% The multiplicative constants for the 109 point FFT

I = sqrt(-1);
u = [
       -1.009259259259259
       -0.096669504712135
       -0.270524477319357*I
        0.039704562727779*I
        0.115409957295789*I
        0.334701798068608
        0.176622794678440
       -0.170441530915683
        0.021401579555952
        0.300116438224959
       -0.107172672593637
        0.936645214537787*I
        0.494269515038399*I
       -0.476971576525395*I
        0.137470328166969*I
        0.072543361542489*I
       -0.070004563236486*I
       -0.537057771352378*I
       -0.283406438290444*I
        0.273488069880941*I
       -1.125450743467288
        0.354402277786248
        0.252075382258991
       -0.032765936098010
        0.248554469000121
       -0.052946232608713
        0.036175452519084
        0.240031783563062
       -0.063460410216613
        1.106731502192097
        0.392798992025334
       -0.130192576768444
       -0.164035721940684
        0.032075448771541
       -0.451761990397406
       -0.468671896406151
        0.811576259753046
        0.328424677301588
       -0.150877998355044
        0.869884601742094
        0.147318748709138
        0.642253994526727
        0.035563627316270
       -0.101263966163239
        0.719638987626222
        0.107117715899004
       -0.484610084759924
       -0.121329434872619
        0.084047321506094
       -0.529841196456105
       -0.523245946388518*I
        0.858208336889710*I
       -0.395947194668952*I
       -0.083562002088984*I
        1.237152737915378*I
       -0.918184924741413*I
       -0.215831857234491*I
        0.414434841245377*I
        0.133922425883739*I
       -0.891908424057627*I
        0.480476957043311*I
       -0.214125493218406*I
       -0.006162548858808*I
       -0.016786807931585*I
       -0.115081437952584*I
        2.755769735834480*I
       -1.642147119384246*I
       -0.048949034556492*I
        0.137236988389273*I
        0.287252635642149*I
        2.277129987248311*I
       -1.661527224857065*I
       -0.370060032760878*I
        0.249759448083204*I
       -2.491339723832748*I
       -1.677633241027596*I
        1.101224781413771*I
        0.139669689105790*I
       -0.128998812157492*I
        0.734695696063533*I
       -1.116261894722981*I
        0.391969391247269*I
        0.222448114612722*I
       -0.026837493150144*I
       -0.762202686778763*I
       -0.679472531253449*I
        0.938679541045778*I
       -0.022187404242249*I
       -0.191840936983471*I
        1.691624073945188*I
        0.598578141992143*I
       -0.443549644097682*I
       -0.066753570123491*I
        0.072892810044539*I
       -0.309807129055475*I
        3.643139447479125
       -0.543909175007147
       -0.944713478103407
       -0.018289247906203
        1.824852500560356
       -2.490007827762621
        1.303857516985950
        0.662633013059579
       -0.202747445927157
        1.469596335910484
        0.134519052092805
       -0.107624507717795
        0.135861168728946
       -0.000455571474751
        0.208915341664259
        0.281605419106737
       -0.204984334992880
       -0.062824073038232
        0.042430731786907
       -0.511146937004218
       -1.616676854289526
        1.742883011898173
        0.807076071388773
       -0.424301589304144
        5.249497997320805
        1.316069515263027
        0.034308999927115
       -0.121713840452119
       -0.302639506366784
        5.127329652917261
       -1.171726941920707
        0.297780120688705
       -0.355305495878435
        0.054679325268209
       -0.252592272521764
       -0.061174652951279
       -0.083415382928033
        0.383586580432902
        0.109226276554707
       -1.865139782303221
        0.288515606610493
       -0.020281082448489
        0.069253495872875
        0.001579924701018
       -0.181103096304761
       -4.911143076789404
        0.771012597413368
       -0.134828235700713
       -0.255227706033334
        4.003427398767021
       -1.653069654247384
        0.169866725026677
        0.355475772851842
        0.106976251424329
       -2.317394051159206
        1.220578256561109
       -0.533879212558218
       -0.102442505727048
        0.049356040219649
       -0.405668021129574
       -0.024448133047175
        0.063679963548609
       -0.173149249720616
       -0.036256901693318
        0.552074813546320
       -0.190040341905743
        0.075088472480456
       -0.002143140944881
       -0.014670218829308
        0.230750011102993
        2.175939977026310
       -0.837965203103847
       -0.224082611896020
        0.226509765112493
       -3.084308465362608
        0.015838495125938
        1.409944915505248
       -0.164257366815163
       -0.265548709898943
        2.498576901705863
       -1.165561528581383
        0.103497748404240
        0.167922978803852
       -0.039932596300364
        0.727725298584531
       -0.551644778039882
        0.386445932193350
        0.220305363897070
       -0.004205698598864
       -0.529017653611440
        0.198819918844677
        0.004575670713660
       -0.040440807944979
        0.016249547601839
       -0.237268112669181
       -0.774818837780654
       -0.378139254353998
        0.245352386135018
       -0.192769087742633
        1.808779815598260
       -0.990936171571323
        0.656687553209203
        1.178727765857691
       -0.097773477752724
       -2.542973795931718
       -0.378197059048303
       -0.758464097995473
       -0.343210639711454
        0.034229956599867
        2.479136007933180
        0.365292586290677
        0.040929928466293
       -0.425299797660517
       -0.001378862777760
        0.700271046703222
        0.027198044113031
        0.307189434399805
       -0.034308479832667
       -0.029347099182593
        0.004968690452792
        0.050552411209905
       -4.286278465567325
        1.170709915427737
        0.456560069589126
       -4.265501717159013
        0.325032558815128
       -0.688877489571484
       -0.338156799680843
        0.121107395883889
        0.014798964741952
        0.514586195876562
        0.218322116530411
        0.058429220302534
        0.001900879900166
       -1.068953768839237
        0.062117397249735
       -0.142458620219881
        0.068331477921149
        0.001861520458874
       -0.057084464363927
       -0.075339320985903
       -0.103921701704488
        0.024916429259215
        0.004365850526918
        0.077433140738796
        0.241422142190250
        1.554805906640441
       -0.472020767187585
       -0.087930327282165
        0.818907300520250
       -4.485570154833123*I
        2.468600279566380*I
       -1.431978315082490*I
       -0.363315002236200*I
        2.728164062243788*I
        5.144707409025369*I
       -3.344832717651105*I
        0.978292812761046*I
        0.872462065398313*I
      -12.122800532046950*I
       -1.127523911396151*I
        2.337141359150046*I
        0.943047578284972*I
       -0.430901296202633*I
        3.764691949697811*I
       -0.784787347075287*I
        0.681866914141655*I
       -0.148793117555337*I
       -0.167122378959195*I
        2.450963477967499*I
        6.991786482883035*I
       -7.197998625501090*I
        0.429055994958383*I
        1.765273301178220*I
      -26.294859423559970*I
       -0.030190239300714*I
        1.103781628101184*I
       -0.290153803381248*I
       -0.174829714588671*I
       -2.579404291421194*I
        1.493659892374988*I
       -2.945441181799660*I
        0.948979562724277*I
        0.485188757578639*I
       -4.127549831429520*I
       -0.989590691368115*I
        1.298712031732482*I
        0.637077987030157*I
       -0.178473993743097*I
        2.136125123950774*I
       -0.467811505525384*I
        0.769986285633902*I
       -0.140804040406568*I
       -0.098269379174258*I
        0.850613656904709*I
       10.135943940977882*I
      -12.287111026328752*I
        0.374172601235076*I
        1.767589913661924*I
      -18.041511687235488*I
        1.505253464711279*I
       -1.190793969222521*I
        0.574044039487913*I
        0.179381572274957*I
       -0.049586590274198*I
       -2.212789100466785*I
        2.096757966483588*I
       -0.642424125161775*I
       -0.452550274325650*I
        5.416783454492157*I
        0.705704867588089*I
       -1.211951130294176*I
       -0.526708521771710*I
        0.203125096648577*I
       -1.966939024549529*I
        0.417532950866890*I
       -0.483951066591852*I
        0.096532385987302*I
        0.088463919377818*I
       -1.100525711624069*I
       -5.709243474620305*I
        6.495036550609947*I
       -0.267742865397820*I
       -1.177621071613381*I
       14.778790370265149*I
       -2.331222841938177*I
        2.256576173143957*I
        0.121393788451160*I
       -0.054855450255790*I
       -1.581921393020065*I
        4.041710825420869*I
       -1.919602457273600*I
       -0.536196479828015*I
        0.181854154731195*I
       -1.391926571063109*I
       -0.546596694666553*I
        1.121042573347495*I
       -0.284667728970482*I
       -0.251214968101177*I
        2.306997157632065*I
       -0.956451086868665*I
        0.403641693359177*I
        0.220285180017063*I
       -0.047159779907468*I
        0.281490633691738*I
        7.362391247492902*I
       -2.854109641262093*I
       -1.640680150700875*I
        0.525076109763023*I
       -5.628116921774177*I
       -1.914271982617228*I
        1.764739333531073*I
        0.521192201141573*I
       -0.094375520295286*I
       -3.569251855609905*I
        6.537035830706745*I
       -3.593348726018005*I
       -2.071128198027672*I
        0.272319494946313*I
        3.123112112468801*I
       -0.342533842466639*I
        0.830830198336618*I
       -0.309914354013260*I
       -0.164663801209148*I
        2.233397573645378*I
       -1.216928830760976*I
        0.809290677897996*I
        0.349097661620388*I
       -0.069071057014509*I
       -0.340259171343007*I
       11.506052638634177*I
       -9.613896394030666*I
       -1.952459903935057*I
        1.037389599385971*I
       -3.257501602075166*I
        1.415164941518468*I
       -1.340438502225010*I
       -0.214195329864244*I
        0.049743656850359*I
        1.717057749543323*I
       -3.526248885375872*I
        1.837650394430535*I
        0.869108225951896*I
       -0.151391216559169*I
       -0.577061847135231*I
        0.296376845711064*I
       -0.650624257228038*I
        0.198194027661248*I
        0.138626256436775*I
       -1.513464910425814*I
        0.724459972543214*I
       -0.404310790419058*I
       -0.189794280545817*I
        0.038743612307326*I
        0.019589512550423*I
       -6.289481295375691*I
        4.156002011764252*I
        1.197713351545310*I
       -0.520821903049665*I
        2.961872841283116*I
        3.408396498385651*I
       -2.362588226355170*I
        0.655292263315665*I
        0.209085226245995*I
       -0.573121334611861*I
       -4.593209117223117*I
        2.632217587462351*I
       -0.221048166466516*I
       -0.527158110064754*I
        6.757363551555029*I
        0.837060303031352*I
       -1.729091966248770*I
       -0.329189924657245*I
        0.341058132151905*I
       -3.035844553664939*I
        0.870619216971976*I
       -0.542754303750416*I
       -0.035746031230863*I
        0.107141079433331*I
       -1.366227055829619*I
       -7.177088865187967*I
        5.026054133381591*I
        0.605812077871246*I
       -1.145174705470621*I
       15.961488172667080*I
        0.972231110958971*I
       -1.434260480816128*I
       -0.115519198880162*I
        0.134602617441978*I
        3.074328073515550*I
       -4.015347861540868*I
        3.269394953908833*I
        0.561074317651697*I
       -0.378754126262476*I
        0.502218859480359*I
        0.666062266917377*I
       -1.064771115034550*I
       -0.163581816508448*I
        0.171568897476123*I
       -2.184761348798076*I
        0.842370168143180*I
       -0.789638481765949*I
       -0.104146810606910*I
        0.083670218094384*I
       -0.255177242780851*I
      -10.820998289806029*I
       10.950503710179708*I
        0.789143651349990*I
       -1.402489756523948*I
       10.649506644655327*I
       -1.460209203114874*I
        1.265616235723766*I
       -0.179924354811834*I
       -0.114562614562658*I
       -0.833735579634563*I
        2.869518992921329*I
       -1.967204180457062*I
       -0.113342050395060*I
        0.301970745442410*I
       -2.419860803678462*I
       -0.501040856649576*I
        0.931287693761107*I
        0.164257247055231*I
       -0.170875676542676*I
        1.740201967487672*I
       -0.570996461705052*I
        0.444130928505455*I
        0.046630947279258*I
       -0.063603765842572*I
        0.540468099536823*I
        5.999362384997998*I
       -5.325519281187100*I
       -0.464985243073745*I
        0.849221487331523*I
       -8.870331605774133*I
];


% The input permutation for the 109 point FFT

ip = [
   1
   2
   90
   74
   67
   98
   23
   106
   81
   36
   64
   49
   22
   17
   8
   79
   76
   27
   26
   46
   82
   16
   28
   6
   10
   39
   4
   50
   77
   7
   99
   3
   70
   38
   24
   86
   45
   102
   52
   71
   18
   97
   43
   33
   15
   48
   42
   53
   51
   91
   54
   31
   55
   11
   19
   109
   21
   37
   44
   13
   88
   5
   30
   75
   47
   62
   89
   94
   103
   32
   35
   84
   85
   65
   29
   95
   83
   105
   101
   72
   107
   61
   34
   104
   12
   108
   41
   73
   87
   25
   66
   9
   59
   40
   93
   14
   68
   78
   96
   63
   69
   58
   60
   20
   57
   80
   56
   100
   92
];


% The output permutation for the 109 point FFT

op = [
   1
   109
   4
   107
   34
   104
   2
   95
   64
   105
   26
   57
   32
   68
   17
   102
   94
   13
   27
   76
   29
   93
   87
   7
   62
   99
   98
   103
   47
   35
   24
   42
   16
   82
   43
   90
   30
   6
   106
   66
   59
   19
   15
   31
   9
   100
   37
   18
   92
   108
   21
   11
   20
   23
   25
   79
   77
   74
   65
   75
   54
   38
   72
   91
   46
   63
   85
   69
   73
   5
   12
   52
   60
   84
   36
   97
   28
   70
   96
   78
   89
   101
   49
   44
   45
   8
   61
   33
   39
   83
   22
   81
   67
   40
   48
   71
   14
   86
   3
   80
   51
   10
   41
   56
   50
   88
   53
   58
   55
];