Properties

Label 120.4.w.c.77.61
Level 120120
Weight 44
Character 120.77
Analytic conductor 7.0807.080
Analytic rank 00
Dimension 128128
Inner twists 88

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [120,4,Mod(53,120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(120, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 2, 3])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("120.53"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 120=2335 120 = 2^{3} \cdot 3 \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 120.w (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [128,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.080229200697.08022920069
Analytic rank: 00
Dimension: 128128
Relative dimension: 6464 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 77.61
Character χ\chi == 120.77
Dual form 120.4.w.c.53.61

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(2.79310+0.445660i)q2+(2.149824.73057i)q3+(7.60277+2.48954i)q4+(4.08469+10.4075i)q5+(8.1128712.2548i)q6+(13.5500+13.5500i)q7+(20.1258+10.3418i)q8+(17.756620.3397i)q9+(6.77075+30.8894i)q1023.6403q11+(28.121530.6134i)q12+(21.993921.9939i)q13+(31.8078+43.8853i)q14+(58.0146+3.05120i)q15+(51.6043+37.8549i)q16+(92.386192.3861i)q17+(40.531264.7242i)q18105.429q19+(5.14516+89.2946i)q20+(93.229534.9693i)q21+(66.029610.5355i)q22+(6.663196.66319i)q23+(92.189372.9735i)q24+(91.6306+85.0226i)q25+(51.629271.2327i)q26+(134.392+40.2721i)q27+(69.2844+136.751i)q28190.191iq29+(160.680+34.3771i)q3030.1383q31+(127.265+128.730i)q32+(50.8223+111.832i)q33+(299.216216.870i)q34+(85.6738+196.369i)q35+(84.3627198.844i)q36+(203.258+203.258i)q37+(294.47446.9856i)q38+(151.326+56.7607i)q39+(25.4242+251.701i)q40+348.549iq41+(275.98356.1240i)q42+(30.675730.6757i)q43+(179.73258.8536i)q44+(139.155267.882i)q45+(15.641421.5805i)q46+(66.6485+66.6485i)q47+(290.015162.737i)q48+24.2070iq49+(293.824+196.640i)q50+(238.426635.652i)q51+(112.460221.969i)q52+(195.204195.204i)q53+(393.317+52.5908i)q54+(96.5634246.036i)q55+(132.573+412.837i)q56+(226.653+498.740i)q57+(84.7607531.222i)q58343.492iq59+(433.476+167.627i)q60+232.915iq61+(84.179213.4314i)q62+(35.0015516.206i)q63+(298.095+416.273i)q64+(139.062318.738i)q65+(191.791+289.708i)q66+(397.741+397.741i)q67+(932.390472.391i)q68+(45.8453+17.1961i)q69+(326.809+510.297i)q70834.762iq71+(147.016592.988i)q72+(334.976334.976i)q73+(658.303+477.135i)q74+(205.216+616.248i)q75+(801.555262.471i)q76+(320.327320.327i)q77+(447.965+91.0981i)q78+906.479iq79+(183.185+691.696i)q80+(98.4075+722.327i)q81+(155.334+973.530i)q82+(690.879+690.879i)q83+(795.86033.7648i)q84+(1338.87+584.136i)q85+(72.009299.3510i)q86+(899.713408.876i)q87+(475.780244.483i)q88+1288.76q89+(508.057686.206i)q90596.035iq91+(34.070467.2471i)q92+(64.7918+142.571i)q93+(215.858+156.453i)q94+(430.6461097.25i)q95+(882.565325.292i)q96+(688.583688.583i)q97+(10.7881+67.6124i)q98+(419.771+480.837i)q99+O(q100)q+(2.79310 + 0.445660i) q^{2} +(2.14982 - 4.73057i) q^{3} +(7.60277 + 2.48954i) q^{4} +(4.08469 + 10.4075i) q^{5} +(8.11287 - 12.2548i) q^{6} +(13.5500 + 13.5500i) q^{7} +(20.1258 + 10.3418i) q^{8} +(-17.7566 - 20.3397i) q^{9} +(6.77075 + 30.8894i) q^{10} -23.6403 q^{11} +(28.1215 - 30.6134i) q^{12} +(-21.9939 - 21.9939i) q^{13} +(31.8078 + 43.8853i) q^{14} +(58.0146 + 3.05120i) q^{15} +(51.6043 + 37.8549i) q^{16} +(92.3861 - 92.3861i) q^{17} +(-40.5312 - 64.7242i) q^{18} -105.429 q^{19} +(5.14516 + 89.2946i) q^{20} +(93.2295 - 34.9693i) q^{21} +(-66.0296 - 10.5355i) q^{22} +(-6.66319 - 6.66319i) q^{23} +(92.1893 - 72.9735i) q^{24} +(-91.6306 + 85.0226i) q^{25} +(-51.6292 - 71.2327i) q^{26} +(-134.392 + 40.2721i) q^{27} +(69.2844 + 136.751i) q^{28} -190.191i q^{29} +(160.680 + 34.3771i) q^{30} -30.1383 q^{31} +(127.265 + 128.730i) q^{32} +(-50.8223 + 111.832i) q^{33} +(299.216 - 216.870i) q^{34} +(-85.6738 + 196.369i) q^{35} +(-84.3627 - 198.844i) q^{36} +(-203.258 + 203.258i) q^{37} +(-294.474 - 46.9856i) q^{38} +(-151.326 + 56.7607i) q^{39} +(-25.4242 + 251.701i) q^{40} +348.549i q^{41} +(275.983 - 56.1240i) q^{42} +(-30.6757 - 30.6757i) q^{43} +(-179.732 - 58.8536i) q^{44} +(139.155 - 267.882i) q^{45} +(-15.6414 - 21.5805i) q^{46} +(-66.6485 + 66.6485i) q^{47} +(290.015 - 162.737i) q^{48} +24.2070i q^{49} +(-293.824 + 196.640i) q^{50} +(-238.426 - 635.652i) q^{51} +(-112.460 - 221.969i) q^{52} +(195.204 - 195.204i) q^{53} +(-393.317 + 52.5908i) q^{54} +(-96.5634 - 246.036i) q^{55} +(132.573 + 412.837i) q^{56} +(-226.653 + 498.740i) q^{57} +(84.7607 - 531.222i) q^{58} -343.492i q^{59} +(433.476 + 167.627i) q^{60} +232.915i q^{61} +(-84.1792 - 13.4314i) q^{62} +(35.0015 - 516.206i) q^{63} +(298.095 + 416.273i) q^{64} +(139.062 - 318.738i) q^{65} +(-191.791 + 289.708i) q^{66} +(-397.741 + 397.741i) q^{67} +(932.390 - 472.391i) q^{68} +(-45.8453 + 17.1961i) q^{69} +(-326.809 + 510.297i) q^{70} -834.762i q^{71} +(-147.016 - 592.988i) q^{72} +(334.976 - 334.976i) q^{73} +(-658.303 + 477.135i) q^{74} +(205.216 + 616.248i) q^{75} +(-801.555 - 262.471i) q^{76} +(-320.327 - 320.327i) q^{77} +(-447.965 + 91.0981i) q^{78} +906.479i q^{79} +(-183.185 + 691.696i) q^{80} +(-98.4075 + 722.327i) q^{81} +(-155.334 + 973.530i) q^{82} +(-690.879 + 690.879i) q^{83} +(795.860 - 33.7648i) q^{84} +(1338.87 + 584.136i) q^{85} +(-72.0092 - 99.3510i) q^{86} +(-899.713 - 408.876i) q^{87} +(-475.780 - 244.483i) q^{88} +1288.76 q^{89} +(508.057 - 686.206i) q^{90} -596.035i q^{91} +(-34.0704 - 67.2471i) q^{92} +(-64.7918 + 142.571i) q^{93} +(-215.858 + 156.453i) q^{94} +(-430.646 - 1097.25i) q^{95} +(882.565 - 325.292i) q^{96} +(-688.583 - 688.583i) q^{97} +(-10.7881 + 67.6124i) q^{98} +(419.771 + 480.837i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 128q4q6144q7156q1056q12+212q15+636q16+220q18188q228q25+908q28+328q30544q311624q331268q36136q40+328q42+3792q97+O(q100) 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/120Z)×\left(\mathbb{Z}/120\mathbb{Z}\right)^\times.

nn 3131 4141 6161 9797
χ(n)\chi(n) 11 1-1 1-1 e(14)e\left(\frac{1}{4}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.79310 + 0.445660i 0.987509 + 0.157565i
33 2.14982 4.73057i 0.413732 0.910399i
44 7.60277 + 2.48954i 0.950347 + 0.311193i
55 4.08469 + 10.4075i 0.365346 + 0.930872i
66 8.11287 12.2548i 0.552011 0.833837i
77 13.5500 + 13.5500i 0.731633 + 0.731633i 0.970943 0.239310i 0.0769212π-0.0769212\pi
−0.239310 + 0.970943i 0.576921π0.576921\pi
88 20.1258 + 10.3418i 0.889443 + 0.457047i
99 −17.7566 20.3397i −0.657651 0.753323i
1010 6.77075 + 30.8894i 0.214110 + 0.976810i
1111 −23.6403 −0.647984 −0.323992 0.946060i 0.605025π-0.605025\pi
−0.323992 + 0.946060i 0.605025π0.605025\pi
1212 28.1215 30.6134i 0.676499 0.736444i
1313 −21.9939 21.9939i −0.469231 0.469231i 0.432435 0.901665i 0.357655π-0.357655\pi
−0.901665 + 0.432435i 0.857655π0.857655\pi
1414 31.8078 + 43.8853i 0.607215 + 0.837774i
1515 58.0146 + 3.05120i 0.998620 + 0.0525212i
1616 51.6043 + 37.8549i 0.806318 + 0.591483i
1717 92.3861 92.3861i 1.31805 1.31805i 0.402740 0.915314i 0.368058π-0.368058\pi
0.915314 0.402740i 0.131942π-0.131942\pi
1818 −40.5312 64.7242i −0.530739 0.847535i
1919 −105.429 −1.27301 −0.636503 0.771274i 0.719620π-0.719620\pi
−0.636503 + 0.771274i 0.719620π0.719620\pi
2020 5.14516 + 89.2946i 0.0575246 + 0.998344i
2121 93.2295 34.9693i 0.968778 0.363378i
2222 −66.0296 10.5355i −0.639889 0.102099i
2323 −6.66319 6.66319i −0.0604075 0.0604075i 0.676258 0.736665i 0.263601π-0.263601\pi
−0.736665 + 0.676258i 0.763601π0.763601\pi
2424 92.1893 72.9735i 0.784086 0.620652i
2525 −91.6306 + 85.0226i −0.733045 + 0.680181i
2626 −51.6292 71.2327i −0.389435 0.537303i
2727 −134.392 + 40.2721i −0.957915 + 0.287051i
2828 69.2844 + 136.751i 0.467626 + 0.922984i
2929 190.191i 1.21785i −0.793228 0.608924i 0.791601π-0.791601\pi
0.793228 0.608924i 0.208399π-0.208399\pi
3030 160.680 + 34.3771i 0.977870 + 0.209212i
3131 −30.1383 −0.174613 −0.0873064 0.996182i 0.527826π-0.527826\pi
−0.0873064 + 0.996182i 0.527826π0.527826\pi
3232 127.265 + 128.730i 0.703049 + 0.711141i
3333 −50.8223 + 111.832i −0.268092 + 0.589923i
3434 299.216 216.870i 1.50927 1.09391i
3535 −85.6738 + 196.369i −0.413757 + 0.948356i
3636 −84.3627 198.844i −0.390568 0.920574i
3737 −203.258 + 203.258i −0.903119 + 0.903119i −0.995705 0.0925854i 0.970487π-0.970487\pi
0.0925854 + 0.995705i 0.470487π0.470487\pi
3838 −294.474 46.9856i −1.25711 0.200581i
3939 −151.326 + 56.7607i −0.621323 + 0.233051i
4040 −25.4242 + 251.701i −0.100498 + 0.994937i
4141 348.549i 1.32766i 0.747882 + 0.663831i 0.231071π0.231071\pi
−0.747882 + 0.663831i 0.768929π0.768929\pi
4242 275.983 56.1240i 1.01393 0.206193i
4343 −30.6757 30.6757i −0.108791 0.108791i 0.650616 0.759407i 0.274511π-0.274511\pi
−0.759407 + 0.650616i 0.774511π0.774511\pi
4444 −179.732 58.8536i −0.615809 0.201648i
4545 139.155 267.882i 0.460976 0.887412i
4646 −15.6414 21.5805i −0.0501348 0.0691710i
4747 −66.6485 + 66.6485i −0.206844 + 0.206844i −0.802925 0.596080i 0.796724π-0.796724\pi
0.596080 + 0.802925i 0.296724π0.296724\pi
4848 290.015 162.737i 0.872085 0.489355i
4949 24.2070i 0.0705743i
5050 −293.824 + 196.640i −0.831060 + 0.556182i
5151 −238.426 635.652i −0.654633 1.74528i
5252 −112.460 221.969i −0.299910 0.591953i
5353 195.204 195.204i 0.505911 0.505911i −0.407358 0.913269i 0.633550π-0.633550\pi
0.913269 + 0.407358i 0.133550π0.133550\pi
5454 −393.317 + 52.5908i −0.991179 + 0.132532i
5555 −96.5634 246.036i −0.236738 0.603190i
5656 132.573 + 412.837i 0.316355 + 0.985136i
5757 −226.653 + 498.740i −0.526684 + 1.15894i
5858 84.7607 531.222i 0.191890 1.20264i
5959 343.492i 0.757946i −0.925408 0.378973i 0.876277π-0.876277\pi
0.925408 0.378973i 0.123723π-0.123723\pi
6060 433.476 + 167.627i 0.932691 + 0.360677i
6161 232.915i 0.488880i 0.969664 + 0.244440i 0.0786041π0.0786041\pi
−0.969664 + 0.244440i 0.921396π0.921396\pi
6262 −84.1792 13.4314i −0.172432 0.0275128i
6363 35.0015 516.206i 0.0699963 1.03232i
6464 298.095 + 416.273i 0.582216 + 0.813034i
6565 139.062 318.738i 0.265362 0.608225i
6666 −191.791 + 289.708i −0.357694 + 0.540313i
6767 −397.741 + 397.741i −0.725251 + 0.725251i −0.969670 0.244418i 0.921403π-0.921403\pi
0.244418 + 0.969670i 0.421403π0.421403\pi
6868 932.390 472.391i 1.66278 0.842439i
6969 −45.8453 + 17.1961i −0.0799874 + 0.0300024i
7070 −326.809 + 510.297i −0.558016 + 0.871316i
7171 834.762i 1.39533i −0.716427 0.697663i 0.754224π-0.754224\pi
0.716427 0.697663i 0.245776π-0.245776\pi
7272 −147.016 592.988i −0.240639 0.970615i
7373 334.976 334.976i 0.537067 0.537067i −0.385599 0.922666i 0.626005π-0.626005\pi
0.922666 + 0.385599i 0.126005π0.126005\pi
7474 −658.303 + 477.135i −1.03414 + 0.749538i
7575 205.216 + 616.248i 0.315951 + 0.948775i
7676 −801.555 262.471i −1.20980 0.396151i
7777 −320.327 320.327i −0.474086 0.474086i
7878 −447.965 + 91.0981i −0.650282 + 0.132241i
7979 906.479i 1.29097i 0.763771 + 0.645487i 0.223345π0.223345\pi
−0.763771 + 0.645487i 0.776655π0.776655\pi
8080 −183.185 + 691.696i −0.256009 + 0.966674i
8181 −98.4075 + 722.327i −0.134990 + 0.990847i
8282 −155.334 + 973.530i −0.209193 + 1.31108i
8383 −690.879 + 690.879i −0.913660 + 0.913660i −0.996558 0.0828977i 0.973583π-0.973583\pi
0.0828977 + 0.996558i 0.473583π0.473583\pi
8484 795.860 33.7648i 1.03376 0.0438576i
8585 1338.87 + 584.136i 1.70849 + 0.745394i
8686 −72.0092 99.3510i −0.0902901 0.124573i
8787 −899.713 408.876i −1.10873 0.503863i
8888 −475.780 244.483i −0.576344 0.296159i
8989 1288.76 1.53493 0.767465 0.641091i 0.221518π-0.221518\pi
0.767465 + 0.641091i 0.221518π0.221518\pi
9090 508.057 686.206i 0.595043 0.803694i
9191 596.035i 0.686609i
9292 −34.0704 67.2471i −0.0386097 0.0762064i
9393 −64.7918 + 142.571i −0.0722430 + 0.158967i
9494 −215.858 + 156.453i −0.236852 + 0.171669i
9595 −430.646 1097.25i −0.465088 1.18501i
9696 882.565 325.292i 0.938296 0.345833i
9797 −688.583 688.583i −0.720773 0.720773i 0.247989 0.968763i 0.420230π-0.420230\pi
−0.968763 + 0.247989i 0.920230π0.920230\pi
9898 −10.7881 + 67.6124i −0.0111200 + 0.0696927i
9999 419.771 + 480.837i 0.426147 + 0.488141i
100100 −908.314 + 418.289i −0.908314 + 0.418289i
101101 1938.57 1.90985 0.954925 0.296848i 0.0959356π-0.0959356\pi
0.954925 + 0.296848i 0.0959356π0.0959356\pi
102102 −382.661 1881.69i −0.371462 1.82662i
103103 280.520 280.520i 0.268354 0.268354i −0.560083 0.828437i 0.689231π-0.689231\pi
0.828437 + 0.560083i 0.189231π0.189231\pi
104104 −215.188 670.100i −0.202893 0.631814i
105105 744.756 + 827.443i 0.692197 + 0.769050i
106106 632.217 458.228i 0.579305 0.419878i
107107 93.1446 + 93.1446i 0.0841555 + 0.0841555i 0.747931 0.663776i 0.231047π-0.231047\pi
−0.663776 + 0.747931i 0.731047π0.731047\pi
108108 −1122.01 28.3945i −0.999680 0.0252988i
109109 1161.91 1.02101 0.510507 0.859874i 0.329458π-0.329458\pi
0.510507 + 0.859874i 0.329458π0.329458\pi
110110 −160.063 730.236i −0.138740 0.632957i
111111 524.559 + 1398.49i 0.448549 + 1.19585i
112112 186.306 + 1212.18i 0.157181 + 1.02268i
113113 61.0136 + 61.0136i 0.0507936 + 0.0507936i 0.732047 0.681254i 0.238565π-0.238565\pi
−0.681254 + 0.732047i 0.738565π0.738565\pi
114114 −855.334 + 1292.02i −0.702714 + 1.06148i
115115 42.1298 96.5640i 0.0341620 0.0783012i
116116 473.489 1445.98i 0.378986 1.15738i
117117 −56.8129 + 837.884i −0.0448919 + 0.662072i
118118 153.081 959.405i 0.119426 0.748478i
119119 2503.67 1.92866
120120 1136.03 + 661.382i 0.864210 + 0.503131i
121121 −772.136 −0.580117
122122 −103.801 + 650.553i −0.0770302 + 0.482773i
123123 1648.83 + 749.316i 1.20870 + 0.549297i
124124 −229.135 75.0306i −0.165943 0.0543383i
125125 −1259.15 606.351i −0.900976 0.433869i
126126 327.815 1426.21i 0.231778 1.00839i
127127 728.509 + 728.509i 0.509014 + 0.509014i 0.914224 0.405210i 0.132802π-0.132802\pi
−0.405210 + 0.914224i 0.632802π0.632802\pi
128128 647.091 + 1295.54i 0.446838 + 0.894615i
129129 −211.060 + 79.1664i −0.144053 + 0.0540326i
130130 530.463 828.293i 0.357882 0.558816i
131131 −1108.11 −0.739052 −0.369526 0.929220i 0.620480π-0.620480\pi
−0.369526 + 0.929220i 0.620480π0.620480\pi
132132 −664.802 + 723.710i −0.438360 + 0.477203i
133133 −1428.57 1428.57i −0.931374 0.931374i
134134 −1288.19 + 933.672i −0.830466 + 0.601918i
135135 −968.080 1234.18i −0.617178 0.786823i
136136 2814.78 903.905i 1.77475 0.569921i
137137 157.161 157.161i 0.0980083 0.0980083i −0.656403 0.754411i 0.727923π-0.727923\pi
0.754411 + 0.656403i 0.227923π0.227923\pi
138138 −135.714 + 27.5988i −0.0837156 + 0.0170244i
139139 1006.99 0.614471 0.307236 0.951633i 0.400596π-0.400596\pi
0.307236 + 0.951633i 0.400596π0.400596\pi
140140 −1140.23 + 1279.66i −0.688335 + 0.772509i
141141 172.003 + 458.567i 0.102733 + 0.273889i
142142 372.021 2331.57i 0.219854 1.37790i
143143 519.941 + 519.941i 0.304054 + 0.304054i
144144 −146.359 1721.79i −0.0846986 0.996407i
145145 1979.41 776.873i 1.13366 0.444936i
146146 1084.90 786.334i 0.614982 0.445736i
147147 114.513 + 52.0405i 0.0642507 + 0.0291989i
148148 −2051.34 + 1039.30i −1.13932 + 0.577232i
149149 1884.11i 1.03592i 0.855405 + 0.517960i 0.173309π0.173309\pi
−0.855405 + 0.517960i 0.826691π0.826691\pi
150150 298.552 + 1812.70i 0.162511 + 0.986707i
151151 34.3422 0.0185081 0.00925407 0.999957i 0.497054π-0.497054\pi
0.00925407 + 0.999957i 0.497054π0.497054\pi
152152 −2121.85 1090.33i −1.13227 0.581824i
153153 −3519.57 238.645i −1.85974 0.126100i
154154 −751.947 1037.46i −0.393465 0.542864i
155155 −123.106 313.663i −0.0637941 0.162542i
156156 −1291.81 + 54.8056i −0.662996 + 0.0281280i
157157 1860.87 1860.87i 0.945945 0.945945i −0.0526676 0.998612i 0.516772π-0.516772\pi
0.998612 + 0.0526676i 0.0167724π0.0167724\pi
158158 −403.982 + 2531.88i −0.203412 + 1.27485i
159159 −503.773 1343.08i −0.251269 0.669892i
160160 −819.916 + 1850.33i −0.405125 + 0.914261i
161161 180.573i 0.0883922i
162162 −596.774 + 1973.67i −0.289426 + 0.957200i
163163 −1488.97 1488.97i −0.715493 0.715493i 0.252186 0.967679i 0.418851π-0.418851\pi
−0.967679 + 0.252186i 0.918851π0.918851\pi
164164 −867.728 + 2649.94i −0.413160 + 1.26174i
165165 −1371.48 72.1314i −0.647089 0.0340328i
166166 −2237.59 + 1621.79i −1.04621 + 0.758287i
167167 −1907.69 + 1907.69i −0.883963 + 0.883963i −0.993935 0.109972i 0.964924π-0.964924\pi
0.109972 + 0.993935i 0.464924π0.464924\pi
168168 2237.96 + 260.375i 1.02775 + 0.119574i
169169 1229.54i 0.559645i
170170 3479.28 + 2228.23i 1.56970 + 1.00528i
171171 1872.06 + 2144.40i 0.837194 + 0.958985i
172172 −156.852 309.589i −0.0695339 0.137244i
173173 −657.105 + 657.105i −0.288779 + 0.288779i −0.836597 0.547818i 0.815459π-0.815459\pi
0.547818 + 0.836597i 0.315459π0.315459\pi
174174 −2330.76 1543.00i −1.01549 0.672266i
175175 −2393.66 89.5384i −1.03396 0.0386769i
176176 −1219.94 894.901i −0.522481 0.383271i
177177 −1624.91 738.444i −0.690033 0.313587i
178178 3599.64 + 574.351i 1.51576 + 0.241851i
179179 2226.47i 0.929687i −0.885393 0.464843i 0.846111π-0.846111\pi
0.885393 0.464843i 0.153889π-0.153889\pi
180180 1724.87 1690.22i 0.714244 0.699897i
181181 759.935i 0.312075i 0.987751 + 0.156037i 0.0498721π0.0498721\pi
−0.987751 + 0.156037i 0.950128π0.950128\pi
182182 265.629 1664.78i 0.108185 0.678033i
183183 1101.82 + 500.724i 0.445075 + 0.202265i
184184 −65.1926 203.011i −0.0261199 0.0813380i
185185 −2945.65 1285.15i −1.17064 0.510737i
186186 −244.508 + 369.340i −0.0963882 + 0.145599i
187187 −2184.04 + 2184.04i −0.854078 + 0.854078i
188188 −672.638 + 340.789i −0.260942 + 0.132205i
189189 −2366.70 1275.33i −0.910859 0.490827i
190190 −713.835 3256.65i −0.272563 1.24349i
191191 109.634i 0.0415333i 0.999784 + 0.0207667i 0.00661071π0.00661071\pi
−0.999784 + 0.0207667i 0.993389π0.993389\pi
192192 2610.06 515.246i 0.981067 0.193670i
193193 857.642 857.642i 0.319868 0.319868i −0.528849 0.848716i 0.677376π-0.677376\pi
0.848716 + 0.528849i 0.177376π0.177376\pi
194194 −1616.40 2230.15i −0.598201 0.825338i
195195 −1208.86 1343.07i −0.443938 0.493228i
196196 −60.2643 + 184.040i −0.0219622 + 0.0670700i
197197 −760.319 760.319i −0.274977 0.274977i 0.556123 0.831100i 0.312288π-0.312288\pi
−0.831100 + 0.556123i 0.812288π0.812288\pi
198198 958.171 + 1530.10i 0.343910 + 0.549189i
199199 5232.87i 1.86406i 0.362378 + 0.932031i 0.381965π0.381965\pi
−0.362378 + 0.932031i 0.618035π0.618035\pi
200200 −2723.42 + 763.522i −0.962876 + 0.269946i
201201 1026.47 + 2736.61i 0.360208 + 0.960328i
202202 5414.61 + 863.943i 1.88599 + 0.300925i
203203 2577.10 2577.10i 0.891019 0.891019i
204204 −230.213 5426.29i −0.0790106 1.86234i
205205 −3627.51 + 1423.72i −1.23588 + 0.485056i
206206 908.536 658.503i 0.307285 0.222719i
207207 −17.2119 + 253.843i −0.00577926 + 0.0852334i
208208 −302.403 1967.55i −0.100807 0.655891i
209209 2492.38 0.824888
210210 1711.42 + 2643.04i 0.562376 + 0.868509i
211211 2462.42i 0.803414i −0.915768 0.401707i 0.868417π-0.868417\pi
0.915768 0.401707i 0.131583π-0.131583\pi
212212 1970.06 998.121i 0.638227 0.323355i
213213 −3948.90 1794.59i −1.27030 0.577291i
214214 218.651 + 301.673i 0.0698443 + 0.0963642i
215215 193.955 444.557i 0.0615239 0.141016i
216216 −3121.23 579.344i −0.983206 0.182497i
217217 −408.375 408.375i −0.127753 0.127753i
218218 3245.32 + 517.816i 1.00826 + 0.160876i
219219 −864.489 2304.76i −0.266743 0.711147i
220220 −121.633 2110.95i −0.0372750 0.646911i
221221 −4063.85 −1.23694
222222 841.890 + 4139.90i 0.254522 + 1.25159i
223223 181.463 181.463i 0.0544919 0.0544919i −0.679336 0.733828i 0.737732π-0.737732\pi
0.733828 + 0.679336i 0.237732π0.237732\pi
224224 −19.8494 + 3468.75i −0.00592073 + 1.03467i
225225 3356.38 + 354.028i 0.994483 + 0.104897i
226226 143.225 + 197.608i 0.0421558 + 0.0581624i
227227 2577.03 + 2577.03i 0.753496 + 0.753496i 0.975130 0.221634i 0.0711391π-0.0711391\pi
−0.221634 + 0.975130i 0.571139π0.571139\pi
228228 −2964.83 + 3227.55i −0.861188 + 0.937498i
229229 2690.23 0.776313 0.388156 0.921593i 0.373112π-0.373112\pi
0.388156 + 0.921593i 0.373112π0.373112\pi
230230 160.707 250.937i 0.0460728 0.0719404i
231231 −2203.97 + 826.685i −0.627752 + 0.235463i
232232 1966.92 3827.75i 0.556614 1.08321i
233233 −2252.87 2252.87i −0.633435 0.633435i 0.315493 0.948928i 0.397830π-0.397830\pi
−0.948928 + 0.315493i 0.897830π0.897830\pi
234234 −532.096 + 2314.97i −0.148650 + 0.646729i
235235 −965.880 421.403i −0.268115 0.116976i
236236 855.138 2611.49i 0.235867 0.720311i
237237 4288.16 + 1948.76i 1.17530 + 0.534117i
238238 6992.99 + 1115.79i 1.90457 + 0.303890i
239239 3833.40 1.03750 0.518749 0.854927i 0.326398π-0.326398\pi
0.518749 + 0.854927i 0.326398π0.326398\pi
240240 2878.30 + 2353.59i 0.774140 + 0.633015i
241241 1641.79 0.438826 0.219413 0.975632i 0.429586π-0.429586\pi
0.219413 + 0.975632i 0.429586π0.429586\pi
242242 −2156.65 344.110i −0.572871 0.0914060i
243243 3205.46 + 2018.39i 0.846216 + 0.532840i
244244 −579.851 + 1770.80i −0.152136 + 0.464605i
245245 −251.933 + 98.8781i −0.0656956 + 0.0257840i
246246 4271.41 + 2827.73i 1.10705 + 0.732884i
247247 2318.80 + 2318.80i 0.597334 + 0.597334i
248248 −606.557 311.684i −0.155308 0.0798063i
249249 1782.99 + 4753.51i 0.453784 + 1.20981i
250250 −3246.71 2254.75i −0.821359 0.570412i
251251 4943.40 1.24313 0.621564 0.783364i 0.286498π-0.286498\pi
0.621564 + 0.783364i 0.286498π0.286498\pi
252252 1551.23 3837.46i 0.387770 0.959275i
253253 157.520 + 157.520i 0.0391431 + 0.0391431i
254254 1710.13 + 2359.46i 0.422453 + 0.582858i
255255 5641.63 5077.85i 1.38546 1.24701i
256256 1230.01 + 3906.95i 0.300297 + 0.953846i
257257 −1468.71 + 1468.71i −0.356481 + 0.356481i −0.862514 0.506033i 0.831111π-0.831111\pi
0.506033 + 0.862514i 0.331111π0.331111\pi
258258 −624.794 + 127.058i −0.150767 + 0.0306600i
259259 −5508.31 −1.32150
260260 1850.77 2077.09i 0.441461 0.495446i
261261 −3868.43 + 3377.15i −0.917433 + 0.800920i
262262 −3095.05 493.840i −0.729821 0.116449i
263263 −538.864 538.864i −0.126341 0.126341i 0.641109 0.767450i 0.278475π-0.278475\pi
−0.767450 + 0.641109i 0.778475π0.778475\pi
264264 −2179.38 + 1725.12i −0.508075 + 0.402172i
265265 2828.92 + 1234.23i 0.655771 + 0.286106i
266266 −3353.48 4626.79i −0.772988 1.06649i
267267 2770.61 6096.59i 0.635050 1.39740i
268268 −4014.13 + 2033.74i −0.914933 + 0.463547i
269269 402.369i 0.0912004i 0.998960 + 0.0456002i 0.0145200π0.0145200\pi
−0.998960 + 0.0456002i 0.985480π0.985480\pi
270270 −2153.92 3878.61i −0.485493 0.874240i
271271 −8159.60 −1.82900 −0.914502 0.404581i 0.867418π-0.867418\pi
−0.914502 + 0.404581i 0.867418π0.867418\pi
272272 8264.79 1270.26i 1.84238 0.283164i
273273 −2819.59 1281.37i −0.625088 0.284072i
274274 509.005 368.924i 0.112227 0.0813414i
275275 2166.17 2009.96i 0.475001 0.440746i
276276 −391.362 + 16.6037i −0.0853523 + 0.00362112i
277277 −333.740 + 333.740i −0.0723916 + 0.0723916i −0.742376 0.669984i 0.766301π-0.766301\pi
0.669984 + 0.742376i 0.266301π0.266301\pi
278278 2812.61 + 448.774i 0.606796 + 0.0968190i
279279 535.153 + 613.004i 0.114834 + 0.131540i
280280 −3755.06 + 3066.07i −0.801457 + 0.654402i
281281 985.762i 0.209273i −0.994511 0.104636i 0.966632π-0.966632\pi
0.994511 0.104636i 0.0333679π-0.0333679\pi
282282 276.057 + 1357.48i 0.0582941 + 0.286655i
283283 5012.19 + 5012.19i 1.05280 + 1.05280i 0.998526 + 0.0542790i 0.0172860π0.0172860\pi
0.0542790 + 0.998526i 0.482714π0.482714\pi
284284 2078.18 6346.51i 0.434216 1.32604i
285285 −6116.43 321.686i −1.27125 0.0668598i
286286 1220.53 + 1683.96i 0.252348 + 0.348164i
287287 −4722.85 + 4722.85i −0.971362 + 0.971362i
288288 358.538 4874.35i 0.0733579 0.997306i
289289 12157.4i 2.47453i
290290 5874.90 1287.74i 1.18961 0.260753i
291291 −4737.72 + 1777.06i −0.954398 + 0.357984i
292292 3380.68 1712.81i 0.677532 0.343269i
293293 684.466 684.466i 0.136474 0.136474i −0.635569 0.772044i 0.719235π-0.719235\pi
0.772044 + 0.635569i 0.219235π0.219235\pi
294294 296.653 + 196.388i 0.0588474 + 0.0389578i
295295 3574.88 1403.06i 0.705550 0.276913i
296296 −6192.78 + 1988.68i −1.21604 + 0.390505i
297297 3177.06 952.045i 0.620713 0.186004i
298298 −839.672 + 5262.50i −0.163225 + 1.02298i
299299 293.099i 0.0566901i
300300 26.0380 + 5196.09i 0.00501101 + 0.999987i
301301 831.313i 0.159190i
302302 95.9211 + 15.3050i 0.0182769 + 0.00291623i
303303 4167.57 9170.53i 0.790166 1.73872i
304304 −5440.61 3991.01i −1.02645 0.752961i
305305 −2424.05 + 951.385i −0.455084 + 0.178610i
306306 −9724.14 2235.09i −1.81664 0.417554i
307307 −1726.29 + 1726.29i −0.320926 + 0.320926i −0.849122 0.528196i 0.822869π-0.822869\pi
0.528196 + 0.849122i 0.322869π0.322869\pi
308308 −1637.91 3232.84i −0.303014 0.598079i
309309 −723.953 1930.09i −0.133282 0.355336i
310310 −204.059 930.955i −0.0373863 0.170564i
311311 4178.94i 0.761949i 0.924585 + 0.380975i 0.124411π0.124411\pi
−0.924585 + 0.380975i 0.875589π0.875589\pi
312312 −3632.57 422.630i −0.659146 0.0766882i
313313 −7559.82 + 7559.82i −1.36520 + 1.36520i −0.498043 + 0.867152i 0.665948π0.665948\pi
−0.867152 + 0.498043i 0.834052π0.834052\pi
314314 6026.89 4368.26i 1.08318 0.785081i
315315 5515.37 1744.27i 0.986526 0.311995i
316316 −2256.72 + 6891.76i −0.401742 + 1.22687i
317317 2832.31 + 2832.31i 0.501825 + 0.501825i 0.912005 0.410180i 0.134534π-0.134534\pi
−0.410180 + 0.912005i 0.634534π0.634534\pi
318318 −808.529 3975.85i −0.142579 0.701116i
319319 4496.18i 0.789146i
320320 −3114.73 + 4802.76i −0.544120 + 0.839007i
321321 640.871 240.383i 0.111433 0.0417972i
322322 80.4742 504.358i 0.0139275 0.0872881i
323323 −9740.20 + 9740.20i −1.67789 + 1.67789i
324324 −2546.44 + 5246.70i −0.436632 + 0.899640i
325325 3885.28 + 145.335i 0.663129 + 0.0248053i
326326 −3495.27 4822.42i −0.593819 0.819292i
327327 2497.89 5496.48i 0.422426 0.929530i
328328 −3604.62 + 7014.82i −0.606804 + 1.18088i
329329 −1806.18 −0.302668
330330 −3798.54 812.685i −0.633644 0.135566i
331331 1899.46i 0.315419i 0.987486 + 0.157709i 0.0504109π0.0504109\pi
−0.987486 + 0.157709i 0.949589π0.949589\pi
332332 −6972.57 + 3532.62i −1.15262 + 0.583969i
333333 7743.38 + 525.041i 1.27428 + 0.0864026i
334334 −6178.56 + 4478.19i −1.01220 + 0.733640i
335335 −5764.13 2514.83i −0.940084 0.410148i
336336 6134.80 + 1724.62i 0.996074 + 0.280018i
337337 −5416.63 5416.63i −0.875556 0.875556i 0.117515 0.993071i 0.462507π-0.462507\pi
−0.993071 + 0.117515i 0.962507π0.962507\pi
338338 547.958 3434.23i 0.0881804 0.552655i
339339 419.797 157.461i 0.0672573 0.0252275i
340340 8724.92 + 7774.24i 1.39169 + 1.24005i
341341 712.479 0.113146
342342 4273.18 + 6823.82i 0.675635 + 1.07892i
343343 4319.66 4319.66i 0.679999 0.679999i
344344 −300.131 934.614i −0.0470406 0.146485i
345345 −366.232 406.893i −0.0571514 0.0634968i
346346 −2128.20 + 1542.51i −0.330673 + 0.239671i
347347 −4397.76 4397.76i −0.680357 0.680357i 0.279723 0.960081i 0.409757π-0.409757\pi
−0.960081 + 0.279723i 0.909757π0.909757\pi
348348 −5822.40 5348.47i −0.896877 0.823873i
349349 11672.4 1.79028 0.895139 0.445787i 0.147076π-0.147076\pi
0.895139 + 0.445787i 0.147076π0.147076\pi
350350 −6645.81 1316.85i −1.01495 0.201110i
351351 3841.53 + 2070.05i 0.584176 + 0.314790i
352352 −3008.59 3043.22i −0.455564 0.460808i
353353 5095.42 + 5095.42i 0.768277 + 0.768277i 0.977803 0.209526i 0.0671921π-0.0671921\pi
−0.209526 + 0.977803i 0.567192π0.567192\pi
354354 −4209.44 2786.70i −0.632003 0.418394i
355355 8687.76 3409.75i 1.29887 0.509777i
356356 9798.18 + 3208.44i 1.45872 + 0.477660i
357357 5382.43 11843.8i 0.797951 1.75585i
358358 992.248 6218.74i 0.146486 0.918074i
359359 −10047.6 −1.47714 −0.738571 0.674176i 0.764499π-0.764499\pi
−0.738571 + 0.674176i 0.764499π0.764499\pi
360360 5570.98 3952.24i 0.815601 0.578614i
361361 4256.33 0.620546
362362 −338.673 + 2122.57i −0.0491720 + 0.308177i
363363 −1659.95 + 3652.64i −0.240013 + 0.528138i
364364 1483.86 4531.52i 0.213668 0.652517i
365365 4854.52 + 2117.97i 0.696156 + 0.303725i
366366 2854.33 + 1889.61i 0.407646 + 0.269867i
367367 5113.00 + 5113.00i 0.727238 + 0.727238i 0.970069 0.242831i 0.0780759π-0.0780759\pi
−0.242831 + 0.970069i 0.578076π0.578076\pi
368368 −91.6152 596.084i −0.0129776 0.0844376i
369369 7089.38 6189.04i 1.00016 0.873139i
370370 −7654.73 4902.32i −1.07554 0.688809i
371371 5290.03 0.740283
372372 −847.535 + 922.636i −0.118125 + 0.128593i
373373 829.354 + 829.354i 0.115127 + 0.115127i 0.762323 0.647196i 0.224059π-0.224059\pi
−0.647196 + 0.762323i 0.724059π0.724059\pi
374374 −7073.56 + 5126.88i −0.977982 + 0.708837i
375375 −5575.33 + 4652.97i −0.767757 + 0.640742i
376376 −2030.62 + 652.088i −0.278514 + 0.0894385i
377377 −4183.04 + 4183.04i −0.571452 + 0.571452i
378378 −6042.07 4616.85i −0.822144 0.628215i
379379 −7284.09 −0.987226 −0.493613 0.869682i 0.664324π-0.664324\pi
−0.493613 + 0.869682i 0.664324π0.664324\pi
380380 −542.450 9414.26i −0.0732292 1.27090i
381381 5012.42 1880.10i 0.674001 0.252810i
382382 −48.8597 + 306.219i −0.00654419 + 0.0410145i
383383 7765.66 + 7765.66i 1.03605 + 1.03605i 0.999325 + 0.0367230i 0.0116919π0.0116919\pi
0.0367230 + 0.999325i 0.488308π0.488308\pi
384384 7519.77 275.933i 0.999327 0.0366696i
385385 2025.35 4642.23i 0.268108 0.614519i
386386 2777.70 2013.26i 0.366272 0.265472i
387387 −79.2391 + 1168.63i −0.0104081 + 0.153501i
388388 −3520.88 6949.40i −0.460685 0.909284i
389389 524.755i 0.0683962i 0.999415 + 0.0341981i 0.0108877π0.0108877\pi
−0.999415 + 0.0341981i 0.989112π0.989112\pi
390390 −2777.90 4290.07i −0.360678 0.557015i
391391 −1231.17 −0.159241
392392 −250.344 + 487.184i −0.0322558 + 0.0627718i
393393 −2382.23 + 5241.98i −0.305770 + 0.672832i
394394 −1784.80 2462.49i −0.228216 0.314869i
395395 −9434.15 + 3702.69i −1.20173 + 0.471652i
396396 1994.36 + 4700.73i 0.253082 + 0.596517i
397397 −7963.26 + 7963.26i −1.00671 + 1.00671i −0.00673471 + 0.999977i 0.502144π0.502144\pi
−0.999977 + 0.00673471i 0.997856π0.997856\pi
398398 −2332.08 + 14615.9i −0.293711 + 1.84078i
399399 −9829.11 + 3686.79i −1.23326 + 0.462582i
400400 −7947.05 + 918.869i −0.993382 + 0.114859i
401401 2609.86i 0.325012i −0.986708 0.162506i 0.948042π-0.948042\pi
0.986708 0.162506i 0.0519577π-0.0519577\pi
402402 1647.44 + 8101.08i 0.204395 + 1.00509i
403403 662.857 + 662.857i 0.0819337 + 0.0819337i
404404 14738.5 + 4826.15i 1.81502 + 0.594332i
405405 −7919.56 + 1926.31i −0.971669 + 0.236344i
406406 8346.59 6049.57i 1.02028 0.739495i
407407 4805.08 4805.08i 0.585207 0.585207i
408408 1775.27 15258.8i 0.215415 1.85152i
409409 9324.88i 1.12735i 0.825997 + 0.563675i 0.190613π0.190613\pi
−0.825997 + 0.563675i 0.809387π0.809387\pi
410410 −10766.5 + 2359.94i −1.29687 + 0.284266i
411411 −405.593 1081.33i −0.0486774 0.129776i
412412 2831.10 1434.36i 0.338539 0.171519i
413413 4654.32 4654.32i 0.554538 0.554538i
414414 −161.202 + 701.337i −0.0191368 + 0.0832581i
415415 −10012.3 4368.27i −1.18430 0.516698i
416416 32.2187 5630.33i 0.00379724 0.663581i
417417 2164.84 4763.62i 0.254227 0.559414i
418418 6961.46 + 1110.75i 0.814584 + 0.129973i
419419 321.911i 0.0375332i 0.999824 + 0.0187666i 0.00597394π0.00597394\pi
−0.999824 + 0.0187666i 0.994026π0.994026\pi
420420 3602.25 + 8144.97i 0.418504 + 0.946271i
421421 2975.11i 0.344413i −0.985061 0.172207i 0.944910π-0.944910\pi
0.985061 0.172207i 0.0550897π-0.0550897\pi
422422 1097.41 6877.79i 0.126590 0.793378i
423423 2539.06 + 172.161i 0.291852 + 0.0197891i
424424 5947.38 1909.87i 0.681204 0.218754i
425425 −610.486 + 16320.3i −0.0696774 + 1.86271i
426426 −10229.9 6772.32i −1.16347 0.770235i
427427 −3156.00 + 3156.00i −0.357681 + 0.357681i
428428 476.270 + 940.045i 0.0537883 + 0.106165i
429429 3577.40 1341.84i 0.402607 0.151013i
430430 739.857 1155.25i 0.0829746 0.129561i
431431 17559.0i 1.96238i −0.193043 0.981190i 0.561836π-0.561836\pi
0.193043 0.981190i 0.438164π-0.438164\pi
432432 −8459.70 3009.17i −0.942170 0.335136i
433433 −4103.34 + 4103.34i −0.455413 + 0.455413i −0.897146 0.441733i 0.854364π-0.854364\pi
0.441733 + 0.897146i 0.354364π0.354364\pi
434434 −958.634 1322.63i −0.106027 0.146286i
435435 580.312 11033.9i 0.0639628 1.21617i
436436 8833.72 + 2892.62i 0.970317 + 0.317732i
437437 702.495 + 702.495i 0.0768991 + 0.0768991i
438438 −1387.46 6822.69i −0.151360 0.744294i
439439 10896.8i 1.18469i −0.805685 0.592344i 0.798203π-0.798203\pi
0.805685 0.592344i 0.201797π-0.201797\pi
440440 601.035 5950.30i 0.0651209 0.644703i
441441 492.363 429.833i 0.0531652 0.0464133i
442442 −11350.7 1811.10i −1.22149 0.194899i
443443 −3646.95 + 3646.95i −0.391133 + 0.391133i −0.875091 0.483958i 0.839199π-0.839199\pi
0.483958 + 0.875091i 0.339199π0.339199\pi
444444 506.491 + 11938.3i 0.0541374 + 1.27606i
445445 5264.21 + 13412.8i 0.560781 + 1.42882i
446446 587.716 425.974i 0.0623972 0.0452252i
447447 8912.91 + 4050.49i 0.943101 + 0.428594i
448448 −1601.33 + 9679.71i −0.168874 + 1.02081i
449449 1995.96 0.209789 0.104895 0.994483i 0.466549π-0.466549\pi
0.104895 + 0.994483i 0.466549π0.466549\pi
450450 9216.92 + 2484.64i 0.965533 + 0.260282i
451451 8239.80i 0.860304i
452452 311.976 + 615.768i 0.0324649 + 0.0640781i
453453 73.8294 162.458i 0.00765741 0.0168498i
454454 6049.41 + 8346.37i 0.625359 + 0.862808i
455455 6203.21 2434.62i 0.639145 0.250850i
456456 −9719.45 + 7693.54i −0.998147 + 0.790094i
457457 3478.05 + 3478.05i 0.356009 + 0.356009i 0.862340 0.506330i 0.168998π-0.168998\pi
−0.506330 + 0.862340i 0.668998π0.668998\pi
458458 7514.08 + 1198.93i 0.766616 + 0.122320i
459459 −8695.35 + 16136.5i −0.884236 + 1.64093i
460460 560.704 629.270i 0.0568325 0.0637824i
461461 858.652 0.0867493 0.0433746 0.999059i 0.486189π-0.486189\pi
0.0433746 + 0.999059i 0.486189π0.486189\pi
462462 −6524.33 + 1326.79i −0.657012 + 0.133610i
463463 2288.18 2288.18i 0.229678 0.229678i −0.582880 0.812558i 0.698074π-0.698074\pi
0.812558 + 0.582880i 0.198074π0.198074\pi
464464 7199.67 9814.69i 0.720336 0.981973i
465465 −1748.46 91.9581i −0.174372 0.00917087i
466466 −5288.47 7296.50i −0.525716 0.725330i
467467 138.937 + 138.937i 0.0137671 + 0.0137671i 0.713957 0.700190i 0.246901π-0.246901\pi
−0.700190 + 0.713957i 0.746901π0.746901\pi
468468 −2517.89 + 6228.81i −0.248695 + 0.615228i
469469 −10778.8 −1.06124
470470 −2509.99 1607.47i −0.246335 0.157760i
471471 −4802.44 12803.5i −0.469819 1.25255i
472472 3552.32 6913.04i 0.346417 0.674149i
473473 725.182 + 725.182i 0.0704945 + 0.0704945i
474474 11108.8 + 7354.15i 1.07646 + 0.712631i
475475 9660.54 8963.87i 0.933171 0.865875i
476476 19034.8 + 6233.00i 1.83290 + 0.600187i
477477 −7436.54 504.236i −0.713827 0.0484012i
478478 10707.1 + 1708.39i 1.02454 + 0.163473i
479479 −4176.86 −0.398425 −0.199213 0.979956i 0.563838π-0.563838\pi
−0.199213 + 0.979956i 0.563838π0.563838\pi
480480 6990.47 + 7856.55i 0.664729 + 0.747085i
481481 8940.86 0.847542
482482 4585.68 + 731.682i 0.433345 + 0.0691436i
483483 −854.213 388.199i −0.0804722 0.0365707i
484484 −5870.38 1922.27i −0.551312 0.180528i
485485 4353.75 9979.05i 0.407616 0.934279i
486486 8053.65 + 7066.12i 0.751689 + 0.659518i
487487 −29.3477 29.3477i −0.00273074 0.00273074i 0.705740 0.708471i 0.250615π-0.250615\pi
−0.708471 + 0.705740i 0.750615π0.750615\pi
488488 −2408.75 + 4687.59i −0.223441 + 0.434830i
489489 −10244.7 + 3842.67i −0.947407 + 0.355361i
490490 −747.740 + 163.899i −0.0689376 + 0.0151106i
491491 −1350.17 −0.124098 −0.0620491 0.998073i 0.519764π-0.519764\pi
−0.0620491 + 0.998073i 0.519764π0.519764\pi
492492 10670.3 + 9801.73i 0.977749 + 0.898162i
493493 −17571.0 17571.0i −1.60519 1.60519i
494494 5443.22 + 7510.01i 0.495753 + 0.683991i
495495 −3289.66 + 6332.82i −0.298705 + 0.575029i
496496 −1555.27 1140.88i −0.140793 0.103280i
497497 11311.1 11311.1i 1.02087 1.02087i
498498 2861.61 + 14071.6i 0.257493 + 1.26619i
499499 6077.90 0.545259 0.272629 0.962119i 0.412107π-0.412107\pi
0.272629 + 0.962119i 0.412107π0.412107\pi
500500 −8063.51 7744.66i −0.721222 0.692704i
501501 4923.29 + 13125.7i 0.439035 + 1.17048i
502502 13807.4 + 2203.08i 1.22760 + 0.195873i
503503 −11674.3 11674.3i −1.03485 1.03485i −0.999370 0.0354794i 0.988704π-0.988704\pi
−0.0354794 0.999370i 0.511296π-0.511296\pi
504504 6042.93 10027.1i 0.534074 0.886194i
505505 7918.46 + 20175.6i 0.697756 + 1.77782i
506506 369.768 + 510.169i 0.0324865 + 0.0448217i
507507 −5816.43 2643.29i −0.509500 0.231543i
508508 3725.03 + 7352.34i 0.325338 + 0.642141i
509509 403.668i 0.0351518i 0.999846 + 0.0175759i 0.00559487π0.00559487\pi
−0.999846 + 0.0175759i 0.994405π0.994405\pi
510510 18020.6 11668.7i 1.56464 1.01313i
511511 9077.86 0.785873
512512 1694.38 + 11460.7i 0.146253 + 0.989247i
513513 14168.8 4245.86i 1.21943 0.365418i
514514 −4756.79 + 3447.70i −0.408196 + 0.295859i
515515 4065.34 + 1773.66i 0.347845 + 0.151761i
516516 −1801.73 + 76.4395i −0.153715 + 0.00652144i
517517 1575.59 1575.59i 0.134032 0.134032i
518518 −15385.2 2454.83i −1.30500 0.208222i
519519 1695.83 + 4521.14i 0.143427 + 0.382381i
520520 6095.06 4976.71i 0.514012 0.419698i
521521 12374.1i 1.04054i −0.854003 0.520268i 0.825832π-0.825832\pi
0.854003 0.520268i 0.174168π-0.174168\pi
522522 −12310.0 + 7708.68i −1.03217 + 0.646360i
523523 −15850.3 15850.3i −1.32521 1.32521i −0.909495 0.415716i 0.863531π-0.863531\pi
−0.415716 0.909495i 0.636469π-0.636469\pi
524524 −8424.70 2758.68i −0.702356 0.229988i
525525 −5569.49 + 11130.9i −0.462995 + 0.925316i
526526 −1264.95 1745.25i −0.104856 0.144670i
527527 −2784.36 + 2784.36i −0.230149 + 0.230149i
528528 −6856.04 + 3847.15i −0.565097 + 0.317094i
529529 12078.2i 0.992702i
530530 7351.41 + 4708.06i 0.602499 + 0.385858i
531531 −6986.52 + 6099.24i −0.570978 + 0.498464i
532532 −7304.61 14417.6i −0.595291 1.17497i
533533 7665.93 7665.93i 0.622980 0.622980i
534534 10455.6 15793.6i 0.847298 1.27988i
535535 −588.932 + 1349.87i −0.0475921 + 0.109084i
536536 −12118.2 + 3891.50i −0.976543 + 0.313595i
537537 −10532.5 4786.49i −0.846386 0.384641i
538538 −179.320 + 1123.86i −0.0143700 + 0.0900612i
539539 572.260i 0.0457310i
540540 −4287.55 11793.3i −0.341679 0.939817i
541541 14672.6i 1.16604i −0.812459 0.583018i 0.801872π-0.801872\pi
0.812459 0.583018i 0.198128π-0.198128\pi
542542 −22790.5 3636.41i −1.80616 0.288187i
543543 3594.93 + 1633.72i 0.284113 + 0.129115i
544544 23650.5 + 135.336i 1.86398 + 0.0106663i
545545 4746.03 + 12092.5i 0.373023 + 0.950433i
546546 −7304.32 4835.56i −0.572520 0.379016i
547547 −14666.6 + 14666.6i −1.14643 + 1.14643i −0.159182 + 0.987249i 0.550886π0.550886\pi
−0.987249 + 0.159182i 0.949114π0.949114\pi
548548 1586.11 803.598i 0.123641 0.0626423i
549549 4737.42 4135.77i 0.368284 0.321512i
550550 6946.09 4648.63i 0.538513 0.360397i
551551 20051.7i 1.55033i
552552 −1100.51 128.039i −0.0848567 0.00987262i
553553 −12282.8 + 12282.8i −0.944519 + 0.944519i
554554 −1080.90 + 783.433i −0.0828937 + 0.0600810i
555555 −12412.1 + 11171.7i −0.949306 + 0.854440i
556556 7655.89 + 2506.94i 0.583961 + 0.191219i
557557 −3265.81 3265.81i −0.248432 0.248432i 0.571895 0.820327i 0.306209π-0.306209\pi
−0.820327 + 0.571895i 0.806209π0.806209\pi
558558 1221.54 + 1950.68i 0.0926739 + 0.147991i
559559 1349.35i 0.102096i
560560 −11854.7 + 6890.33i −0.894556 + 0.519946i
561561 5636.46 + 15027.0i 0.424192 + 1.13091i
562562 439.315 2753.33i 0.0329740 0.206659i
563563 15854.6 15854.6i 1.18684 1.18684i 0.208905 0.977936i 0.433010π-0.433010\pi
0.977936 0.208905i 0.0669898π-0.0669898\pi
564564 166.079 + 3914.59i 0.0123992 + 0.292259i
565565 −385.775 + 884.218i −0.0287251 + 0.0658395i
566566 11765.8 + 16233.3i 0.873769 + 1.20554i
567567 −11121.0 + 8454.14i −0.823700 + 0.626174i
568568 8632.94 16800.3i 0.637729 1.24106i
569569 −15762.7 −1.16135 −0.580674 0.814136i 0.697211π-0.697211\pi
−0.580674 + 0.814136i 0.697211π0.697211\pi
570570 −16940.4 3624.35i −1.24484 0.266329i
571571 16858.9i 1.23559i −0.786339 0.617795i 0.788026π-0.788026\pi
0.786339 0.617795i 0.211974π-0.211974\pi
572572 2658.58 + 5247.41i 0.194337 + 0.383576i
573573 518.633 + 235.694i 0.0378119 + 0.0171837i
574574 −15296.2 + 11086.6i −1.11228 + 0.806176i
575575 1177.07 + 44.0302i 0.0853694 + 0.00319337i
576576 3173.74 13454.8i 0.229582 0.973289i
577577 −6369.66 6369.66i −0.459571 0.459571i 0.438944 0.898515i 0.355353π-0.355353\pi
−0.898515 + 0.438944i 0.855353π0.855353\pi
578578 5418.07 33956.8i 0.389899 2.44362i
579579 −2213.36 5900.91i −0.158867 0.423547i
580580 16983.0 978.563i 1.21583 0.0700562i
581581 −18722.9 −1.33693
582582 −14024.9 + 2852.10i −0.998882 + 0.203133i
583583 −4614.67 + 4614.67i −0.327822 + 0.327822i
584584 10205.9 3277.40i 0.723156 0.232226i
585585 −8952.31 + 2831.22i −0.632705 + 0.200097i
586586 2216.82 1606.74i 0.156273 0.113266i
587587 −7601.19 7601.19i −0.534471 0.534471i 0.387428 0.921900i 0.373363π-0.373363\pi
−0.921900 + 0.387428i 0.873363π0.873363\pi
588588 741.058 + 680.737i 0.0519740 + 0.0477434i
589589 3177.46 0.222283
590590 10610.3 2325.70i 0.740369 0.162284i
591591 −5231.29 + 1962.20i −0.364106 + 0.136572i
592592 −18183.3 + 2794.69i −1.26238 + 0.194022i
593593 −5652.89 5652.89i −0.391461 0.391461i 0.483747 0.875208i 0.339276π-0.339276\pi
−0.875208 + 0.483747i 0.839276π0.839276\pi
594594 9298.13 1243.26i 0.642268 0.0858783i
595595 10226.7 + 26056.9i 0.704630 + 1.79534i
596596 −4690.57 + 14324.4i −0.322371 + 0.984484i
597597 24754.5 + 11249.7i 1.69704 + 0.771223i
598598 −130.622 + 818.653i −0.00893235 + 0.0559819i
599599 7162.66 0.488578 0.244289 0.969702i 0.421445π-0.421445\pi
0.244289 + 0.969702i 0.421445π0.421445\pi
600600 −2242.96 + 14524.8i −0.152614 + 0.988286i
601601 −21472.0 −1.45734 −0.728671 0.684864i 0.759862π-0.759862\pi
−0.728671 + 0.684864i 0.759862π0.759862\pi
602602 370.483 2321.94i 0.0250827 0.157201i
603603 15152.5 + 1027.42i 1.02331 + 0.0693858i
604604 261.096 + 85.4964i 0.0175891 + 0.00575960i
605605 −3153.94 8035.98i −0.211944 0.540015i
606606 15727.4 23756.9i 1.05426 1.59250i
607607 874.002 + 874.002i 0.0584426 + 0.0584426i 0.735724 0.677281i 0.236842π-0.236842\pi
−0.677281 + 0.735724i 0.736842π0.736842\pi
608608 −13417.5 13571.9i −0.894986 0.905288i
609609 −6650.85 17731.4i −0.442539 1.17983i
610610 −7194.60 + 1577.01i −0.477542 + 0.104674i
611611 2931.71 0.194115
612612 −26164.4 10576.5i −1.72816 0.698577i
613613 −4069.30 4069.30i −0.268120 0.268120i 0.560222 0.828342i 0.310716π-0.310716\pi
−0.828342 + 0.560222i 0.810716π0.810716\pi
614614 −5591.02 + 4052.34i −0.367484 + 0.266351i
615615 −1063.49 + 20220.9i −0.0697304 + 1.32583i
616616 −3134.08 9759.59i −0.204993 0.638352i
617617 17088.1 17088.1i 1.11498 1.11498i 0.122508 0.992468i 0.460906π-0.460906\pi
0.992468 0.122508i 0.0390937π-0.0390937\pi
618618 −1161.91 5713.55i −0.0756291 0.371898i
619619 24760.0 1.60773 0.803867 0.594808i 0.202772π-0.202772\pi
0.803867 + 0.594808i 0.202772π0.202772\pi
620620 −155.066 2691.19i −0.0100445 0.174324i
621621 1163.82 + 627.138i 0.0752053 + 0.0405252i
622622 −1862.39 + 11672.2i −0.120056 + 0.752431i
623623 17462.8 + 17462.8i 1.12301 + 1.12301i
624624 −9957.76 2799.34i −0.638829 0.179588i
625625 1167.32 15581.3i 0.0747085 0.997205i
626626 −24484.4 + 17746.2i −1.56325 + 1.13304i
627627 5358.16 11790.4i 0.341283 0.750976i
628628 18780.5 9515.04i 1.19335 0.604604i
629629 37556.4i 2.38072i
630630 16182.3 2413.93i 1.02336 0.152656i
631631 9465.71 0.597185 0.298593 0.954381i 0.403483π-0.403483\pi
0.298593 + 0.954381i 0.403483π0.403483\pi
632632 −9374.62 + 18243.6i −0.590036 + 1.14825i
633633 −11648.7 5293.76i −0.731427 0.332398i
634634 6648.67 + 9173.17i 0.416486 + 0.574626i
635635 −4606.19 + 10557.7i −0.287860 + 0.659792i
636636 −486.420 11465.3i −0.0303268 0.714823i
637637 532.405 532.405i 0.0331156 0.0331156i
638638 −2003.77 + 12558.3i −0.124342 + 0.779289i
639639 −16978.8 + 14822.5i −1.05113 + 0.917637i
640640 −10840.1 + 12026.5i −0.669521 + 0.742793i
641641 2756.35i 0.169843i −0.996388 0.0849214i 0.972936π-0.972936\pi
0.996388 0.0849214i 0.0270639π-0.0270639\pi
642642 1897.14 385.803i 0.116627 0.0237172i
643643 15387.1 + 15387.1i 0.943717 + 0.943717i 0.998498 0.0547818i 0.0174463π-0.0174463\pi
−0.0547818 + 0.998498i 0.517446π0.517446\pi
644644 449.545 1372.86i 0.0275070 0.0840033i
645645 −1686.04 1873.23i −0.102927 0.114354i
646646 −31546.1 + 22864.5i −1.92131 + 1.39256i
647647 17532.0 17532.0i 1.06531 1.06531i 0.0675938 0.997713i 0.478468π-0.478468\pi
0.997713 0.0675938i 0.0215322π-0.0215322\pi
648648 −9450.69 + 13519.7i −0.572929 + 0.819605i
649649 8120.25i 0.491137i
650650 10787.2 + 2137.45i 0.650937 + 0.128981i
651651 −2809.78 + 1053.92i −0.169161 + 0.0634504i
652652 −7613.46 15027.2i −0.457310 0.902623i
653653 −8681.37 + 8681.37i −0.520258 + 0.520258i −0.917649 0.397391i 0.869916π-0.869916\pi
0.397391 + 0.917649i 0.369916π0.369916\pi
654654 9426.40 14239.0i 0.563611 0.851359i
655655 −4526.28 11532.6i −0.270010 0.687963i
656656 −13194.3 + 17986.6i −0.785290 + 1.07052i
657657 −12761.3 865.284i −0.757788 0.0513820i
658658 −5044.83 804.942i −0.298887 0.0476898i
659659 13562.6i 0.801707i −0.916142 0.400853i 0.868714π-0.868714\pi
0.916142 0.400853i 0.131286π-0.131286\pi
660660 −10247.5 3962.76i −0.604368 0.233713i
661661 4458.07i 0.262328i 0.991361 + 0.131164i 0.0418714π0.0418714\pi
−0.991361 + 0.131164i 0.958129π0.958129\pi
662662 −846.513 + 5305.37i −0.0496989 + 0.311479i
663663 −8736.54 + 19224.3i −0.511763 + 1.12611i
664664 −21049.4 + 6759.56i −1.23023 + 0.395063i
665665 9032.52 20703.1i 0.526716 1.20726i
666666 21394.0 + 4917.41i 1.24475 + 0.286105i
667667 −1267.28 + 1267.28i −0.0735672 + 0.0735672i
668668 −19253.1 + 9754.48i −1.11515 + 0.564988i
669669 −468.312 1248.54i −0.0270643 0.0721544i
670670 −14979.0 9593.00i −0.863716 0.553149i
671671 5506.17i 0.316786i
672672 16366.5 + 7551.08i 0.939511 + 0.433466i
673673 8098.65 8098.65i 0.463864 0.463864i −0.436056 0.899920i 0.643625π-0.643625\pi
0.899920 + 0.436056i 0.143625π0.143625\pi
674674 −12715.2 17543.1i −0.726663 1.00258i
675675 8890.36 15116.5i 0.506948 0.861977i
676676 3061.00 9347.92i 0.174158 0.531857i
677677 −21319.0 21319.0i −1.21027 1.21027i −0.970936 0.239337i 0.923070π-0.923070\pi
−0.239337 0.970936i 0.576930π-0.576930\pi
678678 1242.71 252.717i 0.0703921 0.0143149i
679679 18660.7i 1.05468i
680680 20904.9 + 25602.6i 1.17892 + 1.44384i
681681 17731.0 6650.68i 0.997727 0.374236i
682682 1990.02 + 317.523i 0.111733 + 0.0178279i
683683 2724.01 2724.01i 0.152608 0.152608i −0.626674 0.779282i 0.715584π-0.715584\pi
0.779282 + 0.626674i 0.215584π0.215584\pi
684684 8894.29 + 20964.0i 0.497196 + 1.17190i
685685 2277.60 + 993.690i 0.127040 + 0.0554262i
686686 13990.3 10140.1i 0.778648 0.564361i
687687 5783.51 12726.3i 0.321186 0.706754i
688688 −421.774 2744.22i −0.0233720 0.152068i
689689 −8586.56 −0.474778
690690 −841.584 1299.71i −0.0464327 0.0717087i
691691 2093.61i 0.115260i −0.998338 0.0576301i 0.981646π-0.981646\pi
0.998338 0.0576301i 0.0183544π-0.0183544\pi
692692 −6631.72 + 3359.93i −0.364306 + 0.184574i
693693 −827.445 + 12203.3i −0.0453565 + 0.668923i
694694 −10323.5 14243.3i −0.564658 0.779059i
695695 4113.23 + 10480.2i 0.224495 + 0.571994i
696696 −13878.9 17533.6i −0.755861 0.954898i
697697 32201.1 + 32201.1i 1.74993 + 1.74993i
698698 32602.0 + 5201.91i 1.76791 + 0.282085i
699699 −15500.6 + 5814.10i −0.838751 + 0.314606i
700700 −17975.5 6639.85i −0.970587 0.358518i
701701 −12609.8 −0.679411 −0.339706 0.940532i 0.610327π-0.610327\pi
−0.339706 + 0.940532i 0.610327π0.610327\pi
702702 9807.23 + 7493.88i 0.527279 + 0.402904i
703703 21429.3 21429.3i 1.14968 1.14968i
704704 −7047.05 9840.83i −0.377267 0.526833i
705705 −4069.94 + 3663.22i −0.217422 + 0.195695i
706706 11961.2 + 16502.8i 0.637627 + 0.879734i
707707 26267.7 + 26267.7i 1.39731 + 1.39731i
708708 −10515.4 9659.51i −0.558184 0.512749i
709709 4224.57 0.223776 0.111888 0.993721i 0.464310π-0.464310\pi
0.111888 + 0.993721i 0.464310π0.464310\pi
710710 25785.3 5651.97i 1.36297 0.298753i
711711 18437.5 16096.0i 0.972519 0.849010i
712712 25937.4 + 13328.1i 1.36523 + 0.701535i
713713 200.817 + 200.817i 0.0105479 + 0.0105479i
714714 20312.0 30682.1i 1.06464 1.60819i
715715 −3287.47 + 7535.07i −0.171950 + 0.394120i
716716 5542.89 16927.3i 0.289312 0.883525i
717717 8241.10 18134.2i 0.429246 0.944536i
718718 −28064.0 4477.83i −1.45869 0.232745i
719719 3475.57 0.180274 0.0901369 0.995929i 0.471270π-0.471270\pi
0.0901369 + 0.995929i 0.471270π0.471270\pi
720720 17321.6 8556.21i 0.896582 0.442877i
721721 7602.12 0.392673
722722 11888.3 + 1896.88i 0.612795 + 0.0977762i
723723 3529.55 7766.61i 0.181557 0.399507i
724724 −1891.89 + 5777.62i −0.0971155 + 0.296579i
725725 16170.5 + 17427.3i 0.828357 + 0.892737i
726726 −6264.24 + 9462.41i −0.320231 + 0.483723i
727727 −4473.63 4473.63i −0.228223 0.228223i 0.583727 0.811950i 0.301594π-0.301594\pi
−0.811950 + 0.583727i 0.801594π0.801594\pi
728728 6164.07 11995.7i 0.313813 0.610700i
729729 16439.3 10824.5i 0.835204 0.549941i
730730 12615.2 + 8079.17i 0.639604 + 0.409621i
731731 −5668.01 −0.286784
732732 7130.31 + 6549.92i 0.360032 + 0.330727i
733733 302.954 + 302.954i 0.0152658 + 0.0152658i 0.714698 0.699433i 0.246564π-0.246564\pi
−0.699433 + 0.714698i 0.746564π0.746564\pi
734734 12002.4 + 16559.8i 0.603567 + 0.832741i
735735 −73.8604 + 1404.36i −0.00370664 + 0.0704769i
736736 9.76089 1705.75i 0.000488847 0.0854277i
737737 9402.73 9402.73i 0.469951 0.469951i
738738 22559.5 14127.1i 1.12524 0.704643i
739739 20265.7 1.00878 0.504389 0.863477i 0.331718π-0.331718\pi
0.504389 + 0.863477i 0.331718π0.331718\pi
740740 −19195.6 17104.1i −0.953575 0.849672i
741741 15954.2 5984.24i 0.790948 0.296676i
742742 14775.6 + 2357.56i 0.731036 + 0.116642i
743743 −1627.48 1627.48i −0.0803585 0.0803585i 0.665785 0.746144i 0.268097π-0.268097\pi
−0.746144 + 0.665785i 0.768097π0.768097\pi
744744 −2778.43 + 2199.30i −0.136912 + 0.108374i
745745 −19608.8 + 7696.00i −0.964309 + 0.378470i
746746 1946.86 + 2686.08i 0.0955489 + 0.131829i
747747 26319.9 + 1784.63i 1.28915 + 0.0874111i
748748 −22042.0 + 11167.5i −1.07745 + 0.545887i
749749 2524.23i 0.123142i
750750 −17646.1 + 10511.5i −0.859125 + 0.511766i
751751 −34918.2 −1.69665 −0.848324 0.529478i 0.822388π-0.822388\pi
−0.848324 + 0.529478i 0.822388π0.822388\pi
752752 −5962.32 + 916.380i −0.289127 + 0.0444374i
753753 10627.4 23385.1i 0.514322 1.13174i
754754 −13547.8 + 9819.41i −0.654354 + 0.474273i
755755 140.277 + 357.415i 0.00676187 + 0.0172287i
756756 −14818.5 15588.0i −0.712890 0.749908i
757757 −20575.8 + 20575.8i −0.987899 + 0.987899i −0.999928 0.0120287i 0.996171π-0.996171\pi
0.0120287 + 0.999928i 0.496171π0.496171\pi
758758 −20345.2 3246.23i −0.974894 0.155552i
759759 1083.80 406.520i 0.0518305 0.0194410i
760760 2680.45 26536.7i 0.127934 1.26656i
761761 14836.5i 0.706729i 0.935486 + 0.353365i 0.114962π0.114962\pi
−0.935486 + 0.353365i 0.885038π0.885038\pi
762762 14838.1 3017.47i 0.705415 0.143453i
763763 15743.9 + 15743.9i 0.747008 + 0.747008i
764764 −272.940 + 833.525i −0.0129249 + 0.0394711i
765765 −11892.7 37604.6i −0.562066 1.77725i
766766 18229.4 + 25151.1i 0.859862 + 1.18635i
767767 −7554.71 + 7554.71i −0.355651 + 0.355651i
768768 21126.4 + 2580.56i 0.992622 + 0.121247i
769769 5513.84i 0.258562i 0.991608 + 0.129281i 0.0412669π0.0412669\pi
−0.991608 + 0.129281i 0.958733π0.958733\pi
770770 7725.87 12063.6i 0.361586 0.564599i
771771 3790.38 + 10105.3i 0.177052 + 0.472027i
772772 8655.60 4385.32i 0.403526 0.204445i
773773 −6649.85 + 6649.85i −0.309416 + 0.309416i −0.844683 0.535267i 0.820211π-0.820211\pi
0.535267 + 0.844683i 0.320211π0.320211\pi
774774 −742.134 + 3228.78i −0.0344644 + 0.149943i
775775 2761.59 2562.44i 0.127999 0.118768i
776776 −6737.09 20979.5i −0.311659 0.970514i
777777 −11841.8 + 26057.4i −0.546749 + 1.20310i
778778 −233.862 + 1465.69i −0.0107768 + 0.0675419i
779779 36747.2i 1.69012i
780780 −5847.02 13220.6i −0.268406 0.606888i
781781 19734.0i 0.904148i
782782 −3438.78 548.685i −0.157252 0.0250907i
783783 7659.40 + 25560.1i 0.349585 + 1.16660i
784784 −916.352 + 1249.18i −0.0417435 + 0.0569053i
785785 26968.0 + 11765.8i 1.22615 + 0.534956i
786786 −8989.94 + 13579.7i −0.407965 + 0.616249i
787787 17933.4 17933.4i 0.812271 0.812271i −0.172703 0.984974i 0.555250π-0.555250\pi
0.984974 + 0.172703i 0.0552501π0.0552501\pi
788788 −3887.69 7673.39i −0.175753 0.346895i
789789 −3707.59 + 1390.68i −0.167293 + 0.0627495i
790790 −28000.6 + 6137.54i −1.26104 + 0.276410i
791791 1653.47i 0.0743245i
792792 3475.51 + 14018.4i 0.155930 + 0.628942i
793793 5122.69 5122.69i 0.229397 0.229397i
794794 −25791.1 + 18693.2i −1.15276 + 0.835515i
795795 11920.3 10729.1i 0.531784 0.478642i
796796 −13027.5 + 39784.3i −0.580083 + 1.77151i
797797 4707.94 + 4707.94i 0.209239 + 0.209239i 0.803944 0.594705i 0.202731π-0.202731\pi
−0.594705 + 0.803944i 0.702731π0.702731\pi
798798 −29096.7 + 5917.11i −1.29074 + 0.262485i
799799 12314.8i 0.545264i
800800 −22606.4 975.197i −0.999071 0.0430980i
801801 −22884.1 26213.1i −1.00945 1.15630i
802802 1163.11 7289.58i 0.0512105 0.320953i
803803 −7918.92 + 7918.92i −0.348011 + 0.348011i
804804 991.116 + 23361.3i 0.0434751 + 1.02474i
805805 1879.31 737.585i 0.0822818 0.0322937i
806806 1556.02 + 2146.83i 0.0680004 + 0.0938201i
807807 1903.44 + 865.020i 0.0830287 + 0.0377325i
808808 39015.2 + 20048.3i 1.69870 + 0.872891i
809809 −39244.1 −1.70550 −0.852749 0.522320i 0.825067π-0.825067\pi
−0.852749 + 0.522320i 0.825067π0.825067\pi
810810 −22978.6 + 1850.94i −0.996771 + 0.0802908i
811811 16408.3i 0.710448i 0.934781 + 0.355224i 0.115595π0.115595\pi
−0.934781 + 0.355224i 0.884405π0.884405\pi
812812 26008.9 13177.3i 1.12406 0.569498i
813813 −17541.6 + 38599.5i −0.756718 + 1.66512i
814814 15562.5 11279.6i 0.670104 0.485689i
815815 9414.43 21578.4i 0.404630 0.927435i
816816 11758.7 41828.0i 0.504458 1.79445i
817817 3234.11 + 3234.11i 0.138491 + 0.138491i
818818 −4155.73 + 26045.3i −0.177630 + 1.11327i
819819 −12123.2 + 10583.5i −0.517238 + 0.451549i
820820 −31123.5 + 1793.34i −1.32546 + 0.0763733i
821821 7023.21 0.298553 0.149276 0.988796i 0.452306π-0.452306\pi
0.149276 + 0.988796i 0.452306π0.452306\pi
822822 −650.956 3201.00i −0.0276213 0.135825i
823823 −26346.4 + 26346.4i −1.11589 + 1.11589i −0.123552 + 0.992338i 0.539429π0.539429\pi
−0.992338 + 0.123552i 0.960571π0.960571\pi
824824 8546.77 2744.61i 0.361336 0.116035i
825825 −4851.38 14568.3i −0.204731 0.614791i
826826 15074.2 10925.7i 0.634987 0.460236i
827827 1006.50 + 1006.50i 0.0423209 + 0.0423209i 0.727951 0.685630i 0.240473π-0.240473\pi
−0.685630 + 0.727951i 0.740473π0.740473\pi
828828 −762.811 + 1887.06i −0.0320163 + 0.0792028i
829829 −21920.6 −0.918376 −0.459188 0.888339i 0.651860π-0.651860\pi
−0.459188 + 0.888339i 0.651860π0.651860\pi
830830 −26018.6 16663.1i −1.08810 0.696849i
831831 861.300 + 2296.26i 0.0359545 + 0.0958560i
832832 2599.21 15711.7i 0.108307 0.654694i
833833 2236.39 + 2236.39i 0.0930207 + 0.0930207i
834834 8169.55 12340.5i 0.339195 0.512369i
835835 −27646.6 12061.9i −1.14581 0.499904i
836836 18949.0 + 6204.89i 0.783929 + 0.256699i
837837 4050.34 1213.73i 0.167264 0.0501228i
838838 −143.463 + 899.130i −0.00591391 + 0.0370643i
839839 31047.8 1.27758 0.638790 0.769381i 0.279435π-0.279435\pi
0.638790 + 0.769381i 0.279435π0.279435\pi
840840 6431.54 + 24355.1i 0.264178 + 1.00039i
841841 −11783.7 −0.483156
842842 1325.89 8309.77i 0.0542674 0.340111i
843843 −4663.22 2119.21i −0.190522 0.0865829i
844844 6130.32 18721.3i 0.250017 0.763522i
845845 12796.4 5022.30i 0.520958 0.204464i
846846 7015.11 + 1612.42i 0.285088 + 0.0655274i
847847 −10462.5 10462.5i −0.424433 0.424433i
848848 17462.8 2683.94i 0.707163 0.108687i
849849 34485.8 12935.2i 1.39405 0.522893i
850850 −8978.46 + 45312.1i −0.362304 + 1.82846i
851851 2708.69 0.109110
852852 −25554.9 23474.8i −1.02758 0.943936i
853853 1829.37 + 1829.37i 0.0734308 + 0.0734308i 0.742868 0.669438i 0.233465π-0.233465\pi
−0.669438 + 0.742868i 0.733465π0.733465\pi
854854 −10221.5 + 7408.51i −0.409571 + 0.296855i
855855 −14671.0 + 28242.6i −0.586826 + 1.12968i
856856 911.327 + 2837.89i 0.0363884 + 0.113314i
857857 −19889.3 + 19889.3i −0.792774 + 0.792774i −0.981944 0.189170i 0.939420π-0.939420\pi
0.189170 + 0.981944i 0.439420π0.439420\pi
858858 10590.0 2153.59i 0.421372 0.0856902i
859859 −19612.5 −0.779011 −0.389505 0.921024i 0.627354π-0.627354\pi
−0.389505 + 0.921024i 0.627354π0.627354\pi
860860 2581.34 2897.00i 0.102352 0.114869i
861861 12188.5 + 32495.0i 0.482443 + 1.28621i
862862 7825.34 49043.9i 0.309202 1.93787i
863863 −29168.7 29168.7i −1.15054 1.15054i −0.986445 0.164093i 0.947530π-0.947530\pi
−0.164093 0.986445i 0.552470π-0.552470\pi
864864 −22287.7 12175.1i −0.877595 0.479402i
865865 −9522.88 4154.73i −0.374321 0.163312i
866866 −13289.7 + 9632.33i −0.521482 + 0.377967i
867867 −57511.4 26136.2i −2.25281 1.02379i
868868 −2088.12 4121.45i −0.0816535 0.161165i
869869 21429.4i 0.836530i
870870 6538.22 30560.0i 0.254789 1.19090i
871871 17495.7 0.680620
872872 23384.3 + 12016.2i 0.908133 + 0.466651i
873873 −1778.70 + 26232.5i −0.0689574 + 1.01699i
874874 1649.06 + 2275.21i 0.0638220 + 0.0880551i
875875 −8845.49 25277.6i −0.341751 0.976617i
876876 −834.712 19674.8i −0.0321944 0.758845i
877877 −1922.31 + 1922.31i −0.0740158 + 0.0740158i −0.743146 0.669130i 0.766667π-0.766667\pi
0.669130 + 0.743146i 0.266667π0.266667\pi
878878 4856.29 30435.9i 0.186665 1.16989i
879879 −1766.44 4709.39i −0.0677821 0.180710i
880880 4330.56 16351.9i 0.165890 0.626389i
881881 3232.94i 0.123633i 0.998088 + 0.0618163i 0.0196893π0.0196893\pi
−0.998088 + 0.0618163i 0.980311π0.980311\pi
882882 1566.78 981.139i 0.0598142 0.0374565i
883883 −16301.2 16301.2i −0.621269 0.621269i 0.324587 0.945856i 0.394775π-0.394775\pi
−0.945856 + 0.324587i 0.894775π0.894775\pi
884884 −30896.6 10117.1i −1.17552 0.384928i
885885 1048.06 19927.5i 0.0398082 0.756900i
886886 −11811.6 + 8560.99i −0.447876 + 0.324619i
887887 −25995.8 + 25995.8i −0.984051 + 0.984051i −0.999875 0.0158243i 0.994963π-0.994963\pi
0.0158243 + 0.999875i 0.494963π0.494963\pi
888888 −3905.77 + 33570.7i −0.147600 + 1.26865i
889889 19742.6i 0.744822i
890890 8725.90 + 39809.2i 0.328644 + 1.49933i
891891 2326.38 17076.0i 0.0874712 0.642053i
892892 1831.39 927.864i 0.0687437 0.0348287i
893893 7026.70 7026.70i 0.263314 0.263314i
894894 23089.5 + 15285.5i 0.863789 + 0.571839i
895895 23171.9 9094.43i 0.865419 0.339657i
896896 −8786.52 + 26322.7i −0.327608 + 0.981451i
897897 1386.52 + 630.108i 0.0516106 + 0.0234545i
898898 5574.92 + 889.522i 0.207169 + 0.0330554i
899899 5732.04i 0.212652i
900900 24636.4 + 11047.5i 0.912460 + 0.409165i
901901 36068.2i 1.33364i
902902 3672.15 23014.6i 0.135554 0.849558i
903903 −3932.58 1787.17i −0.144926 0.0658619i
904904 596.956 + 1858.94i 0.0219629 + 0.0683930i
905905 −7909.00 + 3104.10i −0.290502 + 0.114015i
906906 278.614 420.858i 0.0102167 0.0154328i
907907 −1900.65 + 1900.65i −0.0695812 + 0.0695812i −0.741041 0.671460i 0.765668π-0.765668\pi
0.671460 + 0.741041i 0.265668π0.265668\pi
908908 13176.9 + 26008.2i 0.481599 + 0.950565i
909909 −34422.4 39429.9i −1.25601 1.43873i
910910 18411.2 4035.60i 0.670687 0.147010i
911911 21899.8i 0.796456i 0.917286 + 0.398228i 0.130375π0.130375\pi
−0.917286 + 0.398228i 0.869625π0.869625\pi
912912 −30576.1 + 17157.2i −1.11017 + 0.622952i
913913 16332.6 16332.6i 0.592037 0.592037i
914914 8164.49 + 11264.5i 0.295468 + 0.407657i
915915 −710.670 + 13512.4i −0.0256765 + 0.488205i
916916 20453.2 + 6697.46i 0.737766 + 0.241583i
917917 −15014.9 15014.9i −0.540715 0.540715i
918918 −31478.4 + 41195.7i −1.13174 + 1.48111i
919919 6800.64i 0.244105i −0.992524 0.122052i 0.961052π-0.961052\pi
0.992524 0.122052i 0.0389476π-0.0389476\pi
920920 1846.54 1507.73i 0.0661725 0.0540308i
921921 4455.12 + 11877.5i 0.159393 + 0.424948i
922922 2398.30 + 382.667i 0.0856656 + 0.0136686i
923923 −18359.6 + 18359.6i −0.654729 + 0.654729i
924924 −18814.4 + 798.210i −0.669857 + 0.0284190i
925925 1343.12 35906.2i 0.0477424 1.27631i
926926 7410.85 5371.35i 0.262998 0.190619i
927927 −10686.8 724.619i −0.378641 0.0256738i
928928 24483.4 24204.8i 0.866063 0.856207i
929929 3940.14 0.139151 0.0695757 0.997577i 0.477835π-0.477835\pi
0.0695757 + 0.997577i 0.477835π0.477835\pi
930930 −4842.64 1036.07i −0.170749 0.0365312i
931931 2552.12i 0.0898415i
932932 −11519.4 22736.7i −0.404862 0.799104i
933933 19768.8 + 8983.96i 0.693678 + 0.315243i
934934 326.145 + 449.983i 0.0114259 + 0.0157643i
935935 −31651.4 13809.2i −1.10707 0.483003i
936936 −9808.63 + 16275.5i −0.342527 + 0.568357i
937937 −13351.3 13351.3i −0.465492 0.465492i 0.434958 0.900451i 0.356763π-0.356763\pi
−0.900451 + 0.434958i 0.856763π0.856763\pi
938938 −30106.3 4803.69i −1.04798 0.167213i
939939 19510.0 + 52014.5i 0.678047 + 1.80770i
940940 −6294.27 5608.43i −0.218400 0.194603i
941941 43783.5 1.51679 0.758395 0.651795i 0.225984π-0.225984\pi
0.758395 + 0.651795i 0.225984π0.225984\pi
942942 −7707.67 37901.6i −0.266592 1.31094i
943943 2322.45 2322.45i 0.0802008 0.0802008i
944944 13002.8 17725.7i 0.448312 0.611145i
945945 3605.64 29840.7i 0.124118 1.02721i
946946 1702.32 + 2348.69i 0.0585065 + 0.0807214i
947947 22126.2 + 22126.2i 0.759245 + 0.759245i 0.976185 0.216940i 0.0696076π-0.0696076\pi
−0.216940 + 0.976185i 0.569608π0.569608\pi
948948 27750.4 + 25491.6i 0.950729 + 0.873342i
949949 −14734.8 −0.504017
950950 30977.7 20731.6i 1.05795 0.708024i
951951 19487.4 7309.50i 0.664482 0.249239i
952952 50388.3 + 25892.4i 1.71544 + 0.881490i
953953 −3751.04 3751.04i −0.127501 0.127501i 0.640477 0.767977i 0.278737π-0.278737\pi
−0.767977 + 0.640477i 0.778737π0.778737\pi
954954 −20546.2 4722.55i −0.697284 0.160271i
955955 −1141.02 + 447.823i −0.0386622 + 0.0151740i
956956 29144.5 + 9543.42i 0.985983 + 0.322862i
957957 21269.5 + 9665.95i 0.718438 + 0.326495i
958958 −11666.4 1861.46i −0.393448 0.0627778i
959959 4259.06 0.143412
960960 16023.7 + 25059.5i 0.538711 + 0.842491i
961961 −28882.7 −0.969510
962962 24972.7 + 3984.58i 0.836955 + 0.133543i
963963 240.604 3548.47i 0.00805127 0.118741i
964964 12482.2 + 4087.32i 0.417037 + 0.136560i
965965 12429.1 + 5422.68i 0.414618 + 0.180893i
966966 −2212.90 1464.97i −0.0737047 0.0487935i
967967 −3625.15 3625.15i −0.120555 0.120555i 0.644255 0.764811i 0.277167π-0.277167\pi
−0.764811 + 0.644255i 0.777167π0.777167\pi
968968 −15539.8 7985.27i −0.515981 0.265141i
969969 25137.1 + 67016.3i 0.833353 + 2.22175i
970970 16607.7 25932.2i 0.549734 0.858383i
971971 −6376.71 −0.210750 −0.105375 0.994433i 0.533604π-0.533604\pi
−0.105375 + 0.994433i 0.533604π0.533604\pi
972972 19345.5 + 23325.5i 0.638383 + 0.769719i
973973 13644.7 + 13644.7i 0.449567 + 0.449567i
974974 −68.8919 95.0501i −0.00226636 0.00312690i
975975 9040.16 18067.2i 0.296940 0.593448i
976976 −8816.96 + 12019.4i −0.289164 + 0.394192i
977977 −6800.26 + 6800.26i −0.222681 + 0.222681i −0.809627 0.586945i 0.800330π-0.800330\pi
0.586945 + 0.809627i 0.300330π0.300330\pi
978978 −30327.0 + 6167.30i −0.991565 + 0.201645i
979979 −30466.8 −0.994609
980980 −2161.55 + 124.549i −0.0704574 + 0.00405976i
981981 −20631.5 23632.9i −0.671471 0.769153i
982982 −3771.15 601.716i −0.122548 0.0195535i
983983 −33279.1 33279.1i −1.07979 1.07979i −0.996527 0.0832671i 0.973465π-0.973465\pi
−0.0832671 0.996527i 0.526535π-0.526535\pi
984984 25434.8 + 32132.5i 0.824017 + 1.04100i
985985 4807.32 11018.7i 0.155507 0.356430i
986986 −41246.9 56908.3i −1.33222 1.83806i
987987 −3882.95 + 8544.25i −0.125224 + 0.275549i
988988 11856.5 + 23402.0i 0.381788 + 0.753560i
989989 408.796i 0.0131435i
990990 −12010.6 + 16222.1i −0.385578 + 0.520780i
991991 36313.9 1.16402 0.582012 0.813180i 0.302266π-0.302266\pi
0.582012 + 0.813180i 0.302266π0.302266\pi
992992 −3835.56 3879.71i −0.122761 0.124174i
993993 8985.52 + 4083.48i 0.287157 + 0.130499i
994994 36633.8 26552.0i 1.16897 0.847262i
995995 −54460.9 + 21374.7i −1.73520 + 0.681028i
996996 1721.57 + 40578.7i 0.0547692 + 1.29095i
997997 10579.3 10579.3i 0.336058 0.336058i −0.518823 0.854881i 0.673630π-0.673630\pi
0.854881 + 0.518823i 0.173630π0.173630\pi
998998 16976.2 + 2708.68i 0.538448 + 0.0859135i
999999 19130.6 35501.8i 0.605871 1.12435i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 120.4.w.c.77.61 yes 128
3.2 odd 2 inner 120.4.w.c.77.4 yes 128
5.3 odd 4 inner 120.4.w.c.53.36 yes 128
8.5 even 2 inner 120.4.w.c.77.29 yes 128
15.8 even 4 inner 120.4.w.c.53.29 yes 128
24.5 odd 2 inner 120.4.w.c.77.36 yes 128
40.13 odd 4 inner 120.4.w.c.53.4 128
120.53 even 4 inner 120.4.w.c.53.61 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.w.c.53.4 128 40.13 odd 4 inner
120.4.w.c.53.29 yes 128 15.8 even 4 inner
120.4.w.c.53.36 yes 128 5.3 odd 4 inner
120.4.w.c.53.61 yes 128 120.53 even 4 inner
120.4.w.c.77.4 yes 128 3.2 odd 2 inner
120.4.w.c.77.29 yes 128 8.5 even 2 inner
120.4.w.c.77.36 yes 128 24.5 odd 2 inner
120.4.w.c.77.61 yes 128 1.1 even 1 trivial