Properties

Label 370.2.x.a.9.9
Level 370370
Weight 22
Character 370.9
Analytic conductor 2.9542.954
Analytic rank 00
Dimension 108108
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [370,2,Mod(9,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 370=2537 370 = 2 \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 370.x (of order 1818, degree 66, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.954464874792.95446487479
Analytic rank: 00
Dimension: 108108
Relative dimension: 1818 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 9.9
Character χ\chi == 370.9
Dual form 370.2.x.a.329.9

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.984808+0.173648i)q2+(2.61244+0.460644i)q3+(0.9396930.342020i)q4+(1.38577+1.75489i)q52.65274q6+(2.091252.49226i)q7+(0.866025+0.500000i)q8+(3.79359+1.38075i)q9+(1.669451.48759i)q10+(0.0622047+0.107742i)q11+(2.612440.460644i)q12+(2.131365.85586i)q13+(1.62670+2.81754i)q14+(2.81188+5.22289i)q15+(0.7660440.642788i)q16+(1.61191+4.42868i)q17+(3.975720.701027i)q18+(0.307373+1.74320i)q19+(1.90241+1.17509i)q20+(6.611325.54755i)q21+(0.07996890.0953032i)q22+(7.341214.23845i)q23+(2.49276+0.907292i)q24+(1.15926+4.86376i)q25+(3.11584+5.39679i)q26+(2.38247+1.37552i)q27+(1.112733.05720i)q28+(1.23037+2.13106i)q29+(3.676114.65527i)q305.35817q31+(0.642788+0.766044i)q32+(0.112876+0.310124i)q33+(0.8183884.64131i)q34+(7.27163+0.216203i)q35+4.03705q36+(2.12868+5.69813i)q371.77009iq38+(2.8705816.2799i)q39+(2.077560.826889i)q40+(3.81283+1.38776i)q41+(5.54755+6.61132i)q422.22479iq43+(0.0953032+0.0799689i)q44+(2.83399+8.57073i)q45+(7.96568+2.89927i)q46+(8.31733+4.80201i)q47+(2.297341.32637i)q48+(0.6224723.53021i)q49+(0.2970624.99117i)q50+(6.25107+10.8272i)q51+(4.005644.77374i)q52+(4.66659+5.56142i)q53+(2.585130.940909i)q54+(0.102873+0.258468i)q55+(0.564949+3.20398i)q56+(1.60599+4.41242i)q57+(1.581731.88504i)q58+(5.603744.70210i)q59+(4.42864+3.94619i)q60+(0.1271590.0462822i)q61+(5.276770.930436i)q62+(11.37456.56709i)q63+(0.5000000.866025i)q64+(7.3227811.8552i)q65+(0.1650130.285811i)q66+(6.98181+8.32060i)q67+4.71291iq68+(17.226114.4544i)q69+(7.19870+1.04979i)q70+(1.013115.74563i)q71+(3.97572+0.701027i)q729.15252iq73+(3.085815.24193i)q74+(5.26895+12.1723i)q75+(0.307373+1.74320i)q76+(0.398606+0.0702850i)q77+(5.65395+15.5341i)q78+(0.898957+0.754314i)q79+(2.18958+0.453562i)q80+(3.687253.09397i)q81+(3.513922.02876i)q82+(1.33054+3.65563i)q83+(4.315237.47420i)q84+(10.0056+3.30844i)q85+(0.386330+2.19099i)q86+(2.23261+6.13404i)q87+(0.1077420.0622047i)q88+(11.3243+9.50225i)q89+(4.279237.94840i)q90+(19.05156.93418i)q91+(8.348121.47200i)q92+(13.99792.46821i)q93+(9.024833.28477i)q94+(3.48507+1.87628i)q95+(2.03212+1.70515i)q96+(1.401740.809293i)q97+(1.22603+3.36849i)q98+(0.0872144+0.494617i)q99+O(q100)q+(-0.984808 + 0.173648i) q^{2} +(2.61244 + 0.460644i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.38577 + 1.75489i) q^{5} -2.65274 q^{6} +(2.09125 - 2.49226i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(3.79359 + 1.38075i) q^{9} +(-1.66945 - 1.48759i) q^{10} +(0.0622047 + 0.107742i) q^{11} +(2.61244 - 0.460644i) q^{12} +(-2.13136 - 5.85586i) q^{13} +(-1.62670 + 2.81754i) q^{14} +(2.81188 + 5.22289i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.61191 + 4.42868i) q^{17} +(-3.97572 - 0.701027i) q^{18} +(-0.307373 + 1.74320i) q^{19} +(1.90241 + 1.17509i) q^{20} +(6.61132 - 5.54755i) q^{21} +(-0.0799689 - 0.0953032i) q^{22} +(-7.34121 - 4.23845i) q^{23} +(-2.49276 + 0.907292i) q^{24} +(-1.15926 + 4.86376i) q^{25} +(3.11584 + 5.39679i) q^{26} +(2.38247 + 1.37552i) q^{27} +(1.11273 - 3.05720i) q^{28} +(1.23037 + 2.13106i) q^{29} +(-3.67611 - 4.65527i) q^{30} -5.35817 q^{31} +(-0.642788 + 0.766044i) q^{32} +(0.112876 + 0.310124i) q^{33} +(0.818388 - 4.64131i) q^{34} +(7.27163 + 0.216203i) q^{35} +4.03705 q^{36} +(2.12868 + 5.69813i) q^{37} -1.77009i q^{38} +(-2.87058 - 16.2799i) q^{39} +(-2.07756 - 0.826889i) q^{40} +(-3.81283 + 1.38776i) q^{41} +(-5.54755 + 6.61132i) q^{42} -2.22479i q^{43} +(0.0953032 + 0.0799689i) q^{44} +(2.83399 + 8.57073i) q^{45} +(7.96568 + 2.89927i) q^{46} +(8.31733 + 4.80201i) q^{47} +(2.29734 - 1.32637i) q^{48} +(-0.622472 - 3.53021i) q^{49} +(0.297062 - 4.99117i) q^{50} +(-6.25107 + 10.8272i) q^{51} +(-4.00564 - 4.77374i) q^{52} +(4.66659 + 5.56142i) q^{53} +(-2.58513 - 0.940909i) q^{54} +(-0.102873 + 0.258468i) q^{55} +(-0.564949 + 3.20398i) q^{56} +(-1.60599 + 4.41242i) q^{57} +(-1.58173 - 1.88504i) q^{58} +(5.60374 - 4.70210i) q^{59} +(4.42864 + 3.94619i) q^{60} +(0.127159 - 0.0462822i) q^{61} +(5.27677 - 0.930436i) q^{62} +(11.3745 - 6.56709i) q^{63} +(0.500000 - 0.866025i) q^{64} +(7.32278 - 11.8552i) q^{65} +(-0.165013 - 0.285811i) q^{66} +(-6.98181 + 8.32060i) q^{67} +4.71291i q^{68} +(-17.2261 - 14.4544i) q^{69} +(-7.19870 + 1.04979i) q^{70} +(1.01311 - 5.74563i) q^{71} +(-3.97572 + 0.701027i) q^{72} -9.15252i q^{73} +(-3.08581 - 5.24193i) q^{74} +(-5.26895 + 12.1723i) q^{75} +(0.307373 + 1.74320i) q^{76} +(0.398606 + 0.0702850i) q^{77} +(5.65395 + 15.5341i) q^{78} +(0.898957 + 0.754314i) q^{79} +(2.18958 + 0.453562i) q^{80} +(-3.68725 - 3.09397i) q^{81} +(3.51392 - 2.02876i) q^{82} +(-1.33054 + 3.65563i) q^{83} +(4.31523 - 7.47420i) q^{84} +(-10.0056 + 3.30844i) q^{85} +(0.386330 + 2.19099i) q^{86} +(2.23261 + 6.13404i) q^{87} +(-0.107742 - 0.0622047i) q^{88} +(-11.3243 + 9.50225i) q^{89} +(-4.27923 - 7.94840i) q^{90} +(-19.0515 - 6.93418i) q^{91} +(-8.34812 - 1.47200i) q^{92} +(-13.9979 - 2.46821i) q^{93} +(-9.02483 - 3.28477i) q^{94} +(-3.48507 + 1.87628i) q^{95} +(-2.03212 + 1.70515i) q^{96} +(-1.40174 - 0.809293i) q^{97} +(1.22603 + 3.36849i) q^{98} +(0.0872144 + 0.494617i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 108q12q9+12q116q14+6q1924q21+30q25+48q26+24q30192q31+12q34+30q35+84q36+24q39+12q40108q41+6q4430q45+90q99+O(q100) 108 q - 12 q^{9} + 12 q^{11} - 6 q^{14} + 6 q^{19} - 24 q^{21} + 30 q^{25} + 48 q^{26} + 24 q^{30} - 192 q^{31} + 12 q^{34} + 30 q^{35} + 84 q^{36} + 24 q^{39} + 12 q^{40} - 108 q^{41} + 6 q^{44} - 30 q^{45}+ \cdots - 90 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/370Z)×\left(\mathbb{Z}/370\mathbb{Z}\right)^\times.

nn 261261 297297
χ(n)\chi(n) e(49)e\left(\frac{4}{9}\right) 1-1

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 −0.984808 + 0.173648i −0.696364 + 0.122788i
33 2.61244 + 0.460644i 1.50829 + 0.265953i 0.865821 0.500354i 0.166797π-0.166797\pi
0.642474 + 0.766307i 0.277908π0.277908\pi
44 0.939693 0.342020i 0.469846 0.171010i
55 1.38577 + 1.75489i 0.619737 + 0.784809i
66 −2.65274 −1.08298
77 2.09125 2.49226i 0.790419 0.941984i −0.208935 0.977930i 0.567000π-0.567000\pi
0.999354 + 0.0359452i 0.0114442π0.0114442\pi
88 −0.866025 + 0.500000i −0.306186 + 0.176777i
99 3.79359 + 1.38075i 1.26453 + 0.460251i
1010 −1.66945 1.48759i −0.527928 0.470417i
1111 0.0622047 + 0.107742i 0.0187554 + 0.0324854i 0.875251 0.483669i 0.160696π-0.160696\pi
−0.856495 + 0.516155i 0.827363π0.827363\pi
1212 2.61244 0.460644i 0.754147 0.132977i
1313 −2.13136 5.85586i −0.591132 1.62412i −0.768407 0.639961i 0.778950π-0.778950\pi
0.177275 0.984161i 0.443272π-0.443272\pi
1414 −1.62670 + 2.81754i −0.434755 + 0.753018i
1515 2.81188 + 5.22289i 0.726024 + 1.34854i
1616 0.766044 0.642788i 0.191511 0.160697i
1717 −1.61191 + 4.42868i −0.390945 + 1.07411i 0.575625 + 0.817713i 0.304759π0.304759\pi
−0.966571 + 0.256400i 0.917464π0.917464\pi
1818 −3.97572 0.701027i −0.937086 0.165234i
1919 −0.307373 + 1.74320i −0.0705162 + 0.399917i 0.929036 + 0.369990i 0.120639π0.120639\pi
−0.999552 + 0.0299275i 0.990472π0.990472\pi
2020 1.90241 + 1.17509i 0.425392 + 0.262758i
2121 6.61132 5.54755i 1.44271 1.21058i
2222 −0.0799689 0.0953032i −0.0170494 0.0203187i
2323 −7.34121 4.23845i −1.53075 0.883778i −0.999327 0.0366706i 0.988325π-0.988325\pi
−0.531421 0.847108i 0.678342π-0.678342\pi
2424 −2.49276 + 0.907292i −0.508833 + 0.185200i
2525 −1.15926 + 4.86376i −0.231851 + 0.972751i
2626 3.11584 + 5.39679i 0.611066 + 1.05840i
2727 2.38247 + 1.37552i 0.458506 + 0.264718i
2828 1.11273 3.05720i 0.210286 0.577757i
2929 1.23037 + 2.13106i 0.228474 + 0.395728i 0.957356 0.288911i 0.0932931π-0.0932931\pi
−0.728882 + 0.684639i 0.759960π0.759960\pi
3030 −3.67611 4.65527i −0.671162 0.849931i
3131 −5.35817 −0.962356 −0.481178 0.876623i 0.659791π-0.659791\pi
−0.481178 + 0.876623i 0.659791π0.659791\pi
3232 −0.642788 + 0.766044i −0.113630 + 0.135419i
3333 0.112876 + 0.310124i 0.0196491 + 0.0539856i
3434 0.818388 4.64131i 0.140352 0.795977i
3535 7.27163 + 0.216203i 1.22913 + 0.0365450i
3636 4.03705 0.672842
3737 2.12868 + 5.69813i 0.349952 + 0.936767i
3838 1.77009i 0.287146i
3939 −2.87058 16.2799i −0.459661 2.60687i
4040 −2.07756 0.826889i −0.328491 0.130743i
4141 −3.81283 + 1.38776i −0.595464 + 0.216731i −0.622131 0.782913i 0.713733π-0.713733\pi
0.0266671 + 0.999644i 0.491511π0.491511\pi
4242 −5.54755 + 6.61132i −0.856006 + 1.02015i
4343 2.22479i 0.339277i −0.985506 0.169639i 0.945740π-0.945740\pi
0.985506 0.169639i 0.0542600π-0.0542600\pi
4444 0.0953032 + 0.0799689i 0.0143675 + 0.0120558i
4545 2.83399 + 8.57073i 0.422467 + 1.27765i
4646 7.96568 + 2.89927i 1.17448 + 0.427474i
4747 8.31733 + 4.80201i 1.21321 + 0.700445i 0.963456 0.267865i 0.0863182π-0.0863182\pi
0.249750 + 0.968310i 0.419652π0.419652\pi
4848 2.29734 1.32637i 0.331593 0.191445i
4949 −0.622472 3.53021i −0.0889245 0.504316i
5050 0.297062 4.99117i 0.0420109 0.705858i
5151 −6.25107 + 10.8272i −0.875324 + 1.51611i
5252 −4.00564 4.77374i −0.555483 0.661998i
5353 4.66659 + 5.56142i 0.641005 + 0.763920i 0.984529 0.175224i 0.0560650π-0.0560650\pi
−0.343524 + 0.939144i 0.611621π0.611621\pi
5454 −2.58513 0.940909i −0.351791 0.128042i
5555 −0.102873 + 0.258468i −0.0138714 + 0.0348518i
5656 −0.564949 + 3.20398i −0.0754944 + 0.428150i
5757 −1.60599 + 4.41242i −0.212718 + 0.584439i
5858 −1.58173 1.88504i −0.207692 0.247517i
5959 5.60374 4.70210i 0.729545 0.612161i −0.200462 0.979701i 0.564244π-0.564244\pi
0.930008 + 0.367540i 0.119800π0.119800\pi
6060 4.42864 + 3.94619i 0.571735 + 0.509451i
6161 0.127159 0.0462822i 0.0162811 0.00592583i −0.333867 0.942620i 0.608354π-0.608354\pi
0.350148 + 0.936694i 0.386131π0.386131\pi
6262 5.27677 0.930436i 0.670150 0.118166i
6363 11.3745 6.56709i 1.43306 0.827376i
6464 0.500000 0.866025i 0.0625000 0.108253i
6565 7.32278 11.8552i 0.908280 1.47046i
6666 −0.165013 0.285811i −0.0203117 0.0351810i
6767 −6.98181 + 8.32060i −0.852964 + 1.01652i 0.146662 + 0.989187i 0.453147π0.453147\pi
−0.999626 + 0.0273364i 0.991297π0.991297\pi
6868 4.71291i 0.571524i
6969 −17.2261 14.4544i −2.07378 1.74011i
7070 −7.19870 + 1.04979i −0.860409 + 0.125474i
7171 1.01311 5.74563i 0.120234 0.681881i −0.863791 0.503851i 0.831916π-0.831916\pi
0.984025 0.178031i 0.0569727π-0.0569727\pi
7272 −3.97572 + 0.701027i −0.468543 + 0.0826168i
7373 9.15252i 1.07122i −0.844465 0.535611i 0.820081π-0.820081\pi
0.844465 0.535611i 0.179919π-0.179919\pi
7474 −3.08581 5.24193i −0.358718 0.609361i
7575 −5.26895 + 12.1723i −0.608406 + 1.40553i
7676 0.307373 + 1.74320i 0.0352581 + 0.199959i
7777 0.398606 + 0.0702850i 0.0454254 + 0.00800972i
7878 5.65395 + 15.5341i 0.640183 + 1.75889i
7979 0.898957 + 0.754314i 0.101141 + 0.0848670i 0.691956 0.721940i 0.256749π-0.256749\pi
−0.590815 + 0.806807i 0.701194π0.701194\pi
8080 2.18958 + 0.453562i 0.244803 + 0.0507098i
8181 −3.68725 3.09397i −0.409695 0.343775i
8282 3.51392 2.02876i 0.388048 0.224039i
8383 −1.33054 + 3.65563i −0.146046 + 0.401257i −0.991048 0.133505i 0.957377π-0.957377\pi
0.845002 + 0.534763i 0.179599π0.179599\pi
8484 4.31523 7.47420i 0.470830 0.815502i
8585 −10.0056 + 3.30844i −1.08526 + 0.358851i
8686 0.386330 + 2.19099i 0.0416591 + 0.236260i
8787 2.23261 + 6.13404i 0.239361 + 0.657638i
8888 −0.107742 0.0622047i −0.0114853 0.00663105i
8989 −11.3243 + 9.50225i −1.20038 + 1.00724i −0.200759 + 0.979641i 0.564341π0.564341\pi
−0.999619 + 0.0275959i 0.991215π0.991215\pi
9090 −4.27923 7.94840i −0.451071 0.837835i
9191 −19.0515 6.93418i −1.99714 0.726899i
9292 −8.34812 1.47200i −0.870352 0.153466i
9393 −13.9979 2.46821i −1.45152 0.255941i
9494 −9.02483 3.28477i −0.930840 0.338798i
9595 −3.48507 + 1.87628i −0.357560 + 0.192502i
9696 −2.03212 + 1.70515i −0.207402 + 0.174031i
9797 −1.40174 0.809293i −0.142325 0.0821712i 0.427147 0.904182i 0.359519π-0.359519\pi
−0.569471 + 0.822011i 0.692852π0.692852\pi
9898 1.22603 + 3.36849i 0.123848 + 0.340269i
9999 0.0872144 + 0.494617i 0.00876538 + 0.0497109i
100100 0.574159 + 4.96692i 0.0574159 + 0.496692i
101101 3.80356 6.58797i 0.378469 0.655527i −0.612371 0.790571i 0.709784π-0.709784\pi
0.990840 + 0.135044i 0.0431174π0.0431174\pi
102102 4.27598 11.7482i 0.423385 1.16324i
103103 0.748500 0.432146i 0.0737519 0.0425807i −0.462671 0.886530i 0.653109π-0.653109\pi
0.536422 + 0.843950i 0.319775π0.319775\pi
104104 4.77374 + 4.00564i 0.468104 + 0.392786i
105105 18.8971 + 3.91445i 1.84417 + 0.382012i
106106 −5.56142 4.66659i −0.540173 0.453259i
107107 −7.01548 19.2749i −0.678212 1.86337i −0.461511 0.887135i 0.652692π-0.652692\pi
−0.216701 0.976238i 0.569530π-0.569530\pi
108108 2.70924 + 0.477712i 0.260697 + 0.0459679i
109109 −2.66608 15.1201i −0.255364 1.44824i −0.795137 0.606429i 0.792601π-0.792601\pi
0.539774 0.841810i 0.318510π-0.318510\pi
110110 0.0564275 0.272405i 0.00538015 0.0259728i
111111 2.93624 + 15.8666i 0.278695 + 1.50599i
112112 3.25341i 0.307418i
113113 −6.37898 + 1.12479i −0.600084 + 0.105811i −0.465435 0.885082i 0.654102π-0.654102\pi
−0.134650 + 0.990893i 0.542991π0.542991\pi
114114 0.815382 4.62426i 0.0763675 0.433102i
115115 −2.73527 18.7565i −0.255065 1.74906i
116116 1.88504 + 1.58173i 0.175021 + 0.146860i
117117 25.1576i 2.32582i
118118 −4.70210 + 5.60374i −0.432863 + 0.515866i
119119 7.66651 + 13.2788i 0.702787 + 1.21726i
120120 −5.04660 3.11722i −0.460690 0.284562i
121121 5.49226 9.51288i 0.499296 0.864807i
122122 −0.117191 + 0.0676601i −0.0106099 + 0.00612566i
123123 −10.6001 + 1.86908i −0.955775 + 0.168529i
124124 −5.03503 + 1.83260i −0.452159 + 0.164573i
125125 −10.1418 + 4.70571i −0.907111 + 0.420891i
126126 −10.0614 + 8.44249i −0.896338 + 0.752117i
127127 7.60677 + 9.06540i 0.674992 + 0.804424i 0.989454 0.144846i 0.0462687π-0.0462687\pi
−0.314462 + 0.949270i 0.601824π0.601824\pi
128128 −0.342020 + 0.939693i −0.0302306 + 0.0830579i
129129 1.02484 5.81213i 0.0902318 0.511730i
130130 −5.15290 + 12.9467i −0.451939 + 1.13550i
131131 18.7130 + 6.81096i 1.63496 + 0.595077i 0.986147 0.165872i 0.0530437π-0.0530437\pi
0.648812 + 0.760948i 0.275266π0.275266\pi
132132 0.212137 + 0.252815i 0.0184642 + 0.0220047i
133133 3.70170 + 4.41152i 0.320978 + 0.382527i
134134 5.43089 9.40657i 0.469157 0.812604i
135135 0.887684 + 6.08712i 0.0763997 + 0.523895i
136136 −0.818388 4.64131i −0.0701762 0.397989i
137137 −9.87870 + 5.70347i −0.843995 + 0.487281i −0.858620 0.512613i 0.828678π-0.828678\pi
0.0146254 + 0.999893i 0.495344π0.495344\pi
138138 19.4744 + 11.2435i 1.65777 + 0.957113i
139139 7.95448 + 2.89519i 0.674690 + 0.245567i 0.656566 0.754269i 0.272008π-0.272008\pi
0.0181240 + 0.999836i 0.494231π0.494231\pi
140140 6.90704 2.28388i 0.583752 0.193023i
141141 19.5165 + 16.3763i 1.64359 + 1.37913i
142142 5.83427i 0.489601i
143143 0.498340 0.593898i 0.0416733 0.0496643i
144144 3.79359 1.38075i 0.316132 0.115063i
145145 −2.03476 + 5.11233i −0.168978 + 0.424556i
146146 1.58932 + 9.01347i 0.131533 + 0.745960i
147147 9.50922i 0.784307i
148148 3.94918 + 4.62644i 0.324621 + 0.380291i
149149 6.02167 0.493314 0.246657 0.969103i 0.420668π-0.420668\pi
0.246657 + 0.969103i 0.420668π0.420668\pi
150150 3.07521 12.9023i 0.251090 1.05347i
151151 3.37427 19.1364i 0.274594 1.55730i −0.465654 0.884967i 0.654181π-0.654181\pi
0.740248 0.672334i 0.234708π-0.234708\pi
152152 −0.605406 1.66334i −0.0491049 0.134915i
153153 −12.2298 + 14.5750i −0.988724 + 1.17831i
154154 −0.404755 −0.0326161
155155 −7.42522 9.40298i −0.596408 0.755266i
156156 −8.26552 14.3163i −0.661771 1.14622i
157157 −1.64797 + 4.52776i −0.131522 + 0.361355i −0.987921 0.154961i 0.950475π-0.950475\pi
0.856398 + 0.516316i 0.172697π0.172697\pi
158158 −1.01628 0.586752i −0.0808513 0.0466795i
159159 9.62935 + 16.6785i 0.763657 + 1.32269i
160160 −2.23508 0.0664544i −0.176699 0.00525368i
161161 −25.9156 + 9.43252i −2.04244 + 0.743386i
162162 4.16850 + 2.40668i 0.327508 + 0.189087i
163163 9.49111 + 11.3111i 0.743401 + 0.885951i 0.996678 0.0814431i 0.0259529π-0.0259529\pi
−0.253277 + 0.967394i 0.581508π0.581508\pi
164164 −3.10825 + 2.60813i −0.242713 + 0.203661i
165165 −0.387811 + 0.627846i −0.0301911 + 0.0488777i
166166 0.675533 3.83114i 0.0524315 0.297354i
167167 13.0721 + 2.30496i 1.01155 + 0.178363i 0.654771 0.755828i 0.272765π-0.272765\pi
0.356775 + 0.934190i 0.383876π0.383876\pi
168168 −2.95179 + 8.10998i −0.227736 + 0.625699i
169169 −19.7898 + 16.6056i −1.52229 + 1.27735i
170170 9.27907 4.99563i 0.711672 0.383147i
171171 −3.57297 + 6.18857i −0.273232 + 0.473252i
172172 −0.760923 2.09062i −0.0580198 0.159408i
173173 2.57744 0.454472i 0.195959 0.0345529i −0.0748071 0.997198i 0.523834π-0.523834\pi
0.270766 + 0.962645i 0.412723π0.412723\pi
174174 −3.26386 5.65316i −0.247432 0.428565i
175175 9.69743 + 13.0605i 0.733057 + 0.987281i
176176 0.116907 + 0.0425506i 0.00881217 + 0.00320737i
177177 16.8055 9.70263i 1.26318 0.729295i
178178 9.50225 11.3243i 0.712224 0.848795i
179179 −0.806271 −0.0602635 −0.0301318 0.999546i 0.509593π-0.509593\pi
−0.0301318 + 0.999546i 0.509593π0.509593\pi
180180 5.59445 + 7.08457i 0.416985 + 0.528053i
181181 7.10400 2.58564i 0.528036 0.192189i −0.0642251 0.997935i 0.520458π-0.520458\pi
0.592261 + 0.805746i 0.298235π0.298235\pi
182182 19.9662 + 3.52057i 1.47999 + 0.260962i
183183 0.353516 0.0623344i 0.0261327 0.00460789i
184184 8.47690 0.624926
185185 −7.04971 + 11.6319i −0.518305 + 0.855196i
186186 14.2139 1.04221
187187 −0.577423 + 0.101815i −0.0422253 + 0.00744546i
188188 9.45811 + 1.66772i 0.689804 + 0.121631i
189189 8.41048 3.06116i 0.611772 0.222667i
190190 3.10631 2.45295i 0.225355 0.177955i
191191 27.3426 1.97844 0.989221 0.146428i 0.0467776π-0.0467776\pi
0.989221 + 0.146428i 0.0467776π0.0467776\pi
192192 1.70515 2.03212i 0.123059 0.146656i
193193 11.7272 6.77071i 0.844143 0.487366i −0.0145271 0.999894i 0.504624π-0.504624\pi
0.858670 + 0.512528i 0.171291π0.171291\pi
194194 1.52097 + 0.553589i 0.109199 + 0.0397454i
195195 24.5914 27.5978i 1.76103 1.97632i
196196 −1.79234 3.10442i −0.128024 0.221744i
197197 −25.3327 + 4.46683i −1.80488 + 0.318249i −0.971959 0.235149i 0.924442π-0.924442\pi
−0.832918 + 0.553397i 0.813331π0.813331\pi
198198 −0.171779 0.471958i −0.0122078 0.0335406i
199199 4.88903 8.46804i 0.346574 0.600284i −0.639065 0.769153i 0.720678π-0.720678\pi
0.985638 + 0.168870i 0.0540116π0.0540116\pi
200200 −1.42793 4.79176i −0.100970 0.338829i
201201 −22.0724 + 18.5210i −1.55687 + 1.30637i
202202 −2.60179 + 7.14836i −0.183061 + 0.502957i
203203 7.88417 + 1.39019i 0.553360 + 0.0975723i
204204 −2.17097 + 12.3122i −0.151999 + 0.862026i
205205 −7.71908 4.76797i −0.539124 0.333009i
206206 −0.662087 + 0.555557i −0.0461298 + 0.0387075i
207207 −21.9973 26.2153i −1.52892 1.82209i
208208 −5.39679 3.11584i −0.374200 0.216044i
209209 −0.206935 + 0.0753183i −0.0143140 + 0.00520988i
210210 −19.2898 0.573532i −1.33112 0.0395775i
211211 −1.59289 2.75897i −0.109659 0.189936i 0.805973 0.591952i 0.201643π-0.201643\pi
−0.915632 + 0.402017i 0.868309π0.868309\pi
212212 6.28727 + 3.62996i 0.431812 + 0.249307i
213213 5.29339 14.5435i 0.362697 0.996502i
214214 10.2559 + 17.7638i 0.701082 + 1.21431i
215215 3.90425 3.08306i 0.266268 0.210263i
216216 −2.75103 −0.187184
217217 −11.2053 + 13.3539i −0.760664 + 0.906524i
218218 5.25114 + 14.4274i 0.355652 + 0.977147i
219219 4.21606 23.9104i 0.284895 1.61572i
220220 −0.00826755 + 0.278065i −0.000557398 + 0.0187472i
221221 29.3693 1.97559
222222 −5.64684 15.1157i −0.378991 1.01450i
223223 5.96950i 0.399747i −0.979822 0.199874i 0.935947π-0.935947\pi
0.979822 0.199874i 0.0640531π-0.0640531\pi
224224 0.564949 + 3.20398i 0.0377472 + 0.214075i
225225 −11.1134 + 16.8504i −0.740892 + 1.12336i
226226 6.08675 2.21540i 0.404885 0.147366i
227227 9.03348 10.7657i 0.599573 0.714543i −0.377842 0.925870i 0.623334π-0.623334\pi
0.977416 + 0.211327i 0.0677784π0.0677784\pi
228228 4.69560i 0.310973i
229229 −13.4234 11.2635i −0.887042 0.744316i 0.0805729 0.996749i 0.474325π-0.474325\pi
−0.967615 + 0.252432i 0.918769π0.918769\pi
230230 5.95075 + 17.9966i 0.392381 + 1.18666i
231231 1.00896 + 0.367231i 0.0663846 + 0.0241620i
232232 −2.13106 1.23037i −0.139911 0.0807777i
233233 8.01457 4.62722i 0.525052 0.303139i −0.213947 0.976845i 0.568632π-0.568632\pi
0.738999 + 0.673706i 0.235299π0.235299\pi
234234 4.36857 + 24.7754i 0.285582 + 1.61962i
235235 3.09896 + 21.2505i 0.202154 + 1.38623i
236236 3.65758 6.33512i 0.238088 0.412381i
237237 2.00100 + 2.38470i 0.129979 + 0.154903i
238238 −9.85587 11.7458i −0.638861 0.761365i
239239 2.11096 + 0.768325i 0.136546 + 0.0496988i 0.409389 0.912360i 0.365742π-0.365742\pi
−0.272843 + 0.962059i 0.587964π0.587964\pi
240240 5.51123 + 2.19353i 0.355749 + 0.141591i
241241 −3.16438 + 17.9461i −0.203836 + 1.15601i 0.695425 + 0.718598i 0.255216π0.255216\pi
−0.899261 + 0.437412i 0.855895π0.855895\pi
242242 −3.75693 + 10.3221i −0.241504 + 0.663528i
243243 −13.5125 16.1036i −0.866828 1.03305i
244244 0.103661 0.0869821i 0.00663623 0.00556846i
245245 5.33252 5.98445i 0.340682 0.382332i
246246 10.1145 3.68136i 0.644874 0.234715i
247247 10.8630 1.91545i 0.691199 0.121877i
248248 4.64031 2.67908i 0.294660 0.170122i
249249 −5.15990 + 8.93722i −0.326996 + 0.566373i
250250 9.17060 6.39533i 0.579999 0.404476i
251251 −7.01443 12.1494i −0.442747 0.766860i 0.555145 0.831753i 0.312663π-0.312663\pi
−0.997892 + 0.0648932i 0.979329π0.979329\pi
252252 8.44249 10.0614i 0.531827 0.633807i
253253 1.05461i 0.0663026i
254254 −9.06540 7.60677i −0.568814 0.477291i
255255 −27.6630 + 4.03410i −1.73233 + 0.252625i
256256 0.173648 0.984808i 0.0108530 0.0615505i
257257 21.0952 3.71965i 1.31588 0.232025i 0.528732 0.848789i 0.322668π-0.322668\pi
0.787148 + 0.616764i 0.211557π0.211557\pi
258258 5.90180i 0.367430i
259259 18.6528 + 6.61102i 1.15903 + 0.410789i
260260 2.82645 13.6448i 0.175289 0.846213i
261261 1.72504 + 9.78321i 0.106778 + 0.605566i
262262 −19.6114 3.45802i −1.21160 0.213637i
263263 4.34907 + 11.9490i 0.268175 + 0.736804i 0.998554 + 0.0537622i 0.0171213π0.0171213\pi
−0.730379 + 0.683042i 0.760656π0.760656\pi
264264 −0.252815 0.212137i −0.0155597 0.0130561i
265265 −3.29283 + 15.8962i −0.202277 + 0.976496i
266266 −4.41152 3.70170i −0.270487 0.226966i
267267 −33.9614 + 19.6076i −2.07840 + 1.19997i
268268 −3.71494 + 10.2067i −0.226926 + 0.623475i
269269 5.81907 10.0789i 0.354795 0.614522i −0.632288 0.774733i 0.717884π-0.717884\pi
0.987083 + 0.160211i 0.0512174π0.0512174\pi
270270 −1.93121 5.84049i −0.117530 0.355441i
271271 −2.78689 15.8052i −0.169292 0.960100i −0.944528 0.328430i 0.893481π-0.893481\pi
0.775237 0.631671i 0.217630π-0.217630\pi
272272 1.61191 + 4.42868i 0.0977363 + 0.268528i
273273 −46.5768 26.8911i −2.81895 1.62752i
274274 8.73823 7.33224i 0.527896 0.442957i
275275 −0.596141 + 0.177648i −0.0359487 + 0.0107126i
276276 −21.1309 7.69103i −1.27193 0.462945i
277277 15.0833 + 2.65958i 0.906265 + 0.159799i 0.607307 0.794467i 0.292250π-0.292250\pi
0.298958 + 0.954266i 0.403361π0.403361\pi
278278 −8.33637 1.46993i −0.499983 0.0881604i
279279 −20.3267 7.39831i −1.21693 0.442925i
280280 −6.40552 + 3.44858i −0.382803 + 0.206092i
281281 −12.5602 + 10.5392i −0.749278 + 0.628719i −0.935312 0.353824i 0.884881π-0.884881\pi
0.186034 + 0.982543i 0.440437π0.440437\pi
282282 −22.0637 12.7385i −1.31388 0.758567i
283283 −0.762634 2.09532i −0.0453339 0.124554i 0.914960 0.403545i 0.132222π-0.132222\pi
−0.960294 + 0.278991i 0.910000π0.910000\pi
284284 −1.01311 5.74563i −0.0601170 0.340941i
285285 −9.96883 + 3.29629i −0.590503 + 0.195255i
286286 −0.387640 + 0.671412i −0.0229216 + 0.0397014i
287287 −4.51494 + 12.4047i −0.266508 + 0.732226i
288288 −3.49619 + 2.01853i −0.206015 + 0.118943i
289289 −3.99223 3.34988i −0.234837 0.197052i
290290 1.11610 5.38800i 0.0655396 0.316394i
291291 −3.28916 2.75993i −0.192814 0.161790i
292292 −3.13035 8.60056i −0.183190 0.503309i
293293 −30.5728 5.39081i −1.78608 0.314935i −0.819845 0.572586i 0.805940π-0.805940\pi
−0.966238 + 0.257652i 0.917051π0.917051\pi
294294 1.65126 + 9.36475i 0.0963034 + 0.546163i
295295 16.0172 + 3.31788i 0.932556 + 0.193175i
296296 −4.69256 3.87039i −0.272749 0.224962i
297297 0.342255i 0.0198596i
298298 −5.93018 + 1.04565i −0.343526 + 0.0605730i
299299 −9.17302 + 52.0228i −0.530489 + 3.00855i
300300 −0.788029 + 13.2403i −0.0454969 + 0.764429i
301301 −5.54474 4.65259i −0.319594 0.268171i
302302 19.4316i 1.11817i
303303 12.9713 15.4586i 0.745182 0.888073i
304304 0.885045 + 1.53294i 0.0507608 + 0.0879203i
305305 0.257434 + 0.159014i 0.0147406 + 0.00910509i
306306 9.51312 16.4772i 0.543829 0.941940i
307307 −16.2296 + 9.37014i −0.926270 + 0.534782i −0.885630 0.464392i 0.846273π-0.846273\pi
−0.0406400 + 0.999174i 0.512940π0.512940\pi
308308 0.398606 0.0702850i 0.0227127 0.00400486i
309309 2.15448 0.784166i 0.122564 0.0446096i
310310 8.94522 + 7.97075i 0.508054 + 0.452708i
311311 −25.3178 + 21.2441i −1.43564 + 1.20464i −0.493357 + 0.869827i 0.664230π0.664230\pi
−0.942283 + 0.334818i 0.891325π0.891325\pi
312312 10.6259 + 12.6635i 0.601576 + 0.716930i
313313 7.88099 21.6528i 0.445460 1.22389i −0.490393 0.871501i 0.663147π-0.663147\pi
0.935853 0.352390i 0.114631π-0.114631\pi
314314 0.836697 4.74515i 0.0472176 0.267784i
315315 27.2871 + 10.8605i 1.53745 + 0.611921i
316316 1.10273 + 0.401362i 0.0620336 + 0.0225784i
317317 9.65872 + 11.5108i 0.542488 + 0.646512i 0.965744 0.259498i 0.0835572π-0.0835572\pi
−0.423256 + 0.906010i 0.639113π0.639113\pi
318318 −12.3793 14.7530i −0.694194 0.827309i
319319 −0.153070 + 0.265124i −0.00857026 + 0.0148441i
320320 2.21266 0.322673i 0.123692 0.0180380i
321321 −9.44869 53.5862i −0.527374 2.99089i
322322 23.8840 13.7894i 1.33100 0.768454i
323323 −7.22462 4.17113i −0.401988 0.232088i
324324 −4.52308 1.64627i −0.251282 0.0914593i
325325 30.9523 3.57797i 1.71692 0.198470i
326326 −11.3111 9.49111i −0.626462 0.525664i
327327 40.7284i 2.25229i
328328 2.60813 3.10825i 0.144010 0.171624i
329329 29.3615 10.6867i 1.61875 0.589177i
330330 0.272895 0.685650i 0.0150224 0.0377438i
331331 0.997568 + 5.65749i 0.0548313 + 0.310964i 0.999872 0.0159885i 0.00508951π-0.00508951\pi
−0.945041 + 0.326952i 0.893978π0.893978\pi
332332 3.89024i 0.213505i
333333 0.207610 + 24.5556i 0.0113770 + 1.34564i
334334 −13.2737 −0.726305
335335 −24.2769 0.721812i −1.32639 0.0394368i
336336 1.49866 8.49935i 0.0817588 0.463677i
337337 10.5449 + 28.9719i 0.574417 + 1.57820i 0.797449 + 0.603387i 0.206182π0.206182\pi
−0.223032 + 0.974811i 0.571595π0.571595\pi
338338 16.6056 19.7898i 0.903226 1.07642i
339339 −17.1829 −0.933245
340340 −8.27062 + 6.53103i −0.448537 + 0.354195i
341341 −0.333304 0.577299i −0.0180494 0.0312625i
342342 2.44406 6.71499i 0.132159 0.363105i
343343 9.62281 + 5.55573i 0.519583 + 0.299981i
344344 1.11239 + 1.92672i 0.0599763 + 0.103882i
345345 1.49436 50.2604i 0.0804538 2.70593i
346346 −2.45936 + 0.895135i −0.132216 + 0.0481227i
347347 1.49886 + 0.865365i 0.0804628 + 0.0464552i 0.539692 0.841863i 0.318541π-0.318541\pi
−0.459229 + 0.888318i 0.651874π0.651874\pi
348348 4.19593 + 5.00052i 0.224926 + 0.268056i
349349 1.92593 1.61604i 0.103092 0.0865048i −0.589785 0.807561i 0.700787π-0.700787\pi
0.692877 + 0.721056i 0.256343π0.256343\pi
350350 −11.8180 11.1781i −0.631701 0.597497i
351351 2.97695 16.8831i 0.158898 0.901153i
352352 −0.122519 0.0216035i −0.00653031 0.00115147i
353353 −5.99902 + 16.4822i −0.319296 + 0.877258i 0.671392 + 0.741103i 0.265697π0.265697\pi
−0.990688 + 0.136155i 0.956525π0.956525\pi
354354 −14.8653 + 12.4735i −0.790082 + 0.662957i
355355 11.4869 6.18426i 0.609660 0.328227i
356356 −7.39144 + 12.8023i −0.391745 + 0.678523i
357357 13.9115 + 38.2216i 0.736276 + 2.02290i
358358 0.794022 0.140007i 0.0419654 0.00739962i
359359 −2.81046 4.86786i −0.148330 0.256916i 0.782280 0.622927i 0.214057π-0.214057\pi
−0.930611 + 0.366011i 0.880723π0.880723\pi
360360 −6.73968 6.00547i −0.355212 0.316516i
361361 14.9099 + 5.42676i 0.784731 + 0.285619i
362362 −6.54708 + 3.77996i −0.344107 + 0.198670i
363363 18.7303 22.3219i 0.983084 1.17159i
364364 −20.2742 −1.06266
365365 16.0616 12.6833i 0.840705 0.663876i
366366 −0.337321 + 0.122775i −0.0176321 + 0.00641755i
367367 26.7060 + 4.70899i 1.39404 + 0.245807i 0.819693 0.572804i 0.194144π-0.194144\pi
0.574349 + 0.818611i 0.305255π0.305255\pi
368368 −8.34812 + 1.47200i −0.435176 + 0.0767332i
369369 −16.3805 −0.852732
370370 4.92275 12.6794i 0.255922 0.659169i
371371 23.6195 1.22626
372372 −13.9979 + 2.46821i −0.725758 + 0.127971i
373373 −29.1022 5.13150i −1.50685 0.265699i −0.641602 0.767037i 0.721730π-0.721730\pi
−0.865251 + 0.501338i 0.832841π0.832841\pi
374374 0.550970 0.200537i 0.0284900 0.0103695i
375375 −28.6626 + 7.62163i −1.48013 + 0.393579i
376376 −9.60402 −0.495289
377377 9.85684 11.7469i 0.507653 0.604997i
378378 −7.75114 + 4.47512i −0.398675 + 0.230175i
379379 22.0060 + 8.00953i 1.13037 + 0.411422i 0.838427 0.545013i 0.183475π-0.183475\pi
0.291945 + 0.956435i 0.405698π0.405698\pi
380380 −2.63317 + 2.95509i −0.135079 + 0.151593i
381381 15.6963 + 27.1868i 0.804147 + 1.39282i
382382 −26.9272 + 4.74800i −1.37772 + 0.242929i
383383 −0.0827565 0.227371i −0.00422866 0.0116181i 0.937560 0.347823i 0.113079π-0.113079\pi
−0.941789 + 0.336205i 0.890857π0.890857\pi
384384 −1.32637 + 2.29734i −0.0676861 + 0.117236i
385385 0.429036 + 0.796907i 0.0218657 + 0.0406142i
386386 −10.3733 + 8.70426i −0.527989 + 0.443035i
387387 3.07188 8.43993i 0.156153 0.429026i
388388 −1.59400 0.281064i −0.0809229 0.0142689i
389389 −0.294635 + 1.67096i −0.0149386 + 0.0847208i −0.991366 0.131127i 0.958140π-0.958140\pi
0.976427 + 0.215848i 0.0692515π0.0692515\pi
390390 −19.4255 + 31.4488i −0.983647 + 1.59247i
391391 30.6041 25.6799i 1.54772 1.29869i
392392 2.30418 + 2.74602i 0.116379 + 0.138695i
393393 45.7491 + 26.4133i 2.30774 + 1.33237i
394394 24.1721 8.79794i 1.21777 0.443234i
395395 −0.0779845 + 2.62288i −0.00392383 + 0.131971i
396396 0.251124 + 0.434959i 0.0126194 + 0.0218575i
397397 7.64307 + 4.41273i 0.383595 + 0.221468i 0.679381 0.733786i 0.262248π-0.262248\pi
−0.295787 + 0.955254i 0.595582π0.595582\pi
398398 −3.34429 + 9.18836i −0.167634 + 0.460571i
399399 7.63835 + 13.2300i 0.382396 + 0.662329i
400400 2.23832 + 4.47101i 0.111916 + 0.223550i
401401 −17.8573 −0.891751 −0.445875 0.895095i 0.647108π-0.647108\pi
−0.445875 + 0.895095i 0.647108π0.647108\pi
402402 18.5210 22.0724i 0.923742 1.10087i
403403 11.4202 + 31.3767i 0.568879 + 1.56298i
404404 1.32096 7.49156i 0.0657204 0.372719i
405405 0.319869 10.7583i 0.0158944 0.534582i
406406 −8.00579 −0.397321
407407 −0.481513 + 0.583799i −0.0238677 + 0.0289378i
408408 12.5021i 0.618948i
409409 −0.621905 3.52700i −0.0307512 0.174399i 0.965564 0.260166i 0.0837772π-0.0837772\pi
−0.996315 + 0.0857667i 0.972666π0.972666\pi
410410 8.42976 + 3.35513i 0.416316 + 0.165698i
411411 −28.4348 + 10.3494i −1.40259 + 0.510500i
412412 0.555557 0.662087i 0.0273703 0.0326187i
413413 23.7992i 1.17108i
414414 26.2153 + 21.9973i 1.28841 + 1.08111i
415415 −8.25904 + 2.73093i −0.405421 + 0.134056i
416416 5.85586 + 2.13136i 0.287107 + 0.104498i
417417 19.4470 + 11.2277i 0.952322 + 0.549823i
418418 0.190713 0.110108i 0.00932806 0.00538556i
419419 0.292638 + 1.65963i 0.0142963 + 0.0810784i 0.991121 0.132962i 0.0424488π-0.0424488\pi
−0.976825 + 0.214040i 0.931338π0.931338\pi
420420 19.0963 2.78482i 0.931805 0.135885i
421421 −5.62872 + 9.74922i −0.274327 + 0.475148i −0.969965 0.243244i 0.921788π-0.921788\pi
0.695638 + 0.718392i 0.255122π0.255122\pi
422422 2.04778 + 2.44046i 0.0996846 + 0.118799i
423423 24.9221 + 29.7010i 1.21175 + 1.44411i
424424 −6.82209 2.48304i −0.331310 0.120587i
425425 −19.6714 12.9739i −0.954204 0.629327i
426426 −2.68752 + 15.2417i −0.130211 + 0.738463i
427427 0.150575 0.413701i 0.00728684 0.0200204i
428428 −13.1848 15.7130i −0.637311 0.759518i
429429 1.57546 1.32197i 0.0760640 0.0638252i
430430 −3.30957 + 3.71418i −0.159602 + 0.179114i
431431 −2.78306 + 1.01295i −0.134055 + 0.0487921i −0.408177 0.912903i 0.633835π-0.633835\pi
0.274121 + 0.961695i 0.411613π0.411613\pi
432432 2.70924 0.477712i 0.130348 0.0229839i
433433 −16.0594 + 9.27188i −0.771764 + 0.445578i −0.833503 0.552514i 0.813668π-0.813668\pi
0.0617397 + 0.998092i 0.480335π0.480335\pi
434434 8.71616 15.0968i 0.418389 0.724671i
435435 −7.67066 + 12.4184i −0.367780 + 0.595416i
436436 −7.67666 13.2964i −0.367645 0.636780i
437437 9.64495 11.4944i 0.461381 0.549852i
438438 24.2793i 1.16011i
439439 8.69993 + 7.30011i 0.415225 + 0.348415i 0.826343 0.563167i 0.190417π-0.190417\pi
−0.411118 + 0.911582i 0.634862π0.634862\pi
440440 −0.0401436 0.275276i −0.00191377 0.0131233i
441441 2.51295 14.2517i 0.119664 0.678650i
442442 −28.9231 + 5.09992i −1.37573 + 0.242579i
443443 8.42323i 0.400200i −0.979775 0.200100i 0.935873π-0.935873\pi
0.979775 0.200100i 0.0641267π-0.0641267\pi
444444 8.18586 + 13.9055i 0.388484 + 0.659925i
445445 −32.3684 6.70496i −1.53441 0.317845i
446446 1.03659 + 5.87881i 0.0490841 + 0.278370i
447447 15.7313 + 2.77385i 0.744063 + 0.131198i
448448 −1.11273 3.05720i −0.0525716 0.144439i
449449 −5.64012 4.73262i −0.266174 0.223346i 0.499926 0.866068i 0.333361π-0.333361\pi
−0.766100 + 0.642722i 0.777805π0.777805\pi
450450 8.01850 18.5243i 0.377996 0.873242i
451451 −0.386695 0.324476i −0.0182088 0.0152790i
452452 −5.60958 + 3.23869i −0.263853 + 0.152335i
453453 17.6302 48.4385i 0.828338 2.27584i
454454 −7.02680 + 12.1708i −0.329784 + 0.571203i
455455 −14.2324 43.0424i −0.667225 2.01786i
456456 −0.815382 4.62426i −0.0381837 0.216551i
457457 −2.39975 6.59326i −0.112256 0.308420i 0.870825 0.491593i 0.163585π-0.163585\pi
−0.983081 + 0.183173i 0.941363π0.941363\pi
458458 15.1753 + 8.76149i 0.709097 + 0.409397i
459459 −9.93205 + 8.33398i −0.463588 + 0.388997i
460460 −8.98542 16.6899i −0.418948 0.778169i
461461 −8.35772 3.04196i −0.389258 0.141678i 0.139975 0.990155i 0.455298π-0.455298\pi
−0.529232 + 0.848477i 0.677520π0.677520\pi
462462 −1.05740 0.186448i −0.0491947 0.00867435i
463463 29.0606 + 5.12417i 1.35056 + 0.238140i 0.801677 0.597758i 0.203941π-0.203941\pi
0.548885 + 0.835898i 0.315053π0.315053\pi
464464 2.31234 + 0.841622i 0.107348 + 0.0390713i
465465 −15.0665 27.9851i −0.698694 1.29778i
466466 −7.08931 + 5.94863i −0.328406 + 0.275565i
467467 −25.2848 14.5982i −1.17004 0.675522i −0.216350 0.976316i 0.569415π-0.569415\pi
−0.953689 + 0.300793i 0.902749π0.902749\pi
468468 −8.60440 23.6404i −0.397739 1.09278i
469469 6.13634 + 34.8009i 0.283350 + 1.60696i
470470 −6.74198 20.3895i −0.310984 0.940497i
471471 −6.39092 + 11.0694i −0.294478 + 0.510051i
472472 −2.50193 + 6.87401i −0.115161 + 0.316402i
473473 0.239703 0.138392i 0.0110215 0.00636329i
474474 −2.38470 2.00100i −0.109533 0.0919091i
475475 −8.12217 3.51580i −0.372671 0.161316i
476476 11.7458 + 9.85587i 0.538366 + 0.451743i
477477 10.0242 + 27.5411i 0.458975 + 1.26102i
478478 −2.21230 0.390089i −0.101188 0.0178422i
479479 0.783733 + 4.44477i 0.0358097 + 0.203087i 0.997464 0.0711792i 0.0226762π-0.0226762\pi
−0.961654 + 0.274266i 0.911565π0.911565\pi
480480 −5.80841 1.20319i −0.265116 0.0549176i
481481 28.8305 24.6100i 1.31456 1.12212i
482482 18.2230i 0.830033i
483483 −72.0481 + 12.7040i −3.27830 + 0.578053i
484484 1.90744 10.8176i 0.0867019 0.491711i
485485 −0.522274 3.58139i −0.0237152 0.162622i
486486 16.1036 + 13.5125i 0.730473 + 0.612940i
487487 21.9873i 0.996338i −0.867080 0.498169i 0.834006π-0.834006\pi
0.867080 0.498169i 0.165994π-0.165994\pi
488488 −0.0869821 + 0.103661i −0.00393750 + 0.00469252i
489489 19.5846 + 33.9215i 0.885646 + 1.53398i
490490 −4.21232 + 6.81951i −0.190293 + 0.308074i
491491 −11.5059 + 19.9287i −0.519252 + 0.899371i 0.480498 + 0.876996i 0.340456π0.340456\pi
−0.999750 + 0.0223747i 0.992877π0.992877\pi
492492 −9.32154 + 5.38179i −0.420247 + 0.242630i
493493 −11.4210 + 2.01384i −0.514378 + 0.0906987i
494494 −10.3654 + 3.77269i −0.466361 + 0.169742i
495495 −0.747138 + 0.838480i −0.0335814 + 0.0376869i
496496 −4.10460 + 3.44417i −0.184302 + 0.154648i
497497 −12.2009 14.5405i −0.547286 0.652230i
498498 3.52958 9.69745i 0.158164 0.434553i
499499 −2.48624 + 14.1002i −0.111299 + 0.631211i 0.877217 + 0.480095i 0.159398π0.159398\pi
−0.988516 + 0.151116i 0.951713π0.951713\pi
500500 −7.92074 + 7.89062i −0.354226 + 0.352879i
501501 33.0882 + 12.0431i 1.47827 + 0.538047i
502502 9.01758 + 10.7467i 0.402474 + 0.479650i
503503 −13.6272 16.2402i −0.607606 0.724116i 0.371281 0.928521i 0.378919π-0.378919\pi
−0.978887 + 0.204404i 0.934474π0.934474\pi
504504 −6.56709 + 11.3745i −0.292522 + 0.506662i
505505 16.8320 2.45461i 0.749015 0.109229i
506506 0.183131 + 1.03859i 0.00814115 + 0.0461708i
507507 −59.3490 + 34.2652i −2.63578 + 1.52177i
508508 10.2486 + 5.91702i 0.454707 + 0.262525i
509509 −33.4117 12.1609i −1.48095 0.539020i −0.529898 0.848062i 0.677770π-0.677770\pi
−0.951049 + 0.309041i 0.899992π0.899992\pi
510510 26.5422 8.77645i 1.17531 0.388628i
511511 −22.8104 19.1402i −1.00907 0.846713i
512512 1.00000i 0.0441942i
513513 −3.13010 + 3.73031i −0.138197 + 0.164697i
514514 −20.1288 + 7.32627i −0.887842 + 0.323148i
515515 1.79562 + 0.714674i 0.0791245 + 0.0314923i
516516 −1.02484 5.81213i −0.0451159 0.255865i
517517 1.19483i 0.0525486i
518518 −19.5174 3.27156i −0.857546 0.143744i
519519 6.94276 0.304753
520520 −0.414122 + 13.9283i −0.0181604 + 0.610796i
521521 −0.796753 + 4.51861i −0.0349064 + 0.197964i −0.997274 0.0737869i 0.976492π-0.976492\pi
0.962368 + 0.271751i 0.0876026π0.0876026\pi
522522 −3.39767 9.33503i −0.148712 0.408583i
523523 −0.554308 + 0.660599i −0.0242382 + 0.0288860i −0.778027 0.628230i 0.783780π-0.783780\pi
0.753789 + 0.657116i 0.228224π0.228224\pi
524524 19.9139 0.869944
525525 19.3177 + 38.5869i 0.843096 + 1.68407i
526526 −6.35791 11.0122i −0.277218 0.480156i
527527 8.63688 23.7296i 0.376228 1.03368i
528528 0.285811 + 0.165013i 0.0124383 + 0.00718128i
529529 24.4289 + 42.3122i 1.06213 + 1.83966i
530530 0.482453 16.2265i 0.0209564 0.704834i
531531 27.7507 10.1004i 1.20428 0.438322i
532532 4.98729 + 2.87941i 0.216226 + 0.124838i
533533 16.2530 + 19.3696i 0.703996 + 0.838989i
534534 30.0406 25.2070i 1.29998 1.09082i
535535 24.1033 39.0220i 1.04208 1.68707i
536536 1.88613 10.6968i 0.0814683 0.462030i
537537 −2.10634 0.371404i −0.0908951 0.0160273i
538538 −3.98048 + 10.9363i −0.171610 + 0.471496i
539539 0.341631 0.286662i 0.0147151 0.0123474i
540540 2.91607 + 5.41641i 0.125488 + 0.233085i
541541 6.93311 12.0085i 0.298078 0.516286i −0.677618 0.735414i 0.736988π-0.736988\pi
0.975696 + 0.219128i 0.0703212π0.0703212\pi
542542 5.48910 + 15.0812i 0.235777 + 0.647792i
543543 19.7499 3.48243i 0.847547 0.149445i
544544 −2.35645 4.08150i −0.101032 0.174993i
545545 22.8394 25.6317i 0.978333 1.09794i
546546 50.5388 + 18.3946i 2.16286 + 0.787216i
547547 −25.1975 + 14.5478i −1.07737 + 0.622018i −0.930185 0.367092i 0.880354π-0.880354\pi
−0.147182 + 0.989109i 0.547020π0.547020\pi
548548 −7.33224 + 8.73823i −0.313218 + 0.373279i
549549 0.546295 0.0233153
550550 0.556236 0.278468i 0.0237180 0.0118739i
551551 −4.09305 + 1.48975i −0.174370 + 0.0634654i
552552 22.1454 + 3.90484i 0.942572 + 0.166201i
553553 3.75989 0.662970i 0.159887 0.0281923i
554554 −15.3159 −0.650712
555555 −23.7751 + 27.1403i −1.00920 + 1.15204i
556556 8.46498 0.358995
557557 −2.68552 + 0.473530i −0.113789 + 0.0200641i −0.230253 0.973131i 0.573955π-0.573955\pi
0.116464 + 0.993195i 0.462844π0.462844\pi
558558 21.3026 + 3.75622i 0.901810 + 0.159013i
559559 −13.0280 + 4.74182i −0.551028 + 0.200558i
560560 5.70937 4.50849i 0.241265 0.190519i
561561 −1.55538 −0.0656684
562562 10.5392 12.5602i 0.444571 0.529820i
563563 −1.29221 + 0.746060i −0.0544603 + 0.0314427i −0.526983 0.849876i 0.676677π-0.676677\pi
0.472523 + 0.881319i 0.343343π0.343343\pi
564564 23.9406 + 8.71365i 1.00808 + 0.366911i
565565 −10.8137 9.63569i −0.454936 0.405377i
566566 1.11490 + 1.93106i 0.0468626 + 0.0811684i
567567 −15.4219 + 2.71930i −0.647661 + 0.114200i
568568 1.99544 + 5.48242i 0.0837267 + 0.230037i
569569 0.464658 0.804812i 0.0194795 0.0337395i −0.856121 0.516775i 0.827132π-0.827132\pi
0.875601 + 0.483035i 0.160466π0.160466\pi
570570 9.24499 4.97728i 0.387230 0.208475i
571571 −10.4105 + 8.73548i −0.435667 + 0.365568i −0.834085 0.551636i 0.814004π-0.814004\pi
0.398418 + 0.917204i 0.369559π0.369559\pi
572572 0.265161 0.728524i 0.0110869 0.0304611i
573573 71.4310 + 12.5952i 2.98407 + 0.526173i
574574 2.29229 13.0002i 0.0956785 0.542620i
575575 29.1251 30.7924i 1.21460 1.28413i
576576 3.09256 2.59497i 0.128857 0.108124i
577577 7.04419 + 8.39494i 0.293254 + 0.349486i 0.892475 0.451098i 0.148967π-0.148967\pi
−0.599221 + 0.800584i 0.704523π0.704523\pi
578578 4.51328 + 2.60574i 0.187728 + 0.108385i
579579 33.7556 12.2860i 1.40283 0.510590i
580580 −0.163527 + 5.49995i −0.00679008 + 0.228373i
581581 6.32827 + 10.9609i 0.262541 + 0.454734i
582582 3.71845 + 2.14685i 0.154135 + 0.0889896i
583583 −0.308914 + 0.848733i −0.0127939 + 0.0351509i
584584 4.57626 + 7.92632i 0.189367 + 0.327993i
585585 44.1487 34.8628i 1.82533 1.44140i
586586 31.0444 1.28243
587587 −12.1206 + 14.4448i −0.500271 + 0.596200i −0.955799 0.294022i 0.905006π-0.905006\pi
0.455528 + 0.890222i 0.349451π0.349451\pi
588588 −3.25234 8.93574i −0.134124 0.368504i
589589 1.64696 9.34035i 0.0678616 0.384862i
590590 −16.3500 0.486125i −0.673118 0.0200134i
591591 −68.2377 −2.80693
592592 5.29335 + 2.99674i 0.217555 + 0.123165i
593593 22.9711i 0.943311i 0.881783 + 0.471655i 0.156343π0.156343\pi
−0.881783 + 0.471655i 0.843657π0.843657\pi
594594 −0.0594319 0.337055i −0.00243852 0.0138295i
595595 −12.6787 + 31.8552i −0.519776 + 1.30594i
596596 5.65852 2.05953i 0.231782 0.0843617i
597597 16.6731 19.8702i 0.682383 0.813232i
598598 52.8253i 2.16019i
599599 13.2057 + 11.0809i 0.539570 + 0.452753i 0.871391 0.490589i 0.163219π-0.163219\pi
−0.331821 + 0.943342i 0.607663π0.607663\pi
600600 −1.52310 13.1760i −0.0621801 0.537907i
601601 −17.2811 6.28980i −0.704910 0.256566i −0.0354044 0.999373i 0.511272π-0.511272\pi
−0.669506 + 0.742807i 0.733494π0.733494\pi
602602 6.26842 + 3.61907i 0.255482 + 0.147502i
603603 −37.9748 + 21.9248i −1.54645 + 0.892846i
604604 −3.37427 19.1364i −0.137297 0.778650i
605605 24.3051 3.54441i 0.988141 0.144101i
606606 −10.0899 + 17.4762i −0.409873 + 0.709922i
607607 20.1792 + 24.0486i 0.819049 + 0.976104i 0.999973 0.00739272i 0.00235320π-0.00235320\pi
−0.180924 + 0.983497i 0.557909π0.557909\pi
608608 −1.13779 1.35597i −0.0461436 0.0549917i
609609 19.9566 + 7.26359i 0.808680 + 0.294336i
610610 −0.281136 0.111895i −0.0113829 0.00453049i
611611 10.3927 58.9399i 0.420443 2.38445i
612612 −6.50736 + 17.8788i −0.263044 + 0.722709i
613613 −3.34601 3.98762i −0.135144 0.161058i 0.694228 0.719755i 0.255746π-0.255746\pi
−0.829372 + 0.558697i 0.811302π0.811302\pi
614614 14.3559 12.0460i 0.579357 0.486138i
615615 −17.9693 16.0118i −0.724593 0.645658i
616616 −0.380345 + 0.138434i −0.0153245 + 0.00557768i
617617 −10.8427 + 1.91187i −0.436513 + 0.0769689i −0.387586 0.921833i 0.626691π-0.626691\pi
−0.0489263 + 0.998802i 0.515580π0.515580\pi
618618 −1.98558 + 1.14637i −0.0798717 + 0.0461139i
619619 −12.3360 + 21.3667i −0.495828 + 0.858799i −0.999988 0.00481106i 0.998469π-0.998469\pi
0.504161 + 0.863610i 0.331802π0.331802\pi
620620 −10.1934 6.29634i −0.409378 0.252867i
621621 −11.6601 20.1959i −0.467905 0.810435i
622622 21.2441 25.3178i 0.851813 1.01515i
623623 48.0948i 1.92688i
624624 −12.6635 10.6259i −0.506946 0.425378i
625625 −22.3123 11.2767i −0.892490 0.451067i
626626 −4.00128 + 22.6924i −0.159924 + 0.906971i
627627 −0.575302 + 0.101441i −0.0229753 + 0.00405117i
628628 4.81835i 0.192273i
629629 −28.6665 + 0.242366i −1.14301 + 0.00966378i
630630 −28.7584 5.95717i −1.14576 0.237339i
631631 −2.77327 15.7280i −0.110402 0.626122i −0.988924 0.148420i 0.952581π-0.952581\pi
0.878522 0.477702i 0.158530π-0.158530\pi
632632 −1.15568 0.203777i −0.0459703 0.00810581i
633633 −2.89044 7.94142i −0.114885 0.315643i
634634 −11.5108 9.65872i −0.457153 0.383597i
635635 −5.36747 + 25.9116i −0.213002 + 1.02827i
636636 14.7530 + 12.3793i 0.584996 + 0.490870i
637637 −19.3457 + 11.1693i −0.766505 + 0.442542i
638638 0.104706 0.287677i 0.00414534 0.0113892i
639639 11.7766 20.3977i 0.465876 0.806921i
640640 −2.12302 + 0.701996i −0.0839196 + 0.0277488i
641641 1.88975 + 10.7173i 0.0746405 + 0.423307i 0.999115 + 0.0420632i 0.0133931π0.0133931\pi
−0.924474 + 0.381244i 0.875496π0.875496\pi
642642 18.6103 + 51.1313i 0.734489 + 2.01799i
643643 −17.8979 10.3334i −0.705825 0.407508i 0.103689 0.994610i 0.466935π-0.466935\pi
−0.809513 + 0.587102i 0.800269π0.800269\pi
644644 −21.1266 + 17.7273i −0.832505 + 0.698555i
645645 11.6198 6.25584i 0.457530 0.246323i
646646 7.83917 + 2.85322i 0.308428 + 0.112259i
647647 −26.6214 4.69407i −1.04660 0.184543i −0.376194 0.926541i 0.622767π-0.622767\pi
−0.670402 + 0.741998i 0.733878π0.733878\pi
648648 4.74024 + 0.835832i 0.186214 + 0.0328346i
649649 0.855192 + 0.311264i 0.0335692 + 0.0122182i
650650 −29.8607 + 8.89841i −1.17123 + 0.349024i
651651 −35.4246 + 29.7247i −1.38840 + 1.16500i
652652 12.7873 + 7.38277i 0.500791 + 0.289132i
653653 1.25703 + 3.45366i 0.0491914 + 0.135152i 0.961855 0.273559i 0.0882007π-0.0882007\pi
−0.912664 + 0.408711i 0.865979π0.865979\pi
654654 7.07242 + 40.1097i 0.276553 + 1.56841i
655655 13.9795 + 42.2776i 0.546224 + 1.65192i
656656 −2.02876 + 3.51392i −0.0792099 + 0.137196i
657657 12.6374 34.7209i 0.493031 1.35459i
658658 −27.0597 + 15.6229i −1.05490 + 0.609044i
659659 −17.3527 14.5606i −0.675965 0.567202i 0.238859 0.971054i 0.423227π-0.423227\pi
−0.914824 + 0.403852i 0.867671π0.867671\pi
660660 −0.149688 + 0.722621i −0.00582658 + 0.0281280i
661661 −24.4097 20.4821i −0.949426 0.796663i 0.0297746 0.999557i 0.490521π-0.490521\pi
−0.979201 + 0.202893i 0.934965π0.934965\pi
662662 −1.96483 5.39831i −0.0763651 0.209811i
663663 76.7256 + 13.5288i 2.97978 + 0.525415i
664664 −0.675533 3.83114i −0.0262158 0.148677i
665665 −2.61199 + 12.6094i −0.101289 + 0.488973i
666666 −4.46848 24.1464i −0.173150 0.935656i
667667 20.8594i 0.807681i
668668 13.0721 2.30496i 0.505773 0.0891814i
669669 2.74981 15.5950i 0.106314 0.602936i
670670 24.0335 3.50480i 0.928493 0.135402i
671671 0.0128964 + 0.0108214i 0.000497862 + 0.000417756i
672672 8.63046i 0.332927i
673673 6.08410 7.25075i 0.234525 0.279496i −0.635927 0.771749i 0.719382π-0.719382\pi
0.870452 + 0.492253i 0.163827π0.163827\pi
674674 −15.4156 26.7006i −0.593787 1.02847i
675675 −9.45207 + 9.99316i −0.363810 + 0.384637i
676676 −12.9169 + 22.3727i −0.496803 + 0.860488i
677677 30.5077 17.6136i 1.17250 0.676946i 0.218236 0.975896i 0.429970π-0.429970\pi
0.954269 + 0.298950i 0.0966364π0.0966364\pi
678678 16.9218 2.98377i 0.649878 0.114591i
679679 −4.94835 + 1.80105i −0.189900 + 0.0691180i
680680 7.01087 7.86798i 0.268854 0.301723i
681681 28.5586 23.9635i 1.09437 0.918284i
682682 0.428487 + 0.510651i 0.0164076 + 0.0195538i
683683 3.38068 9.28834i 0.129358 0.355408i −0.858058 0.513553i 0.828329π-0.828329\pi
0.987416 + 0.158145i 0.0505512π0.0505512\pi
684684 −1.24088 + 7.03738i −0.0474462 + 0.269081i
685685 −23.6986 9.43228i −0.905477 0.360389i
686686 −10.4414 3.80034i −0.398653 0.145098i
687687 −29.8793 35.6088i −1.13997 1.35856i
688688 −1.43007 1.70429i −0.0545208 0.0649753i
689689 22.6207 39.1802i 0.861781 1.49265i
690690 7.25596 + 49.7563i 0.276230 + 1.89419i
691691 1.40211 + 7.95176i 0.0533388 + 0.302499i 0.999793 0.0203384i 0.00647437π-0.00647437\pi
−0.946454 + 0.322838i 0.895363π0.895363\pi
692692 2.26656 1.30860i 0.0861617 0.0497455i
693693 1.41510 + 0.817009i 0.0537552 + 0.0310356i
694694 −1.62635 0.591944i −0.0617355 0.0224699i
695695 5.94238 + 17.9713i 0.225407 + 0.681690i
696696 −5.00052 4.19593i −0.189544 0.159046i
697697 19.1227i 0.724326i
698698 −1.61604 + 1.92593i −0.0611682 + 0.0728974i
699699 23.0691 8.39647i 0.872554 0.317584i
700700 13.5796 + 8.95614i 0.513259 + 0.338510i
701701 6.64346 + 37.6769i 0.250920 + 1.42304i 0.806332 + 0.591463i 0.201449π0.201449\pi
−0.555412 + 0.831575i 0.687440π0.687440\pi
702702 17.1435i 0.647042i
703703 −10.5873 + 1.95926i −0.399307 + 0.0738947i
704704 0.124409 0.00468886
705705 −1.69306 + 56.9432i −0.0637643 + 2.14460i
706706 3.04578 17.2735i 0.114630 0.650097i
707707 −8.46469 23.2565i −0.318347 0.874652i
708708 12.4735 14.8653i 0.468782 0.558672i
709709 −7.80154 −0.292993 −0.146497 0.989211i 0.546800π-0.546800\pi
−0.146497 + 0.989211i 0.546800π0.546800\pi
710710 −10.2385 + 8.08499i −0.384243 + 0.303424i
711711 2.36875 + 4.10279i 0.0888351 + 0.153867i
712712 5.05604 13.8914i 0.189483 0.520601i
713713 39.3355 + 22.7103i 1.47312 + 0.850509i
714714 −20.3373 35.2252i −0.761104 1.31827i
715715 1.73281 + 0.0515207i 0.0648035 + 0.00192676i
716716 −0.757647 + 0.275761i −0.0283146 + 0.0103057i
717717 5.16083 + 2.97960i 0.192735 + 0.111275i
718718 3.61306 + 4.30587i 0.134838 + 0.160694i
719719 9.50555 7.97610i 0.354497 0.297458i −0.448096 0.893986i 0.647898π-0.647898\pi
0.802593 + 0.596527i 0.203453π0.203453\pi
720720 7.68013 + 4.74391i 0.286221 + 0.176795i
721721 0.488281 2.76918i 0.0181845 0.103130i
722722 −15.6257 2.75524i −0.581529 0.102539i
723723 −16.5335 + 45.4255i −0.614889 + 1.68939i
724724 5.79123 4.85942i 0.215229 0.180599i
725725 −11.7913 + 3.51377i −0.437917 + 0.130498i
726726 −14.5696 + 25.2352i −0.540727 + 0.936567i
727727 5.43556 + 14.9341i 0.201594 + 0.553874i 0.998755 0.0498929i 0.0158880π-0.0158880\pi
−0.797161 + 0.603767i 0.793666π0.793666\pi
728728 19.9662 3.52057i 0.739996 0.130481i
729729 −20.6626 35.7887i −0.765281 1.32551i
730730 −13.6152 + 15.2797i −0.503921 + 0.565528i
731731 9.85288 + 3.58616i 0.364422 + 0.132639i
732732 0.310877 0.179485i 0.0114903 0.00663395i
733733 −33.4889 + 39.9105i −1.23694 + 1.47413i −0.409755 + 0.912196i 0.634386π0.634386\pi
−0.827184 + 0.561931i 0.810059π0.810059\pi
734734 −27.1180 −1.00094
735735 16.6876 13.1776i 0.615532 0.486064i
736736 7.96568 2.89927i 0.293619 0.106869i
737737 −1.33078 0.234652i −0.0490198 0.00864352i
738738 16.1316 2.84444i 0.593812 0.104705i
739739 16.1448 0.593895 0.296947 0.954894i 0.404031π-0.404031\pi
0.296947 + 0.954894i 0.404031π0.404031\pi
740740 −2.64621 + 13.3416i −0.0972767 + 0.490446i
741741 29.2614 1.07495
742742 −23.2607 + 4.10148i −0.853926 + 0.150570i
743743 −31.3707 5.53150i −1.15088 0.202931i −0.434520 0.900662i 0.643082π-0.643082\pi
−0.716360 + 0.697731i 0.754193π0.754193\pi
744744 13.3567 4.86142i 0.489679 0.178228i
745745 8.34468 + 10.5673i 0.305725 + 0.387158i
746746 29.5511 1.08194
747747 −10.0950 + 12.0308i −0.369358 + 0.440184i
748748 −0.507777 + 0.293165i −0.0185662 + 0.0107192i
749749 −62.7091 22.8242i −2.29134 0.833979i
750750 26.9036 12.4830i 0.982382 0.455816i
751751 3.87246 + 6.70730i 0.141308 + 0.244753i 0.927990 0.372606i 0.121536π-0.121536\pi
−0.786681 + 0.617359i 0.788202π0.788202\pi
752752 9.45811 1.66772i 0.344902 0.0608155i
753753 −12.7283 34.9706i −0.463844 1.27440i
754754 −7.66726 + 13.2801i −0.279225 + 0.483632i
755755 38.2583 20.5973i 1.39236 0.749613i
756756 6.85628 5.75310i 0.249361 0.209238i
757757 14.6997 40.3870i 0.534269 1.46789i −0.319675 0.947527i 0.603574π-0.603574\pi
0.853944 0.520365i 0.174204π-0.174204\pi
758758 −23.0625 4.06654i −0.837668 0.147704i
759759 0.485799 2.75510i 0.0176334 0.100004i
760760 2.08002 3.36744i 0.0754502 0.122150i
761761 −2.77362 + 2.32734i −0.100544 + 0.0843660i −0.691674 0.722210i 0.743126π-0.743126\pi
0.591130 + 0.806576i 0.298682π0.298682\pi
762762 −20.1788 24.0482i −0.731001 0.871174i
763763 −43.2585 24.9753i −1.56606 0.904167i
764764 25.6937 9.35173i 0.929564 0.338334i
765765 −42.5252 1.26438i −1.53750 0.0457137i
766766 0.120982 + 0.209547i 0.00437125 + 0.00757123i
767767 −39.4784 22.7929i −1.42548 0.823003i
768768 0.907292 2.49276i 0.0327391 0.0899499i
769769 20.1460 + 34.8940i 0.726485 + 1.25831i 0.958360 + 0.285563i 0.0921806π0.0921806\pi
−0.231875 + 0.972746i 0.574486π0.574486\pi
770770 −0.560899 0.710299i −0.0202134 0.0255974i
771771 56.8233 2.04644
772772 8.70426 10.3733i 0.313273 0.373344i
773773 14.2847 + 39.2469i 0.513784 + 1.41161i 0.877264 + 0.480009i 0.159367π0.159367\pi
−0.363479 + 0.931602i 0.618411π0.618411\pi
774774 −1.55964 + 8.84514i −0.0560600 + 0.317932i
775775 6.21149 26.0608i 0.223123 0.936133i
776776 1.61859 0.0581038
777777 45.6841 + 25.8632i 1.63891 + 0.927838i
778778 1.69673i 0.0608308i
779779 −1.24717 7.07307i −0.0446846 0.253419i
780780 13.6693 34.3442i 0.489441 1.22972i
781781 0.682065 0.248251i 0.0244062 0.00888314i
782782 −25.6799 + 30.6041i −0.918312 + 1.09440i
783783 6.76958i 0.241925i
784784 −2.74602 2.30418i −0.0980721 0.0822922i
785785 −10.2294 + 3.38246i −0.365104 + 0.120725i
786786 −49.6407 18.0677i −1.77063 0.644455i
787787 5.89312 + 3.40240i 0.210067 + 0.121282i 0.601343 0.798991i 0.294633π-0.294633\pi
−0.391275 + 0.920274i 0.627966π0.627966\pi
788788 −22.2772 + 12.8617i −0.793591 + 0.458180i
789789 5.85747 + 33.2194i 0.208531 + 1.18264i
790790 −0.378658 2.59657i −0.0134720 0.0923819i
791791 −10.5368 + 18.2503i −0.374645 + 0.648905i
792792 −0.322839 0.384744i −0.0114716 0.0136713i
793793 −0.542044 0.645983i −0.0192486 0.0229395i
794794 −8.29321 3.01848i −0.294315 0.107122i
795795 −15.9248 + 40.0111i −0.564795 + 1.41905i
796796 1.69794 9.62950i 0.0601819 0.341309i
797797 −15.2588 + 41.9231i −0.540493 + 1.48499i 0.305706 + 0.952126i 0.401108π0.401108\pi
−0.846199 + 0.532867i 0.821115π0.821115\pi
798798 −9.81967 11.7026i −0.347613 0.414269i
799799 −34.6733 + 29.0944i −1.22665 + 1.02929i
800800 −2.98070 4.01440i −0.105384 0.141931i
801801 −56.0802 + 20.4115i −1.98149 + 0.721205i
802802 17.5860 3.10089i 0.620983 0.109496i
803803 0.986109 0.569330i 0.0347990 0.0200912i
804804 −14.4068 + 24.9532i −0.508087 + 0.880032i
805805 −52.4662 32.4076i −1.84919 1.14222i
806806 −16.6952 28.9169i −0.588063 1.01855i
807807 19.8448 23.6501i 0.698569 0.832522i
808808 7.60713i 0.267618i
809809 16.3379 + 13.7092i 0.574411 + 0.481988i 0.883106 0.469173i 0.155448π-0.155448\pi
−0.308695 + 0.951161i 0.599892π0.599892\pi
810810 1.55314 + 10.6504i 0.0545719 + 0.374216i
811811 0.598461 3.39404i 0.0210148 0.119181i −0.972496 0.232920i 0.925172π-0.925172\pi
0.993511 + 0.113740i 0.0362829π0.0362829\pi
812812 7.88417 1.39019i 0.276680 0.0487861i
813813 42.5741i 1.49314i
814814 0.372822 0.658543i 0.0130674 0.0230819i
815815 −6.69709 + 32.3304i −0.234589 + 1.13248i
816816 2.17097 + 12.3122i 0.0759993 + 0.431013i
817817 3.87825 + 0.683840i 0.135683 + 0.0239245i
818818 1.22491 + 3.36542i 0.0428281 + 0.117669i
819819 −62.6992 52.6108i −2.19089 1.83837i
820820 −8.88430 1.84034i −0.310253 0.0642675i
821821 −32.5122 27.2810i −1.13468 0.952114i −0.135433 0.990787i 0.543243π-0.543243\pi
−0.999252 + 0.0386729i 0.987687π0.987687\pi
822822 26.2057 15.1299i 0.914028 0.527714i
823823 14.9362 41.0368i 0.520642 1.43045i −0.349166 0.937061i 0.613535π-0.613535\pi
0.869808 0.493391i 0.164243π-0.164243\pi
824824 −0.432146 + 0.748500i −0.0150545 + 0.0260752i
825825 −1.63922 + 0.189488i −0.0570702 + 0.00659711i
826826 4.13269 + 23.4377i 0.143795 + 0.815501i
827827 −9.38199 25.7768i −0.326244 0.896348i −0.989053 0.147559i 0.952858π-0.952858\pi
0.662809 0.748788i 0.269364π-0.269364\pi
828828 −29.6369 17.1109i −1.02995 0.594643i
829829 28.8267 24.1885i 1.00119 0.840100i 0.0140429 0.999901i 0.495530π-0.495530\pi
0.987149 + 0.159802i 0.0510854π0.0510854\pi
830830 7.65935 4.12361i 0.265860 0.143133i
831831 38.1790 + 13.8960i 1.32442 + 0.482048i
832832 −6.13700 1.08212i −0.212762 0.0375157i
833833 16.6376 + 2.93365i 0.576457 + 0.101645i
834834 −21.1012 7.68021i −0.730674 0.265944i
835835 14.0700 + 26.1341i 0.486912 + 0.904409i
836836 −0.168695 + 0.141552i −0.00583445 + 0.00489568i
837837 −12.7657 7.37025i −0.441246 0.254753i
838838 −0.576385 1.58360i −0.0199109 0.0547047i
839839 −7.07968 40.1508i −0.244418 1.38616i −0.821841 0.569716i 0.807053π-0.807053\pi
0.577424 0.816445i 0.304058π-0.304058\pi
840840 −18.3226 + 6.05855i −0.632190 + 0.209040i
841841 11.4724 19.8707i 0.395599 0.685198i
842842 3.85027 10.5785i 0.132689 0.364560i
843843 −37.6676 + 21.7474i −1.29734 + 0.749021i
844844 −2.44046 2.04778i −0.0840039 0.0704877i
845845 −56.5652 11.7172i −1.94590 0.403085i
846846 −29.7010 24.9221i −1.02114 0.856840i
847847 −12.2228 33.5819i −0.419981 1.15389i
848848 7.14962 + 1.26067i 0.245519 + 0.0432916i
849849 −1.02714 5.82521i −0.0352514 0.199921i
850850 21.6255 + 9.36090i 0.741747 + 0.321076i
851851 8.52419 50.8535i 0.292205 1.74324i
852852 15.4768i 0.530227i
853853 16.9093 2.98157i 0.578964 0.102087i 0.123505 0.992344i 0.460586π-0.460586\pi
0.455459 + 0.890257i 0.349475π0.349475\pi
854854 −0.0764489 + 0.433563i −0.00261603 + 0.0148362i
855855 −15.8116 + 2.30580i −0.540745 + 0.0788568i
856856 15.7130 + 13.1848i 0.537060 + 0.450647i
857857 10.2382i 0.349729i −0.984593 0.174864i 0.944051π-0.944051\pi
0.984593 0.174864i 0.0559487π-0.0559487\pi
858858 −1.32197 + 1.57546i −0.0451313 + 0.0537853i
859859 −13.9161 24.1035i −0.474813 0.822400i 0.524771 0.851243i 0.324151π-0.324151\pi
−0.999584 + 0.0288434i 0.990818π0.990818\pi
860860 2.61433 4.23246i 0.0891479 0.144326i
861861 −17.5092 + 30.3268i −0.596711 + 1.03353i
862862 2.56488 1.48084i 0.0873602 0.0504374i
863863 20.3816 3.59383i 0.693799 0.122335i 0.184381 0.982855i 0.440972π-0.440972\pi
0.509418 + 0.860519i 0.329861π0.329861\pi
864864 −2.58513 + 0.940909i −0.0879478 + 0.0320104i
865865 4.36930 + 3.89332i 0.148561 + 0.132377i
866866 14.2053 11.9197i 0.482717 0.405048i
867867 −8.88637 10.5904i −0.301797 0.359667i
868868 −5.96220 + 16.3810i −0.202370 + 0.556008i
869869 −0.0253518 + 0.143777i −0.000860000 + 0.00487731i
870870 5.39769 13.5617i 0.182999 0.459785i
871871 63.6050 + 23.1503i 2.15517 + 0.784419i
872872 9.86892 + 11.7613i 0.334204 + 0.398289i
873873 −4.20018 5.00557i −0.142154 0.169413i
874874 −7.50244 + 12.9946i −0.253774 + 0.439549i
875875 −9.48124 + 35.1168i −0.320524 + 1.18716i
876876 −4.21606 23.9104i −0.142447 0.807859i
877877 −12.1853 + 7.03519i −0.411469 + 0.237562i −0.691421 0.722452i 0.743015π-0.743015\pi
0.279952 + 0.960014i 0.409682π0.409682\pi
878878 −9.83541 5.67848i −0.331929 0.191639i
879879 −77.3865 28.1664i −2.61018 0.950028i
880880 0.0873349 + 0.264124i 0.00294406 + 0.00890360i
881881 −8.43965 7.08171i −0.284339 0.238589i 0.489451 0.872031i 0.337197π-0.337197\pi
−0.773790 + 0.633442i 0.781642π0.781642\pi
882882 14.4715i 0.487281i
883883 17.9615 21.4057i 0.604452 0.720358i −0.373862 0.927484i 0.621967π-0.621967\pi
0.978314 + 0.207126i 0.0664112π0.0664112\pi
884884 27.5981 10.0449i 0.928225 0.337846i
885885 40.3156 + 16.0460i 1.35519 + 0.539381i
886886 1.46268 + 8.29527i 0.0491397 + 0.278685i
887887 15.5073i 0.520683i −0.965517 0.260341i 0.916165π-0.916165\pi
0.965517 0.260341i 0.0838351π-0.0838351\pi
888888 −10.4762 12.2728i −0.351557 0.411847i
889889 38.5010 1.29128
890890 33.0409 + 0.982387i 1.10753 + 0.0329297i
891891 0.103985 0.589731i 0.00348364 0.0197567i
892892 −2.04169 5.60949i −0.0683608 0.187820i
893893 −10.9274 + 13.0227i −0.365671 + 0.435789i
894894 −15.9739 −0.534249
895895 −1.11731 1.41491i −0.0373476 0.0472954i
896896 1.62670 + 2.81754i 0.0543444 + 0.0941272i
897897 −47.9280 + 131.681i −1.60027 + 4.39670i
898898 6.37625 + 3.68133i 0.212778 + 0.122847i
899899 −6.59253 11.4186i −0.219873 0.380831i
900900 −4.67998 + 19.6352i −0.155999 + 0.654508i
901901 −32.1519 + 11.7023i −1.07113 + 0.389861i
902902 0.437165 + 0.252397i 0.0145560 + 0.00840392i
903903 −12.3421 14.7088i −0.410721 0.489478i
904904 4.96197 4.16358i 0.165033 0.138479i
905905 14.3821 + 8.88359i 0.478076 + 0.295301i
906906 −8.95107 + 50.7641i −0.297380 + 1.68652i
907907 43.1993 + 7.61721i 1.43441 + 0.252925i 0.836205 0.548418i 0.184770π-0.184770\pi
0.598205 + 0.801343i 0.295881π0.295881\pi
908908 4.80661 13.2061i 0.159513 0.438259i
909909 23.5255 19.7402i 0.780292 0.654743i
910910 21.4904 + 39.9171i 0.712400 + 1.32324i
911911 −4.77070 + 8.26310i −0.158060 + 0.273769i −0.934169 0.356830i 0.883857π-0.883857\pi
0.776109 + 0.630599i 0.217191π0.217191\pi
912912 1.60599 + 4.41242i 0.0531796 + 0.146110i
913913 −0.476630 + 0.0840427i −0.0157741 + 0.00278141i
914914 3.50820 + 6.07638i 0.116041 + 0.200989i
915915 0.599284 + 0.533999i 0.0198117 + 0.0176535i
916916 −16.4662 5.99321i −0.544059 0.198021i
917917 56.1082 32.3941i 1.85286 1.06975i
918918 8.33398 9.93205i 0.275062 0.327806i
919919 48.1342 1.58780 0.793901 0.608048i 0.208047π-0.208047\pi
0.793901 + 0.608048i 0.208047π0.208047\pi
920920 11.7471 + 14.8760i 0.387290 + 0.490447i
921921 −46.7151 + 17.0029i −1.53932 + 0.560265i
922922 8.75897 + 1.54444i 0.288461 + 0.0508635i
923923 −35.8049 + 6.31337i −1.17853 + 0.207807i
924924 1.07371 0.0353225
925925 −30.1820 + 3.74777i −0.992379 + 0.123226i
926926 −29.5089 −0.969724
927927 3.43619 0.605893i 0.112859 0.0199001i
928928 −2.42336 0.427303i −0.0795505 0.0140269i
929929 43.2031 15.7246i 1.41745 0.515909i 0.484141 0.874990i 0.339132π-0.339132\pi
0.933306 + 0.359081i 0.116910π0.116910\pi
930930 19.6972 + 24.9437i 0.645897 + 0.817936i
931931 6.34519 0.207955
932932 5.94863 7.08931i 0.194854 0.232218i
933933 −75.9273 + 43.8366i −2.48575 + 1.43515i
934934 27.4356 + 9.98573i 0.897719 + 0.326743i
935935 −0.978852 0.872218i −0.0320119 0.0285246i
936936 12.5788 + 21.7871i 0.411151 + 0.712134i
937937 25.3840 4.47588i 0.829259 0.146221i 0.257122 0.966379i 0.417226π-0.417226\pi
0.572137 + 0.820158i 0.306115π0.306115\pi
938938 −12.0862 33.2067i −0.394630 1.08424i
939939 30.5629 52.9365i 0.997383 1.72752i
940940 10.1802 + 18.9090i 0.332040 + 0.616744i
941941 −34.0940 + 28.6083i −1.11143 + 0.932603i −0.998140 0.0609589i 0.980584π-0.980584\pi
−0.113292 + 0.993562i 0.536140π0.536140\pi
942942 4.37165 12.0110i 0.142436 0.391340i
943943 33.8727 + 5.97268i 1.10305 + 0.194497i
944944 1.27027 7.20403i 0.0413436 0.234471i
945945 17.0270 + 10.5174i 0.553889 + 0.342129i
946946 −0.212029 + 0.177914i −0.00689367 + 0.00578448i
947947 19.8592 + 23.6673i 0.645339 + 0.769085i 0.985203 0.171390i 0.0548257π-0.0548257\pi
−0.339865 + 0.940474i 0.610381π0.610381\pi
948948 2.69594 + 1.55650i 0.0875602 + 0.0505529i
949949 −53.5959 + 19.5073i −1.73980 + 0.633234i
950950 8.60929 + 2.05199i 0.279322 + 0.0665752i
951951 19.9305 + 34.5206i 0.646290 + 1.11941i
952952 −13.2788 7.66651i −0.430368 0.248473i
953953 17.0316 46.7940i 0.551708 1.51581i −0.279668 0.960097i 0.590224π-0.590224\pi
0.831377 0.555709i 0.187553π-0.187553\pi
954954 −14.6543 25.3821i −0.474452 0.821774i
955955 37.8907 + 47.9832i 1.22611 + 1.55270i
956956 2.24643 0.0726548
957957 −0.522014 + 0.622112i −0.0168743 + 0.0201100i
958958 −1.54365 4.24115i −0.0498732 0.137025i
959959 −6.44434 + 36.5477i −0.208099 + 1.18019i
960960 5.92910 + 0.176286i 0.191361 + 0.00568962i
961961 −2.29002 −0.0738716
962962 −24.1190 + 29.2425i −0.777628 + 0.942815i
963963 82.8076i 2.66844i
964964 3.16438 + 17.9461i 0.101918 + 0.578005i
965965 28.1331 + 11.1973i 0.905637 + 0.360452i
966966 68.7475 25.0221i 2.21192 0.805071i
967967 −30.8841 + 36.8062i −0.993165 + 1.18361i −0.0101746 + 0.999948i 0.503239π0.503239\pi
−0.982990 + 0.183659i 0.941206π0.941206\pi
968968 10.9845i 0.353056i
969969 −16.9525 14.2248i −0.544592 0.456967i
970970 1.13624 + 3.43628i 0.0364825 + 0.110332i
971971 1.99793 + 0.727189i 0.0641168 + 0.0233366i 0.373879 0.927477i 0.378027π-0.378027\pi
−0.309763 + 0.950814i 0.600250π0.600250\pi
972972 −18.2054 10.5109i −0.583937 0.337136i
973973 23.8504 13.7700i 0.764608 0.441446i
974974 3.81805 + 21.6532i 0.122338 + 0.693814i
975975 82.5092 + 4.91074i 2.64241 + 0.157269i
976976 0.0676601 0.117191i 0.00216575 0.00375118i
977977 13.1442 + 15.6647i 0.420522 + 0.501158i 0.934163 0.356847i 0.116148π-0.116148\pi
−0.513641 + 0.858005i 0.671704π0.671704\pi
978978 −25.1775 30.0054i −0.805087 0.959465i
979979 −1.72822 0.629020i −0.0552341 0.0201036i
980980 2.96413 7.44737i 0.0946855 0.237898i
981981 10.7631 61.0405i 0.343639 1.94887i
982982 7.87047 21.6239i 0.251157 0.690047i
983983 2.93803 + 3.50141i 0.0937087 + 0.111678i 0.810861 0.585239i 0.198999π-0.198999\pi
−0.717152 + 0.696917i 0.754555π0.754555\pi
984984 8.24538 6.91870i 0.262853 0.220560i
985985 −42.9441 38.2659i −1.36831 1.21925i
986986 10.8978 3.96649i 0.347058 0.126319i
987987 81.6279 14.3932i 2.59824 0.458141i
988988 9.55280 5.51531i 0.303915 0.175465i
989989 −9.42966 + 16.3326i −0.299846 + 0.519348i
990990 0.590187 0.955481i 0.0187574 0.0303672i
991991 −22.4132 38.8207i −0.711977 1.23318i −0.964114 0.265489i 0.914467π-0.914467\pi
0.252137 0.967692i 0.418867π-0.418867\pi
992992 3.44417 4.10460i 0.109352 0.130321i
993993 15.2394i 0.483607i
994994 14.5405 + 12.2009i 0.461197 + 0.386990i
995995 21.6355 3.15511i 0.685893 0.100024i
996996 −1.79202 + 10.1630i −0.0567822 + 0.322028i
997997 −29.3514 + 5.17544i −0.929567 + 0.163908i −0.617876 0.786276i 0.712007π-0.712007\pi
−0.311691 + 0.950183i 0.600895π0.600895\pi
998998 14.3177i 0.453219i
999999 −2.76638 + 16.5036i −0.0875244 + 0.522152i
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 370.2.x.a.9.9 108
5.4 even 2 inner 370.2.x.a.9.10 yes 108
37.33 even 9 inner 370.2.x.a.329.10 yes 108
185.144 even 18 inner 370.2.x.a.329.9 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.x.a.9.9 108 1.1 even 1 trivial
370.2.x.a.9.10 yes 108 5.4 even 2 inner
370.2.x.a.329.9 yes 108 185.144 even 18 inner
370.2.x.a.329.10 yes 108 37.33 even 9 inner