi\\m7$F^`m$\"39+++[gEG;bJGh$F^jl$\"3'**** **>?`0\">Fg_m7$Fc`m$!3-+++Ys#=-#Fg`m7$$!3'HGpiGs')H$F^jl$!3]*****4jq,; &Fg`m7$Fi`m$!3g*****\\'RtrmFg`m7$$!3G..\"4-8X)HF^jl$!3f*****\\XK.;&Fg` m7$F^am$!3*)******)>43-#Fg`m7$$!3LC8bbPNqEF^jl$\"3#******zb?A\">Fg_mFb am7$$!3mWB>!\\%>cBF^jl$!3f*****H)*H-9%Fi\\m7$Fgam$!3-+++jZX\"=#Fg_m7$$ !3qlL$[AN?/#F^jl$\"35+++zS+]?(Fi\\m7$$!3!pS :Tp;PT\"F^jl$\"3,+++J'H&)3%F^fl7$Ffbm$\"3k******\\d,&f%Fi\\m7$$!3gFkvG ub*4\"F^jl$!3/+++qp\"4h#F^fl7$F[cm$!39+++_VXOHFi\\m7$$!3y#[uRj\")R&yF] cm$\"3/+++()p>f=F^fl7$Facm$\"31+++HO-fQUu9F^fl7$Fecm$!3@+++e2:q#)F^fl7$$!3b'*[zEjzq:F]cm$\"37+++*o8&48F^f lFhcm7$$\"3b'*[zEjzq:F]cm$!33+++?T^48F^fl7$Fjcm$\"3>+++;&\\,F)F^fl7$$ \"3n*o%Q!)*)Q7ZF]cm$\"3'******4rAWZ\"F^fl7$F_dm$!32+++WQ-fc)>f=F^fl7$Fddm$\"3#)*****R@ak$HFi\\m7$$\"3 gFkvGub*4\"F^jl$\"3\"******HV;4h#F^fl7$Fidm$!39+++Pd,&f%Fi\\m7$$\"3!pS :Tp;PT\"F^jl$!3#)*****\\FI&)3%F^fl7$F^em$\"3()******e-+0sFi\\m7$$\"3/' Qu%ff(ys\"F^jl$\"3]*****zk?B]t=\"Fg_m7$$\"3qlL $[AN?/#F^jl$!3!******4*>!)=:Fi\\m7$Fhem$\"3-+++UZX\"=#Fg_m7$$\"3mWB>! \\%>cBF^jl$\"3g******p)H-9%Fi\\m7$F]fm$!3K+++f`].]Fg_m7$$\"3LC8bbPNqEF ^jl$!3%)*****zd?A\">Fg_m7$FbfmF`am7$$\"3G..\"4-8X)HF^jl$\"3`+++`CLg^Fg `m7$Fgfm$\"3H+++gRtrmFg`m7$$\"3'HGpiGs')H$F^jl$\"3G+++F1EG;bJGh$F^jl$!3'******4=`0\">Fg_m7$F`gm$!3J+++]g\"GTJ#F^fl7$Fihm$\"3,+++'=tt&QFi\\m7$$\"3yP@yVry( \\&F^jl$!3++++Bk'z\\\"F^fl7$F^im$!3'******RU*e2HFi\\m7$$\"3W<694k%>\"e F^jl$\"3'*******)G\"[A5F^fl7$Fcim$\"3:++++bcgAFi\\m7$$\"3S'4+Xn0h7'F^j l$!3u*****>npAF(F\\x7$Fhim$!35+++xV,,=Fi\\m7$$\"3Ov!f)R\\ESkF^jl$\"3%* *****fw%)[M&F\\x7$F\\jm$\"3$*******o**fj9Fi\\m7$$\"3-b!=_?CWv'F^jl$!3. +++>U-NSF\\x7$Fajm$!3%******\\bo!47Fi\\m7$$\"3pMqdqMeoqF^jl$\"3++++Q4' [6$F\\x7$Ffjm$\"32+++Zbp75Fi\\m7$$\"3O9g$ftUFQ(F^jl$!3.+++JXJ]CF\\x7$F [[n$!3$)*****zR&*Ge)F^fl7$$\"3g#*\\H,?!pp(F^jl$\"3++++<;%*e>F\\x7$F`[n $\"3))*****phJ*[tF^fl7$$\"3FsRlm716!)F^jl$!3%******Rtt\")e\"F\\x7$Fe[n $!3x******[!4)[jF^fl7$$\"3%>&H,K0AD$)F^jl$\"3&********Q\"\\.8F\\x7$Fj[ n$\"3O+++X6=GbF^fl7$$\"3gJ>P(zz$R')F^jl$!32+++rkX\"3\"F\\x7$F_\\n$!35+ ++s@ZZ[F^fl7$$\"3&)44ti!RN&*)F^jl$\"3B+++W$R$f!*FL7$Fd\\n$\"3B+++IdMxU F^fl7$$\"3_*))*3G$)pn#*F^jl$!3S+++;&zYl(FL7$Fi\\n$!3-+++iZo&z$F^fl7$$ \"3=p)[Mfd=e*F^jl$\"3S+++'3)\\=lFL7$F^]n$\"3#)*****RpybQ$F^fl7$$\"3')[ y!)eo,'*)*F^jl$!3C+++fj3!f&FL7$Fc]n$!3'******pB=R.$F^fl7$$\"3r#o;Ch<5- \"F*$\"3y******fM$[#[FL7$Fh]n$\"3y*****f\"yUIFF^fl7$$\"3n!e_*QNV_5F*$! 3!)*****4%f#*)=%FL7$F]^n$!3z*****z)>'pY#F^fl7$$\"3ky%)[l%\\Q3\"F*$\"3! ******zYDkl$FL7$Fb^n$\"3++++m1+PAF^fl7$$\"3hwV-#Rl_6\"F*$!3++++!yVw?$F L7$Fg^n$!37+++m(z_.#F^fl7$$\"3Vu-c=8oY6F*$\"3++++7$fp#GFL7$F\\_n$\"32+ ++%37v&=F^fl7$$\"3Rsh4Xs4y6F*$!3#)******z!R?]#FL7$Fa_n$!3)******>@z,q \"F^fl7$$\"3Pq?jrJ^47F*$\"3!******R[MMA#FL7$Ff_n$\"3#******fsx.c\"F^fl 7$$\"3Loz;)4H4C\"F*$!34+++)opJ)>FL7$F[`n$!3++++svoN9F^fl7$$\"3:mQqC]Ms 7F*$\"3%*******\\b.vM@y*F\\x7$$\"3&eN$QdYUH9F*$!3-+++DT6n5FL7$Fian$ !3;+++MReS3Y\"F*$\"3)*)****zVQ\\r*F27$F^bn$\"3&*** ***Hxk1])F\\x7$$\"3y^^X5lD#\\\"F*$!3?+++;gbl))F27$Fcbn$!3b*****>\"oQVz F\\x7$$\"3g\\5*pVsO_\"F*$\"3N+++(Hk$3\")F27$Fhbn$\"3%******>n3PV(F\\x7 $$\"3rZp_j$)3b:F*$!3i*****f!*y8V(F27$F]cn$!32+++]iempF\\x7$$\"3`XG1!H/ le\"F*$\"3]+++]P4DoF27$Fbcn$\"3W******o/gPlF\\x7$$\"3OV()f;-#zh\"F*$!3 l*****\\(=7!G'F27$Fgcn$!3]+++vV(G9'F\\x7$$\"3ZTY8VhL\\;F*$\"3T+++voH*y &F27$F\\dn$\"32++++++zdF\\x7$$\"3HR0np?v!o\"F*$!3k*****\\iSmM&F27$Fadn $!3()*****>cwHW&F\\x7$$\"37Pk?'*z;7F*$\"3?+++QM** *>$F27$Fdfn$\"3-+++G=t!o$F\\x7$$\"3uAx&>[z?$>F*$!3(******zKE+*HF27$Fif n$!3u*****Hj$z#\\$F\\x7$$\"3d?O\\3a\\j>F*$\"3!)*****\\il%)z#F27$F^gn$ \"3A+++9%HpJ$F\\x7$$\"3o=&H]L6\\*>F*$!3u******e3t@EF27$Fcgn$!39+++Qf;_ JF\\x7$$\"3];achsKE?F*$\"32+++7y:fCF27$Fhgn$\"3#)*****R)Ri(*HF\\x7$$\" 3h985)=Vx0#F*$!3&******\\(oH4BF27$F]hn$!31+++iS\\_GF\\x7$$\"3V7sj9\"f \"*3#F*$\"3-+++](o9<#F27$Fbhn$\"3'******><^gr#F\\x7$$\"3E5J:#F*$\"3(******zV[ `#>F27$F\\in$\"3&)*****>cTmY#F\\x7$$\"3>1\\C%*oS$=#F*$!37+++7`W:=F27$F ain$!3%******pz@DN#F\\x7$$\"3-/3y?G#[@#F*$\"3$******\\i!R9?;F27$F[jn$!32+++.2&H9#F\\x7 $$\"3&**f_QnawF#F*$\"3))*****R4@G`\"F27$F`jn$\"3\"******>UAm/#F\\x7$$ \"31)\\)Q+124BF*$!30+++]7G^9F27$Fejn$!3&)******o/Sb>F\\x7$$\"3)eRCp_'[ SBF*$\"3/+++D\"GeP\"F27$Fjjn$\"3;+++m(\\*o=F\\x7$$\"3r$HgMX->P#F*$!3'* *****R%)*308F27$F_[o$!3(******RMEpy\"F\\x7$$\"3#=>'**z$=LS#F*$\"3))*** **p/$fR7F27$Fd[o$\"3;+++.F/41kO%))F`\\p7$Ff]o$!3-+++1k**e7F\\x7$$\"3FvLG#zX Yl#F*$\"3\"******\\(ozc%)F`\\p7$F[^o$\"3********=<'e?\"F\\x7$$\"34t#>) =<1'o#F*$!3!)*******\\(=#4)F`\\p7$F`^o$!3(********\\7]:\"F\\x7$$\"3#4< b`kxur#F*$\"3v******\\PM_xF`\\p7$Fe^o$\"30+++>#*H16F\\x7$$\"3uo5*=d$*) [FF*$!3Q++++DJIuF`\\p7$Fj^o$!3&******HX4'f5F\\x7$$\"38npU)\\4.y#F*$\"3 ]+++](oz7(F`\\p7$F__o$\"3-+++y+\"[,\"F\\x7$$\"3'\\'G'\\UD<\"GF*$!3y*** **zVtx%oF`\\p7$Fd_o$!3D+++Z0&zr*FL7$$\"3yi()\\^89VGF*$\"3&*******\\i?z lF`\\p7$Fi_o$\"3[*****>n`XI*FL7$$\"3hgY.ysbuGF*$!3S+++1*y$GjF`\\p7$F^` o$!3]+++D\"Gp!*)FL7$$\"3We0d/K(f!HF*$\"3s*****f:gC4'F`\\p7$Fc`o$\"3%** *****\\P9C&)FL7$$\"3#oX168*QPHF*$!3()*****4y+_'eF`\\p7$Fh`o$!3<+++J&H` :)FL7$$\"3laBkd]!)oHF*$\"3%)*****4G)yhcF`\\p7$F]ao$\"3U+++`>m*z(FL7$$ \"3[_#yT)4A+IF*$!31++++D;iaF`\\p7$Fbao$!3I+++y]ScuFL7$$\"3I]Tr5pjJIF*$ \"3o*****>nyfF&F`\\p7$Fgao$\"3r*****pHzZ7(FL7$$\"37[+DPG0jIF*$!3D+++mZ 2+^F`\\p7$F\\bo$!3M+++%4YT!oFL7$$\"3%f%fyj(oW4$F*$\"3y*****z2&3R\\F`\\ p7$Fabo$\"37+++p/(Q\\'FL7$$\"3MW=K!p%)e7$F*$!3)******R4'4%y%F`\\p7$Ffb o$!3E+++GQJ$>'FL7$$\"3!fFL7$$\"3**RORVlr)=$F*$!3o*****f:l&*\\%F`\\p7$F`co$!3Q+++A\\8> cFL7$$\"3#y`H*pC8?KF*$\"3!)*****>c^DP%F`\\p7$Feco$\"37+++](eXM&FL7$$\" 3kNaY'R[:D$F*$!3$)*****>19.D%F`\\p7$Fjco$!3s*****zoMv2&FL7$$\"3.M8+BV' HG$F*$\"3++++cEiNTF`\\p7$F_do$\"3p*****49\\w\"[FL7$$\"3'=BP&\\-Q9LF*$! 39+++pHkDSF`\\p7$Fddo$!33+++f3\\kXFL7$$\"3oHJ2whzXLF*$\"3)*******=#*RJ RF`\\p7$Fido$\"3k******\\Pk\"yDTQFL7$$\"3sB3obR/SMF*$!32+++iSwlOF`\\p7$Fheo$!3z*******\\()4h$F L7$$\"3b@n@#))f9Z$F*$\"3s*****zo/`e$F`\\p7$F]fo$\"3-+++]P\\&Q$FL7$$\"3 Q>Ev3e(G]$F*$!3-+++D\"yg^$F`\\p7$Fbfo$!3/+++\"GjW;$FL7$$\"3?<&)GNX$F`\\p7$Fgfo$\"3#******fl(fZHFL7$$\"3-:W#=m2dc$F*$! 36+++ilZ*Q$F`\\p7$F\\go$!33+++v=_MFFL7$$\"3%GJg$)eBrf$F*$\"3()******* \\7[L$F`\\p7$Fago$\"33+++QM-DDFL7$$\"3C6i*[^R&GOF*$!3H+++vVt#G$F`\\p7$ Ffgo$!3(*******\\(=(=BFL7$$\"314@VTa&*fOF*$\"35+++]7GQKF`\\p7$F[ho$\"3 ))*****\\i!R:@FL7$$\"3)o+ozOr8p$F*$!3x********\\7.KF`\\p7$F`ho$!3++++D cw9>FL7$$\"3s/R]%H(yAPF*$\"3A+++++DcJF`\\p7$Feho$\"3'******\\P%[;cy$F *$\"3A+++]i:!4$F`\\p7$F_io$\"3(******zo/jK\"FL7$$\"3w)f6T2Nq\"QF*$!3x* ****\\7yq1$F`\\p7$Fdio$!3)*******=#\\Q8\"FL7$$\"3e'\\Z1+^%[QF*$\"3&)** ******\\7UIF`\\p7$Fiio$\"3a*****zV)*oU*F27$$\"3S%R$=Fp')zQF*$!31+++]i: @IF`\\p7$F^jo$!3Q+++v$4w_(F27$$\"3B#H>P&GG6RF*$\"3))******\\iS1IF`\\p7 $Fcjo$\"3W++++voPcF27$$\"3i!>b-y)pURF*$!3?+++QMF&*HF`\\p7$Fhjo$!3.+++i lsaPF27$$\"3X)3\"z1Z6uRF*$\"3t*****z=#f))HF`\\p7$F][p$\"35+++%4rh(=F27 $$\"3G')pKL1`0SF*$!3v*****4GQl)HF`\\p-Fb[p6&Fd[pF+Fe[pF+-F$6$7gu7$$!#] F,$\"3.p\"Fi\\m7$$!3GL LLe%G?y%F^jl$!38hMc#=*=p^Fi\\m7$$!3'o;/,\\9Yt%F^jl$!3%*[WeL:iksFi\\m7$ $!3X+](=_+so%F^jl$!3lRFg_m7$ $!3x$3_De_U3%F^jl$!3+UP(obp>@#Fg_m7$$!35+]7GCadSF^jl$!3pN8\"Qpd8L#Fg_m 7$$!3W;zptA$3.%F^jl$!3DBH)*Qn!)*G#Fg_m7$$!3[L3F>@7/SF^jl$!3(4LV@2[(p?F g_m7$$!3`]P%['>TxRF^jl$!3![z55\\iMm\"Fg_m7$$!3'om;/\"=q]RF^jl$!3h#Ge3u SZ2\"Fg_m7$$!37++D\")ok^QF^jl$\"3^lXKD-#*yAFg_m7$$!3QLL3_>f_PF^jl$\"3D hQAS'HnQ&Fg_m7$$!33mmmT0&ps$F^jl$\"3X_vW2/4$o&Fg_m7$$!3]***\\7848q$F^j l$\"3k]]0\\x%)GcFg_m7$$!3\"HLL3sncn$F^jl$\"3qq#3&pb$z:&Fg_m7$$!3KmmT5j -]OF^jl$\"3\"4vvseyI@%Fg_m7$$!39LLe*[V()f$F^jl$\"3$Q!oT&G>UM(Fi\\m7$$! 3(****\\(o1YZNF^jl$!3-!fg(f:8#)\\Fg_m7$$!3kLL3-RU%\\$F^jl$!3$[(R2>N+78 Fg`m7$$!3hmmTNrQTMF^jl$!3m['4iXJSI#Fg`m7$$!3e***\\(o.N)Q$F^jl$!3'>!fQy kW$R$Fg`m7$$!3DLL3-OJNLF^jl$!3*4P/ls;gZ%Fg`m7$$!3*******\\#pW#G$F^jl$! 3!4IG(4i1NaFg`m7$$!3umm\"zC!eHKF^jl$!3&)p$3$QLpnhFg`m7$$!3Y+]P4p9.KF^j l$!3G*p&3NpZ@kFg`m7$$!3[LL$3d8n<$F^jl$!3E_]dsHZ*e'Fg`m7$$!3***\\i:!p\\ jJF^jl$!3'*4(3nRG'RmFg`m7$$!3\\m;HK-G]JF^jl$!3x!*z'*zCmmmFg`m7$$!3OL3- jN1PJF^jl$!3#ouhD3r.n'Fg`m7$$!3')***\\P*o%Q7$F^jl$!3(\\7?LFD2l'Fg`m7$$ !3mm\"H#=qYpIF^jl$!3F`sF0'*=IjFg`m7$$!34L$3F9(3:IF^jl$!3M]aX`BjgcFg`m7 $$!3`*\\(=nsqgHF^jl$!3k7#y'*\\'>CZFg`m7$$!3Kmmm\"RFj!HF^jl$!3[:9v')[1K OFg`m7$$!3DL$3xcH%eGF^jl$!3q!G!*f=1*QEFg`m7$$!3$)***\\PuJ0\"GF^jl$!3T7 PQXU\\+RjiFF^jl$!3G=z*z4W\"R))Fg_m7$$!3+LL$e4OZr#F^jl$! 3H_bR'p$*\\O#Fg_m7$$!3r**\\i!\\93m#F^jl$\"3B)QXYh#*4h#Fg_m7$$!3UmmT&)G *og#F^jl$\"38PnZ[D\"e;&Fg_m7$$!3x*\\7G3K*zDF^jl$\"3HE>7\"=_Lj&Fg_m7$$! 38L$3-GrHb#F^jl$\"3Ef-mjpAYcFg_m7$$!3[mTgx/,EDF^jl$\"3w_?b#\\&R#G&Fg_m 7$$!3[*****\\n\\!*\\#F^jl$\"38\"o]eF_gi%Fg_m7$$!3a******\\Ow!R#F^jl$\" 3%>E!f74EVtFi\\m7$$!3$******\\ixCG#F^jl$!366k()p]A5?Fg_m7$$!3*)****\\7 #*QcAF^jl$!3gP`;7CKWAFg_m7$$!3%)*******z+.B#F^jl$!3Z:\\#y(zn2BFg_m7$$! 3z****\\(Q7U?#F^jl$!3=!eCT_Dd@#Fg_m7$$!3v*****\\(R7y@F^jl$!3O'Q(*Hx`7* >Fg_m7$$!3m******\\r%f7#F^jl$!3%fInh7F0E\"Fg_m7$$!3c*****\\KqP2#F^jl$! 3+P^[_%y*pOFi\\m7$$!3-L3Fp()QE?F^jl$\"3k#\\;+W;z#QFi\\m7$$!3\\m;a8s+z> F^jl$\"3?j#)Rdix6$*Fi\\m7$$!3A$3xcV;`&>F^jl$\"3;Ah>+[Z.6Fg_m7$$!3'**\\ 7ylD;$>F^jl$\"3dt=v`&*4-7Fg_m7$$!3L;z%*z[$z!>F^jl$\"3!3\"y(RvLyA\"Fg_m 7$$!31LL3-TC%)=F^jl$\"3\"GgWO ]c$)oPMFi\\m7$$!3.mmm\"4z)e;F^jl$!3O\")))[!QK`s&Fi\\m7$$!3PmmTg1:6;F^j l$!3.bm-dB.lsFi\\m7$$!3Omm;HAUj:F^jl$!3-R`G+`RoqFi\\m7$$!3_mm\"zz$p::F ^jl$!3:XlClV@1aFi\\m7$$!3ommmm`'zY\"F^jl$!3,)f\")*[\"eu\"GFi\\m7$$!3H#)*F^fl7$$!3x(***\\iXg#G'F ]cm$\"3!38rJ^j(e]F'>(F^fl7$$!3:jm;/'= ><#F]cm$!3zf=7\"fi]5#F^fl7$$!3%G*GLLe*e$\\Fg_m$\"3z;HJC()[3>F\\x7$$\"3 zrm;zRQb@F]cm$\"3C[Y0/IZ\"*>F^fl7$$\"310+](=>Y2%F]cm$\"3Fz>d&4b6i(F^fl 7$$\"3Qpmm\"zXu9'F]cm$!3&>Pxq$oFx;Fi\\m7$$\"3q-+++&y))G)F]cm$\"3E:&y'[ L4`')F^fl7$$\"3I++]i_QQ5F^jl$\"3K[E.6VaP@Fi\\m7$$\"3C+](=-N(R6F^jl$!3t l>,!GX?F\"Fi\\m7$$\"3>++D\"y%3T7F^jl$!3e:-@lA*GR%Fi\\m7$$\"3#***\\P4kh `8F^jl$!3f6iL-js%G$Fi\\m7$$\"3l****\\P![hY\"F^jl$\"3i:UGR,Q4FFi\\m7$$ \"32L$eRP0n^\"F^jl$\"3L%\\60T$G`aFi\\m7$$\"3\\mmT5FEn:F^jl$\"3[E/h7Z5W rFi\\m7$$\"3#***\\(o/?yh\"F^jl$\"3a#)o[a*=i:(Fi\\m7$$\"3MLLL$Qx$o;F^jl $\"33XG^@!zL@&Fi\\m7$$\"34nm;z)Qjx\"F^jl$!3$o>=\"3DP.RFi\\m7$$\"3$3++] P+V)=F^jl$!3t&Q@i;A`=\"Fg_m7$$\"3+%ek`md(3>F^jl$!3w[S?HC7G7Fg_m7$$\"3= n\"Hd&\\@L>F^jl$!3/!)Ga5Pz(>\"Fg_m7$$\"3N]P4YAnd>F^jl$!3eZ*RaB>'*3\"Fg _m7$$\"3_L$ek`H@)>F^jl$!3Ca^PB]*4.*Fi\\m7$$\"3')*\\(=rAk6/!*o)Fi\\m7$$\"3yKLe9S8& \\#F^jl$!3K?!zJ%p`6XFg_m7$$\"3Hm;aQ?V@DF^jl$!3*=rTIC)=*=&Fg_m7$$\"3!)* ***\\i+tZDF^jl$!3SO0\">IKCg&Fg_m7$$\"3KL$ek3GSd#F^jl$!3yrQ<+jZscFg_m7$ $\"3%om;/6E.g#F^jl$!3wJD]j%HaK&Fg_m7$$\"3(QLL$e@#Hl#F^jl$!3Ib0#yj]68$F g_m7$$\"3!4+]i?=bq#F^jl$\"34#\\r.U)HP8Fg_m7$$\"3&R$3xc/%pv#F^jl$\"3_.v #p3(4uzFg_m7$$\"3*pm\"H2FO3GF^jl$\"3;M8E$)[Wg;Fg`m7$$\"3/+D\"y&\\yfGF^ jl$\"3_4E8^BhmEFg`m7$$\"33LLL3s?6HF^jl$\"3k5yH[zBLPFg`m7$$\"3(**\\i!R: /lHF^jl$\"3;P)4u]Mh![Fg`m7$$\"3%om\"zpe()=IF^jl$\"3M\"HAMJyqr&Fg`m7$$ \"3sL3_+-rsIF^jl$\"3:c1e/yJ/KF^jl$\"3RR&)eqU+7kFg`m7$$\"3GM$e*[ACIKF ^jl$\"3PZ0M?mHghFg`m7$$\"3v+D\"y5\"4#G$F^jl$\"3;BK?uU'3W&Fg`m7$$\"3%zm mm'*RRL$F^jl$\"3B\"p#3SB%H]%Fg`m7$$\"3Kn;a8H'pQ$F^jl$\"3&)*\\wm%HMAMFg `m7$$\"3TnmTge)*RMF^jl$\"3rG9@l/)>L#Fg`m7$$\"3]n;H2)3I\\$F^jl$\"3=-iV= :XO8Fg`m7$$\"3(ommTvJga$F^jl$\"3lC?n:>1t^Fg_m7$$\"3_L3FWch)f$F^jl$!391 QHK*)oHsFi\\m7$$\"3(3+vV`*>^OF^jl$!3uqIaANNnUFg_m7$$\"3>%3F%z9\\xOF^jl $!3E0%[>Pqk?&Fg_m7$$\"3Ao\"zWU$y.PF^jl$!3$)fAzW%\\7l&Fg_m7$$\"3a^7`p`2 IPF^jl$!3$pV$HQ)RVm&Fg_m7$$\"3'[L$e9tOcPF^jl$!3E$*oBQ\"oxJ&Fg_m7$$\"3' zm\"H#e0I&QF^jl$!3?bpp)R$yEAFg_m7$$\"32,++]Qk\\RF^jl$\"3HskF8B&y/\"Fg_ m7$$\"3,oT5SMLxRF^jl$\"3&HE%[=U*>m\"Fg_m7$$\"3BM$3-.B]+%F^jl$\"3$f9se( >>!3#Fg_m7$$\"3Y+DJ?ErKSF^jl$\"3ijpb:)=%)H#Fg_m7$$\"3SnmT5ASgSF^jl$\"3 1([;82yeK#Fg_m7$$\"3MM3_+=4)3%F^jl$\"35$Q&zM3*H=#Fg_m7$$\"3d+]i!R\"y:T F^jl$\"3ys41T=%*)*=Fg_m7$$\"3!o;H2)4ZVTF^jl$\"3?*Hef*R&*3:Fg_m7$$\"3uL L$3dg6<%F^jl$\"3;H#HSGm90\"Fg_m7$$\"3=n;zpBp?UF^jl$\"31Q%o#oCtg=Fi\\m7 $$\"3i++voTAqUF^jl$!3Q^PFG&eXs&Fi\\m7$$\"3)p;H#o+*\\H%F^jl$!3e/.t1sEQ' )Fi\\m7$$\"31M$3x'fv>VF^jl$!39CPldz;!3\"Fg_m7$$\"38,v=n=_WVF^jl$!3=)G^ iC;a@\"Fg_m7$$\"3]nmmmxGpVF^jl$!3ilW=%**y%o7Fg_m7$$\"3SM$eRA5\\Z%F^jl$ !3*4%\\'*=p3rsFi\\m7$$\"3J,+D\"oK0e%F^jl$\"3L(os6+mF(HFi\\m7$$\"3q,]il (z5j%F^jl$\"3m%G=-Dr\"Fi\\m7$$\"#]F,$!3. " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "28 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }