Properties

Label 91.2.q.a.43.4
Level 9191
Weight 22
Character 91.43
Analytic conductor 0.7270.727
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(36,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.36");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 91=713 91 = 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 91.q (of order 66, degree 22, 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: 0.7266386583940.726638658394
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 12.0.58891012706304.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x125x102x9+15x8+2x730x6+4x5+60x416x380x2+64 x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 43.4
Root 1.081050.911778i-1.08105 - 0.911778i of defining polynomial
Character χ\chi == 91.43
Dual form 91.2.q.a.36.4

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+(0.713220+0.411778i)q2+(1.33015+2.30388i)q3+(0.6608781.14467i)q4+3.16209iq5+(1.89737+1.09545i)q6+(0.8660250.500000i)q72.73565iq8+(2.038583.53092i)q9+(1.30208+2.25527i)q10+(5.14653+2.97135i)q11+3.51626q12+(0.07661933.60474i)q13+0.823556q14+(7.285084.20604i)q15+(0.195274+0.338225i)q16+(1.349822.33796i)q173.35776iq18+(1.694850.978524i)q19+(3.619562.08976i)q20+2.66029iq21+(2.44707+4.23845i)q22+(1.36471+2.36374i)q23+(6.30261+3.63882i)q244.99883q25+(1.429702.60252i)q26+2.86554q27+(1.144670.660878i)q28+(2.999235.19481i)q29+(3.463915.99967i)q30+1.15155iq31+(5.01684+2.89647i)q32+(13.6913+7.90465i)q332.22331iq34+(1.58105+2.73845i)q35+(2.69450+4.66701i)q36+(5.633103.25227i)q37+1.61174q38+(8.40680+4.61830i)q39+8.65038q40+(3.233511.86687i)q41+(1.09545+1.89737i)q42+(3.49562+6.05460i)q437.85479iq44+(11.16516.44617i)q45+(1.94667+1.12391i)q460.456071iq47+(0.5194870.899778i)q48+(0.5000000.866025i)q49+(3.565272.05841i)q50+7.18184q51+(4.07561+2.46999i)q52+0.399286q53+(2.04376+1.17997i)q54+(9.39568+16.2738i)q55+(1.367832.36914i)q56+5.20632iq57+(4.278222.47003i)q58+(4.162002.40293i)q59+11.1187iq60+(0.578514+1.00201i)q61+(0.474182+0.821308i)q62+(3.530922.03858i)q633.98971q64+(11.39850.242277i)q6513.0199q66+(5.437933.13959i)q67+(1.78413+3.09021i)q68+(3.630526.28825i)q69+2.60416iq70+(3.903352.25360i)q71+(9.65936+5.57684i)q728.30575iq73+(2.678434.63917i)q74+(6.6491711.5167i)q75+(2.240181.29337i)q76+5.94270q77+(4.09418+6.75560i)q787.91410q79+(1.069500.617476i)q80+(2.304143.99089i)q81+(1.537472.66298i)q826.19795iq83+(3.045171.75813i)q84+(7.392844.26826i)q85+5.75769iq86+(7.97882+13.8197i)q87+(8.1285714.0791i)q88+(3.08423+1.78068i)q89+10.6176q90+(1.868723.08348i)q91+3.60762q92+(2.653031.53173i)q93+(0.1878000.325279i)q94+(3.09418+5.35928i)q9515.4109iq96+(2.96831+1.71375i)q97+(0.7132200.411778i)q9824.2293iq99+O(q100)q+(0.713220 + 0.411778i) q^{2} +(-1.33015 + 2.30388i) q^{3} +(-0.660878 - 1.14467i) q^{4} +3.16209i q^{5} +(-1.89737 + 1.09545i) q^{6} +(0.866025 - 0.500000i) q^{7} -2.73565i q^{8} +(-2.03858 - 3.53092i) q^{9} +(-1.30208 + 2.25527i) q^{10} +(5.14653 + 2.97135i) q^{11} +3.51626 q^{12} +(-0.0766193 - 3.60474i) q^{13} +0.823556 q^{14} +(-7.28508 - 4.20604i) q^{15} +(-0.195274 + 0.338225i) q^{16} +(-1.34982 - 2.33796i) q^{17} -3.35776i q^{18} +(1.69485 - 0.978524i) q^{19} +(3.61956 - 2.08976i) q^{20} +2.66029i q^{21} +(2.44707 + 4.23845i) q^{22} +(-1.36471 + 2.36374i) q^{23} +(6.30261 + 3.63882i) q^{24} -4.99883 q^{25} +(1.42970 - 2.60252i) q^{26} +2.86554 q^{27} +(-1.14467 - 0.660878i) q^{28} +(2.99923 - 5.19481i) q^{29} +(-3.46391 - 5.99967i) q^{30} +1.15155i q^{31} +(-5.01684 + 2.89647i) q^{32} +(-13.6913 + 7.90465i) q^{33} -2.22331i q^{34} +(1.58105 + 2.73845i) q^{35} +(-2.69450 + 4.66701i) q^{36} +(-5.63310 - 3.25227i) q^{37} +1.61174 q^{38} +(8.40680 + 4.61830i) q^{39} +8.65038 q^{40} +(-3.23351 - 1.86687i) q^{41} +(-1.09545 + 1.89737i) q^{42} +(3.49562 + 6.05460i) q^{43} -7.85479i q^{44} +(11.1651 - 6.44617i) q^{45} +(-1.94667 + 1.12391i) q^{46} -0.456071i q^{47} +(-0.519487 - 0.899778i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.56527 - 2.05841i) q^{50} +7.18184 q^{51} +(-4.07561 + 2.46999i) q^{52} +0.399286 q^{53} +(2.04376 + 1.17997i) q^{54} +(-9.39568 + 16.2738i) q^{55} +(-1.36783 - 2.36914i) q^{56} +5.20632i q^{57} +(4.27822 - 2.47003i) q^{58} +(4.16200 - 2.40293i) q^{59} +11.1187i q^{60} +(0.578514 + 1.00201i) q^{61} +(-0.474182 + 0.821308i) q^{62} +(-3.53092 - 2.03858i) q^{63} -3.98971 q^{64} +(11.3985 - 0.242277i) q^{65} -13.0199 q^{66} +(-5.43793 - 3.13959i) q^{67} +(-1.78413 + 3.09021i) q^{68} +(-3.63052 - 6.28825i) q^{69} +2.60416i q^{70} +(3.90335 - 2.25360i) q^{71} +(-9.65936 + 5.57684i) q^{72} -8.30575i q^{73} +(-2.67843 - 4.63917i) q^{74} +(6.64917 - 11.5167i) q^{75} +(-2.24018 - 1.29337i) q^{76} +5.94270 q^{77} +(4.09418 + 6.75560i) q^{78} -7.91410 q^{79} +(-1.06950 - 0.617476i) q^{80} +(2.30414 - 3.99089i) q^{81} +(-1.53747 - 2.66298i) q^{82} -6.19795i q^{83} +(3.04517 - 1.75813i) q^{84} +(7.39284 - 4.26826i) q^{85} +5.75769i q^{86} +(7.97882 + 13.8197i) q^{87} +(8.12857 - 14.0791i) q^{88} +(3.08423 + 1.78068i) q^{89} +10.6176 q^{90} +(-1.86872 - 3.08348i) q^{91} +3.60762 q^{92} +(-2.65303 - 1.53173i) q^{93} +(0.187800 - 0.325279i) q^{94} +(3.09418 + 5.35928i) q^{95} -15.4109i q^{96} +(-2.96831 + 1.71375i) q^{97} +(0.713220 - 0.411778i) q^{98} -24.2293i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+4q418q64q9+12q10+6q114q12+4q138q14+6q158q164q1712q20+6q2212q23+12q2420q2542q26+12q27++6q97+O(q100) 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27}+ \cdots + 6 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/91Z)×\left(\mathbb{Z}/91\mathbb{Z}\right)^\times.

nn 1515 6666
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) 11

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 0.713220 + 0.411778i 0.504323 + 0.291171i 0.730497 0.682916i 0.239288π-0.239288\pi
−0.226174 + 0.974087i 0.572622π0.572622\pi
33 −1.33015 + 2.30388i −0.767960 + 1.33015i 0.170707 + 0.985322i 0.445395π0.445395\pi
−0.938667 + 0.344824i 0.887939π0.887939\pi
44 −0.660878 1.14467i −0.330439 0.572337i
55 3.16209i 1.41413i 0.707148 + 0.707065i 0.249981π0.249981\pi
−0.707148 + 0.707065i 0.750019π0.750019\pi
66 −1.89737 + 1.09545i −0.774600 + 0.447215i
77 0.866025 0.500000i 0.327327 0.188982i
88 2.73565i 0.967199i
99 −2.03858 3.53092i −0.679526 1.17697i
1010 −1.30208 + 2.25527i −0.411754 + 0.713179i
1111 5.14653 + 2.97135i 1.55174 + 0.895895i 0.998001 + 0.0632025i 0.0201314π0.0201314\pi
0.553735 + 0.832693i 0.313202π0.313202\pi
1212 3.51626 1.01506
1313 −0.0766193 3.60474i −0.0212504 0.999774i
1414 0.823556 0.220105
1515 −7.28508 4.20604i −1.88100 1.08600i
1616 −0.195274 + 0.338225i −0.0488186 + 0.0845563i
1717 −1.34982 2.33796i −0.327380 0.567038i 0.654611 0.755966i 0.272832π-0.272832\pi
−0.981991 + 0.188927i 0.939499π0.939499\pi
1818 3.35776i 0.791433i
1919 1.69485 0.978524i 0.388826 0.224489i −0.292825 0.956166i 0.594595π-0.594595\pi
0.681651 + 0.731677i 0.261262π0.261262\pi
2020 3.61956 2.08976i 0.809359 0.467284i
2121 2.66029i 0.580523i
2222 2.44707 + 4.23845i 0.521717 + 0.903641i
2323 −1.36471 + 2.36374i −0.284561 + 0.492874i −0.972503 0.232892i 0.925181π-0.925181\pi
0.687941 + 0.725766i 0.258515π0.258515\pi
2424 6.30261 + 3.63882i 1.28652 + 0.742770i
2525 −4.99883 −0.999766
2626 1.42970 2.60252i 0.280388 0.510397i
2727 2.86554 0.551474
2828 −1.14467 0.660878i −0.216323 0.124894i
2929 2.99923 5.19481i 0.556942 0.964652i −0.440807 0.897602i 0.645308π-0.645308\pi
0.997750 0.0670505i 0.0213589π-0.0213589\pi
3030 −3.46391 5.99967i −0.632421 1.09539i
3131 1.15155i 0.206824i 0.994639 + 0.103412i 0.0329760π0.0329760\pi
−0.994639 + 0.103412i 0.967024π0.967024\pi
3232 −5.01684 + 2.89647i −0.886860 + 0.512029i
3333 −13.6913 + 7.90465i −2.38334 + 1.37602i
3434 2.22331i 0.381294i
3535 1.58105 + 2.73845i 0.267246 + 0.462883i
3636 −2.69450 + 4.66701i −0.449083 + 0.777835i
3737 −5.63310 3.25227i −0.926075 0.534670i −0.0405072 0.999179i 0.512897π-0.512897\pi
−0.885568 + 0.464509i 0.846231π0.846231\pi
3838 1.61174 0.261459
3939 8.40680 + 4.61830i 1.34617 + 0.739521i
4040 8.65038 1.36775
4141 −3.23351 1.86687i −0.504990 0.291556i 0.225782 0.974178i 0.427506π-0.427506\pi
−0.730772 + 0.682622i 0.760840π0.760840\pi
4242 −1.09545 + 1.89737i −0.169032 + 0.292771i
4343 3.49562 + 6.05460i 0.533078 + 0.923318i 0.999254 + 0.0386258i 0.0122980π0.0122980\pi
−0.466176 + 0.884692i 0.654369π0.654369\pi
4444 7.85479i 1.18415i
4545 11.1651 6.44617i 1.66439 0.960938i
4646 −1.94667 + 1.12391i −0.287021 + 0.165712i
4747 0.456071i 0.0665248i −0.999447 0.0332624i 0.989410π-0.989410\pi
0.999447 0.0332624i 0.0105897π-0.0105897\pi
4848 −0.519487 0.899778i −0.0749815 0.129872i
4949 0.500000 0.866025i 0.0714286 0.123718i
5050 −3.56527 2.05841i −0.504205 0.291103i
5151 7.18184 1.00566
5252 −4.07561 + 2.46999i −0.565186 + 0.342527i
5353 0.399286 0.0548462 0.0274231 0.999624i 0.491270π-0.491270\pi
0.0274231 + 0.999624i 0.491270π0.491270\pi
5454 2.04376 + 1.17997i 0.278121 + 0.160573i
5555 −9.39568 + 16.2738i −1.26691 + 2.19436i
5656 −1.36783 2.36914i −0.182783 0.316590i
5757 5.20632i 0.689594i
5858 4.27822 2.47003i 0.561758 0.324331i
5959 4.16200 2.40293i 0.541846 0.312835i −0.203981 0.978975i 0.565388π-0.565388\pi
0.745827 + 0.666140i 0.232055π0.232055\pi
6060 11.1187i 1.43542i
6161 0.578514 + 1.00201i 0.0740711 + 0.128295i 0.900682 0.434479i 0.143067π-0.143067\pi
−0.826611 + 0.562774i 0.809734π0.809734\pi
6262 −0.474182 + 0.821308i −0.0602212 + 0.104306i
6363 −3.53092 2.03858i −0.444854 0.256837i
6464 −3.98971 −0.498714
6565 11.3985 0.242277i 1.41381 0.0300508i
6666 −13.0199 −1.60263
6767 −5.43793 3.13959i −0.664349 0.383562i 0.129583 0.991569i 0.458636π-0.458636\pi
−0.793932 + 0.608007i 0.791969π0.791969\pi
6868 −1.78413 + 3.09021i −0.216358 + 0.374743i
6969 −3.63052 6.28825i −0.437063 0.757016i
7070 2.60416i 0.311257i
7171 3.90335 2.25360i 0.463242 0.267453i −0.250165 0.968203i 0.580485π-0.580485\pi
0.713406 + 0.700751i 0.247151π0.247151\pi
7272 −9.65936 + 5.57684i −1.13837 + 0.657236i
7373 8.30575i 0.972115i −0.873927 0.486057i 0.838435π-0.838435\pi
0.873927 0.486057i 0.161565π-0.161565\pi
7474 −2.67843 4.63917i −0.311361 0.539293i
7575 6.64917 11.5167i 0.767780 1.32983i
7676 −2.24018 1.29337i −0.256966 0.148360i
7777 5.94270 0.677233
7878 4.09418 + 6.75560i 0.463575 + 0.764921i
7979 −7.91410 −0.890405 −0.445203 0.895430i 0.646868π-0.646868\pi
−0.445203 + 0.895430i 0.646868π0.646868\pi
8080 −1.06950 0.617476i −0.119574 0.0690359i
8181 2.30414 3.99089i 0.256016 0.443432i
8282 −1.53747 2.66298i −0.169785 0.294077i
8383 6.19795i 0.680313i −0.940369 0.340156i 0.889520π-0.889520\pi
0.940369 0.340156i 0.110480π-0.110480\pi
8484 3.04517 1.75813i 0.332255 0.191827i
8585 7.39284 4.26826i 0.801866 0.462958i
8686 5.75769i 0.620867i
8787 7.97882 + 13.8197i 0.855419 + 1.48163i
8888 8.12857 14.0791i 0.866509 1.50084i
8989 3.08423 + 1.78068i 0.326928 + 0.188752i 0.654476 0.756083i 0.272889π-0.272889\pi
−0.327549 + 0.944834i 0.606222π0.606222\pi
9090 10.6176 1.11919
9191 −1.86872 3.08348i −0.195895 0.323237i
9292 3.60762 0.376120
9393 −2.65303 1.53173i −0.275106 0.158833i
9494 0.187800 0.325279i 0.0193701 0.0335500i
9595 3.09418 + 5.35928i 0.317457 + 0.549851i
9696 15.4109i 1.57287i
9797 −2.96831 + 1.71375i −0.301386 + 0.174005i −0.643065 0.765811i 0.722338π-0.722338\pi
0.341679 + 0.939817i 0.389004π0.389004\pi
9898 0.713220 0.411778i 0.0720461 0.0415959i
9999 24.2293i 2.43513i
100100 3.30361 + 5.72203i 0.330361 + 0.572203i
101101 −6.66474 + 11.5437i −0.663167 + 1.14864i 0.316612 + 0.948555i 0.397455π0.397455\pi
−0.979779 + 0.200084i 0.935879π0.935879\pi
102102 5.12223 + 2.95732i 0.507177 + 0.292819i
103103 −11.6450 −1.14741 −0.573706 0.819061i 0.694495π-0.694495\pi
−0.573706 + 0.819061i 0.694495π0.694495\pi
104104 −9.86130 + 0.209604i −0.966981 + 0.0205533i
105105 −8.41209 −0.820936
106106 0.284779 + 0.164417i 0.0276602 + 0.0159696i
107107 −1.96483 + 3.40318i −0.189947 + 0.328998i −0.945232 0.326398i 0.894165π-0.894165\pi
0.755285 + 0.655396i 0.227498π0.227498\pi
108108 −1.89377 3.28011i −0.182228 0.315629i
109109 11.2533i 1.07787i −0.842346 0.538936i 0.818826π-0.818826\pi
0.842346 0.538936i 0.181174π-0.181174\pi
110110 −13.4024 + 7.73787i −1.27787 + 0.737777i
111111 14.9857 8.65199i 1.42238 0.821210i
112112 0.390549i 0.0369034i
113113 2.88709 + 5.00059i 0.271595 + 0.470416i 0.969270 0.245998i 0.0791157π-0.0791157\pi
−0.697676 + 0.716414i 0.745782π0.745782\pi
114114 −2.14385 + 3.71325i −0.200790 + 0.347778i
115115 −7.47437 4.31533i −0.696989 0.402407i
116116 −7.92849 −0.736142
117117 −12.5718 + 7.61907i −1.16227 + 0.704383i
118118 3.95790 0.364354
119119 −2.33796 1.34982i −0.214320 0.123738i
120120 −11.5063 + 19.9294i −1.05037 + 1.81930i
121121 12.1578 + 21.0580i 1.10526 + 1.91436i
122122 0.952877i 0.0862694i
123123 8.60209 4.96642i 0.775625 0.447807i
124124 1.31815 0.761033i 0.118373 0.0683428i
125125 0.00370455i 0.000331345i
126126 −1.67888 2.90791i −0.149567 0.259057i
127127 3.06558 5.30975i 0.272027 0.471164i −0.697354 0.716727i 0.745639π-0.745639\pi
0.969381 + 0.245563i 0.0789728π0.0789728\pi
128128 7.18812 + 4.15007i 0.635346 + 0.366817i
129129 −18.5988 −1.63753
130130 8.22942 + 4.52086i 0.721767 + 0.396506i
131131 10.2217 0.893073 0.446537 0.894765i 0.352657π-0.352657\pi
0.446537 + 0.894765i 0.352657π0.352657\pi
132132 18.0965 + 10.4480i 1.57510 + 0.909383i
133133 0.978524 1.69485i 0.0848488 0.146962i
134134 −2.58563 4.47844i −0.223364 0.386878i
135135 9.06111i 0.779856i
136136 −6.39584 + 3.69264i −0.548439 + 0.316641i
137137 −17.2751 + 9.97376i −1.47591 + 0.852116i −0.999631 0.0271788i 0.991348π-0.991348\pi
−0.476278 + 0.879295i 0.658014π0.658014\pi
138138 5.97987i 0.509041i
139139 10.1637 + 17.6041i 0.862077 + 1.49316i 0.869921 + 0.493192i 0.164170π0.164170\pi
−0.00784365 + 0.999969i 0.502497π0.502497\pi
140140 2.08976 3.61956i 0.176617 0.305909i
141141 1.05073 + 0.606641i 0.0884877 + 0.0510884i
142142 3.71193 0.311498
143143 10.3166 18.7795i 0.862718 1.57042i
144144 1.59233 0.132694
145145 16.4265 + 9.48383i 1.36414 + 0.787589i
146146 3.42013 5.92383i 0.283052 0.490260i
147147 1.33015 + 2.30388i 0.109709 + 0.190021i
148148 8.59741i 0.706703i
149149 −9.28046 + 5.35808i −0.760285 + 0.438951i −0.829398 0.558658i 0.811316π-0.811316\pi
0.0691132 + 0.997609i 0.477983π0.477983\pi
150150 9.48465 5.47597i 0.774418 0.447111i
151151 8.74416i 0.711590i 0.934564 + 0.355795i 0.115790π0.115790\pi
−0.934564 + 0.355795i 0.884210π0.884210\pi
152152 −2.67690 4.63653i −0.217125 0.376072i
153153 −5.50343 + 9.53222i −0.444926 + 0.770634i
154154 4.23845 + 2.44707i 0.341544 + 0.197191i
155155 −3.64130 −0.292476
156156 −0.269413 12.6752i −0.0215703 1.01483i
157157 6.50734 0.519342 0.259671 0.965697i 0.416386π-0.416386\pi
0.259671 + 0.965697i 0.416386π0.416386\pi
158158 −5.64449 3.25885i −0.449052 0.259260i
159159 −0.531109 + 0.919907i −0.0421197 + 0.0729534i
160160 −9.15891 15.8637i −0.724075 1.25414i
161161 2.72941i 0.215108i
162162 3.28672 1.89759i 0.258229 0.149089i
163163 2.26264 1.30634i 0.177224 0.102320i −0.408764 0.912640i 0.634040π-0.634040\pi
0.585988 + 0.810320i 0.300707π0.300707\pi
164164 4.93509i 0.385366i
165165 −24.9952 43.2930i −1.94588 3.37036i
166166 2.55218 4.42050i 0.198087 0.343097i
167167 −3.36558 1.94312i −0.260436 0.150363i 0.364097 0.931361i 0.381378π-0.381378\pi
−0.624534 + 0.780998i 0.714711π0.714711\pi
168168 7.27763 0.561482
169169 −12.9883 + 0.552385i −0.999097 + 0.0424911i
170170 7.03030 0.539200
171171 −6.91018 3.98959i −0.528434 0.305092i
172172 4.62036 8.00270i 0.352299 0.610200i
173173 6.98838 + 12.1042i 0.531317 + 0.920267i 0.999332 + 0.0365470i 0.0116358π0.0116358\pi
−0.468015 + 0.883720i 0.655031π0.655031\pi
174174 13.1420i 0.996293i
175175 −4.32911 + 2.49941i −0.327250 + 0.188938i
176176 −2.00997 + 1.16046i −0.151507 + 0.0874727i
177177 12.7850i 0.960979i
178178 1.46649 + 2.54004i 0.109918 + 0.190384i
179179 −12.6422 + 21.8968i −0.944919 + 1.63665i −0.189005 + 0.981976i 0.560526π0.560526\pi
−0.755914 + 0.654671i 0.772807π0.772807\pi
180180 −14.7575 8.52026i −1.09996 0.635063i
181181 −0.864474 −0.0642559 −0.0321279 0.999484i 0.510228π-0.510228\pi
−0.0321279 + 0.999484i 0.510228π0.510228\pi
182182 −0.0631003 2.96870i −0.00467730 0.220055i
183183 −3.07803 −0.227535
184184 6.46638 + 3.73336i 0.476708 + 0.275227i
185185 10.2840 17.8124i 0.756093 1.30959i
186186 −1.26146 2.18492i −0.0924950 0.160206i
187187 16.0432i 1.17319i
188188 −0.522052 + 0.301407i −0.0380746 + 0.0219824i
189189 2.48163 1.43277i 0.180512 0.104219i
190190 5.09647i 0.369737i
191191 −7.33382 12.7026i −0.530657 0.919125i −0.999360 0.0357690i 0.988612π-0.988612\pi
0.468703 0.883356i 0.344721π-0.344721\pi
192192 5.30690 9.19182i 0.382993 0.663363i
193193 14.2859 + 8.24794i 1.02832 + 0.593700i 0.916503 0.400029i 0.131000π-0.131000\pi
0.111816 + 0.993729i 0.464333π0.464333\pi
194194 −2.82275 −0.202661
195195 −14.6035 + 26.5831i −1.04578 + 1.90365i
196196 −1.32176 −0.0944111
197197 9.53510 + 5.50509i 0.679348 + 0.392222i 0.799609 0.600521i 0.205040π-0.205040\pi
−0.120262 + 0.992742i 0.538373π0.538373\pi
198198 9.97709 17.2808i 0.709041 1.22809i
199199 −10.6059 18.3699i −0.751829 1.30221i −0.946935 0.321425i 0.895838π-0.895838\pi
0.195106 0.980782i 0.437495π-0.437495\pi
200200 13.6751i 0.966972i
201201 14.4665 8.35223i 1.02039 0.589121i
202202 −9.50686 + 5.48879i −0.668901 + 0.386190i
203203 5.99845i 0.421009i
204204 −4.74632 8.22086i −0.332309 0.575576i
205205 5.90322 10.2247i 0.412299 0.714122i
206206 −8.30542 4.79514i −0.578666 0.334093i
207207 11.1282 0.773466
208208 1.23417 + 0.677998i 0.0855746 + 0.0470107i
209209 11.6301 0.804474
210210 −5.99967 3.46391i −0.414017 0.239033i
211211 8.96788 15.5328i 0.617375 1.06932i −0.372588 0.927997i 0.621530π-0.621530\pi
0.989963 0.141327i 0.0451370π-0.0451370\pi
212212 −0.263879 0.457052i −0.0181233 0.0313905i
213213 11.9905i 0.821572i
214214 −2.80271 + 1.61815i −0.191589 + 0.110614i
215215 −19.1452 + 11.0535i −1.30569 + 0.753842i
216216 7.83913i 0.533385i
217217 0.575774 + 0.997270i 0.0390861 + 0.0676991i
218218 4.63387 8.02610i 0.313845 0.543596i
219219 19.1355 + 11.0479i 1.29305 + 0.746545i
220220 24.8376 1.67455
221221 −8.32431 + 5.04488i −0.559953 + 0.339356i
222222 14.2508 0.956451
223223 −13.8834 8.01558i −0.929700 0.536763i −0.0429835 0.999076i 0.513686π-0.513686\pi
−0.886717 + 0.462313i 0.847020π0.847020\pi
224224 −2.89647 + 5.01684i −0.193529 + 0.335201i
225225 10.1905 + 17.6505i 0.679366 + 1.17670i
226226 4.75536i 0.316322i
227227 −14.1812 + 8.18751i −0.941239 + 0.543424i −0.890348 0.455280i 0.849539π-0.849539\pi
−0.0508902 + 0.998704i 0.516206π0.516206\pi
228228 5.95954 3.44074i 0.394680 0.227869i
229229 27.0104i 1.78490i −0.451148 0.892449i 0.648985π-0.648985\pi
0.451148 0.892449i 0.351015π-0.351015\pi
230230 −3.55392 6.15556i −0.234338 0.405886i
231231 −7.90465 + 13.6913i −0.520088 + 0.900819i
232232 −14.2112 8.20484i −0.933011 0.538674i
233233 −11.5681 −0.757853 −0.378926 0.925427i 0.623707π-0.623707\pi
−0.378926 + 0.925427i 0.623707π0.623707\pi
234234 −12.1039 + 0.257269i −0.791254 + 0.0168182i
235235 1.44214 0.0940747
236236 −5.50114 3.17609i −0.358094 0.206746i
237237 10.5269 18.2331i 0.683796 1.18437i
238238 −1.11165 1.92544i −0.0720578 0.124808i
239239 14.6731i 0.949122i 0.880223 + 0.474561i 0.157393π0.157393\pi
−0.880223 + 0.474561i 0.842607π0.842607\pi
240240 2.84518 1.64267i 0.183656 0.106034i
241241 12.4246 7.17334i 0.800338 0.462076i −0.0432510 0.999064i 0.513772π-0.513772\pi
0.843589 + 0.536989i 0.180438π0.180438\pi
242242 20.0253i 1.28727i
243243 10.4280 + 18.0618i 0.668956 + 1.15867i
244244 0.764654 1.32442i 0.0489519 0.0847872i
245245 2.73845 + 1.58105i 0.174953 + 0.101009i
246246 8.18025 0.521554
247247 −3.65718 6.03453i −0.232701 0.383968i
248248 3.15024 0.200040
249249 14.2793 + 8.24417i 0.904916 + 0.522453i
250250 −0.00152545 + 0.00264216i −9.64781e−5 + 0.000167105i
251251 4.30726 + 7.46040i 0.271872 + 0.470896i 0.969341 0.245719i 0.0790239π-0.0790239\pi
−0.697469 + 0.716615i 0.745691π0.745691\pi
252252 5.38900i 0.339475i
253253 −14.0470 + 8.11004i −0.883128 + 0.509874i
254254 4.37287 2.52468i 0.274378 0.158412i
255255 22.7096i 1.42213i
256256 7.40753 + 12.8302i 0.462970 + 0.801888i
257257 5.18197 8.97544i 0.323243 0.559873i −0.657912 0.753094i 0.728560π-0.728560\pi
0.981155 + 0.193222i 0.0618936π0.0618936\pi
258258 −13.2650 7.65856i −0.825844 0.476801i
259259 −6.50454 −0.404172
260260 −7.81035 12.8875i −0.484377 0.799247i
261261 −24.4566 −1.51383
262262 7.29032 + 4.20907i 0.450397 + 0.260037i
263263 11.0413 19.1241i 0.680835 1.17924i −0.293891 0.955839i 0.594950π-0.594950\pi
0.974726 0.223403i 0.0717165π-0.0717165\pi
264264 21.6244 + 37.4545i 1.33089 + 2.30517i
265265 1.26258i 0.0775596i
266266 1.39581 0.805869i 0.0855824 0.0494110i
267267 −8.20495 + 4.73713i −0.502135 + 0.289908i
268268 8.29954i 0.506975i
269269 −6.46995 11.2063i −0.394480 0.683259i 0.598555 0.801082i 0.295742π-0.295742\pi
−0.993035 + 0.117823i 0.962409π0.962409\pi
270270 −3.73117 + 6.46257i −0.227072 + 0.393299i
271271 −15.3069 8.83745i −0.929829 0.536837i −0.0430712 0.999072i 0.513714π-0.513714\pi
−0.886757 + 0.462235i 0.847048π0.847048\pi
272272 1.05434 0.0639289
273273 9.58965 0.203830i 0.580392 0.0123363i
274274 −16.4279 −0.992446
275275 −25.7266 14.8533i −1.55137 0.895685i
276276 −4.79866 + 8.31152i −0.288845 + 0.500295i
277277 −9.00751 15.6015i −0.541209 0.937401i −0.998835 0.0482562i 0.984634π-0.984634\pi
0.457626 0.889145i 0.348700π-0.348700\pi
278278 16.7408i 1.00405i
279279 4.06602 2.34752i 0.243426 0.140542i
280280 7.49145 4.32519i 0.447700 0.258480i
281281 2.44178i 0.145665i −0.997344 0.0728323i 0.976796π-0.976796\pi
0.997344 0.0728323i 0.0232038π-0.0232038\pi
282282 0.499603 + 0.865337i 0.0297509 + 0.0515301i
283283 −14.3620 + 24.8757i −0.853732 + 1.47871i 0.0240853 + 0.999710i 0.492333π0.492333\pi
−0.877817 + 0.478996i 0.841001π0.841001\pi
284284 −5.15927 2.97871i −0.306146 0.176754i
285285 −16.4629 −0.975176
286286 15.0910 9.14580i 0.892350 0.540802i
287287 −3.73374 −0.220396
288288 20.4544 + 11.8094i 1.20529 + 0.695873i
289289 4.85596 8.41078i 0.285645 0.494752i
290290 7.81046 + 13.5281i 0.458646 + 0.794399i
291291 9.11818i 0.534517i
292292 −9.50738 + 5.48909i −0.556377 + 0.321225i
293293 25.4013 14.6654i 1.48396 0.856763i 0.484124 0.874999i 0.339138π-0.339138\pi
0.999834 + 0.0182359i 0.00580499π0.00580499\pi
294294 2.19090i 0.127776i
295295 7.59829 + 13.1606i 0.442390 + 0.766241i
296296 −8.89708 + 15.4102i −0.517132 + 0.895699i
297297 14.7476 + 8.51453i 0.855742 + 0.494063i
298298 −8.82535 −0.511239
299299 8.62523 + 4.73830i 0.498810 + 0.274023i
300300 −17.5772 −1.01482
301301 6.05460 + 3.49562i 0.348981 + 0.201484i
302302 −3.60065 + 6.23651i −0.207194 + 0.358871i
303303 −17.7302 30.7096i −1.01857 1.76422i
304304 0.764323i 0.0438369i
305305 −3.16846 + 1.82931i −0.181426 + 0.104746i
306306 −7.85032 + 4.53238i −0.448773 + 0.259099i
307307 7.06910i 0.403455i 0.979442 + 0.201728i 0.0646555π0.0646555\pi
−0.979442 + 0.201728i 0.935344π0.935344\pi
308308 −3.92740 6.80245i −0.223784 0.387606i
309309 15.4895 26.8286i 0.881166 1.52623i
310310 −2.59705 1.49941i −0.147503 0.0851607i
311311 22.2686 1.26274 0.631368 0.775483i 0.282494π-0.282494\pi
0.631368 + 0.775483i 0.282494π0.282494\pi
312312 12.6341 22.9981i 0.715264 1.30201i
313313 −28.0840 −1.58740 −0.793700 0.608309i 0.791848π-0.791848\pi
−0.793700 + 0.608309i 0.791848π0.791848\pi
314314 4.64117 + 2.67958i 0.261916 + 0.151217i
315315 6.44617 11.1651i 0.363200 0.629082i
316316 5.23025 + 9.05906i 0.294225 + 0.509612i
317317 19.5155i 1.09610i 0.836446 + 0.548049i 0.184629π0.184629\pi
−0.836446 + 0.548049i 0.815371π0.815371\pi
318318 −0.757595 + 0.437398i −0.0424838 + 0.0245281i
319319 30.8712 17.8235i 1.72845 0.997924i
320320 12.6158i 0.705247i
321321 −5.22702 9.05346i −0.291744 0.505315i
322322 −1.12391 + 1.94667i −0.0626332 + 0.108484i
323323 −4.57550 2.64167i −0.254588 0.146986i
324324 −6.09102 −0.338390
325325 0.383007 + 18.0195i 0.0212454 + 0.999540i
326326 2.15168 0.119171
327327 25.9263 + 14.9686i 1.43373 + 0.827764i
328328 −5.10711 + 8.84577i −0.281993 + 0.488426i
329329 −0.228035 0.394969i −0.0125720 0.0217753i
330330 41.1700i 2.26633i
331331 13.5367 7.81539i 0.744042 0.429573i −0.0794953 0.996835i 0.525331π-0.525331\pi
0.823537 + 0.567263i 0.191998π0.191998\pi
332332 −7.09463 + 4.09609i −0.389368 + 0.224802i
333333 26.5200i 1.45329i
334334 −1.60027 2.77174i −0.0875627 0.151663i
335335 9.92767 17.1952i 0.542407 0.939476i
336336 −0.899778 0.519487i −0.0490869 0.0283403i
337337 21.7501 1.18480 0.592401 0.805643i 0.298180π-0.298180\pi
0.592401 + 0.805643i 0.298180π0.298180\pi
338338 −9.49095 4.95431i −0.516240 0.269479i
339339 −15.3610 −0.834295
340340 −9.77153 5.64160i −0.529936 0.305959i
341341 −3.42165 + 5.92647i −0.185293 + 0.320937i
342342 −3.28565 5.69092i −0.177668 0.307730i
343343 1.00000i 0.0539949i
344344 16.5633 9.56281i 0.893032 0.515592i
345345 19.8840 11.4800i 1.07052 0.618065i
346346 11.5106i 0.618816i
347347 7.97952 + 13.8209i 0.428363 + 0.741946i 0.996728 0.0808303i 0.0257572π-0.0257572\pi
−0.568365 + 0.822777i 0.692424π0.692424\pi
348348 10.5460 18.2663i 0.565327 0.979176i
349349 5.90375 + 3.40853i 0.316021 + 0.182455i 0.649617 0.760261i 0.274929π-0.274929\pi
−0.333597 + 0.942716i 0.608262π0.608262\pi
350350 −4.11682 −0.220053
351351 −0.219556 10.3295i −0.0117190 0.551349i
352352 −34.4257 −1.83490
353353 12.1272 + 7.00163i 0.645465 + 0.372659i 0.786716 0.617314i 0.211779π-0.211779\pi
−0.141252 + 0.989974i 0.545113π0.545113\pi
354354 −5.26458 + 9.11852i −0.279809 + 0.484644i
355355 7.12608 + 12.3427i 0.378213 + 0.655085i
356356 4.70725i 0.249484i
357357 6.21965 3.59092i 0.329179 0.190052i
358358 −18.0333 + 10.4115i −0.953088 + 0.550266i
359359 5.41494i 0.285789i −0.989738 0.142895i 0.954359π-0.954359\pi
0.989738 0.142895i 0.0456410π-0.0456410\pi
360360 −17.6345 30.5438i −0.929418 1.60980i
361361 −7.58498 + 13.1376i −0.399210 + 0.691451i
362362 −0.616561 0.355972i −0.0324057 0.0187094i
363363 −64.6867 −3.39517
364364 −2.29459 + 4.17688i −0.120269 + 0.218928i
365365 26.2636 1.37470
366366 −2.19531 1.26747i −0.114751 0.0662515i
367367 −15.0159 + 26.0083i −0.783822 + 1.35762i 0.145878 + 0.989303i 0.453399π0.453399\pi
−0.929700 + 0.368317i 0.879934π0.879934\pi
368368 −0.532985 0.923157i −0.0277838 0.0481229i
369369 15.2230i 0.792480i
370370 14.6695 8.46943i 0.762630 0.440305i
371371 0.345792 0.199643i 0.0179526 0.0103649i
372372 4.04914i 0.209938i
373373 −10.7049 18.5414i −0.554278 0.960037i −0.997959 0.0638526i 0.979661π-0.979661\pi
0.443682 0.896184i 0.353672π-0.353672\pi
374374 6.60622 11.4423i 0.341599 0.591668i
375375 −0.00853484 0.00492759i −0.000440737 0.000254460i
376376 −1.24765 −0.0643427
377377 −18.9557 10.4134i −0.976270 0.536317i
378378 2.35994 0.121382
379379 −8.20693 4.73827i −0.421562 0.243389i 0.274184 0.961677i 0.411592π-0.411592\pi
−0.695745 + 0.718289i 0.744926π0.744926\pi
380380 4.08975 7.08366i 0.209800 0.363384i
381381 8.15535 + 14.1255i 0.417811 + 0.723670i
382382 12.0796i 0.618048i
383383 −4.70304 + 2.71530i −0.240314 + 0.138746i −0.615321 0.788277i 0.710974π-0.710974\pi
0.375007 + 0.927022i 0.377640π0.377640\pi
384384 −19.1225 + 11.0404i −0.975842 + 0.563402i
385385 18.7914i 0.957696i
386386 6.79264 + 11.7652i 0.345736 + 0.598833i
387387 14.2522 24.6855i 0.724480 1.25484i
388388 3.92338 + 2.26516i 0.199179 + 0.114996i
389389 10.6422 0.539580 0.269790 0.962919i 0.413046π-0.413046\pi
0.269790 + 0.962919i 0.413046π0.413046\pi
390390 −21.3618 + 12.9462i −1.08170 + 0.655556i
391391 7.36845 0.372638
392392 −2.36914 1.36783i −0.119660 0.0690856i
393393 −13.5963 + 23.5495i −0.685845 + 1.18792i
394394 4.53375 + 7.85269i 0.228407 + 0.395613i
395395 25.0251i 1.25915i
396396 −27.7346 + 16.0126i −1.39372 + 0.804663i
397397 32.2035 18.5927i 1.61625 0.933140i 0.628367 0.777917i 0.283724π-0.283724\pi
0.987879 0.155223i 0.0496097π-0.0496097\pi
398398 17.4690i 0.875644i
399399 2.60316 + 4.50880i 0.130321 + 0.225723i
400400 0.976143 1.69073i 0.0488072 0.0845365i
401401 −0.776487 0.448305i −0.0387759 0.0223873i 0.480487 0.877002i 0.340460π-0.340460\pi
−0.519263 + 0.854615i 0.673793π0.673793\pi
402402 13.7571 0.686139
403403 4.15103 0.0882308i 0.206777 0.00439509i
404404 17.6183 0.876545
405405 12.6196 + 7.28590i 0.627071 + 0.362039i
406406 2.47003 4.27822i 0.122586 0.212324i
407407 −19.3273 33.4758i −0.958016 1.65933i
408408 19.6470i 0.972672i
409409 21.2846 12.2886i 1.05245 0.607635i 0.129119 0.991629i 0.458785π-0.458785\pi
0.923335 + 0.383995i 0.125452π0.125452\pi
410410 8.42059 4.86163i 0.415863 0.240099i
411411 53.0662i 2.61756i
412412 7.69589 + 13.3297i 0.379149 + 0.656706i
413413 2.40293 4.16200i 0.118241 0.204799i
414414 7.93689 + 4.58237i 0.390077 + 0.225211i
415415 19.5985 0.962052
416416 10.8254 + 17.8624i 0.530759 + 0.875778i
417417 −54.0770 −2.64816
418418 8.29486 + 4.78904i 0.405715 + 0.234239i
419419 3.82279 6.62126i 0.186755 0.323470i −0.757411 0.652938i 0.773536π-0.773536\pi
0.944167 + 0.329468i 0.106869π0.106869\pi
420420 5.55936 + 9.62910i 0.271269 + 0.469852i
421421 25.0780i 1.22223i −0.791544 0.611113i 0.790722π-0.790722\pi
0.791544 0.611113i 0.209278π-0.209278\pi
422422 12.7922 7.38555i 0.622712 0.359523i
423423 −1.61035 + 0.929736i −0.0782979 + 0.0452053i
424424 1.09231i 0.0530471i
425425 6.74753 + 11.6871i 0.327303 + 0.566906i
426426 −4.93741 + 8.55184i −0.239218 + 0.414338i
427427 1.00201 + 0.578514i 0.0484909 + 0.0279962i
428428 5.19405 0.251064
429429 29.5432 + 48.7478i 1.42636 + 2.35356i
430430 −18.2063 −0.877987
431431 6.71520 + 3.87702i 0.323460 + 0.186750i 0.652934 0.757415i 0.273538π-0.273538\pi
−0.329474 + 0.944165i 0.606871π0.606871\pi
432432 −0.559567 + 0.969199i −0.0269222 + 0.0466306i
433433 17.9880 + 31.1561i 0.864448 + 1.49727i 0.867594 + 0.497273i 0.165665π0.165665\pi
−0.00314644 + 0.999995i 0.501002π0.501002\pi
434434 0.948365i 0.0455230i
435435 −43.6992 + 25.2298i −2.09522 + 1.20967i
436436 −12.8814 + 7.43707i −0.616907 + 0.356171i
437437 5.34160i 0.255523i
438438 9.09853 + 15.7591i 0.434745 + 0.753000i
439439 −14.1175 + 24.4523i −0.673792 + 1.16704i 0.303028 + 0.952982i 0.402002π0.402002\pi
−0.976820 + 0.214061i 0.931331π0.931331\pi
440440 44.5194 + 25.7033i 2.12238 + 1.22536i
441441 −4.07715 −0.194150
442442 −8.01444 + 0.170348i −0.381208 + 0.00810264i
443443 28.7918 1.36794 0.683970 0.729511i 0.260252π-0.260252\pi
0.683970 + 0.729511i 0.260252π0.260252\pi
444444 −19.8074 11.4358i −0.940018 0.542720i
445445 −5.63068 + 9.75262i −0.266920 + 0.462319i
446446 −6.60128 11.4337i −0.312579 0.541404i
447447 28.5081i 1.34839i
448448 −3.45519 + 1.99486i −0.163243 + 0.0942481i
449449 −25.2795 + 14.5951i −1.19301 + 0.688785i −0.958988 0.283446i 0.908522π-0.908522\pi
−0.234023 + 0.972231i 0.575189π0.575189\pi
450450 16.7849i 0.791247i
451451 −11.0942 19.2158i −0.522408 0.904836i
452452 3.81603 6.60955i 0.179491 0.310887i
453453 −20.1455 11.6310i −0.946518 0.546473i
454454 −13.4858 −0.632918
455455 9.75026 5.90907i 0.457099 0.277022i
456456 14.2427 0.666974
457457 −27.4399 15.8424i −1.28358 0.741077i −0.306081 0.952006i 0.599018π-0.599018\pi
−0.977501 + 0.210929i 0.932351π0.932351\pi
458458 11.1223 19.2644i 0.519711 0.900165i
459459 −3.86797 6.69952i −0.180541 0.312707i
460460 11.4076i 0.531883i
461461 −19.1407 + 11.0509i −0.891471 + 0.514691i −0.874424 0.485163i 0.838760π-0.838760\pi
−0.0170480 + 0.999855i 0.505427π0.505427\pi
462462 −11.2755 + 6.50993i −0.524585 + 0.302869i
463463 38.8811i 1.80696i 0.428632 + 0.903479i 0.358996π0.358996\pi
−0.428632 + 0.903479i 0.641004π0.641004\pi
464464 1.17134 + 2.02883i 0.0543783 + 0.0941860i
465465 4.84346 8.38913i 0.224610 0.389036i
466466 −8.25062 4.76350i −0.382202 0.220665i
467467 −13.2823 −0.614632 −0.307316 0.951607i 0.599431π-0.599431\pi
−0.307316 + 0.951607i 0.599431π0.599431\pi
468468 17.0298 + 9.35538i 0.787203 + 0.432453i
469469 −6.27918 −0.289946
470470 1.02856 + 0.593841i 0.0474440 + 0.0273918i
471471 −8.65571 + 14.9921i −0.398834 + 0.690801i
472472 −6.57358 11.3858i −0.302574 0.524073i
473473 41.5469i 1.91033i
474474 15.0160 8.66949i 0.689708 0.398203i
475475 −8.47228 + 4.89147i −0.388735 + 0.224436i
476476 3.56827i 0.163551i
477477 −0.813975 1.40985i −0.0372694 0.0645524i
478478 −6.04205 + 10.4651i −0.276357 + 0.478664i
479479 5.74618 + 3.31756i 0.262550 + 0.151583i 0.625497 0.780226i 0.284896π-0.284896\pi
−0.362947 + 0.931810i 0.618230π0.618230\pi
480480 48.7307 2.22424
481481 −11.2920 + 20.5550i −0.514870 + 0.937228i
482482 11.8153 0.538172
483483 −6.28825 3.63052i −0.286125 0.165194i
484484 16.0697 27.8335i 0.730439 1.26516i
485485 −5.41905 9.38607i −0.246066 0.426200i
486486 17.1761i 0.779123i
487487 28.9860 16.7351i 1.31348 0.758338i 0.330809 0.943698i 0.392678π-0.392678\pi
0.982671 + 0.185359i 0.0593449π0.0593449\pi
488488 2.74116 1.58261i 0.124087 0.0716415i
489489 6.95047i 0.314311i
490490 1.30208 + 2.25527i 0.0588220 + 0.101883i
491491 −18.6643 + 32.3276i −0.842310 + 1.45892i 0.0456264 + 0.998959i 0.485472π0.485472\pi
−0.887937 + 0.459966i 0.847862π0.847862\pi
492492 −11.3699 6.56439i −0.512593 0.295946i
493493 −16.1937 −0.729327
494494 −0.123490 5.80989i −0.00555609 0.261399i
495495 76.6152 3.44360
496496 −0.389483 0.224868i −0.0174883 0.0100969i
497497 2.25360 3.90335i 0.101088 0.175089i
498498 6.78954 + 11.7598i 0.304246 + 0.526970i
499499 34.1327i 1.52799i 0.645223 + 0.763994i 0.276764π0.276764\pi
−0.645223 + 0.763994i 0.723236π0.723236\pi
500500 0.00424050 0.00244826i 0.000189641 0.000109489i
501501 8.95342 5.16926i 0.400009 0.230946i
502502 7.09454i 0.316645i
503503 −7.65447 13.2579i −0.341296 0.591142i 0.643378 0.765549i 0.277533π-0.277533\pi
−0.984674 + 0.174407i 0.944199π0.944199\pi
504504 −5.57684 + 9.65936i −0.248412 + 0.430262i
505505 −36.5022 21.0745i −1.62433 0.937805i
506506 −13.3581 −0.593842
507507 16.0037 30.6581i 0.710747 1.36158i
508508 −8.10390 −0.359553
509509 −16.0189 9.24851i −0.710025 0.409933i 0.101046 0.994882i 0.467781π-0.467781\pi
−0.811070 + 0.584949i 0.801115π0.801115\pi
510510 −9.35133 + 16.1970i −0.414084 + 0.717214i
511511 −4.15288 7.19299i −0.183712 0.318199i
512512 4.39924i 0.194421i
513513 4.85668 2.80400i 0.214427 0.123800i
514514 7.39178 4.26765i 0.326037 0.188238i
515515 36.8224i 1.62259i
516516 12.2915 + 21.2895i 0.541104 + 0.937219i
517517 1.35515 2.34718i 0.0595992 0.103229i
518518 −4.63917 2.67843i −0.203833 0.117683i
519519 −37.1823 −1.63212
520520 −0.662786 31.1824i −0.0290651 1.36744i
521521 23.5865 1.03334 0.516671 0.856184i 0.327171π-0.327171\pi
0.516671 + 0.856184i 0.327171π0.327171\pi
522522 −17.4430 10.0707i −0.763457 0.440782i
523523 −6.15294 + 10.6572i −0.269049 + 0.466007i −0.968617 0.248560i 0.920043π-0.920043\pi
0.699567 + 0.714567i 0.253376π0.253376\pi
524524 −6.75529 11.7005i −0.295106 0.511139i
525525 13.2983i 0.580387i
526526 15.7498 9.09312i 0.686722 0.396479i
527527 2.69227 1.55438i 0.117277 0.0677101i
528528 6.17431i 0.268702i
529529 7.77515 + 13.4670i 0.338050 + 0.585520i
530530 −0.519902 + 0.900497i −0.0225831 + 0.0391151i
531531 −16.9691 9.79712i −0.736397 0.425159i
532532 −2.58674 −0.112149
533533 −6.48183 + 11.7990i −0.280759 + 0.511072i
534534 −7.80259 −0.337651
535535 −10.7612 6.21297i −0.465246 0.268610i
536536 −8.58883 + 14.8763i −0.370981 + 0.642558i
537537 −33.6318 58.2520i −1.45132 2.51376i
538538 10.6567i 0.459444i
539539 5.14653 2.97135i 0.221677 0.127985i
540540 10.3720 5.98829i 0.446341 0.257695i
541541 19.4411i 0.835838i −0.908484 0.417919i 0.862760π-0.862760\pi
0.908484 0.417919i 0.137240π-0.137240\pi
542542 −7.27813 12.6061i −0.312623 0.541478i
543543 1.14988 1.99165i 0.0493460 0.0854697i
544544 13.5437 + 7.81944i 0.580680 + 0.335256i
545545 35.5841 1.52425
546546 6.92347 + 3.80343i 0.296297 + 0.162772i
547547 40.2163 1.71953 0.859763 0.510693i 0.170611π-0.170611\pi
0.859763 + 0.510693i 0.170611π0.170611\pi
548548 22.8334 + 13.1829i 0.975395 + 0.563145i
549549 2.35869 4.08537i 0.100666 0.174359i
550550 −12.2325 21.1873i −0.521595 0.903429i
551551 11.7393i 0.500109i
552552 −17.2024 + 9.93184i −0.732185 + 0.422727i
553553 −6.85381 + 3.95705i −0.291454 + 0.168271i
554554 14.8364i 0.630337i
555555 27.3584 + 47.3861i 1.16130 + 2.01143i
556556 13.4340 23.2683i 0.569727 0.986797i
557557 6.89702 + 3.98199i 0.292236 + 0.168722i 0.638950 0.769248i 0.279369π-0.279369\pi
−0.346714 + 0.937971i 0.612703π0.612703\pi
558558 3.86663 0.163687
559559 21.5574 13.0647i 0.911781 0.552578i
560560 −1.23495 −0.0521862
561561 36.9615 + 21.3397i 1.56052 + 0.900965i
562562 1.00547 1.74153i 0.0424133 0.0734620i
563563 −0.711981 1.23319i −0.0300064 0.0519726i 0.850632 0.525761i 0.176219π-0.176219\pi
−0.880639 + 0.473789i 0.842886π0.842886\pi
564564 1.60366i 0.0675263i
565565 −15.8123 + 9.12924i −0.665229 + 0.384070i
566566 −20.4865 + 11.8279i −0.861113 + 0.497164i
567567 4.60828i 0.193530i
568568 −6.16506 10.6782i −0.258680 0.448047i
569569 −9.25946 + 16.0379i −0.388177 + 0.672342i −0.992204 0.124622i 0.960228π-0.960228\pi
0.604028 + 0.796963i 0.293562π0.293562\pi
570570 −11.7417 6.77904i −0.491804 0.283943i
571571 −4.35766 −0.182362 −0.0911812 0.995834i 0.529064π-0.529064\pi
−0.0911812 + 0.995834i 0.529064π0.529064\pi
572572 −28.3145 + 0.601828i −1.18389 + 0.0251637i
573573 39.0202 1.63009
574574 −2.66298 1.53747i −0.111151 0.0641729i
575575 6.82194 11.8159i 0.284494 0.492759i
576576 8.13334 + 14.0874i 0.338889 + 0.586973i
577577 9.56416i 0.398161i −0.979983 0.199081i 0.936204π-0.936204\pi
0.979983 0.199081i 0.0637955π-0.0637955\pi
578578 6.92674 3.99916i 0.288115 0.166343i
579579 −38.0046 + 21.9419i −1.57942 + 0.911876i
580580 25.0706i 1.04100i
581581 −3.09897 5.36758i −0.128567 0.222685i
582582 3.75466 6.50327i 0.155636 0.269569i
583583 2.05494 + 1.18642i 0.0851068 + 0.0491364i
584584 −22.7216 −0.940228
585585 −24.0922 39.7533i −0.996090 1.64360i
586586 24.1556 0.997859
587587 −2.04428 1.18027i −0.0843765 0.0487148i 0.457218 0.889355i 0.348846π-0.348846\pi
−0.541595 + 0.840640i 0.682179π0.682179\pi
588588 1.75813 3.04517i 0.0725040 0.125581i
589589 1.12682 + 1.95171i 0.0464297 + 0.0804186i
590590 12.5152i 0.515244i
591591 −25.3661 + 14.6452i −1.04342 + 0.602421i
592592 2.20000 1.27017i 0.0904194 0.0522037i
593593 40.4292i 1.66023i −0.557594 0.830114i 0.688275π-0.688275\pi
0.557594 0.830114i 0.311725π-0.311725\pi
594594 7.01219 + 12.1455i 0.287714 + 0.498335i
595595 4.26826 7.39284i 0.174982 0.303077i
596596 12.2665 + 7.08207i 0.502455 + 0.290093i
597597 56.4294 2.30950
598598 4.20056 + 6.93114i 0.171774 + 0.283435i
599599 −38.5873 −1.57663 −0.788316 0.615270i 0.789047π-0.789047\pi
−0.788316 + 0.615270i 0.789047π0.789047\pi
600600 −31.5057 18.1898i −1.28621 0.742596i
601601 −4.08115 + 7.06877i −0.166474 + 0.288341i −0.937178 0.348852i 0.886571π-0.886571\pi
0.770704 + 0.637193i 0.219905π0.219905\pi
602602 2.87884 + 4.98630i 0.117333 + 0.203226i
603603 25.6012i 1.04256i
604604 10.0092 5.77882i 0.407269 0.235137i
605605 −66.5872 + 38.4442i −2.70716 + 1.56298i
606606 29.2036i 1.18631i
607607 −3.79263 6.56902i −0.153938 0.266628i 0.778734 0.627354i 0.215862π-0.215862\pi
−0.932672 + 0.360726i 0.882529π0.882529\pi
608608 −5.66853 + 9.81819i −0.229889 + 0.398180i
609609 13.8197 + 7.97882i 0.560003 + 0.323318i
610610 −3.01308 −0.121996
611611 −1.64402 + 0.0349438i −0.0665098 + 0.00141368i
612612 14.5484 0.588083
613613 −13.4908 7.78892i −0.544889 0.314592i 0.202169 0.979351i 0.435201π-0.435201\pi
−0.747058 + 0.664759i 0.768534π0.768534\pi
614614 −2.91090 + 5.04183i −0.117474 + 0.203472i
615615 15.7043 + 27.2006i 0.633258 + 1.09683i
616616 16.2571i 0.655019i
617617 20.6709 11.9343i 0.832177 0.480458i −0.0224202 0.999749i 0.507137π-0.507137\pi
0.854598 + 0.519291i 0.173804π0.173804\pi
618618 22.0948 12.7565i 0.888785 0.513140i
619619 19.4963i 0.783622i 0.920046 + 0.391811i 0.128151π0.128151\pi
−0.920046 + 0.391811i 0.871849π0.871849\pi
620620 2.40646 + 4.16810i 0.0966456 + 0.167395i
621621 −3.91063 + 6.77341i −0.156928 + 0.271807i
622622 15.8824 + 9.16972i 0.636827 + 0.367672i
623623 3.56136 0.142683
624624 −3.20366 + 1.94155i −0.128249 + 0.0777244i
625625 −25.0059 −1.00023
626626 −20.0301 11.5644i −0.800562 0.462205i
627627 −15.4698 + 26.7945i −0.617804 + 1.07007i
628628 −4.30055 7.44878i −0.171611 0.297239i
629629 17.5599i 0.700161i
630630 9.19508 5.30878i 0.366341 0.211507i
631631 −22.2239 + 12.8309i −0.884718 + 0.510792i −0.872211 0.489130i 0.837314π-0.837314\pi
−0.0125066 + 0.999922i 0.503981π0.503981\pi
632632 21.6502i 0.861199i
633633 23.8572 + 41.3219i 0.948238 + 1.64240i
634634 −8.03604 + 13.9188i −0.319152 + 0.552788i
635635 16.7899 + 9.69366i 0.666287 + 0.384681i
636636 1.40399 0.0556719
637637 −3.16010 1.73601i −0.125208 0.0687834i
638638 29.3573 1.16227
639639 −15.9145 9.18826i −0.629569 0.363482i
640640 −13.1229 + 22.7295i −0.518728 + 0.898463i
641641 −0.553020 0.957859i −0.0218430 0.0378332i 0.854897 0.518797i 0.173620π-0.173620\pi
−0.876740 + 0.480964i 0.840287π0.840287\pi
642642 8.60949i 0.339789i
643643 10.9437 6.31833i 0.431576 0.249171i −0.268442 0.963296i 0.586509π-0.586509\pi
0.700018 + 0.714125i 0.253175π0.253175\pi
644644 3.12429 1.80381i 0.123114 0.0710801i
645645 58.8110i 2.31568i
646646 −2.17556 3.76818i −0.0855962 0.148257i
647647 12.8574 22.2697i 0.505477 0.875512i −0.494503 0.869176i 0.664650π-0.664650\pi
0.999980 0.00633579i 0.00201676π-0.00201676\pi
648648 −10.9177 6.30332i −0.428887 0.247618i
649649 28.5598 1.12107
650650 −7.14685 + 13.0096i −0.280323 + 0.510277i
651651 −3.06345 −0.120066
652652 −2.99066 1.72666i −0.117123 0.0676211i
653653 −12.6303 + 21.8764i −0.494263 + 0.856089i −0.999978 0.00661158i 0.997895π-0.997895\pi
0.505715 + 0.862701i 0.331229π0.331229\pi
654654 12.3275 + 21.3518i 0.482041 + 0.834920i
655655 32.3219i 1.26292i
656656 1.26285 0.729104i 0.0493058 0.0284667i
657657 −29.3269 + 16.9319i −1.14415 + 0.660577i
658658 0.375600i 0.0146424i
659659 −11.4882 19.8982i −0.447517 0.775123i 0.550707 0.834699i 0.314358π-0.314358\pi
−0.998224 + 0.0595764i 0.981025π0.981025\pi
660660 −33.0376 + 57.2228i −1.28599 + 2.22739i
661661 26.3554 + 15.2163i 1.02511 + 0.591845i 0.915579 0.402138i 0.131733π-0.131733\pi
0.109528 + 0.993984i 0.465066π0.465066\pi
662662 12.8728 0.500316
663663 −0.550267 25.8886i −0.0213706 1.00543i
664664 −16.9554 −0.657998
665665 5.35928 + 3.09418i 0.207824 + 0.119987i
666666 −10.9204 + 18.9146i −0.423155 + 0.732926i
667667 8.18613 + 14.1788i 0.316968 + 0.549005i
668668 5.13665i 0.198743i
669669 36.9339 21.3238i 1.42795 0.824425i
670670 14.1612 8.17600i 0.547096 0.315866i
671671 6.87586i 0.265440i
672672 −7.70546 13.3462i −0.297245 0.514843i
673673 5.41933 9.38656i 0.208900 0.361825i −0.742468 0.669881i 0.766345π-0.766345\pi
0.951368 + 0.308056i 0.0996784π0.0996784\pi
674674 15.5126 + 8.95620i 0.597523 + 0.344980i
675675 −14.3244 −0.551345
676676 9.21595 + 14.5023i 0.354460 + 0.557779i
677677 −18.1209 −0.696442 −0.348221 0.937412i 0.613214π-0.613214\pi
−0.348221 + 0.937412i 0.613214π0.613214\pi
678678 −10.9558 6.32532i −0.420754 0.242923i
679679 −1.71375 + 2.96831i −0.0657679 + 0.113913i
680680 −11.6765 20.2242i −0.447772 0.775564i
681681 43.5624i 1.66931i
682682 −4.88078 + 2.81792i −0.186895 + 0.107904i
683683 32.7662 18.9176i 1.25376 0.723861i 0.281909 0.959441i 0.409032π-0.409032\pi
0.971855 + 0.235580i 0.0756990π0.0756990\pi
684684 10.5465i 0.403257i
685685 −31.5380 54.6254i −1.20500 2.08713i
686686 0.411778 0.713220i 0.0157218 0.0272309i
687687 62.2288 + 35.9278i 2.37418 + 1.37073i
688688 −2.73042 −0.104096
689689 −0.0305930 1.43932i −0.00116550 0.0548338i
690690 18.9089 0.719850
691691 26.0034 + 15.0131i 0.989216 + 0.571124i 0.905040 0.425327i 0.139841π-0.139841\pi
0.0841761 + 0.996451i 0.473174π0.473174\pi
692692 9.23693 15.9988i 0.351135 0.608184i
693693 −12.1146 20.9832i −0.460197 0.797085i
694694 13.1432i 0.498907i
695695 −55.6658 + 32.1387i −2.11152 + 1.21909i
696696 37.8059 21.8273i 1.43303 0.827360i
697697 10.0798i 0.381798i
698698 2.80712 + 4.86207i 0.106251 + 0.184032i
699699 15.3873 26.6516i 0.582001 1.00805i
700700 5.72203 + 3.30361i 0.216272 + 0.124865i
701701 0.116177 0.00438796 0.00219398 0.999998i 0.499302π-0.499302\pi
0.00219398 + 0.999998i 0.499302π0.499302\pi
702702 4.09688 7.45764i 0.154627 0.281470i
703703 −12.7297 −0.480110
704704 −20.5332 11.8548i −0.773873 0.446796i
705705 −1.91825 + 3.32251i −0.0722456 + 0.125133i
706706 5.76624 + 9.98741i 0.217015 + 0.375881i
707707 13.3295i 0.501307i
708708 14.6347 8.44932i 0.550004 0.317545i
709709 5.82829 3.36497i 0.218886 0.126374i −0.386548 0.922269i 0.626333π-0.626333\pi
0.605434 + 0.795895i 0.292999π0.292999\pi
710710 11.7375i 0.440499i
711711 16.1335 + 27.9440i 0.605053 + 1.04798i
712712 4.87132 8.43738i 0.182561 0.316204i
713713 −2.72196 1.57153i −0.101938 0.0588541i
714714 5.91465 0.221350
715715 59.3826 + 32.6221i 2.22078 + 1.22000i
716716 33.4197 1.24895
717717 −33.8050 19.5173i −1.26247 0.728888i
718718 2.22975 3.86204i 0.0832136 0.144130i
719719 23.4039 + 40.5367i 0.872818 + 1.51177i 0.859069 + 0.511860i 0.171043π0.171043\pi
0.0137492 + 0.999905i 0.495623π0.495623\pi
720720 5.03509i 0.187647i
721721 −10.0848 + 5.82248i −0.375579 + 0.216840i
722722 −10.8195 + 6.24666i −0.402661 + 0.232476i
723723 38.1664i 1.41942i
724724 0.571312 + 0.989541i 0.0212326 + 0.0367760i
725725 −14.9926 + 25.9680i −0.556812 + 0.964426i
726726 −46.1359 26.6366i −1.71226 0.988576i
727727 13.3362 0.494611 0.247305 0.968938i 0.420455π-0.420455\pi
0.247305 + 0.968938i 0.420455π0.420455\pi
728728 −8.43534 + 5.11217i −0.312634 + 0.189470i
729729 −41.6582 −1.54290
730730 18.7317 + 10.8148i 0.693291 + 0.400272i
731731 9.43694 16.3453i 0.349038 0.604551i
732732 2.03420 + 3.52334i 0.0751863 + 0.130226i
733733 29.4612i 1.08817i −0.839029 0.544087i 0.816876π-0.816876\pi
0.839029 0.544087i 0.183124π-0.183124\pi
734734 −21.4193 + 12.3664i −0.790599 + 0.456453i
735735 −7.28508 + 4.20604i −0.268714 + 0.155142i
736736 15.8113i 0.582814i
737737 −18.6576 32.3160i −0.687263 1.19037i
738738 −6.26851 + 10.8574i −0.230747 + 0.399666i
739739 −10.4184 6.01509i −0.383249 0.221269i 0.295982 0.955193i 0.404353π-0.404353\pi
−0.679231 + 0.733925i 0.737686π0.737686\pi
740740 −27.1858 −0.999370
741741 18.7674 0.398904i 0.689438 0.0146541i
742742 0.328834 0.0120719
743743 −18.9509 10.9413i −0.695242 0.401398i 0.110331 0.993895i 0.464809π-0.464809\pi
−0.805573 + 0.592497i 0.798142π0.798142\pi
744744 −4.19027 + 7.25777i −0.153623 + 0.266083i
745745 −16.9427 29.3457i −0.620734 1.07514i
746746 17.6321i 0.645558i
747747 −21.8844 + 12.6350i −0.800710 + 0.462290i
748748 −18.3642 + 10.6026i −0.671461 + 0.387668i
749749 3.92966i 0.143587i
750750 −0.00405815 0.00702892i −0.000148183 0.000256660i
751751 17.3746 30.0937i 0.634008 1.09813i −0.352717 0.935730i 0.614742π-0.614742\pi
0.986724 0.162403i 0.0519245π-0.0519245\pi
752752 0.154255 + 0.0890590i 0.00562509 + 0.00324765i
753753 −22.9172 −0.835147
754754 −9.23160 15.2326i −0.336195 0.554739i
755755 −27.6498 −1.00628
756756 −3.28011 1.89377i −0.119297 0.0688759i
757757 −21.9632 + 38.0413i −0.798265 + 1.38264i 0.122481 + 0.992471i 0.460915π0.460915\pi
−0.920745 + 0.390164i 0.872418π0.872418\pi
758758 −3.90223 6.75887i −0.141736 0.245493i
759759 43.1502i 1.56625i
760760 14.6611 8.46461i 0.531815 0.307044i
761761 0.122449 0.0706957i 0.00443876 0.00256272i −0.497779 0.867304i 0.665851π-0.665851\pi
0.502218 + 0.864741i 0.332518π0.332518\pi
762762 13.4328i 0.486618i
763763 −5.62666 9.74566i −0.203699 0.352817i
764764 −9.69352 + 16.7897i −0.350699 + 0.607429i
765765 −30.1418 17.4024i −1.08978 0.629183i
766766 −4.47241 −0.161595
767767 −8.98082 14.8188i −0.324279 0.535076i
768768 −39.4124 −1.42217
769769 11.8200 + 6.82429i 0.426241 + 0.246090i 0.697744 0.716347i 0.254187π-0.254187\pi
−0.271503 + 0.962438i 0.587521π0.587521\pi
770770 −7.73787 + 13.4024i −0.278853 + 0.482988i
771771 13.7856 + 23.8773i 0.496475 + 0.859920i
772772 21.8035i 0.784726i
773773 15.2328 8.79469i 0.547887 0.316323i −0.200382 0.979718i 0.564218π-0.564218\pi
0.748269 + 0.663395i 0.230885π0.230885\pi
774774 20.3299 11.7375i 0.730744 0.421895i
775775 5.75639i 0.206776i
776776 4.68824 + 8.12026i 0.168298 + 0.291500i
777777 8.65199 14.9857i 0.310388 0.537608i
778778 7.59022 + 4.38221i 0.272123 + 0.157110i
779779 −7.30711 −0.261804
780780 40.0801 0.851909i 1.43510 0.0305032i
781781 26.7849 0.958439
782782 5.25533 + 3.03416i 0.187930 + 0.108501i
783783 8.59441 14.8860i 0.307139 0.531981i
784784 0.195274 + 0.338225i 0.00697409 + 0.0120795i
785785 20.5768i 0.734418i
786786 −19.3944 + 11.1973i −0.691774 + 0.399396i
787787 2.57075 1.48422i 0.0916374 0.0529069i −0.453481 0.891266i 0.649818π-0.649818\pi
0.545118 + 0.838359i 0.316485π0.316485\pi
788788 14.5528i 0.518421i
789789 29.3731 + 50.8756i 1.04571 + 1.81122i
790790 10.3048 17.8484i 0.366628 0.635018i
791791 5.00059 + 2.88709i 0.177800 + 0.102653i
792792 −66.2829 −2.35526
793793 3.56768 2.16216i 0.126692 0.0767807i
794794 30.6242 1.08681
795795 −2.90883 1.67941i −0.103166 0.0595627i
796796 −14.0184 + 24.2805i −0.496867 + 0.860600i
797797 4.72611 + 8.18586i 0.167407 + 0.289958i 0.937508 0.347965i 0.113127π-0.113127\pi
−0.770100 + 0.637923i 0.779794π0.779794\pi
798798 4.28770i 0.151783i
799799 −1.06628 + 0.615614i −0.0377221 + 0.0217789i
800800 25.0783 14.4790i 0.886652 0.511909i
801801 14.5202i 0.513047i
802802 −0.369204 0.639481i −0.0130371 0.0225809i
803803 24.6793 42.7458i 0.870913 1.50847i
804804 −19.1212 11.0396i −0.674351 0.389337i
805805 −8.63066 −0.304191
806806 2.99693 + 1.64637i 0.105562 + 0.0579911i
807807 34.4239 1.21178
808808 31.5795 + 18.2324i 1.11096 + 0.641414i
809809 0.581273 1.00679i 0.0204365 0.0353970i −0.855626 0.517594i 0.826828π-0.826828\pi
0.876063 + 0.482197i 0.160161π0.160161\pi
810810 6.00035 + 10.3929i 0.210831 + 0.365170i
811811 19.5561i 0.686706i −0.939206 0.343353i 0.888437π-0.888437\pi
0.939206 0.343353i 0.111563π-0.111563\pi
812812 −6.86627 + 3.96424i −0.240959 + 0.139118i
813813 40.7209 23.5102i 1.42814 0.824538i
814814 31.8342i 1.11579i
815815 4.13075 + 7.15467i 0.144694 + 0.250617i
816816 −1.40243 + 2.42908i −0.0490949 + 0.0850348i
817817 11.8491 + 6.84111i 0.414549 + 0.239340i
818818 20.2408 0.707702
819819 −7.07800 + 12.8842i −0.247325 + 0.450211i
820820 −15.6052 −0.544958
821821 10.9283 + 6.30945i 0.381400 + 0.220201i 0.678427 0.734668i 0.262662π-0.262662\pi
−0.297027 + 0.954869i 0.595995π0.595995\pi
822822 21.8515 37.8479i 0.762159 1.32010i
823823 −3.28404 5.68812i −0.114474 0.198275i 0.803095 0.595851i 0.203185π-0.203185\pi
−0.917570 + 0.397575i 0.869852π0.869852\pi
824824 31.8565i 1.10978i
825825 68.4403 39.5140i 2.38278 1.37570i
826826 3.42764 1.97895i 0.119263 0.0688564i
827827 17.3050i 0.601754i 0.953663 + 0.300877i 0.0972794π0.0972794\pi
−0.953663 + 0.300877i 0.902721π0.902721\pi
828828 −7.35441 12.7382i −0.255583 0.442683i
829829 −1.87837 + 3.25343i −0.0652385 + 0.112996i −0.896800 0.442437i 0.854114π-0.854114\pi
0.831561 + 0.555433i 0.187447π0.187447\pi
830830 13.9780 + 8.07022i 0.485185 + 0.280122i
831831 47.9252 1.66251
832832 0.305689 + 14.3819i 0.0105979 + 0.498602i
833833 −2.69964 −0.0935371
834834 −38.5688 22.2677i −1.33553 0.771068i
835835 6.14432 10.6423i 0.212633 0.368291i
836836 −7.68610 13.3127i −0.265829 0.460430i
837837 3.29981i 0.114058i
838838 5.45298 3.14828i 0.188370 0.108756i
839839 −40.1340 + 23.1714i −1.38558 + 0.799965i −0.992813 0.119674i 0.961815π-0.961815\pi
−0.392766 + 0.919638i 0.628482π0.628482\pi
840840 23.0125i 0.794008i
841841 −3.49071 6.04609i −0.120369 0.208486i
842842 10.3266 17.8861i 0.355877 0.616396i
843843 5.62558 + 3.24793i 0.193755 + 0.111865i
844844 −23.7067 −0.816018
845845 −1.74669 41.0701i −0.0600880 1.41285i
846846 −1.53138 −0.0526499
847847 21.0580 + 12.1578i 0.723560 + 0.417748i
848848 −0.0779704 + 0.135049i −0.00267751 + 0.00463759i
849849 −38.2071 66.1766i −1.31126 2.27118i
850850 11.1139i 0.381205i
851851 15.3751 8.87679i 0.527050 0.304293i
852852 13.7252 7.92423i 0.470216 0.271479i
853853 15.3103i 0.524215i 0.965039 + 0.262107i 0.0844174π0.0844174\pi
−0.965039 + 0.262107i 0.915583π0.915583\pi
854854 0.476438 + 0.825215i 0.0163034 + 0.0282383i
855855 12.6155 21.8506i 0.431440 0.747275i
856856 9.30993 + 5.37509i 0.318207 + 0.183717i
857857 −2.59248 −0.0885574 −0.0442787 0.999019i 0.514099π-0.514099\pi
−0.0442787 + 0.999019i 0.514099π0.514099\pi
858858 0.997571 + 46.9331i 0.0340565 + 1.60227i
859859 −13.7738 −0.469955 −0.234978 0.972001i 0.575502π-0.575502\pi
−0.234978 + 0.972001i 0.575502π0.575502\pi
860860 25.3053 + 14.6100i 0.862903 + 0.498197i
861861 4.96642 8.60209i 0.169255 0.293159i
862862 3.19294 + 5.53034i 0.108752 + 0.188364i
863863 29.7592i 1.01302i −0.862235 0.506508i 0.830936π-0.830936\pi
0.862235 0.506508i 0.169064π-0.169064\pi
864864 −14.3760 + 8.29996i −0.489080 + 0.282370i
865865 −38.2747 + 22.0979i −1.30138 + 0.751351i
866866 29.6282i 1.00681i
867867 12.9183 + 22.3751i 0.438728 + 0.759899i
868868 0.761033 1.31815i 0.0258311 0.0447408i
869869 −40.7301 23.5155i −1.38167 0.797710i
870870 −41.5562 −1.40889
871871 −10.9007 + 19.8429i −0.369358 + 0.672350i
872872 −30.7852 −1.04252
873873 12.1023 + 6.98724i 0.409599 + 0.236482i
874874 −2.19955 + 3.80974i −0.0744009 + 0.128866i
875875 0.00185228 + 0.00320824i 6.26183e−5 + 0.000108458i
876876 29.2051i 0.986750i
877877 −1.24995 + 0.721660i −0.0422079 + 0.0243687i −0.520955 0.853584i 0.674424π-0.674424\pi
0.478748 + 0.877953i 0.341091π0.341091\pi
878878 −20.1378 + 11.6266i −0.679618 + 0.392378i
879879 78.0286i 2.63184i
880880 −3.66947 6.35571i −0.123698 0.214251i
881881 −17.9402 + 31.0733i −0.604420 + 1.04689i 0.387723 + 0.921776i 0.373262π0.373262\pi
−0.992143 + 0.125110i 0.960072π0.960072\pi
882882 −2.90791 1.67888i −0.0979144 0.0565309i
883883 10.5626 0.355458 0.177729 0.984079i 0.443125π-0.443125\pi
0.177729 + 0.984079i 0.443125π0.443125\pi
884884 11.2761 + 6.19456i 0.379256 + 0.208346i
885885 −40.4273 −1.35895
886886 20.5349 + 11.8558i 0.689883 + 0.398304i
887887 −6.11401 + 10.5898i −0.205288 + 0.355570i −0.950225 0.311566i 0.899147π-0.899147\pi
0.744936 + 0.667136i 0.232480π0.232480\pi
888888 −23.6688 40.9956i −0.794274 1.37572i
889889 6.13117i 0.205633i
890890 −8.03183 + 4.63718i −0.269228 + 0.155439i
891891 23.7166 13.6928i 0.794537 0.458726i
892892 21.1893i 0.709469i
893893 −0.446276 0.772973i −0.0149341 0.0258666i
894894 11.7390 20.3326i 0.392611 0.680022i
895895 −69.2399 39.9757i −2.31443 1.33624i
896896 8.30013 0.277288
897897 −22.3893 + 13.5689i −0.747557 + 0.453051i
898898 −24.0398 −0.802217
899899 5.98208 + 3.45375i 0.199513 + 0.115189i
900900 13.4693 23.3296i 0.448978 0.777653i
901901 −0.538965 0.933515i −0.0179555 0.0310999i
902902 18.2735i 0.608440i
903903 −16.1070 + 9.29938i −0.536008 + 0.309464i
904904 13.6799 7.89807i 0.454985 0.262686i
905905 2.73355i 0.0908662i
906906 −9.57879 16.5909i −0.318234 0.551197i
907907 2.26278 3.91924i 0.0751343 0.130136i −0.826010 0.563655i 0.809395π-0.809395\pi
0.901145 + 0.433519i 0.142728π0.142728\pi
908908 18.7441 + 10.8219i 0.622044 + 0.359137i
909909 54.3464 1.80256
910910 9.38731 0.199529i 0.311186 0.00661432i
911911 −57.2723 −1.89751 −0.948757 0.316006i 0.897658π-0.897658\pi
−0.948757 + 0.316006i 0.897658π0.897658\pi
912912 −1.76091 1.01666i −0.0583095 0.0336650i
913913 18.4163 31.8979i 0.609489 1.05567i
914914 −13.0471 22.5983i −0.431560 0.747484i
915915 9.73302i 0.321764i
916916 −30.9181 + 17.8506i −1.02156 + 0.589800i
917917 8.85224 5.11084i 0.292327 0.168775i
918918 6.37098i 0.210274i
919919 20.3775 + 35.2949i 0.672193 + 1.16427i 0.977281 + 0.211948i 0.0679809π0.0679809\pi
−0.305088 + 0.952324i 0.598686π0.598686\pi
920920 −11.8052 + 20.4473i −0.389207 + 0.674127i
921921 −16.2864 9.40294i −0.536654 0.309837i
922922 −18.2021 −0.599453
923923 −8.42270 13.8979i −0.277236 0.457454i
924924 20.8960 0.687429
925925 28.1589 + 16.2575i 0.925858 + 0.534545i
926926 −16.0104 + 27.7308i −0.526134 + 0.911291i
927927 23.7391 + 41.1174i 0.779696 + 1.35047i
928928 34.7487i 1.14068i
929929 45.2751 26.1396i 1.48543 0.857611i 0.485564 0.874201i 0.338614π-0.338614\pi
0.999862 + 0.0165897i 0.00528089π0.00528089\pi
930930 6.90891 3.98886i 0.226552 0.130800i
931931 1.95705i 0.0641397i
932932 7.64511 + 13.2417i 0.250424 + 0.433747i
933933 −29.6205 + 51.3042i −0.969731 + 1.67962i
934934 −9.47322 5.46937i −0.309973 0.178963i
935935 50.7300 1.65905
936936 20.8431 + 34.3922i 0.681279 + 1.12414i
937937 −6.38634 −0.208633 −0.104316 0.994544i 0.533265π-0.533265\pi
−0.104316 + 0.994544i 0.533265π0.533265\pi
938938 −4.47844 2.58563i −0.146226 0.0844238i
939939 37.3558 64.7021i 1.21906 2.11147i
940940 −0.953077 1.65078i −0.0310859 0.0538424i
941941 25.3711i 0.827073i 0.910488 + 0.413536i 0.135707π0.135707\pi
−0.910488 + 0.413536i 0.864293π0.864293\pi
942942 −12.3469 + 7.12846i −0.402282 + 0.232258i
943943 8.82560 5.09546i 0.287401 0.165931i
944944 1.87692i 0.0610887i
945945 4.53056 + 7.84715i 0.147379 + 0.255268i
946946 −17.1081 + 29.6321i −0.556232 + 0.963422i
947947 23.5612 + 13.6031i 0.765635 + 0.442040i 0.831315 0.555801i 0.187588π-0.187588\pi
−0.0656800 + 0.997841i 0.520922π0.520922\pi
948948 −27.8280 −0.903811
949949 −29.9401 + 0.636381i −0.971895 + 0.0206578i
950950 −8.05681 −0.261397
951951 −44.9613 25.9584i −1.45797 0.841760i
952952 −3.69264 + 6.39584i −0.119679 + 0.207290i
953953 13.2939 + 23.0258i 0.430633 + 0.745878i 0.996928 0.0783248i 0.0249571π-0.0249571\pi
−0.566295 + 0.824203i 0.691624π0.691624\pi
954954 1.34071i 0.0434070i
955955 40.1667 23.1902i 1.29976 0.750418i
956956 16.7959 9.69711i 0.543218 0.313627i
957957 94.8314i 3.06546i
958958 2.73220 + 4.73230i 0.0882732 + 0.152894i
959959 −9.97376 + 17.2751i −0.322070 + 0.557841i
960960 29.0654 + 16.7809i 0.938082 + 0.541602i
961961 29.6739 0.957224
962962 −16.5178 + 10.0105i −0.532554 + 0.322751i
963963 16.0218 0.516296
964964 −16.4223 9.48141i −0.528926 0.305376i
965965 −26.0808 + 45.1732i −0.839569 + 1.45418i
966966 −2.98994 5.17872i −0.0961996 0.166623i
967967 35.2467i 1.13346i −0.823904 0.566729i 0.808209π-0.808209\pi
0.823904 0.566729i 0.191791π-0.191791\pi
968968 57.6073 33.2596i 1.85157 1.06900i
969969 12.1722 7.02760i 0.391026 0.225759i
970970 8.92578i 0.286590i
971971 −18.4891 32.0241i −0.593344 1.02770i −0.993778 0.111377i 0.964474π-0.964474\pi
0.400434 0.916326i 0.368859π-0.368859\pi
972972 13.7833 23.8733i 0.442098 0.765737i
973973 17.6041 + 10.1637i 0.564362 + 0.325834i
974974 27.5645 0.883224
975975 −42.0241 23.0861i −1.34585 0.739347i
976976 −0.451876 −0.0144642
977977 −21.4363 12.3762i −0.685807 0.395951i 0.116232 0.993222i 0.462918π-0.462918\pi
−0.802039 + 0.597271i 0.796252π0.796252\pi
978978 −2.86205 + 4.95721i −0.0915182 + 0.158514i
979979 10.5820 + 18.3286i 0.338204 + 0.585786i
980980 4.17951i 0.133510i
981981 −39.7346 + 22.9408i −1.26863 + 0.732442i
982982 −26.6236 + 15.3711i −0.849593 + 0.490513i
983983 4.55736i 0.145357i −0.997355 0.0726786i 0.976845π-0.976845\pi
0.997355 0.0726786i 0.0231547π-0.0231547\pi
984984 −13.5864 23.5323i −0.433119 0.750183i
985985 −17.4076 + 30.1509i −0.554652 + 0.960686i
986986 −11.5497 6.66820i −0.367816 0.212359i
987987 1.21328 0.0386192
988988 −4.49062 + 8.17436i −0.142866 + 0.260061i
989989 −19.0820 −0.606773
990990 54.6436 + 31.5485i 1.73669 + 1.00268i
991991 13.5982 23.5527i 0.431960 0.748176i −0.565082 0.825034i 0.691156π-0.691156\pi
0.997042 + 0.0768584i 0.0244890π0.0244890\pi
992992 −3.33543 5.77713i −0.105900 0.183424i
993993 41.5824i 1.31958i
994994 3.21462 1.85596i 0.101962 0.0588676i
995995 58.0873 33.5367i 1.84149 1.06319i
996996 21.7936i 0.690556i
997997 15.1137 + 26.1777i 0.478656 + 0.829057i 0.999700 0.0244727i 0.00779070π-0.00779070\pi
−0.521044 + 0.853530i 0.674457π0.674457\pi
998998 −14.0551 + 24.3441i −0.444906 + 0.770600i
999999 −16.1419 9.31952i −0.510707 0.294857i
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 91.2.q.a.43.4 yes 12
3.2 odd 2 819.2.ct.a.316.3 12
4.3 odd 2 1456.2.cc.c.225.6 12
7.2 even 3 637.2.k.h.459.3 12
7.3 odd 6 637.2.u.i.30.3 12
7.4 even 3 637.2.u.h.30.3 12
7.5 odd 6 637.2.k.g.459.3 12
7.6 odd 2 637.2.q.h.589.4 12
13.4 even 6 1183.2.c.i.337.8 12
13.6 odd 12 1183.2.a.p.1.2 6
13.7 odd 12 1183.2.a.m.1.5 6
13.9 even 3 1183.2.c.i.337.5 12
13.10 even 6 inner 91.2.q.a.36.4 12
39.23 odd 6 819.2.ct.a.127.3 12
52.23 odd 6 1456.2.cc.c.673.6 12
91.6 even 12 8281.2.a.ch.1.2 6
91.10 odd 6 637.2.k.g.569.4 12
91.20 even 12 8281.2.a.by.1.5 6
91.23 even 6 637.2.u.h.361.3 12
91.62 odd 6 637.2.q.h.491.4 12
91.75 odd 6 637.2.u.i.361.3 12
91.88 even 6 637.2.k.h.569.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.4 12 13.10 even 6 inner
91.2.q.a.43.4 yes 12 1.1 even 1 trivial
637.2.k.g.459.3 12 7.5 odd 6
637.2.k.g.569.4 12 91.10 odd 6
637.2.k.h.459.3 12 7.2 even 3
637.2.k.h.569.4 12 91.88 even 6
637.2.q.h.491.4 12 91.62 odd 6
637.2.q.h.589.4 12 7.6 odd 2
637.2.u.h.30.3 12 7.4 even 3
637.2.u.h.361.3 12 91.23 even 6
637.2.u.i.30.3 12 7.3 odd 6
637.2.u.i.361.3 12 91.75 odd 6
819.2.ct.a.127.3 12 39.23 odd 6
819.2.ct.a.316.3 12 3.2 odd 2
1183.2.a.m.1.5 6 13.7 odd 12
1183.2.a.p.1.2 6 13.6 odd 12
1183.2.c.i.337.5 12 13.9 even 3
1183.2.c.i.337.8 12 13.4 even 6
1456.2.cc.c.225.6 12 4.3 odd 2
1456.2.cc.c.673.6 12 52.23 odd 6
8281.2.a.by.1.5 6 91.20 even 12
8281.2.a.ch.1.2 6 91.6 even 12