Properties

Label 637.2.bc.c.31.19
Level 637637
Weight 22
Character 637.31
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 112112
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(31,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.bc (of order 1212, degree 44, not 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: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 112112
Relative dimension: 2828 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 31.19
Character χ\chi == 637.31
Dual form 637.2.bc.c.411.19

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+(1.43251+0.383841i)q2+(0.7659950.442247i)q3+(0.172712+0.0997153i)q4+(1.01546+3.78973i)q5+(0.9275460.927546i)q6+(1.888211.88821i)q8+(1.108831.92056i)q9+(2.90931+5.03907i)q10+(2.51265+0.673262i)q11+(0.08819760.152763i)q12+(3.365141.29454i)q13+(2.453832.45383i)q15+(2.179543.77508i)q16+(0.680066+1.17791i)q17+(0.8512323.17684i)q18+(0.8285973.09237i)q19+(0.553276+0.553276i)q203.85783q22+(1.39284+0.804158i)q23+(0.611303+2.28141i)q24+(9.000815.19662i)q25+(4.323713.14612i)q26+4.61500iq27+9.34669q29+(4.457032.57327i)q30+(8.22399+2.20361i)q31+(0.2909321.08577i)q32+(2.22242+0.595497i)q33+(1.42633+1.42633i)q340.442271iq36+(1.24632+4.65133i)q37+(2.373954.11181i)q38+(2.00517+2.47983i)q39+(9.073205.23842i)q40+(2.146282.14628i)q41+11.5495iq43+(0.5010990.134269i)q44+(8.404382.25195i)q45+(2.30394+0.617338i)q46+(9.583912.56800i)q47+3.85559iq48+(10.899110.8991i)q50+(1.041850.601515i)q51+(0.4521140.559138i)q52+(1.511732.61840i)q53+(1.77143+6.61105i)q5410.2059iq55+(2.00229+2.00229i)q57+(13.3893+3.58764i)q58+(0.0670618+0.250278i)q59+(0.6684910.179122i)q60+(0.288679+0.166669i)q6112.6268q62+7.05112iq64+(8.3231111.4384i)q65+(2.95508+1.70611i)q66+(0.272292+1.01621i)q67+(0.234911+0.135626i)q68+1.42255q69+(0.333748+0.333748i)q71+(1.53270+5.72013i)q72+(2.17380+8.11275i)q73+(3.57074+6.18470i)q74+(4.59638+7.96117i)q75+(0.4514650.451465i)q76+(1.92058+4.32207i)q78+(1.451622.51428i)q79+(16.51984.42646i)q80+(1.28553+2.22661i)q81+(2.250743.89840i)q82+(3.84570+3.84570i)q83+(3.773383.77338i)q85+(4.43317+16.5448i)q86+(7.159514.13355i)q87+(6.01566+3.47314i)q88+(7.14176+1.91363i)q89+12.9038q900.320747q92+(7.27408+1.94908i)q93+(12.74347.35740i)q94+(10.8778+6.28033i)q95+(0.257328+0.960361i)q96+(7.45885+7.45885i)q97+(4.07915+4.07915i)q99+O(q100)q+(1.43251 + 0.383841i) q^{2} +(-0.765995 - 0.442247i) q^{3} +(0.172712 + 0.0997153i) q^{4} +(-1.01546 + 3.78973i) q^{5} +(-0.927546 - 0.927546i) q^{6} +(-1.88821 - 1.88821i) q^{8} +(-1.10883 - 1.92056i) q^{9} +(-2.90931 + 5.03907i) q^{10} +(-2.51265 + 0.673262i) q^{11} +(-0.0881976 - 0.152763i) q^{12} +(-3.36514 - 1.29454i) q^{13} +(2.45383 - 2.45383i) q^{15} +(-2.17954 - 3.77508i) q^{16} +(-0.680066 + 1.17791i) q^{17} +(-0.851232 - 3.17684i) q^{18} +(0.828597 - 3.09237i) q^{19} +(-0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +(-1.39284 + 0.804158i) q^{23} +(0.611303 + 2.28141i) q^{24} +(-9.00081 - 5.19662i) q^{25} +(-4.32371 - 3.14612i) q^{26} +4.61500i q^{27} +9.34669 q^{29} +(4.45703 - 2.57327i) q^{30} +(-8.22399 + 2.20361i) q^{31} +(-0.290932 - 1.08577i) q^{32} +(2.22242 + 0.595497i) q^{33} +(-1.42633 + 1.42633i) q^{34} -0.442271i q^{36} +(-1.24632 + 4.65133i) q^{37} +(2.37395 - 4.11181i) q^{38} +(2.00517 + 2.47983i) q^{39} +(9.07320 - 5.23842i) q^{40} +(-2.14628 - 2.14628i) q^{41} +11.5495i q^{43} +(-0.501099 - 0.134269i) q^{44} +(8.40438 - 2.25195i) q^{45} +(-2.30394 + 0.617338i) q^{46} +(-9.58391 - 2.56800i) q^{47} +3.85559i q^{48} +(-10.8991 - 10.8991i) q^{50} +(1.04185 - 0.601515i) q^{51} +(-0.452114 - 0.559138i) q^{52} +(1.51173 - 2.61840i) q^{53} +(-1.77143 + 6.61105i) q^{54} -10.2059i q^{55} +(-2.00229 + 2.00229i) q^{57} +(13.3893 + 3.58764i) q^{58} +(0.0670618 + 0.250278i) q^{59} +(0.668491 - 0.179122i) q^{60} +(-0.288679 + 0.166669i) q^{61} -12.6268 q^{62} +7.05112i q^{64} +(8.32311 - 11.4384i) q^{65} +(2.95508 + 1.70611i) q^{66} +(0.272292 + 1.01621i) q^{67} +(-0.234911 + 0.135626i) q^{68} +1.42255 q^{69} +(-0.333748 + 0.333748i) q^{71} +(-1.53270 + 5.72013i) q^{72} +(2.17380 + 8.11275i) q^{73} +(-3.57074 + 6.18470i) q^{74} +(4.59638 + 7.96117i) q^{75} +(0.451465 - 0.451465i) q^{76} +(1.92058 + 4.32207i) q^{78} +(-1.45162 - 2.51428i) q^{79} +(16.5198 - 4.42646i) q^{80} +(-1.28553 + 2.22661i) q^{81} +(-2.25074 - 3.89840i) q^{82} +(3.84570 + 3.84570i) q^{83} +(-3.77338 - 3.77338i) q^{85} +(-4.43317 + 16.5448i) q^{86} +(-7.15951 - 4.13355i) q^{87} +(6.01566 + 3.47314i) q^{88} +(7.14176 + 1.91363i) q^{89} +12.9038 q^{90} -0.320747 q^{92} +(7.27408 + 1.94908i) q^{93} +(-12.7434 - 7.35740i) q^{94} +(10.8778 + 6.28033i) q^{95} +(-0.257328 + 0.960361i) q^{96} +(7.45885 + 7.45885i) q^{97} +(4.07915 + 4.07915i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 112q+56q9+16q11+96q15+56q16+32q1896q29+32q39+64q4432q4680q50+16q53192q5772q58+64q6032q65+64q71208q72+64q93+O(q100) 112 q + 56 q^{9} + 16 q^{11} + 96 q^{15} + 56 q^{16} + 32 q^{18} - 96 q^{29} + 32 q^{39} + 64 q^{44} - 32 q^{46} - 80 q^{50} + 16 q^{53} - 192 q^{57} - 72 q^{58} + 64 q^{60} - 32 q^{65} + 64 q^{71} - 208 q^{72}+ \cdots - 64 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.43251 + 0.383841i 1.01294 + 0.271417i 0.726858 0.686788i 0.240980π-0.240980\pi
0.286083 + 0.958205i 0.407647π0.407647\pi
33 −0.765995 0.442247i −0.442247 0.255332i 0.262303 0.964986i 0.415518π-0.415518\pi
−0.704550 + 0.709654i 0.748851π0.748851\pi
44 0.172712 + 0.0997153i 0.0863560 + 0.0498576i
55 −1.01546 + 3.78973i −0.454126 + 1.69482i 0.236519 + 0.971627i 0.423993π0.423993\pi
−0.690645 + 0.723194i 0.742673π0.742673\pi
66 −0.927546 0.927546i −0.378669 0.378669i
77 0 0
88 −1.88821 1.88821i −0.667583 0.667583i
99 −1.10883 1.92056i −0.369612 0.640186i
1010 −2.90931 + 5.03907i −0.920005 + 1.59350i
1111 −2.51265 + 0.673262i −0.757592 + 0.202996i −0.616883 0.787055i 0.711605π-0.711605\pi
−0.140709 + 0.990051i 0.544938π0.544938\pi
1212 −0.0881976 0.152763i −0.0254605 0.0440988i
1313 −3.36514 1.29454i −0.933322 0.359041i
1414 0 0
1515 2.45383 2.45383i 0.633577 0.633577i
1616 −2.17954 3.77508i −0.544886 0.943770i
1717 −0.680066 + 1.17791i −0.164940 + 0.285685i −0.936634 0.350309i 0.886076π-0.886076\pi
0.771694 + 0.635994i 0.219410π0.219410\pi
1818 −0.851232 3.17684i −0.200637 0.748789i
1919 0.828597 3.09237i 0.190093 0.709437i −0.803389 0.595454i 0.796972π-0.796972\pi
0.993483 0.113984i 0.0363611π-0.0363611\pi
2020 −0.553276 + 0.553276i −0.123716 + 0.123716i
2121 0 0
2222 −3.85783 −0.822492
2323 −1.39284 + 0.804158i −0.290428 + 0.167679i −0.638135 0.769925i 0.720294π-0.720294\pi
0.347707 + 0.937603i 0.386960π0.386960\pi
2424 0.611303 + 2.28141i 0.124782 + 0.465692i
2525 −9.00081 5.19662i −1.80016 1.03932i
2626 −4.32371 3.14612i −0.847950 0.617006i
2727 4.61500i 0.888157i
2828 0 0
2929 9.34669 1.73564 0.867818 0.496882i 0.165522π-0.165522\pi
0.867818 + 0.496882i 0.165522π0.165522\pi
3030 4.45703 2.57327i 0.813739 0.469813i
3131 −8.22399 + 2.20361i −1.47707 + 0.395781i −0.905350 0.424666i 0.860391π-0.860391\pi
−0.571723 + 0.820447i 0.693725π0.693725\pi
3232 −0.290932 1.08577i −0.0514300 0.191939i
3333 2.22242 + 0.595497i 0.386874 + 0.103663i
3434 −1.42633 + 1.42633i −0.244614 + 0.244614i
3535 0 0
3636 0.442271i 0.0737118i
3737 −1.24632 + 4.65133i −0.204894 + 0.764673i 0.784588 + 0.620017i 0.212874π0.212874\pi
−0.989482 + 0.144656i 0.953792π0.953792\pi
3838 2.37395 4.11181i 0.385106 0.667023i
3939 2.00517 + 2.47983i 0.321085 + 0.397091i
4040 9.07320 5.23842i 1.43460 0.828266i
4141 −2.14628 2.14628i −0.335192 0.335192i 0.519362 0.854554i 0.326170π-0.326170\pi
−0.854554 + 0.519362i 0.826170π0.826170\pi
4242 0 0
4343 11.5495i 1.76128i 0.473786 + 0.880640i 0.342887π0.342887\pi
−0.473786 + 0.880640i 0.657113π0.657113\pi
4444 −0.501099 0.134269i −0.0755435 0.0202418i
4545 8.40438 2.25195i 1.25285 0.335700i
4646 −2.30394 + 0.617338i −0.339697 + 0.0910215i
4747 −9.58391 2.56800i −1.39796 0.374582i −0.520347 0.853955i 0.674197π-0.674197\pi
−0.877611 + 0.479374i 0.840864π0.840864\pi
4848 3.85559i 0.556507i
4949 0 0
5050 −10.8991 10.8991i −1.54137 1.54137i
5151 1.04185 0.601515i 0.145889 0.0842289i
5252 −0.452114 0.559138i −0.0626970 0.0775385i
5353 1.51173 2.61840i 0.207652 0.359665i −0.743322 0.668934i 0.766751π-0.766751\pi
0.950975 + 0.309269i 0.100084π0.100084\pi
5454 −1.77143 + 6.61105i −0.241061 + 0.899650i
5555 10.2059i 1.37617i
5656 0 0
5757 −2.00229 + 2.00229i −0.265210 + 0.265210i
5858 13.3893 + 3.58764i 1.75810 + 0.471080i
5959 0.0670618 + 0.250278i 0.00873071 + 0.0325834i 0.970154 0.242491i 0.0779643π-0.0779643\pi
−0.961423 + 0.275074i 0.911298π0.911298\pi
6060 0.668491 0.179122i 0.0863018 0.0231245i
6161 −0.288679 + 0.166669i −0.0369616 + 0.0213398i −0.518367 0.855158i 0.673460π-0.673460\pi
0.481405 + 0.876498i 0.340127π0.340127\pi
6262 −12.6268 −1.60361
6363 0 0
6464 7.05112i 0.881390i
6565 8.32311 11.4384i 1.03236 1.41876i
6666 2.95508 + 1.70611i 0.363745 + 0.210008i
6767 0.272292 + 1.01621i 0.0332658 + 0.124150i 0.980562 0.196209i 0.0628632π-0.0628632\pi
−0.947296 + 0.320359i 0.896196π0.896196\pi
6868 −0.234911 + 0.135626i −0.0284871 + 0.0164471i
6969 1.42255 0.171255
7070 0 0
7171 −0.333748 + 0.333748i −0.0396086 + 0.0396086i −0.726634 0.687025i 0.758916π-0.758916\pi
0.687025 + 0.726634i 0.258916π0.258916\pi
7272 −1.53270 + 5.72013i −0.180631 + 0.674123i
7373 2.17380 + 8.11275i 0.254425 + 0.949525i 0.968410 + 0.249365i 0.0802217π0.0802217\pi
−0.713985 + 0.700161i 0.753112π0.753112\pi
7474 −3.57074 + 6.18470i −0.415090 + 0.718957i
7575 4.59638 + 7.96117i 0.530744 + 0.919276i
7676 0.451465 0.451465i 0.0517866 0.0517866i
7777 0 0
7878 1.92058 + 4.32207i 0.217462 + 0.489378i
7979 −1.45162 2.51428i −0.163320 0.282878i 0.772738 0.634726i 0.218887π-0.218887\pi
−0.936057 + 0.351847i 0.885554π0.885554\pi
8080 16.5198 4.42646i 1.84697 0.494894i
8181 −1.28553 + 2.22661i −0.142837 + 0.247401i
8282 −2.25074 3.89840i −0.248553 0.430506i
8383 3.84570 + 3.84570i 0.422120 + 0.422120i 0.885933 0.463813i 0.153519π-0.153519\pi
−0.463813 + 0.885933i 0.653519π0.653519\pi
8484 0 0
8585 −3.77338 3.77338i −0.409281 0.409281i
8686 −4.43317 + 16.5448i −0.478041 + 1.78407i
8787 −7.15951 4.13355i −0.767580 0.443163i
8888 6.01566 + 3.47314i 0.641272 + 0.370238i
8989 7.14176 + 1.91363i 0.757025 + 0.202844i 0.616632 0.787251i 0.288497π-0.288497\pi
0.140393 + 0.990096i 0.455163π0.455163\pi
9090 12.9038 1.36018
9191 0 0
9292 −0.320747 −0.0334402
9393 7.27408 + 1.94908i 0.754287 + 0.202111i
9494 −12.7434 7.35740i −1.31438 0.758858i
9595 10.8778 + 6.28033i 1.11604 + 0.644348i
9696 −0.257328 + 0.960361i −0.0262634 + 0.0980164i
9797 7.45885 + 7.45885i 0.757332 + 0.757332i 0.975836 0.218504i 0.0701178π-0.0701178\pi
−0.218504 + 0.975836i 0.570118π0.570118\pi
9898 0 0
9999 4.07915 + 4.07915i 0.409970 + 0.409970i
100100 −1.03636 1.79504i −0.103636 0.179504i
101101 0.104651 0.181261i 0.0104132 0.0180362i −0.860772 0.508991i 0.830019π-0.830019\pi
0.871185 + 0.490955i 0.163352π0.163352\pi
102102 1.72336 0.461772i 0.170638 0.0457222i
103103 −8.17798 14.1647i −0.805800 1.39569i −0.915749 0.401750i 0.868402π-0.868402\pi
0.109949 0.993937i 0.464931π-0.464931\pi
104104 3.90973 + 8.79845i 0.383380 + 0.862759i
105105 0 0
106106 3.17063 3.17063i 0.307958 0.307958i
107107 −8.52958 14.7737i −0.824585 1.42822i −0.902236 0.431243i 0.858075π-0.858075\pi
0.0776502 0.996981i 0.475258π-0.475258\pi
108108 −0.460186 + 0.797066i −0.0442814 + 0.0766977i
109109 −1.81493 6.77341i −0.173839 0.648775i −0.996747 0.0806001i 0.974316π-0.974316\pi
0.822908 0.568175i 0.192350π-0.192350\pi
110110 3.91746 14.6201i 0.373515 1.39398i
111111 3.01171 3.01171i 0.285859 0.285859i
112112 0 0
113113 4.56982 0.429892 0.214946 0.976626i 0.431042π-0.431042\pi
0.214946 + 0.976626i 0.431042π0.431042\pi
114114 −3.63687 + 2.09975i −0.340624 + 0.196660i
115115 −1.63318 6.09509i −0.152294 0.568370i
116116 1.61428 + 0.932007i 0.149883 + 0.0865347i
117117 1.24515 + 7.89838i 0.115114 + 0.730205i
118118 0.384268i 0.0353747i
119119 0 0
120120 −9.26670 −0.845930
121121 −3.66616 + 2.11666i −0.333287 + 0.192424i
122122 −0.477511 + 0.127949i −0.0432318 + 0.0115839i
123123 0.694851 + 2.59322i 0.0626526 + 0.233823i
124124 −1.64012 0.439468i −0.147287 0.0394654i
125125 14.9623 14.9623i 1.33827 1.33827i
126126 0 0
127127 10.4126i 0.923968i −0.886888 0.461984i 0.847138π-0.847138\pi
0.886888 0.461984i 0.152862π-0.152862\pi
128128 −3.28837 + 12.2724i −0.290654 + 1.08473i
129129 5.10773 8.84684i 0.449710 0.778921i
130130 16.3135 13.1910i 1.43079 1.15692i
131131 15.1481 8.74577i 1.32350 0.764121i 0.339212 0.940710i 0.389840π-0.389840\pi
0.984285 + 0.176589i 0.0565063π0.0565063\pi
132132 0.324459 + 0.324459i 0.0282405 + 0.0282405i
133133 0 0
134134 1.56025i 0.134785i
135135 −17.4896 4.68633i −1.50527 0.403335i
136136 3.50824 0.940031i 0.300829 0.0806070i
137137 19.4448 5.21021i 1.66128 0.445138i 0.698540 0.715571i 0.253833π-0.253833\pi
0.962739 + 0.270433i 0.0871668π0.0871668\pi
138138 2.03782 + 0.546032i 0.173471 + 0.0464813i
139139 14.6578i 1.24326i −0.783310 0.621631i 0.786470π-0.786470\pi
0.783310 0.621631i 0.213530π-0.213530\pi
140140 0 0
141141 6.20554 + 6.20554i 0.522600 + 0.522600i
142142 −0.606204 + 0.349992i −0.0508715 + 0.0293707i
143143 9.32698 + 0.987101i 0.779961 + 0.0825455i
144144 −4.83351 + 8.37188i −0.402792 + 0.697657i
145145 −9.49115 + 35.4215i −0.788197 + 2.94159i
146146 12.4560i 1.03087i
147147 0 0
148148 −0.679062 + 0.679062i −0.0558186 + 0.0558186i
149149 −21.1240 5.66017i −1.73055 0.463699i −0.750239 0.661166i 0.770062π-0.770062\pi
−0.980310 + 0.197467i 0.936728π0.936728\pi
150150 3.52856 + 13.1688i 0.288106 + 1.07523i
151151 −13.0689 + 3.50181i −1.06353 + 0.284973i −0.747834 0.663886i 0.768906π-0.768906\pi
−0.315700 + 0.948859i 0.602239π0.602239\pi
152152 −7.40360 + 4.27447i −0.600511 + 0.346705i
153153 3.01632 0.243855
154154 0 0
155155 33.4044i 2.68311i
156156 0.0990399 + 0.628243i 0.00792954 + 0.0502997i
157157 −11.1379 6.43044i −0.888897 0.513205i −0.0153156 0.999883i 0.504875π-0.504875\pi
−0.873582 + 0.486678i 0.838209π0.838209\pi
158158 −1.11438 4.15893i −0.0886554 0.330867i
159159 −2.31596 + 1.33712i −0.183667 + 0.106040i
160160 4.41022 0.348659
161161 0 0
162162 −2.69621 + 2.69621i −0.211834 + 0.211834i
163163 −2.77257 + 10.3474i −0.217164 + 0.810468i 0.768229 + 0.640175i 0.221138π0.221138\pi
−0.985393 + 0.170293i 0.945529π0.945529\pi
164164 −0.156671 0.584704i −0.0122339 0.0456577i
165165 −4.51355 + 7.81769i −0.351379 + 0.608607i
166166 4.03288 + 6.98516i 0.313012 + 0.542153i
167167 −6.07140 + 6.07140i −0.469819 + 0.469819i −0.901856 0.432037i 0.857795π-0.857795\pi
0.432037 + 0.901856i 0.357795π0.357795\pi
168168 0 0
169169 9.64834 + 8.71261i 0.742180 + 0.670201i
170170 −3.95705 6.85380i −0.303492 0.525663i
171171 −6.85785 + 1.83755i −0.524433 + 0.140521i
172172 −1.15166 + 1.99473i −0.0878132 + 0.152097i
173173 1.77614 + 3.07637i 0.135037 + 0.233892i 0.925612 0.378474i 0.123551π-0.123551\pi
−0.790574 + 0.612366i 0.790218π0.790218\pi
174174 −8.66948 8.66948i −0.657232 0.657232i
175175 0 0
176176 8.01805 + 8.01805i 0.604383 + 0.604383i
177177 0.0593158 0.221370i 0.00445845 0.0166392i
178178 9.49615 + 5.48260i 0.711766 + 0.410938i
179179 14.9201 + 8.61412i 1.11518 + 0.643850i 0.940166 0.340716i 0.110670π-0.110670\pi
0.175014 + 0.984566i 0.444003π0.444003\pi
180180 1.67609 + 0.449107i 0.124928 + 0.0334744i
181181 −6.21868 −0.462231 −0.231115 0.972926i 0.574238π-0.574238\pi
−0.231115 + 0.972926i 0.574238π0.574238\pi
182182 0 0
183183 0.294836 0.0217949
184184 4.14840 + 1.11156i 0.305824 + 0.0819453i
185185 −16.3617 9.44644i −1.20294 0.694516i
186186 9.67208 + 5.58418i 0.709192 + 0.409452i
187187 0.915725 3.41753i 0.0669644 0.249915i
188188 −1.39919 1.39919i −0.102046 0.102046i
189189 0 0
190190 13.1720 + 13.1720i 0.955599 + 0.955599i
191191 6.15368 + 10.6585i 0.445264 + 0.771221i 0.998071 0.0620893i 0.0197763π-0.0197763\pi
−0.552806 + 0.833310i 0.686443π0.686443\pi
192192 3.11834 5.40112i 0.225047 0.389792i
193193 −20.7241 + 5.55301i −1.49176 + 0.399715i −0.910329 0.413885i 0.864172π-0.864172\pi
−0.581426 + 0.813599i 0.697505π0.697505\pi
194194 7.82190 + 13.5479i 0.561579 + 0.972684i
195195 −11.4341 + 5.08091i −0.818812 + 0.363852i
196196 0 0
197197 −1.42501 + 1.42501i −0.101528 + 0.101528i −0.756046 0.654518i 0.772872π-0.772872\pi
0.654518 + 0.756046i 0.272872π0.272872\pi
198198 4.27769 + 7.40918i 0.304002 + 0.526548i
199199 −3.33814 + 5.78184i −0.236635 + 0.409863i −0.959747 0.280868i 0.909378π-0.909378\pi
0.723112 + 0.690731i 0.242711π0.242711\pi
200200 7.18310 + 26.8077i 0.507922 + 1.89559i
201201 0.240841 0.898832i 0.0169876 0.0633987i
202202 0.219490 0.219490i 0.0154432 0.0154432i
203203 0 0
204204 0.239921 0.0167978
205205 10.3133 5.95437i 0.720310 0.415871i
206206 −6.27809 23.4301i −0.437415 1.63246i
207207 3.08886 + 1.78336i 0.214691 + 0.123952i
208208 2.44748 + 15.5252i 0.169702 + 1.07648i
209209 8.32789i 0.576052i
210210 0 0
211211 −18.9896 −1.30730 −0.653648 0.756798i 0.726762π-0.726762\pi
−0.653648 + 0.756798i 0.726762π0.726762\pi
212212 0.522188 0.301486i 0.0358640 0.0207061i
213213 0.403248 0.108050i 0.0276301 0.00740346i
214214 −6.54800 24.4375i −0.447612 1.67051i
215215 −43.7695 11.7280i −2.98505 0.799843i
216216 8.71408 8.71408i 0.592918 0.592918i
217217 0 0
218218 10.3996i 0.704353i
219219 1.92272 7.17568i 0.129925 0.484888i
220220 1.01769 1.76269i 0.0686125 0.118840i
221221 3.81337 3.08346i 0.256515 0.207416i
222222 5.47034 3.15830i 0.367145 0.211971i
223223 −2.04467 2.04467i −0.136921 0.136921i 0.635324 0.772245i 0.280866π-0.280866\pi
−0.772245 + 0.635324i 0.780866π0.780866\pi
224224 0 0
225225 23.0488i 1.53658i
226226 6.54633 + 1.75408i 0.435455 + 0.116680i
227227 −6.34006 + 1.69881i −0.420805 + 0.112754i −0.463007 0.886355i 0.653229π-0.653229\pi
0.0422019 + 0.999109i 0.486563π0.486563\pi
228228 −0.545479 + 0.146161i −0.0361252 + 0.00967972i
229229 1.37763 + 0.369136i 0.0910366 + 0.0243932i 0.304050 0.952656i 0.401661π-0.401661\pi
−0.213013 + 0.977049i 0.568328π0.568328\pi
230230 9.35819i 0.617060i
231231 0 0
232232 −17.6485 17.6485i −1.15868 1.15868i
233233 −7.35621 + 4.24711i −0.481921 + 0.278237i −0.721217 0.692709i 0.756417π-0.756417\pi
0.239295 + 0.970947i 0.423084π0.423084\pi
234234 −1.24803 + 11.7925i −0.0815864 + 0.770898i
235235 19.4641 33.7128i 1.26970 2.19918i
236236 −0.0133742 + 0.0499131i −0.000870585 + 0.00324907i
237237 2.56790i 0.166803i
238238 0 0
239239 −4.64810 + 4.64810i −0.300661 + 0.300661i −0.841272 0.540612i 0.818193π-0.818193\pi
0.540612 + 0.841272i 0.318193π0.318193\pi
240240 −14.6117 3.91518i −0.943179 0.252724i
241241 2.79130 + 10.4173i 0.179803 + 0.671034i 0.995683 + 0.0928137i 0.0295861π0.0295861\pi
−0.815880 + 0.578221i 0.803747π0.803747\pi
242242 −6.06429 + 1.62492i −0.389827 + 0.104454i
243243 13.9595 8.05955i 0.895505 0.517020i
244244 −0.0664778 −0.00425580
245245 0 0
246246 3.98154i 0.253854i
247247 −6.79154 + 9.33359i −0.432135 + 0.593882i
248248 19.6895 + 11.3677i 1.25028 + 0.721852i
249249 −1.24504 4.64654i −0.0789009 0.294462i
250250 27.1769 15.6906i 1.71882 0.992361i
251251 −28.0524 −1.77065 −0.885327 0.464968i 0.846066π-0.846066\pi
−0.885327 + 0.464968i 0.846066π0.846066\pi
252252 0 0
253253 2.95831 2.95831i 0.185988 0.185988i
254254 3.99678 14.9162i 0.250780 0.935925i
255255 1.22162 + 4.55916i 0.0765010 + 0.285506i
256256 −2.37016 + 4.10524i −0.148135 + 0.256578i
257257 −7.06032 12.2288i −0.440411 0.762813i 0.557309 0.830305i 0.311834π-0.311834\pi
−0.997720 + 0.0674915i 0.978500π0.978500\pi
258258 10.7127 10.7127i 0.666942 0.666942i
259259 0 0
260260 2.57809 1.14561i 0.159886 0.0710479i
261261 −10.3639 17.9509i −0.641511 1.11113i
262262 25.0569 6.71397i 1.54802 0.414790i
263263 −11.1615 + 19.3323i −0.688248 + 1.19208i 0.284157 + 0.958778i 0.408286π0.408286\pi
−0.972404 + 0.233302i 0.925047π0.925047\pi
264264 −3.07198 5.32082i −0.189067 0.327474i
265265 8.38793 + 8.38793i 0.515267 + 0.515267i
266266 0 0
267267 −4.62426 4.62426i −0.283000 0.283000i
268268 −0.0543034 + 0.202663i −0.00331711 + 0.0123796i
269269 −10.2451 5.91503i −0.624656 0.360645i 0.154023 0.988067i 0.450777π-0.450777\pi
−0.778680 + 0.627422i 0.784110π0.784110\pi
270270 −23.2553 13.4265i −1.41527 0.817109i
271271 −4.77450 1.27932i −0.290030 0.0777134i 0.110870 0.993835i 0.464636π-0.464636\pi
−0.400901 + 0.916121i 0.631303π0.631303\pi
272272 5.92893 0.359494
273273 0 0
274274 29.8548 1.80359
275275 26.1145 + 6.99737i 1.57477 + 0.421957i
276276 0.245691 + 0.141850i 0.0147889 + 0.00853835i
277277 0.730512 + 0.421761i 0.0438922 + 0.0253412i 0.521786 0.853077i 0.325266π-0.325266\pi
−0.477893 + 0.878418i 0.658599π0.658599\pi
278278 5.62628 20.9976i 0.337442 1.25935i
279279 13.3512 + 13.3512i 0.799316 + 0.799316i
280280 0 0
281281 −6.80029 6.80029i −0.405671 0.405671i 0.474555 0.880226i 0.342609π-0.342609\pi
−0.880226 + 0.474555i 0.842609π0.842609\pi
282282 6.50758 + 11.2715i 0.387521 + 0.671206i
283283 9.91175 17.1677i 0.589192 1.02051i −0.405146 0.914252i 0.632779π-0.632779\pi
0.994338 0.106259i 0.0338873π-0.0338873\pi
284284 −0.0909219 + 0.0243625i −0.00539522 + 0.00144565i
285285 −5.55491 9.62139i −0.329045 0.569922i
286286 12.9821 + 4.99411i 0.767650 + 0.295308i
287287 0 0
288288 −1.76270 + 1.76270i −0.103868 + 0.103868i
289289 7.57502 + 13.1203i 0.445589 + 0.771784i
290290 −27.1924 + 47.0987i −1.59679 + 2.76573i
291291 −2.41478 9.01210i −0.141557 0.528299i
292292 −0.433523 + 1.61793i −0.0253700 + 0.0946822i
293293 −6.47711 + 6.47711i −0.378397 + 0.378397i −0.870524 0.492127i 0.836220π-0.836220\pi
0.492127 + 0.870524i 0.336220π0.336220\pi
294294 0 0
295295 −1.01659 −0.0591879
296296 11.1360 6.42936i 0.647266 0.373699i
297297 −3.10710 11.5959i −0.180292 0.672861i
298298 −28.0879 16.2165i −1.62709 0.939399i
299299 5.72813 0.903015i 0.331266 0.0522227i
300300 1.83332i 0.105847i
301301 0 0
302302 −20.0656 −1.15464
303303 −0.160325 + 0.0925634i −0.00921040 + 0.00531763i
304304 −13.4799 + 3.61193i −0.773125 + 0.207158i
305305 −0.338490 1.26326i −0.0193819 0.0723342i
306306 4.32092 + 1.15779i 0.247011 + 0.0661863i
307307 −17.9487 + 17.9487i −1.02438 + 1.02438i −0.0246898 + 0.999695i 0.507860π0.507860\pi
−0.999695 + 0.0246898i 0.992140π0.992140\pi
308308 0 0
309309 14.4668i 0.822985i
310310 12.8220 47.8523i 0.728240 2.71783i
311311 6.73937 11.6729i 0.382155 0.661912i −0.609215 0.793005i 0.708515π-0.708515\pi
0.991370 + 0.131093i 0.0418488π0.0418488\pi
312312 0.896260 8.46863i 0.0507407 0.479442i
313313 5.61548 3.24210i 0.317406 0.183254i −0.332830 0.942987i 0.608003π-0.608003\pi
0.650236 + 0.759733i 0.274670π0.274670\pi
314314 −13.4869 13.4869i −0.761108 0.761108i
315315 0 0
316316 0.578994i 0.0325710i
317317 30.2378 + 8.10220i 1.69833 + 0.455065i 0.972517 0.232832i 0.0747992π-0.0747992\pi
0.725808 + 0.687897i 0.241466π0.241466\pi
318318 −3.83088 + 1.02648i −0.214825 + 0.0575623i
319319 −23.4849 + 6.29277i −1.31490 + 0.352327i
320320 −26.7219 7.16010i −1.49380 0.400262i
321321 15.0887i 0.842171i
322322 0 0
323323 3.07902 + 3.07902i 0.171322 + 0.171322i
324324 −0.444054 + 0.256374i −0.0246696 + 0.0142430i
325325 23.5618 + 29.1393i 1.30697 + 1.61636i
326326 −7.94348 + 13.7585i −0.439949 + 0.762013i
327327 −1.60530 + 5.99104i −0.0887730 + 0.331306i
328328 8.10523i 0.447537i
329329 0 0
330330 −9.46647 + 9.46647i −0.521112 + 0.521112i
331331 12.0897 + 3.23943i 0.664512 + 0.178055i 0.575281 0.817956i 0.304893π-0.304893\pi
0.0892305 + 0.996011i 0.471559π0.471559\pi
332332 0.280723 + 1.04767i 0.0154067 + 0.0574985i
333333 10.3151 2.76392i 0.565264 0.151462i
334334 −11.0278 + 6.36691i −0.603415 + 0.348382i
335335 −4.12767 −0.225518
336336 0 0
337337 4.54349i 0.247500i −0.992313 0.123750i 0.960508π-0.960508\pi
0.992313 0.123750i 0.0394920π-0.0394920\pi
338338 10.4771 + 16.1844i 0.569880 + 0.880314i
339339 −3.50046 2.02099i −0.190119 0.109765i
340340 −0.275444 1.02797i −0.0149381 0.0557496i
341341 19.1804 11.0738i 1.03868 0.599680i
342342 −10.5293 −0.569359
343343 0 0
344344 21.8078 21.8078i 1.17580 1.17580i
345345 −1.44453 + 5.39108i −0.0777711 + 0.290246i
346346 1.36351 + 5.08869i 0.0733028 + 0.273570i
347347 5.56642 9.64133i 0.298821 0.517574i −0.677045 0.735941i 0.736740π-0.736740\pi
0.975867 + 0.218368i 0.0700732π0.0700732\pi
348348 −0.824356 1.42783i −0.0441901 0.0765395i
349349 16.7058 16.7058i 0.894240 0.894240i −0.100679 0.994919i 0.532101π-0.532101\pi
0.994919 + 0.100679i 0.0321014π0.0321014\pi
350350 0 0
351351 5.97430 15.5301i 0.318885 0.828937i
352352 1.46202 + 2.53229i 0.0779259 + 0.134972i
353353 5.91578 1.58513i 0.314865 0.0843678i −0.0979257 0.995194i 0.531221π-0.531221\pi
0.412791 + 0.910826i 0.364554π0.364554\pi
354354 0.169942 0.294347i 0.00903229 0.0156444i
355355 −0.925909 1.60372i −0.0491421 0.0851167i
356356 1.04265 + 1.04265i 0.0552603 + 0.0552603i
357357 0 0
358358 18.0668 + 18.0668i 0.954860 + 0.954860i
359359 5.62963 21.0100i 0.297120 1.10887i −0.642399 0.766371i 0.722061π-0.722061\pi
0.939519 0.342497i 0.111273π-0.111273\pi
360360 −20.1214 11.6171i −1.06049 0.612274i
361361 7.57833 + 4.37535i 0.398859 + 0.230282i
362362 −8.90835 2.38698i −0.468212 0.125457i
363363 3.74435 0.196527
364364 0 0
365365 −32.9526 −1.72482
366366 0.422356 + 0.113170i 0.0220769 + 0.00591549i
367367 14.0740 + 8.12564i 0.734658 + 0.424155i 0.820124 0.572186i 0.193905π-0.193905\pi
−0.0854660 + 0.996341i 0.527238π0.527238\pi
368368 6.07153 + 3.50540i 0.316500 + 0.182731i
369369 −1.74218 + 6.50191i −0.0906944 + 0.338476i
370370 −19.8124 19.8124i −1.03000 1.03000i
371371 0 0
372372 1.06197 + 1.06197i 0.0550604 + 0.0550604i
373373 −2.10783 3.65087i −0.109139 0.189035i 0.806283 0.591531i 0.201476π-0.201476\pi
−0.915422 + 0.402496i 0.868143π0.868143\pi
374374 2.62358 4.54417i 0.135662 0.234973i
375375 −18.0781 + 4.84402i −0.933551 + 0.250144i
376376 13.2475 + 22.9454i 0.683188 + 1.18332i
377377 −31.4529 12.0997i −1.61991 0.623164i
378378 0 0
379379 18.1305 18.1305i 0.931303 0.931303i −0.0664849 0.997787i 0.521178π-0.521178\pi
0.997787 + 0.0664849i 0.0211784π0.0211784\pi
380380 1.25249 + 2.16937i 0.0642513 + 0.111287i
381381 −4.60494 + 7.97599i −0.235918 + 0.408623i
382382 4.72407 + 17.6305i 0.241704 + 0.902053i
383383 −6.07450 + 22.6703i −0.310392 + 1.15840i 0.617811 + 0.786327i 0.288020π0.288020\pi
−0.928203 + 0.372073i 0.878647π0.878647\pi
384384 7.94630 7.94630i 0.405508 0.405508i
385385 0 0
386386 −31.8191 −1.61955
387387 22.1815 12.8065i 1.12755 0.650989i
388388 0.544471 + 2.03199i 0.0276413 + 0.103159i
389389 −16.8646 9.73676i −0.855067 0.493673i 0.00729024 0.999973i 0.497679π-0.497679\pi
−0.862357 + 0.506300i 0.831013π0.831013\pi
390390 −18.3297 + 2.88961i −0.928163 + 0.146321i
391391 2.18752i 0.110628i
392392 0 0
393393 −15.4712 −0.780417
394394 −2.58833 + 1.49437i −0.130398 + 0.0752855i
395395 11.0025 2.94811i 0.553596 0.148336i
396396 0.297764 + 1.11127i 0.0149632 + 0.0558435i
397397 11.5515 + 3.09522i 0.579755 + 0.155345i 0.536767 0.843731i 0.319646π-0.319646\pi
0.0429883 + 0.999076i 0.486312π0.486312\pi
398398 −7.00124 + 7.00124i −0.350941 + 0.350941i
399399 0 0
400400 45.3051i 2.26525i
401401 −2.43214 + 9.07687i −0.121455 + 0.453277i −0.999689 0.0249551i 0.992056π-0.992056\pi
0.878233 + 0.478233i 0.158722π0.158722\pi
402402 0.690017 1.19514i 0.0344149 0.0596084i
403403 30.5276 + 3.23082i 1.52069 + 0.160939i
404404 0.0361490 0.0208706i 0.00179848 0.00103835i
405405 −7.13285 7.13285i −0.354434 0.354434i
406406 0 0
407407 12.5262i 0.620903i
408408 −3.10302 0.831452i −0.153623 0.0411630i
409409 −18.6466 + 4.99635i −0.922017 + 0.247054i −0.688447 0.725286i 0.741707π-0.741707\pi
−0.233570 + 0.972340i 0.575041π0.575041\pi
410410 17.0594 4.57106i 0.842505 0.225749i
411411 −17.1988 4.60840i −0.848354 0.227316i
412412 3.26188i 0.160701i
413413 0 0
414414 3.74032 + 3.74032i 0.183827 + 0.183827i
415415 −18.4793 + 10.6690i −0.907114 + 0.523723i
416416 −0.426549 + 4.03040i −0.0209133 + 0.197607i
417417 −6.48239 + 11.2278i −0.317444 + 0.549829i
418418 −3.19659 + 11.9298i −0.156350 + 0.583507i
419419 24.1967i 1.18208i −0.806641 0.591042i 0.798717π-0.798717\pi
0.806641 0.591042i 0.201283π-0.201283\pi
420420 0 0
421421 −16.9872 + 16.9872i −0.827906 + 0.827906i −0.987227 0.159321i 0.949070π-0.949070\pi
0.159321 + 0.987227i 0.449070π0.449070\pi
422422 −27.2028 7.28898i −1.32421 0.354822i
423423 5.69498 + 21.2540i 0.276899 + 1.03340i
424424 −7.79855 + 2.08961i −0.378731 + 0.101481i
425425 12.2423 7.06809i 0.593838 0.342853i
426426 0.619132 0.0299971
427427 0 0
428428 3.40212i 0.164448i
429429 −6.70787 4.88094i −0.323859 0.235654i
430430 −58.1987 33.6010i −2.80659 1.62039i
431431 −7.10522 26.5171i −0.342247 1.27728i −0.895796 0.444465i 0.853394π-0.853394\pi
0.553549 0.832816i 0.313273π-0.313273\pi
432432 17.4220 10.0586i 0.838216 0.483945i
433433 26.0271 1.25078 0.625391 0.780312i 0.284940π-0.284940\pi
0.625391 + 0.780312i 0.284940π0.284940\pi
434434 0 0
435435 22.9352 22.9352i 1.09966 1.09966i
436436 0.361952 1.35082i 0.0173344 0.0646928i
437437 1.33265 + 4.97350i 0.0637491 + 0.237915i
438438 5.50864 9.54125i 0.263213 0.455899i
439439 1.85272 + 3.20901i 0.0884257 + 0.153158i 0.906846 0.421463i 0.138483π-0.138483\pi
−0.818420 + 0.574620i 0.805150π0.805150\pi
440440 −19.2709 + 19.2709i −0.918706 + 0.918706i
441441 0 0
442442 6.64626 2.95337i 0.316130 0.140477i
443443 −1.34404 2.32795i −0.0638573 0.110604i 0.832329 0.554282i 0.187007π-0.187007\pi
−0.896187 + 0.443678i 0.853674π0.853674\pi
444444 0.820472 0.219845i 0.0389379 0.0104334i
445445 −14.5043 + 25.1222i −0.687570 + 1.19091i
446446 −2.14419 3.71384i −0.101530 0.175855i
447447 13.6777 + 13.6777i 0.646934 + 0.646934i
448448 0 0
449449 24.6366 + 24.6366i 1.16267 + 1.16267i 0.983888 + 0.178784i 0.0572164π0.0572164\pi
0.178784 + 0.983888i 0.442784π0.442784\pi
450450 −8.84706 + 33.0177i −0.417054 + 1.55647i
451451 6.83784 + 3.94783i 0.321981 + 0.185896i
452452 0.789262 + 0.455681i 0.0371238 + 0.0214334i
453453 11.5594 + 3.09733i 0.543108 + 0.145525i
454454 −9.73430 −0.456854
455455 0 0
456456 7.56149 0.354099
457457 −6.58491 1.76442i −0.308029 0.0825361i 0.101493 0.994836i 0.467638π-0.467638\pi
−0.409522 + 0.912300i 0.634305π0.634305\pi
458458 1.83179 + 1.05758i 0.0855939 + 0.0494177i
459459 −5.43605 3.13850i −0.253733 0.146493i
460460 0.325705 1.21555i 0.0151861 0.0566752i
461461 −5.06375 5.06375i −0.235842 0.235842i 0.579284 0.815126i 0.303332π-0.303332\pi
−0.815126 + 0.579284i 0.803332π0.803332\pi
462462 0 0
463463 −14.8196 14.8196i −0.688725 0.688725i 0.273226 0.961950i 0.411909π-0.411909\pi
−0.961950 + 0.273226i 0.911909π0.911909\pi
464464 −20.3715 35.2845i −0.945724 1.63804i
465465 −14.7730 + 25.5876i −0.685082 + 1.18660i
466466 −12.1681 + 3.26043i −0.563676 + 0.151036i
467467 0.228257 + 0.395352i 0.0105625 + 0.0182947i 0.871258 0.490825i 0.163304π-0.163304\pi
−0.860696 + 0.509119i 0.829971π0.829971\pi
468468 −0.572537 + 1.48830i −0.0264655 + 0.0687969i
469469 0 0
470470 40.8229 40.8229i 1.88302 1.88302i
471471 5.68769 + 9.85137i 0.262075 + 0.453927i
472472 0.345951 0.599204i 0.0159237 0.0275806i
473473 −7.77583 29.0198i −0.357533 1.33433i
474474 −0.985664 + 3.67855i −0.0452731 + 0.168961i
475475 −23.5279 + 23.5279i −1.07953 + 1.07953i
476476 0 0
477477 −6.70504 −0.307003
478478 −8.44260 + 4.87434i −0.386155 + 0.222947i
479479 −8.50540 31.7426i −0.388622 1.45036i −0.832378 0.554209i 0.813021π-0.813021\pi
0.443756 0.896148i 0.353646π-0.353646\pi
480480 −3.37821 1.95041i −0.154193 0.0890236i
481481 10.2154 14.0390i 0.465780 0.640121i
482482 15.9943i 0.728519i
483483 0 0
484484 −0.844253 −0.0383751
485485 −35.8412 + 20.6929i −1.62747 + 0.939617i
486486 23.0908 6.18717i 1.04742 0.280656i
487487 2.99178 + 11.1655i 0.135571 + 0.505956i 0.999995 + 0.00319321i 0.00101643π0.00101643\pi
−0.864424 + 0.502763i 0.832317π0.832317\pi
488488 0.859792 + 0.230381i 0.0389210 + 0.0104288i
489489 6.69986 6.69986i 0.302978 0.302978i
490490 0 0
491491 0.946627i 0.0427207i −0.999772 0.0213603i 0.993200π-0.993200\pi
0.999772 0.0213603i 0.00679973π-0.00679973\pi
492492 −0.138575 + 0.517167i −0.00624743 + 0.0233157i
493493 −6.35636 + 11.0095i −0.286276 + 0.495845i
494494 −13.3116 + 10.7636i −0.598917 + 0.484279i
495495 −19.6011 + 11.3167i −0.881004 + 0.508648i
496496 26.2434 + 26.2434i 1.17836 + 1.17836i
497497 0 0
498498 7.13412i 0.319688i
499499 −21.2427 5.69198i −0.950956 0.254808i −0.250188 0.968197i 0.580492π-0.580492\pi
−0.700768 + 0.713389i 0.747159π0.747159\pi
500500 4.07615 1.09220i 0.182291 0.0488447i
501501 7.33572 1.96560i 0.327736 0.0878165i
502502 −40.1855 10.7677i −1.79357 0.480585i
503503 1.12263i 0.0500556i 0.999687 + 0.0250278i 0.00796742π0.00796742\pi
−0.999687 + 0.0250278i 0.992033π0.992033\pi
504504 0 0
505505 0.580663 + 0.580663i 0.0258392 + 0.0258392i
506506 5.37335 3.10230i 0.238875 0.137914i
507507 −3.53744 10.9408i −0.157103 0.485897i
508508 1.03829 1.79838i 0.0460669 0.0797902i
509509 −4.97409 + 18.5635i −0.220473 + 0.822815i 0.763695 + 0.645577i 0.223383π0.223383\pi
−0.984168 + 0.177238i 0.943284π0.943284\pi
510510 6.99997i 0.309964i
511511 0 0
512512 12.9970 12.9970i 0.574390 0.574390i
513513 14.2713 + 3.82398i 0.630092 + 0.168833i
514514 −5.42008 20.2280i −0.239069 0.892219i
515515 61.9848 16.6088i 2.73137 0.731870i
516516 1.76433 1.01864i 0.0776703 0.0448430i
517517 25.8099 1.13512
518518 0 0
519519 3.14197i 0.137917i
520520 −37.3139 + 5.88238i −1.63632 + 0.257960i
521521 19.3198 + 11.1543i 0.846416 + 0.488678i 0.859440 0.511237i 0.170813π-0.170813\pi
−0.0130243 + 0.999915i 0.504146π0.504146\pi
522522 −7.95620 29.6930i −0.348234 1.29963i
523523 15.3793 8.87924i 0.672489 0.388262i −0.124530 0.992216i 0.539742π-0.539742\pi
0.797019 + 0.603954i 0.206409π0.206409\pi
524524 3.48835 0.152389
525525 0 0
526526 −23.4095 + 23.4095i −1.02070 + 1.02070i
527527 2.99720 11.1857i 0.130560 0.487257i
528528 −2.59582 9.68774i −0.112969 0.421605i
529529 −10.2067 + 17.6785i −0.443768 + 0.768628i
530530 8.79620 + 15.2355i 0.382082 + 0.661786i
531531 0.406313 0.406313i 0.0176325 0.0176325i
532532 0 0
533533 4.44408 + 10.0010i 0.192494 + 0.433190i
534534 −4.84933 8.39929i −0.209851 0.363473i
535535 64.6497 17.3228i 2.79505 0.748931i
536536 1.40467 2.43296i 0.0606725 0.105088i
537537 −7.61914 13.1967i −0.328790 0.569482i
538538 −12.4059 12.4059i −0.534854 0.534854i
539539 0 0
540540 −2.55337 2.55337i −0.109879 0.109879i
541541 3.43267 12.8109i 0.147582 0.550783i −0.852045 0.523468i 0.824638π-0.824638\pi
0.999627 0.0273145i 0.00869555π-0.00869555\pi
542542 −6.34848 3.66530i −0.272691 0.157438i
543543 4.76348 + 2.75019i 0.204420 + 0.118022i
544544 1.47680 + 0.395706i 0.0633171 + 0.0169658i
545545 27.5124 1.17850
546546 0 0
547547 −14.0683 −0.601515 −0.300757 0.953701i 0.597239π-0.597239\pi
−0.300757 + 0.953701i 0.597239π0.597239\pi
548548 3.87788 + 1.03908i 0.165655 + 0.0443871i
549549 0.640195 + 0.369617i 0.0273229 + 0.0157749i
550550 34.7236 + 20.0477i 1.48062 + 0.854835i
551551 7.74464 28.9034i 0.329933 1.23133i
552552 −2.68607 2.68607i −0.114327 0.114327i
553553 0 0
554554 0.884579 + 0.884579i 0.0375822 + 0.0375822i
555555 8.35532 + 14.4718i 0.354664 + 0.614295i
556556 1.46161 2.53158i 0.0619861 0.107363i
557557 16.4161 4.39869i 0.695574 0.186379i 0.106327 0.994331i 0.466091π-0.466091\pi
0.589247 + 0.807953i 0.299424π0.299424\pi
558558 14.0011 + 24.2505i 0.592712 + 1.02661i
559559 14.9513 38.8656i 0.632371 1.64384i
560560 0 0
561561 −2.21283 + 2.21283i −0.0934260 + 0.0934260i
562562 −7.13128 12.3517i −0.300815 0.521026i
563563 −8.62337 + 14.9361i −0.363432 + 0.629482i −0.988523 0.151069i 0.951728π-0.951728\pi
0.625091 + 0.780552i 0.285062π0.285062\pi
564564 0.452983 + 1.69056i 0.0190740 + 0.0711853i
565565 −4.64045 + 17.3184i −0.195225 + 0.728590i
566566 20.7884 20.7884i 0.873800 0.873800i
567567 0 0
568568 1.26037 0.0528840
569569 −13.5496 + 7.82285i −0.568028 + 0.327951i −0.756361 0.654154i 0.773025π-0.773025\pi
0.188333 + 0.982105i 0.439691π0.439691\pi
570570 −4.26441 15.9150i −0.178616 0.666605i
571571 10.5267 + 6.07757i 0.440527 + 0.254338i 0.703821 0.710377i 0.251476π-0.251476\pi
−0.263294 + 0.964716i 0.584809π0.584809\pi
572572 1.51245 + 1.10053i 0.0632387 + 0.0460153i
573573 10.8858i 0.454760i
574574 0 0
575575 16.7156 0.697089
576576 13.5421 7.81853i 0.564253 0.325772i
577577 −37.7804 + 10.1232i −1.57282 + 0.421435i −0.936693 0.350151i 0.886130π-0.886130\pi
−0.636125 + 0.771586i 0.719464π0.719464\pi
578578 5.81521 + 21.7026i 0.241881 + 0.902711i
579579 18.3304 + 4.91161i 0.761785 + 0.204120i
580580 −5.17130 + 5.17130i −0.214726 + 0.214726i
581581 0 0
582582 13.8369i 0.573556i
583583 −2.03558 + 7.59690i −0.0843053 + 0.314632i
584584 11.2140 19.4232i 0.464037 0.803736i
585585 −31.1971 3.30168i −1.28984 0.136508i
586586 −11.7647 + 6.79237i −0.485996 + 0.280590i
587587 6.17868 + 6.17868i 0.255021 + 0.255021i 0.823026 0.568004i 0.192284π-0.192284\pi
−0.568004 + 0.823026i 0.692284π0.692284\pi
588588 0 0
589589 27.2575i 1.12313i
590590 −1.45627 0.390207i −0.0599538 0.0160646i
591591 1.72176 0.461345i 0.0708239 0.0189772i
592592 20.2755 5.43281i 0.833320 0.223287i
593593 32.6629 + 8.75200i 1.34130 + 0.359402i 0.856918 0.515453i 0.172376π-0.172376\pi
0.484387 + 0.874854i 0.339043π0.339043\pi
594594 17.8039i 0.730502i
595595 0 0
596596 −3.08397 3.08397i −0.126324 0.126324i
597597 5.11400 2.95257i 0.209302 0.120841i
598598 8.55224 + 0.905108i 0.349727 + 0.0370126i
599599 −5.13357 + 8.89161i −0.209752 + 0.363301i −0.951636 0.307227i 0.900599π-0.900599\pi
0.741884 + 0.670528i 0.233932π0.233932\pi
600600 6.35342 23.7113i 0.259377 0.968009i
601601 4.09959i 0.167226i −0.996498 0.0836128i 0.973354π-0.973354\pi
0.996498 0.0836128i 0.0266459π-0.0266459\pi
602602 0 0
603603 1.64976 1.64976i 0.0671835 0.0671835i
604604 −2.60634 0.698368i −0.106051 0.0284162i
605605 −4.29875 16.0432i −0.174769 0.652247i
606606 −0.265197 + 0.0710593i −0.0107729 + 0.00288658i
607607 −6.28556 + 3.62897i −0.255123 + 0.147295i −0.622108 0.782932i 0.713723π-0.713723\pi
0.366985 + 0.930227i 0.380390π0.380390\pi
608608 −3.59867 −0.145946
609609 0 0
610610 1.93957i 0.0785308i
611611 28.9268 + 21.0484i 1.17025 + 0.851529i
612612 0.520955 + 0.300773i 0.0210583 + 0.0121580i
613613 5.57436 + 20.8038i 0.225146 + 0.840257i 0.982346 + 0.187073i 0.0599002π0.0599002\pi
−0.757200 + 0.653183i 0.773433π0.773433\pi
614614 −32.6012 + 18.8223i −1.31568 + 0.759606i
615615 −10.5332 −0.424740
616616 0 0
617617 −28.5301 + 28.5301i −1.14858 + 1.14858i −0.161748 + 0.986832i 0.551713π0.551713\pi
−0.986832 + 0.161748i 0.948287π0.948287\pi
618618 −5.55294 + 20.7238i −0.223372 + 0.833635i
619619 8.91786 + 33.2819i 0.358439 + 1.33771i 0.876101 + 0.482128i 0.160136π0.160136\pi
−0.517662 + 0.855585i 0.673197π0.673197\pi
620620 3.33093 5.76934i 0.133773 0.231702i
621621 −3.71119 6.42797i −0.148925 0.257946i
622622 14.1348 14.1348i 0.566754 0.566754i
623623 0 0
624624 4.99121 12.9746i 0.199808 0.519400i
625625 15.5266 + 26.8929i 0.621065 + 1.07572i
626626 9.28871 2.48890i 0.371252 0.0994766i
627627 3.68299 6.37912i 0.147084 0.254758i
628628 −1.28243 2.22123i −0.0511744 0.0886366i
629629 −4.63126 4.63126i −0.184660 0.184660i
630630 0 0
631631 −26.1762 26.1762i −1.04206 1.04206i −0.999076 0.0429839i 0.986314π-0.986314\pi
−0.0429839 0.999076i 0.513686π-0.513686\pi
632632 −2.00652 + 7.48844i −0.0798151 + 0.297874i
633633 14.5459 + 8.39809i 0.578148 + 0.333794i
634634 40.2062 + 23.2130i 1.59679 + 0.921907i
635635 39.4610 + 10.5735i 1.56596 + 0.419598i
636636 −0.533325 −0.0211477
637637 0 0
638638 −36.0579 −1.42755
639639 1.01105 + 0.270911i 0.0399966 + 0.0107171i
640640 −43.1698 24.9241i −1.70644 0.985212i
641641 10.1134 + 5.83896i 0.399454 + 0.230625i 0.686248 0.727367i 0.259256π-0.259256\pi
−0.286794 + 0.957992i 0.592590π0.592590\pi
642642 −5.79167 + 21.6148i −0.228579 + 0.853069i
643643 12.8214 + 12.8214i 0.505627 + 0.505627i 0.913181 0.407554i 0.133618π-0.133618\pi
−0.407554 + 0.913181i 0.633618π0.633618\pi
644644 0 0
645645 28.3405 + 28.3405i 1.11591 + 1.11591i
646646 3.22889 + 5.59260i 0.127039 + 0.220038i
647647 5.73484 9.93304i 0.225460 0.390508i −0.730997 0.682380i 0.760945π-0.760945\pi
0.956457 + 0.291872i 0.0942782π0.0942782\pi
648648 6.63165 1.77695i 0.260516 0.0698050i
649649 −0.337005 0.583711i −0.0132286 0.0229126i
650650 22.5677 + 50.7864i 0.885178 + 1.99200i
651651 0 0
652652 −1.51064 + 1.51064i −0.0591614 + 0.0591614i
653653 4.47691 + 7.75423i 0.175195 + 0.303446i 0.940229 0.340544i 0.110611π-0.110611\pi
−0.765034 + 0.643990i 0.777278π0.777278\pi
654654 −4.59922 + 7.96608i −0.179844 + 0.311498i
655655 17.7619 + 66.2883i 0.694014 + 2.59010i
656656 −3.42446 + 12.7803i −0.133703 + 0.498986i
657657 13.1706 13.1706i 0.513835 0.513835i
658658 0 0
659659 22.2313 0.866009 0.433005 0.901392i 0.357453π-0.357453\pi
0.433005 + 0.901392i 0.357453π0.357453\pi
660660 −1.55909 + 0.900139i −0.0606874 + 0.0350379i
661661 0.636436 + 2.37521i 0.0247545 + 0.0923850i 0.977198 0.212330i 0.0681053π-0.0681053\pi
−0.952443 + 0.304715i 0.901439π0.901439\pi
662662 16.0753 + 9.28107i 0.624784 + 0.360719i
663663 −4.28467 + 0.675460i −0.166403 + 0.0262327i
664664 14.5230i 0.563600i
665665 0 0
666666 15.8374 0.613688
667667 −13.0185 + 7.51622i −0.504077 + 0.291029i
668668 −1.65401 + 0.443192i −0.0639957 + 0.0171476i
669669 0.661955 + 2.47045i 0.0255927 + 0.0955132i
670670 −5.91294 1.58437i −0.228437 0.0612094i
671671 0.613137 0.613137i 0.0236699 0.0236699i
672672 0 0
673673 6.44000i 0.248244i −0.992267 0.124122i 0.960389π-0.960389\pi
0.992267 0.124122i 0.0396114π-0.0396114\pi
674674 1.74398 6.50861i 0.0671755 0.250702i
675675 23.9824 41.5387i 0.923083 1.59883i
676676 0.797602 + 2.46686i 0.0306770 + 0.0948792i
677677 4.00871 2.31443i 0.154067 0.0889507i −0.420984 0.907068i 0.638315π-0.638315\pi
0.575052 + 0.818117i 0.304982π0.304982\pi
678678 −4.23871 4.23871i −0.162787 0.162787i
679679 0 0
680680 14.2499i 0.546458i
681681 5.60775 + 1.50259i 0.214889 + 0.0575795i
682682 31.7268 8.50116i 1.21488 0.325526i
683683 −17.5171 + 4.69368i −0.670272 + 0.179599i −0.577877 0.816124i 0.696119π-0.696119\pi
−0.0923945 + 0.995722i 0.529452π0.529452\pi
684684 −1.36766 0.366464i −0.0522939 0.0140121i
685685 78.9813i 3.01772i
686686 0 0
687687 −0.892011 0.892011i −0.0340323 0.0340323i
688688 43.6002 25.1726i 1.66224 0.959697i
689689 −8.47681 + 6.85428i −0.322941 + 0.261127i
690690 −4.13863 + 7.16832i −0.157555 + 0.272893i
691691 0.159887 0.596708i 0.00608240 0.0226998i −0.962818 0.270151i 0.912926π-0.912926\pi
0.968900 + 0.247451i 0.0795930π0.0795930\pi
692692 0.708433i 0.0269306i
693693 0 0
694694 11.6747 11.6747i 0.443166 0.443166i
695695 55.5493 + 14.8844i 2.10711 + 0.564597i
696696 5.71366 + 21.3237i 0.216576 + 0.808271i
697697 3.98773 1.06851i 0.151046 0.0404726i
698698 30.3436 17.5189i 1.14852 0.663101i
699699 7.51309 0.284171
700700 0 0
701701 14.4452i 0.545586i −0.962073 0.272793i 0.912053π-0.912053\pi
0.962073 0.272793i 0.0879474π-0.0879474\pi
702702 14.5194 19.9539i 0.547998 0.753113i
703703 13.3509 + 7.70815i 0.503539 + 0.290718i
704704 −4.74725 17.7170i −0.178919 0.667734i
705705 −29.8188 + 17.2159i −1.12304 + 0.648388i
706706 9.08287 0.341838
707707 0 0
708708 0.0323185 0.0323185i 0.00121460 0.00121460i
709709 0.851819 3.17903i 0.0319907 0.119391i −0.948084 0.318020i 0.896982π-0.896982\pi
0.980075 + 0.198629i 0.0636488π0.0636488\pi
710710 −0.710803 2.65275i −0.0266760 0.0995561i
711711 −3.21921 + 5.57583i −0.120730 + 0.209110i
712712 −9.87181 17.0985i −0.369962 0.640792i
713713 9.68268 9.68268i 0.362619 0.362619i
714714 0 0
715715 −13.2120 + 34.3444i −0.494100 + 1.28441i
716716 1.71792 + 2.97552i 0.0642016 + 0.111201i
717717 5.61603 1.50481i 0.209734 0.0561982i
718718 16.1290 27.9363i 0.601930 1.04257i
719719 −24.6176 42.6390i −0.918083 1.59017i −0.802323 0.596890i 0.796403π-0.796403\pi
−0.115760 0.993277i 0.536930π-0.536930\pi
720720 −26.8190 26.8190i −0.999485 0.999485i
721721 0 0
722722 9.17662 + 9.17662i 0.341518 + 0.341518i
723723 2.46889 9.21401i 0.0918188 0.342673i
724724 −1.07404 0.620097i −0.0399164 0.0230457i
725725 −84.1277 48.5712i −3.12443 1.80389i
726726 5.36383 + 1.43723i 0.199070 + 0.0533408i
727727 −34.0096 −1.26135 −0.630674 0.776048i 0.717221π-0.717221\pi
−0.630674 + 0.776048i 0.717221π0.717221\pi
728728 0 0
729729 −6.54406 −0.242372
730730 −47.2050 12.6485i −1.74714 0.468144i
731731 −13.6042 7.85441i −0.503171 0.290506i
732732 0.0509216 + 0.0293996i 0.00188212 + 0.00108664i
733733 9.70406 36.2160i 0.358428 1.33767i −0.517688 0.855569i 0.673207π-0.673207\pi
0.876116 0.482101i 0.160126π-0.160126\pi
734734 17.0423 + 17.0423i 0.629042 + 0.629042i
735735 0 0
736736 1.27836 + 1.27836i 0.0471208 + 0.0471208i
737737 −1.36835 2.37005i −0.0504038 0.0873020i
738738 −4.99140 + 8.64536i −0.183736 + 0.318240i
739739 −4.13697 + 1.10850i −0.152181 + 0.0407767i −0.334105 0.942536i 0.608434π-0.608434\pi
0.181924 + 0.983313i 0.441767π0.441767\pi
740740 −1.88391 3.26302i −0.0692538 0.119951i
741741 9.33004 4.14595i 0.342748 0.152305i
742742 0 0
743743 −25.3436 + 25.3436i −0.929767 + 0.929767i −0.997691 0.0679234i 0.978363π-0.978363\pi
0.0679234 + 0.997691i 0.478363π0.478363\pi
744744 −10.0547 17.4153i −0.368623 0.638474i
745745 42.9011 74.3069i 1.57177 2.72239i
746746 −1.61814 6.03899i −0.0592444 0.221103i
747747 3.12164 11.6501i 0.114215 0.426256i
748748 0.498937 0.498937i 0.0182429 0.0182429i
749749 0 0
750750 −27.7565 −1.01352
751751 −39.9450 + 23.0623i −1.45761 + 0.841554i −0.998894 0.0470273i 0.985025π-0.985025\pi
−0.458720 + 0.888581i 0.651692π0.651692\pi
752752 11.1941 + 41.7771i 0.408209 + 1.52346i
753753 21.4880 + 12.4061i 0.783067 + 0.452104i
754754 −40.4124 29.4058i −1.47173 1.07090i
755755 53.0837i 1.93191i
756756 0 0
757757 −38.5756 −1.40205 −0.701027 0.713135i 0.747275π-0.747275\pi
−0.701027 + 0.713135i 0.747275π0.747275\pi
758758 32.9315 19.0130i 1.19612 0.690583i
759759 −3.57436 + 0.957747i −0.129741 + 0.0347640i
760760 −8.68107 32.3982i −0.314896 1.17521i
761761 −9.60394 2.57337i −0.348142 0.0932845i 0.0805104 0.996754i 0.474345π-0.474345\pi
−0.428653 + 0.903469i 0.641012π0.641012\pi
762762 −9.65816 + 9.65816i −0.349878 + 0.349878i
763763 0 0
764764 2.45446i 0.0887993i
765765 −3.06294 + 11.4311i −0.110741 + 0.413291i
766766 −17.4036 + 30.1439i −0.628818 + 1.08914i
767767 0.0983225 0.929035i 0.00355022 0.0335455i
768768 3.63106 2.09640i 0.131025 0.0756472i
769769 28.4649 + 28.4649i 1.02647 + 1.02647i 0.999640 + 0.0268295i 0.00854111π0.00854111\pi
0.0268295 + 0.999640i 0.491459π0.491459\pi
770770 0 0
771771 12.4896i 0.449803i
772772 −4.13302 1.10744i −0.148751 0.0398577i
773773 24.6946 6.61690i 0.888203 0.237993i 0.214260 0.976777i 0.431266π-0.431266\pi
0.673943 + 0.738783i 0.264599π0.264599\pi
774774 36.6909 9.83129i 1.31883 0.353379i
775775 85.4739 + 22.9027i 3.07031 + 0.822688i
776776 28.1677i 1.01116i
777777 0 0
778778 −20.4214 20.4214i −0.732141 0.732141i
779779 −8.41547 + 4.85867i −0.301515 + 0.174080i
780780 −2.48145 0.262619i −0.0888500 0.00940326i
781781 0.613891 1.06329i 0.0219667 0.0380475i
782782 0.839661 3.13366i 0.0300262 0.112059i
783783 43.1350i 1.54152i
784784 0 0
785785 35.6797 35.6797i 1.27346 1.27346i
786786 −22.1627 5.93847i −0.790516 0.211818i
787787 4.69577 + 17.5248i 0.167386 + 0.624693i 0.997724 + 0.0674326i 0.0214808π0.0214808\pi
−0.830338 + 0.557260i 0.811853π0.811853\pi
788788 −0.388213 + 0.104021i −0.0138295 + 0.00370561i
789789 17.0993 9.87229i 0.608751 0.351463i
790790 16.8928 0.601020
791791 0 0
792792 15.4046i 0.547378i
793793 1.18721 0.187158i 0.0421589 0.00664617i
794794 15.3597 + 8.86791i 0.545094 + 0.314710i
795795 −2.71557 10.1347i −0.0963114 0.359439i
796796 −1.15307 + 0.665728i −0.0408696 + 0.0235961i
797797 6.98547 0.247438 0.123719 0.992317i 0.460518π-0.460518\pi
0.123719 + 0.992317i 0.460518π0.460518\pi
798798 0 0
799799 9.54256 9.54256i 0.337592 0.337592i
800800 −3.02373 + 11.2847i −0.106905 + 0.398975i
801801 −4.24380 15.8381i −0.149947 0.559611i
802802 −6.96815 + 12.0692i −0.246054 + 0.426178i
803803 −10.9240 18.9209i −0.385500 0.667706i
804804 0.131223 0.131223i 0.00462789 0.00462789i
805805 0 0
806806 42.4910 + 16.3459i 1.49668 + 0.575761i
807807 5.23181 + 9.06176i 0.184168 + 0.318989i
808808 −0.539862 + 0.144656i −0.0189923 + 0.00508897i
809809 −1.00660 + 1.74348i −0.0353902 + 0.0612976i −0.883178 0.469038i 0.844601π-0.844601\pi
0.847788 + 0.530336i 0.177934π0.177934\pi
810810 −7.48003 12.9558i −0.262821 0.455220i
811811 −19.2255 19.2255i −0.675097 0.675097i 0.283790 0.958887i 0.408408π-0.408408\pi
−0.958887 + 0.283790i 0.908408π0.908408\pi
812812 0 0
813813 3.09147 + 3.09147i 0.108422 + 0.108422i
814814 4.80809 17.9440i 0.168523 0.628938i
815815 −36.3983 21.0146i −1.27498 0.736109i
816816 −4.54153 2.62206i −0.158985 0.0917903i
817817 35.7152 + 9.56987i 1.24952 + 0.334807i
818818 −28.6294 −1.00100
819819 0 0
820820 2.37497 0.0829374
821821 −9.31280 2.49536i −0.325019 0.0870885i 0.0926203 0.995702i 0.470476π-0.470476\pi
−0.417639 + 0.908613i 0.637142π0.637142\pi
822822 −22.8686 13.2032i −0.797635 0.460515i
823823 −15.6607 9.04171i −0.545898 0.315174i 0.201568 0.979475i 0.435396π-0.435396\pi
−0.747466 + 0.664300i 0.768730π0.768730\pi
824824 −11.3041 + 42.1876i −0.393798 + 1.46967i
825825 −16.9090 16.9090i −0.588697 0.588697i
826826 0 0
827827 12.8291 + 12.8291i 0.446111 + 0.446111i 0.894059 0.447949i 0.147845π-0.147845\pi
−0.447949 + 0.894059i 0.647845π0.647845\pi
828828 0.355656 + 0.616014i 0.0123599 + 0.0214080i
829829 −14.1033 + 24.4277i −0.489829 + 0.848409i −0.999931 0.0117047i 0.996274π-0.996274\pi
0.510102 + 0.860114i 0.329608π0.329608\pi
830830 −30.5671 + 8.19043i −1.06100 + 0.284294i
831831 −0.373046 0.646134i −0.0129408 0.0224141i
832832 9.12795 23.7280i 0.316455 0.822621i
833833 0 0
834834 −13.5958 + 13.5958i −0.470785 + 0.470785i
835835 −16.8438 29.1742i −0.582902 1.00962i
836836 −0.830418 + 1.43833i −0.0287206 + 0.0497455i
837837 −10.1697 37.9537i −0.351515 1.31187i
838838 9.28767 34.6620i 0.320837 1.19738i
839839 −7.67294 + 7.67294i −0.264899 + 0.264899i −0.827041 0.562142i 0.809978π-0.809978\pi
0.562142 + 0.827041i 0.309978π0.309978\pi
840840 0 0
841841 58.3606 2.01243
842842 −30.8548 + 17.8140i −1.06333 + 0.613912i
843843 2.20158 + 8.21639i 0.0758263 + 0.282988i
844844 −3.27973 1.89355i −0.112893 0.0651787i
845845 −42.8160 + 27.7174i −1.47291 + 0.953506i
846846 32.6326i 1.12193i
847847 0 0
848848 −13.1796 −0.452588
849849 −15.1847 + 8.76689i −0.521137 + 0.300879i
850850 20.2503 5.42604i 0.694579 0.186112i
851851 −2.00448 7.48080i −0.0687125 0.256439i
852852 0.0804200 + 0.0215485i 0.00275514 + 0.000738238i
853853 −10.4908 + 10.4908i −0.359198 + 0.359198i −0.863517 0.504319i 0.831744π-0.831744\pi
0.504319 + 0.863517i 0.331744π0.331744\pi
854854 0 0
855855 27.8554i 0.952634i
856856 −11.7901 + 44.0014i −0.402979 + 1.50394i
857857 −8.61727 + 14.9255i −0.294360 + 0.509847i −0.974836 0.222924i 0.928440π-0.928440\pi
0.680476 + 0.732771i 0.261773π0.261773\pi
858858 −7.73561 9.56678i −0.264090 0.326604i
859859 −32.5438 + 18.7892i −1.11038 + 0.641079i −0.938928 0.344113i 0.888180π-0.888180\pi
−0.171453 + 0.985192i 0.554846π0.554846\pi
860860 −6.39005 6.39005i −0.217899 0.217899i
861861 0 0
862862 40.7133i 1.38670i
863863 −1.19297 0.319657i −0.0406093 0.0108812i 0.238457 0.971153i 0.423358π-0.423358\pi
−0.279067 + 0.960272i 0.590025π0.590025\pi
864864 5.01085 1.34265i 0.170472 0.0456779i
865865 −13.4622 + 3.60719i −0.457729 + 0.122648i
866866 37.2842 + 9.99026i 1.26697 + 0.339483i
867867 13.4001i 0.455092i
868868 0 0
869869 5.34017 + 5.34017i 0.181153 + 0.181153i
870870 41.6585 24.0515i 1.41236 0.815424i
871871 0.399221 3.77218i 0.0135271 0.127815i
872872 −9.36265 + 16.2166i −0.317059 + 0.549163i
873873 6.05452 22.5958i 0.204915 0.764752i
874874 7.63614i 0.258296i
875875 0 0
876876 1.04760 1.04760i 0.0353952 0.0353952i
877877 45.7327 + 12.2540i 1.54428 + 0.413789i 0.927646 0.373460i 0.121829π-0.121829\pi
0.616636 + 0.787249i 0.288495π0.288495\pi
878878 1.42230 + 5.30810i 0.0480004 + 0.179140i
879879 7.82591 2.09695i 0.263962 0.0707283i
880880 −38.5282 + 22.2443i −1.29879 + 0.749855i
881881 −25.5041 −0.859255 −0.429627 0.903006i 0.641355π-0.641355\pi
−0.429627 + 0.903006i 0.641355π0.641355\pi
882882 0 0
883883 34.7968i 1.17101i 0.810670 + 0.585503i 0.199103π0.199103\pi
−0.810670 + 0.585503i 0.800897π0.800897\pi
884884 0.966081 0.152299i 0.0324928 0.00512236i
885885 0.778700 + 0.449582i 0.0261757 + 0.0151125i
886886 −1.03180 3.85071i −0.0346638 0.129367i
887887 −39.3189 + 22.7008i −1.32020 + 0.762217i −0.983760 0.179488i 0.942556π-0.942556\pi
−0.336439 + 0.941705i 0.609223π0.609223\pi
888888 −11.3735 −0.381669
889889 0 0
890890 −30.4205 + 30.4205i −1.01970 + 1.01970i
891891 1.73100 6.46018i 0.0579907 0.216424i
892892 −0.149254 0.557023i −0.00499739 0.0186505i
893893 −15.8824 + 27.5091i −0.531484 + 0.920558i
894894 14.3434 + 24.8436i 0.479717 + 0.830894i
895895 −47.7959 + 47.7959i −1.59764 + 1.59764i
896896 0 0
897897 −4.78707 1.84154i −0.159836 0.0614873i
898898 25.8357 + 44.7488i 0.862149 + 1.49329i
899899 −76.8671 + 20.5965i −2.56366 + 0.686931i
900900 −2.29831 + 3.98080i −0.0766105 + 0.132693i
901901 2.05616 + 3.56137i 0.0685005 + 0.118646i
902902 8.27996 + 8.27996i 0.275693 + 0.275693i
903903 0 0
904904 −8.62877 8.62877i −0.286989 0.286989i
905905 6.31480 23.5671i 0.209911 0.783398i
906906 15.3701 + 8.87394i 0.510638 + 0.294817i
907907 −0.0976763 0.0563935i −0.00324329 0.00187251i 0.498377 0.866960i 0.333929π-0.333929\pi
−0.501621 + 0.865088i 0.667263π0.667263\pi
908908 −1.26440 0.338796i −0.0419607 0.0112433i
909909 −0.464163 −0.0153953
910910 0 0
911911 −0.606928 −0.0201084 −0.0100542 0.999949i 0.503200π-0.503200\pi
−0.0100542 + 0.999949i 0.503200π0.503200\pi
912912 11.9229 + 3.19473i 0.394807 + 0.105788i
913913 −12.2521 7.07372i −0.405484 0.234106i
914914 −8.75571 5.05511i −0.289613 0.167208i
915915 −0.299393 + 1.11735i −0.00989762 + 0.0369384i
916916 0.201125 + 0.201125i 0.00664536 + 0.00664536i
917917 0 0
918918 −6.58253 6.58253i −0.217256 0.217256i
919919 −24.4824 42.4048i −0.807600 1.39880i −0.914522 0.404536i 0.867433π-0.867433\pi
0.106922 0.994267i 0.465900π-0.465900\pi
920920 −8.42503 + 14.5926i −0.277765 + 0.481103i
921921 21.6863 5.81084i 0.714589 0.191474i
922922 −5.31022 9.19757i −0.174883 0.302906i
923923 1.55516 0.691058i 0.0511886 0.0227465i
924924 0 0
925925 35.3890 35.3890i 1.16358 1.16358i
926926 −15.5409 26.9176i −0.510706 0.884568i
927927 −18.1361 + 31.4126i −0.595666 + 1.03172i
928928 −2.71925 10.1484i −0.0892638 0.333137i
929929 −4.07062 + 15.1918i −0.133553 + 0.498426i −1.00000 0.000843401i 0.999732π-0.999732\pi
0.866447 + 0.499269i 0.166398π0.166398\pi
930930 −30.9841 + 30.9841i −1.01601 + 1.01601i
931931 0 0
932932 −1.69401 −0.0554890
933933 −10.3247 + 5.96094i −0.338014 + 0.195152i
934934 0.175229 + 0.653962i 0.00573366 + 0.0213983i
935935 12.0217 + 6.94071i 0.393150 + 0.226985i
936936 12.5627 17.2649i 0.410624 0.564320i
937937 2.27169i 0.0742129i 0.999311 + 0.0371065i 0.0118141π0.0118141\pi
−0.999311 + 0.0371065i 0.988186π0.988186\pi
938938 0 0
939939 −5.73524 −0.187163
940940 6.72336 3.88173i 0.219292 0.126608i
941941 −27.5932 + 7.39357i −0.899512 + 0.241023i −0.678807 0.734317i 0.737502π-0.737502\pi
−0.220705 + 0.975341i 0.570836π0.570836\pi
942942 4.36634 + 16.2954i 0.142263 + 0.530933i
943943 4.71537 + 1.26348i 0.153554 + 0.0411446i
944944 0.798656 0.798656i 0.0259940 0.0259940i
945945 0 0
946946 44.5559i 1.44864i
947947 −0.196990 + 0.735176i −0.00640131 + 0.0238900i −0.969053 0.246854i 0.920603π-0.920603\pi
0.962651 + 0.270744i 0.0872698π0.0872698\pi
948948 −0.256059 + 0.443506i −0.00831640 + 0.0144044i
949949 3.18712 30.1146i 0.103458 0.977562i
950950 −42.7350 + 24.6731i −1.38651 + 0.800500i
951951 −19.5788 19.5788i −0.634887 0.634887i
952952 0 0
953953 7.93535i 0.257051i 0.991706 + 0.128526i 0.0410244π0.0410244\pi
−0.991706 + 0.128526i 0.958976π0.958976\pi
954954 −9.60507 2.57367i −0.310976 0.0833257i
955955 −46.6416 + 12.4976i −1.50929 + 0.404412i
956956 −1.26627 + 0.339296i −0.0409540 + 0.0109736i
957957 20.7723 + 5.56592i 0.671473 + 0.179921i
958958 48.7364i 1.57460i
959959 0 0
960960 17.3023 + 17.3023i 0.558429 + 0.558429i
961961 35.9314 20.7450i 1.15908 0.669194i
962962 20.0224 16.1899i 0.645547 0.521984i
963963 −18.9158 + 32.7631i −0.609553 + 1.05578i
964964 −0.556670 + 2.07752i −0.0179291 + 0.0669124i
965965 84.1778i 2.70978i
966966 0 0
967967 −1.26298 + 1.26298i −0.0406147 + 0.0406147i −0.727122 0.686508i 0.759143π-0.759143\pi
0.686508 + 0.727122i 0.259143π0.259143\pi
968968 10.9192 + 2.92578i 0.350956 + 0.0940383i
969969 −0.996826 3.72021i −0.0320227 0.119510i
970970 −59.2858 + 15.8856i −1.90355 + 0.510055i
971971 0.300693 0.173605i 0.00964970 0.00557126i −0.495167 0.868798i 0.664893π-0.664893\pi
0.504817 + 0.863226i 0.331560π0.331560\pi
972972 3.21464 0.103110
973973 0 0
974974 17.1431i 0.549299i
975975 −5.16142 32.7406i −0.165298 1.04854i
976976 1.25838 + 0.726525i 0.0402797 + 0.0232555i
977977 −2.88386 10.7627i −0.0922627 0.344329i 0.904328 0.426839i 0.140373π-0.140373\pi
−0.996590 + 0.0825101i 0.973706π0.973706\pi
978978 12.1693 7.02596i 0.389132 0.224666i
979979 −19.2331 −0.614693
980980 0 0
981981 −10.9963 + 10.9963i −0.351084 + 0.351084i
982982 0.363354 1.35606i 0.0115951 0.0432735i
983983 8.67608 + 32.3796i 0.276724 + 1.03275i 0.954677 + 0.297643i 0.0962006π0.0962006\pi
−0.677953 + 0.735105i 0.737133π0.737133\pi
984984 3.58452 6.20857i 0.114270 0.197922i
985985 −3.95339 6.84747i −0.125965 0.218178i
986986 −13.3315 + 13.3315i −0.424561 + 0.424561i
987987 0 0
988988 −2.10368 + 0.934803i −0.0669270 + 0.0297400i
989989 −9.28761 16.0866i −0.295329 0.511525i
990990 −32.4227 + 8.68762i −1.03046 + 0.276111i
991991 −17.8999 + 31.0035i −0.568608 + 0.984858i 0.428096 + 0.903733i 0.359184π0.359184\pi
−0.996704 + 0.0811244i 0.974149π0.974149\pi
992992 4.78525 + 8.28829i 0.151932 + 0.263154i
993993 −7.82804 7.82804i −0.248415 0.248415i
994994 0 0
995995 −18.5219 18.5219i −0.587183 0.587183i
996996 0.248298 0.926661i 0.00786763 0.0293624i
997997 53.9761 + 31.1631i 1.70944 + 0.986946i 0.935247 + 0.353996i 0.115177π0.115177\pi
0.774193 + 0.632949i 0.218156π0.218156\pi
998998 −28.2457 16.3077i −0.894102 0.516210i
999999 −21.4659 5.75176i −0.679150 0.181978i
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 637.2.bc.c.31.19 112
7.2 even 3 inner 637.2.bc.c.460.10 112
7.3 odd 6 637.2.i.b.538.9 yes 56
7.4 even 3 637.2.i.b.538.10 yes 56
7.5 odd 6 inner 637.2.bc.c.460.9 112
7.6 odd 2 inner 637.2.bc.c.31.20 112
13.8 odd 4 inner 637.2.bc.c.619.9 112
91.34 even 4 inner 637.2.bc.c.619.10 112
91.47 even 12 inner 637.2.bc.c.411.19 112
91.60 odd 12 637.2.i.b.489.10 yes 56
91.73 even 12 637.2.i.b.489.9 56
91.86 odd 12 inner 637.2.bc.c.411.20 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.i.b.489.9 56 91.73 even 12
637.2.i.b.489.10 yes 56 91.60 odd 12
637.2.i.b.538.9 yes 56 7.3 odd 6
637.2.i.b.538.10 yes 56 7.4 even 3
637.2.bc.c.31.19 112 1.1 even 1 trivial
637.2.bc.c.31.20 112 7.6 odd 2 inner
637.2.bc.c.411.19 112 91.47 even 12 inner
637.2.bc.c.411.20 112 91.86 odd 12 inner
637.2.bc.c.460.9 112 7.5 odd 6 inner
637.2.bc.c.460.10 112 7.2 even 3 inner
637.2.bc.c.619.9 112 13.8 odd 4 inner
637.2.bc.c.619.10 112 91.34 even 4 inner