Properties

Label 961.2.g.l.732.2
Level 961961
Weight 22
Character 961.732
Analytic conductor 7.6747.674
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [961,2,Mod(235,961)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(961, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("961.235");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 961=312 961 = 31^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 961.g (of order 1515, degree 88, 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: 7.673623634257.67362363425
Analytic rank: 00
Dimension: 1616
Relative dimension: 22 over Q(ζ15)\Q(\zeta_{15})
Coefficient field: Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16+19x14+140x12+511x10+979x8+956x6+410x4+44x2+1 x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 31)
Sato-Tate group: SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Embedding invariants

Embedding label 732.2
Root 1.83925i-1.83925i of defining polynomial
Character χ\chi == 961.732
Dual form 961.2.g.l.235.2

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+(0.557811+0.405274i)q2+(0.824384+0.367040i)q3+(0.4711271.44998i)q4+(1.85376+3.21080i)q5+(0.311099+0.538840i)q6+(0.5108100.567312i)q7+(0.7509692.31124i)q8+(1.462501.62427i)q9+(2.33530+1.03974i)q10+(4.025690.855686i)q11+(0.1438101.36826i)q12+(0.3041522.89381i)q13+(0.5148520.109435i)q14+(2.70670+1.96653i)q15+(1.11127+0.807384i)q16+(1.279930.272057i)q17+(0.1575251.49875i)q18+(0.3971603.77873i)q19+(5.52896+1.17522i)q20+(0.6293300.280196i)q21+(1.898792.10882i)q22+(1.014493.12228i)q23+(1.467401.62972i)q24+(4.372847.57398i)q25+(1.003131.73747i)q26+(1.446064.45052i)q27+(1.063250.473389i)q28+(3.96065+2.87758i)q292.30681q305.80746q32+(3.004642.18300i)q33+(0.824217+0.366965i)q34+(0.874609+2.69177i)q35+(1.66614+2.88584i)q36+(5.206399.01773i)q37+(1.752961.94686i)q38+(0.8114052.49725i)q39+(6.02884+6.69570i)q40+(0.6905910.307471i)q41+(0.464603+0.0987545i)q42+(0.748099+7.11768i)q43+(0.655882+6.24030i)q44+(7.926341.68480i)q45+(1.831271.33050i)q46+(0.7087530.514939i)q47+(1.21245+0.257715i)q48+(0.670783+6.38208i)q49+(0.6303155.99705i)q50+(1.15501+0.245505i)q51+(4.05268+1.80437i)q52+(2.392612.65727i)q53+(0.9970493.06860i)q54+(10.210111.3395i)q55+(0.9275951.60664i)q56+(1.714352.96935i)q57+(1.04309+3.21029i)q58+(0.847103+0.377155i)q59+(4.12664+2.99818i)q602.31704q611.66853q63+(1.016930.738843i)q64+(9.85528+4.38785i)q65+(0.7913112.43540i)q66+(1.043451.80731i)q67+(0.9974881.72770i)q68+(1.982332.20160i)q69+(0.603037+1.85596i)q70+(5.176455.74903i)q71+(4.85238+2.16042i)q72+(5.533851.17626i)q73+(0.7504667.14021i)q74+(0.8249507.84887i)q75+(5.66619+1.20439i)q76+(2.54180+1.84673i)q77+(1.464681.06415i)q78+(13.7867+2.93046i)q79+(0.5323285.06476i)q80+(0.243989+2.32140i)q81+(0.509829+0.108368i)q82+(12.88805.73812i)q83+(0.7027730.780508i)q84+(1.49916+4.61393i)q85+(3.30191+3.66714i)q86+(2.20891+3.82595i)q87+(5.00086+8.66175i)q88+(1.37043+4.21776i)q89+(5.10420+2.27254i)q90+(1.797061.30564i)q915.00520q92+0.604042q94+(11.3965+8.28005i)q95+(4.787582.13157i)q96+(1.630885.01933i)q97+(2.21232+3.83184i)q98+(4.49770+7.79025i)q99+O(q100)q+(0.557811 + 0.405274i) q^{2} +(0.824384 + 0.367040i) q^{3} +(-0.471127 - 1.44998i) q^{4} +(-1.85376 + 3.21080i) q^{5} +(0.311099 + 0.538840i) q^{6} +(0.510810 - 0.567312i) q^{7} +(0.750969 - 2.31124i) q^{8} +(-1.46250 - 1.62427i) q^{9} +(-2.33530 + 1.03974i) q^{10} +(-4.02569 - 0.855686i) q^{11} +(0.143810 - 1.36826i) q^{12} +(-0.304152 - 2.89381i) q^{13} +(0.514852 - 0.109435i) q^{14} +(-2.70670 + 1.96653i) q^{15} +(-1.11127 + 0.807384i) q^{16} +(1.27993 - 0.272057i) q^{17} +(-0.157525 - 1.49875i) q^{18} +(0.397160 - 3.77873i) q^{19} +(5.52896 + 1.17522i) q^{20} +(0.629330 - 0.280196i) q^{21} +(-1.89879 - 2.10882i) q^{22} +(1.01449 - 3.12228i) q^{23} +(1.46740 - 1.62972i) q^{24} +(-4.37284 - 7.57398i) q^{25} +(1.00313 - 1.73747i) q^{26} +(-1.44606 - 4.45052i) q^{27} +(-1.06325 - 0.473389i) q^{28} +(3.96065 + 2.87758i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(-3.00464 - 2.18300i) q^{33} +(0.824217 + 0.366965i) q^{34} +(0.874609 + 2.69177i) q^{35} +(-1.66614 + 2.88584i) q^{36} +(-5.20639 - 9.01773i) q^{37} +(1.75296 - 1.94686i) q^{38} +(0.811405 - 2.49725i) q^{39} +(6.02884 + 6.69570i) q^{40} +(0.690591 - 0.307471i) q^{41} +(0.464603 + 0.0987545i) q^{42} +(-0.748099 + 7.11768i) q^{43} +(0.655882 + 6.24030i) q^{44} +(7.92634 - 1.68480i) q^{45} +(1.83127 - 1.33050i) q^{46} +(0.708753 - 0.514939i) q^{47} +(-1.21245 + 0.257715i) q^{48} +(0.670783 + 6.38208i) q^{49} +(0.630315 - 5.99705i) q^{50} +(1.15501 + 0.245505i) q^{51} +(-4.05268 + 1.80437i) q^{52} +(-2.39261 - 2.65727i) q^{53} +(0.997049 - 3.06860i) q^{54} +(10.2101 - 11.3395i) q^{55} +(-0.927595 - 1.60664i) q^{56} +(1.71435 - 2.96935i) q^{57} +(1.04309 + 3.21029i) q^{58} +(0.847103 + 0.377155i) q^{59} +(4.12664 + 2.99818i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(-1.01693 - 0.738843i) q^{64} +(9.85528 + 4.38785i) q^{65} +(-0.791311 - 2.43540i) q^{66} +(1.04345 - 1.80731i) q^{67} +(-0.997488 - 1.72770i) q^{68} +(1.98233 - 2.20160i) q^{69} +(-0.603037 + 1.85596i) q^{70} +(-5.17645 - 5.74903i) q^{71} +(-4.85238 + 2.16042i) q^{72} +(-5.53385 - 1.17626i) q^{73} +(0.750466 - 7.14021i) q^{74} +(-0.824950 - 7.84887i) q^{75} +(-5.66619 + 1.20439i) q^{76} +(-2.54180 + 1.84673i) q^{77} +(1.46468 - 1.06415i) q^{78} +(-13.7867 + 2.93046i) q^{79} +(-0.532328 - 5.06476i) q^{80} +(-0.243989 + 2.32140i) q^{81} +(0.509829 + 0.108368i) q^{82} +(12.8880 - 5.73812i) q^{83} +(-0.702773 - 0.780508i) q^{84} +(-1.49916 + 4.61393i) q^{85} +(-3.30191 + 3.66714i) q^{86} +(2.20891 + 3.82595i) q^{87} +(-5.00086 + 8.66175i) q^{88} +(1.37043 + 4.21776i) q^{89} +(5.10420 + 2.27254i) q^{90} +(-1.79706 - 1.30564i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(11.3965 + 8.28005i) q^{95} +(-4.78758 - 2.13157i) q^{96} +(-1.63088 - 5.01933i) q^{97} +(-2.21232 + 3.83184i) q^{98} +(4.49770 + 7.79025i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q6q2+12q314q43q511q6+2q7+17q810q92q10+7q115q12+7q136q1414q152q16+6q173q18+16q19+6q99+O(q100) 16 q - 6 q^{2} + 12 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} + 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 14 q^{15} - 2 q^{16} + 6 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/961Z)×\left(\mathbb{Z}/961\mathbb{Z}\right)^\times.

nn 33
χ(n)\chi(n) e(215)e\left(\frac{2}{15}\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 0.557811 + 0.405274i 0.394432 + 0.286572i 0.767269 0.641325i 0.221615π-0.221615\pi
−0.372837 + 0.927897i 0.621615π0.621615\pi
33 0.824384 + 0.367040i 0.475958 + 0.211910i 0.630673 0.776049i 0.282779π-0.282779\pi
−0.154714 + 0.987959i 0.549446π0.549446\pi
44 −0.471127 1.44998i −0.235564 0.724990i
55 −1.85376 + 3.21080i −0.829026 + 1.43591i 0.0697774 + 0.997563i 0.477771π0.477771\pi
−0.898803 + 0.438352i 0.855562π0.855562\pi
66 0.311099 + 0.538840i 0.127006 + 0.219981i
77 0.510810 0.567312i 0.193068 0.214424i −0.638836 0.769343i 0.720584π-0.720584\pi
0.831905 + 0.554919i 0.187251π0.187251\pi
88 0.750969 2.31124i 0.265508 0.817148i
99 −1.46250 1.62427i −0.487500 0.541424i
1010 −2.33530 + 1.03974i −0.738487 + 0.328796i
1111 −4.02569 0.855686i −1.21379 0.257999i −0.443842 0.896105i 0.646385π-0.646385\pi
−0.769948 + 0.638106i 0.779718π0.779718\pi
1212 0.143810 1.36826i 0.0415145 0.394984i
1313 −0.304152 2.89381i −0.0843565 0.802599i −0.952141 0.305658i 0.901123π-0.901123\pi
0.867785 0.496940i 0.165543π-0.165543\pi
1414 0.514852 0.109435i 0.137600 0.0292478i
1515 −2.70670 + 1.96653i −0.698867 + 0.507757i
1616 −1.11127 + 0.807384i −0.277817 + 0.201846i
1717 1.27993 0.272057i 0.310429 0.0659836i −0.0500631 0.998746i 0.515942π-0.515942\pi
0.360492 + 0.932762i 0.382609π0.382609\pi
1818 −0.157525 1.49875i −0.0371290 0.353259i
1919 0.397160 3.77873i 0.0911148 0.866900i −0.849538 0.527528i 0.823119π-0.823119\pi
0.940652 0.339371i 0.110214π-0.110214\pi
2020 5.52896 + 1.17522i 1.23631 + 0.262786i
2121 0.629330 0.280196i 0.137331 0.0611437i
2222 −1.89879 2.10882i −0.404823 0.449601i
2323 1.01449 3.12228i 0.211536 0.651040i −0.787846 0.615873i 0.788804π-0.788804\pi
0.999381 0.0351674i 0.0111964π-0.0111964\pi
2424 1.46740 1.62972i 0.299533 0.332665i
2525 −4.37284 7.57398i −0.874568 1.51480i
2626 1.00313 1.73747i 0.196729 0.340745i
2727 −1.44606 4.45052i −0.278295 0.856503i
2828 −1.06325 0.473389i −0.200935 0.0894620i
2929 3.96065 + 2.87758i 0.735474 + 0.534353i 0.891290 0.453433i 0.149801π-0.149801\pi
−0.155816 + 0.987786i 0.549801π0.549801\pi
3030 −2.30681 −0.421164
3131 0 0
3232 −5.80746 −1.02662
3333 −3.00464 2.18300i −0.523041 0.380012i
3434 0.824217 + 0.366965i 0.141352 + 0.0629340i
3535 0.874609 + 2.69177i 0.147836 + 0.454992i
3636 −1.66614 + 2.88584i −0.277690 + 0.480973i
3737 −5.20639 9.01773i −0.855925 1.48251i −0.875784 0.482704i 0.839655π-0.839655\pi
0.0198583 0.999803i 0.493679π-0.493679\pi
3838 1.75296 1.94686i 0.284368 0.315822i
3939 0.811405 2.49725i 0.129929 0.399880i
4040 6.02884 + 6.69570i 0.953243 + 1.05868i
4141 0.690591 0.307471i 0.107852 0.0480189i −0.352101 0.935962i 0.614533π-0.614533\pi
0.459953 + 0.887943i 0.347866π0.347866\pi
4242 0.464603 + 0.0987545i 0.0716898 + 0.0152381i
4343 −0.748099 + 7.11768i −0.114084 + 1.08544i 0.776343 + 0.630311i 0.217072π0.217072\pi
−0.890427 + 0.455126i 0.849594π0.849594\pi
4444 0.655882 + 6.24030i 0.0988780 + 0.940761i
4545 7.92634 1.68480i 1.18159 0.251154i
4646 1.83127 1.33050i 0.270006 0.196171i
4747 0.708753 0.514939i 0.103382 0.0751116i −0.534893 0.844920i 0.679648π-0.679648\pi
0.638275 + 0.769808i 0.279648π0.279648\pi
4848 −1.21245 + 0.257715i −0.175003 + 0.0371980i
4949 0.670783 + 6.38208i 0.0958262 + 0.911725i
5050 0.630315 5.99705i 0.0891400 0.848111i
5151 1.15501 + 0.245505i 0.161734 + 0.0343776i
5252 −4.05268 + 1.80437i −0.562005 + 0.250221i
5353 −2.39261 2.65727i −0.328651 0.365004i 0.556062 0.831141i 0.312312π-0.312312\pi
−0.884712 + 0.466138i 0.845645π0.845645\pi
5454 0.997049 3.06860i 0.135681 0.417584i
5555 10.2101 11.3395i 1.37673 1.52901i
5656 −0.927595 1.60664i −0.123955 0.214696i
5757 1.71435 2.96935i 0.227072 0.393300i
5858 1.04309 + 3.21029i 0.136964 + 0.421532i
5959 0.847103 + 0.377155i 0.110283 + 0.0491014i 0.461137 0.887329i 0.347442π-0.347442\pi
−0.350853 + 0.936430i 0.614108π0.614108\pi
6060 4.12664 + 2.99818i 0.532746 + 0.387063i
6161 −2.31704 −0.296666 −0.148333 0.988937i 0.547391π-0.547391\pi
−0.148333 + 0.988937i 0.547391π0.547391\pi
6262 0 0
6363 −1.66853 −0.210215
6464 −1.01693 0.738843i −0.127116 0.0923554i
6565 9.85528 + 4.38785i 1.22240 + 0.544246i
6666 −0.791311 2.43540i −0.0974036 0.299778i
6767 1.04345 1.80731i 0.127478 0.220798i −0.795221 0.606320i 0.792645π-0.792645\pi
0.922699 + 0.385522i 0.125979π0.125979\pi
6868 −0.997488 1.72770i −0.120963 0.209514i
6969 1.98233 2.20160i 0.238644 0.265041i
7070 −0.603037 + 1.85596i −0.0720767 + 0.221829i
7171 −5.17645 5.74903i −0.614332 0.682284i 0.353051 0.935604i 0.385144π-0.385144\pi
−0.967383 + 0.253320i 0.918478π0.918478\pi
7272 −4.85238 + 2.16042i −0.571858 + 0.254608i
7373 −5.53385 1.17626i −0.647688 0.137670i −0.127658 0.991818i 0.540746π-0.540746\pi
−0.520030 + 0.854148i 0.674079π0.674079\pi
7474 0.750466 7.14021i 0.0872399 0.830032i
7575 −0.824950 7.84887i −0.0952570 0.906310i
7676 −5.66619 + 1.20439i −0.649957 + 0.138153i
7777 −2.54180 + 1.84673i −0.289665 + 0.210454i
7878 1.46468 1.06415i 0.165842 0.120492i
7979 −13.7867 + 2.93046i −1.55113 + 0.329702i −0.902257 0.431198i 0.858091π-0.858091\pi
−0.648869 + 0.760900i 0.724758π0.724758\pi
8080 −0.532328 5.06476i −0.0595161 0.566257i
8181 −0.243989 + 2.32140i −0.0271098 + 0.257933i
8282 0.509829 + 0.108368i 0.0563012 + 0.0119672i
8383 12.8880 5.73812i 1.41465 0.629841i 0.449913 0.893072i 0.351455π-0.351455\pi
0.964733 + 0.263231i 0.0847883π0.0847883\pi
8484 −0.702773 0.780508i −0.0766788 0.0851604i
8585 −1.49916 + 4.61393i −0.162606 + 0.500451i
8686 −3.30191 + 3.66714i −0.356054 + 0.395438i
8787 2.20891 + 3.82595i 0.236820 + 0.410184i
8888 −5.00086 + 8.66175i −0.533094 + 0.923346i
8989 1.37043 + 4.21776i 0.145266 + 0.447081i 0.997045 0.0768191i 0.0244764π-0.0244764\pi
−0.851780 + 0.523900i 0.824476π0.824476\pi
9090 5.10420 + 2.27254i 0.538030 + 0.239547i
9191 −1.79706 1.30564i −0.188383 0.136868i
9292 −5.00520 −0.521828
9393 0 0
9494 0.604042 0.0623021
9595 11.3965 + 8.28005i 1.16926 + 0.849515i
9696 −4.78758 2.13157i −0.488630 0.217552i
9797 −1.63088 5.01933i −0.165591 0.509636i 0.833489 0.552537i 0.186340π-0.186340\pi
−0.999079 + 0.0429007i 0.986340π0.986340\pi
9898 −2.21232 + 3.83184i −0.223478 + 0.387075i
9999 4.49770 + 7.79025i 0.452036 + 0.782949i
100100 −8.92196 + 9.90884i −0.892196 + 0.990884i
101101 1.17656 3.62108i 0.117072 0.360311i −0.875301 0.483578i 0.839337π-0.839337\pi
0.992374 + 0.123267i 0.0393371π0.0393371\pi
102102 0.544781 + 0.605040i 0.0539413 + 0.0599079i
103103 −5.70573 + 2.54035i −0.562202 + 0.250308i −0.668104 0.744068i 0.732894π-0.732894\pi
0.105902 + 0.994377i 0.466227π0.466227\pi
104104 −6.91671 1.47019i −0.678239 0.144164i
105105 −0.266972 + 2.54007i −0.0260538 + 0.247885i
106106 −0.257707 2.45192i −0.0250307 0.238151i
107107 −2.27653 + 0.483890i −0.220080 + 0.0467795i −0.316632 0.948548i 0.602552π-0.602552\pi
0.0965518 + 0.995328i 0.469219π0.469219\pi
108108 −5.77189 + 4.19352i −0.555400 + 0.403522i
109109 −1.19478 + 0.868057i −0.114439 + 0.0831448i −0.643533 0.765419i 0.722532π-0.722532\pi
0.529094 + 0.848563i 0.322532π0.322532\pi
110110 10.2909 2.18740i 0.981197 0.208560i
111111 −0.982202 9.34503i −0.0932265 0.886991i
112112 −0.109609 + 1.04286i −0.0103570 + 0.0985407i
113113 −6.24112 1.32659i −0.587115 0.124795i −0.0952299 0.995455i 0.530359π-0.530359\pi
−0.491885 + 0.870660i 0.663692π0.663692\pi
114114 2.15969 0.961554i 0.202273 0.0900578i
115115 8.14440 + 9.04528i 0.759470 + 0.843476i
116116 2.30647 7.09857i 0.214150 0.659086i
117117 −4.25551 + 4.72623i −0.393422 + 0.436940i
118118 0.319673 + 0.553690i 0.0294283 + 0.0509713i
119119 0.499460 0.865089i 0.0457854 0.0793026i
120120 2.51249 + 7.73265i 0.229358 + 0.705891i
121121 5.42495 + 2.41534i 0.493178 + 0.219577i
122122 −1.29247 0.939035i −0.117015 0.0850162i
123123 0.682166 0.0615089
124124 0 0
125125 13.8872 1.24211
126126 −0.930724 0.676211i −0.0829155 0.0602417i
127127 1.30821 + 0.582453i 0.116085 + 0.0516843i 0.463957 0.885858i 0.346429π-0.346429\pi
−0.347872 + 0.937542i 0.613096π0.613096\pi
128128 3.32139 + 10.2222i 0.293572 + 0.903521i
129129 −3.22919 + 5.59312i −0.284314 + 0.492447i
130130 3.71911 + 6.44168i 0.326187 + 0.564973i
131131 4.21077 4.67654i 0.367897 0.408591i −0.530564 0.847645i 0.678020π-0.678020\pi
0.898461 + 0.439054i 0.144686π0.144686\pi
132132 −1.74974 + 5.38514i −0.152295 + 0.468717i
133133 −1.94084 2.15553i −0.168293 0.186908i
134134 1.31450 0.585254i 0.113556 0.0505582i
135135 16.9704 + 3.60717i 1.46058 + 0.310456i
136136 0.332396 3.16254i 0.0285027 0.271185i
137137 1.33273 + 12.6801i 0.113863 + 1.08333i 0.891001 + 0.454001i 0.150004π0.150004\pi
−0.777139 + 0.629330i 0.783330π0.783330\pi
138138 1.99802 0.424691i 0.170082 0.0361521i
139139 15.1397 10.9997i 1.28414 0.932979i 0.284466 0.958686i 0.408184π-0.408184\pi
0.999670 + 0.0257067i 0.00818361π0.00818361\pi
140140 3.49096 2.53633i 0.295040 0.214359i
141141 0.773288 0.164367i 0.0651226 0.0138422i
142142 −0.557552 5.30475i −0.0467887 0.445165i
143143 −1.25177 + 11.9098i −0.104679 + 0.995950i
144144 2.93664 + 0.624203i 0.244720 + 0.0520169i
145145 −16.5814 + 7.38253i −1.37701 + 0.613086i
146146 −2.61014 2.89885i −0.216017 0.239911i
147147 −1.78949 + 5.50749i −0.147595 + 0.454250i
148148 −10.6227 + 11.7977i −0.873178 + 0.969762i
149149 10.0677 + 17.4377i 0.824774 + 1.42855i 0.902092 + 0.431545i 0.142031π0.142031\pi
−0.0773172 + 0.997007i 0.524635π0.524635\pi
150150 2.72078 4.71252i 0.222150 0.384776i
151151 −4.75035 14.6201i −0.386578 1.18977i −0.935329 0.353779i 0.884896π-0.884896\pi
0.548751 0.835986i 0.315104π-0.315104\pi
152152 −8.43531 3.75564i −0.684194 0.304623i
153153 −2.31379 1.68107i −0.187059 0.135906i
154154 −2.16628 −0.174564
155155 0 0
156156 −4.00324 −0.320515
157157 −12.2544 8.90334i −0.978008 0.710564i −0.0207452 0.999785i 0.506604π-0.506604\pi
−0.957262 + 0.289221i 0.906604π0.906604\pi
158158 −8.87802 3.95275i −0.706298 0.314464i
159159 −0.997111 3.06879i −0.0790760 0.243371i
160160 10.7656 18.6466i 0.851098 1.47414i
161161 −1.25310 2.17042i −0.0987577 0.171053i
162162 −1.07690 + 1.19602i −0.0846093 + 0.0939681i
163163 −0.322882 + 0.993730i −0.0252901 + 0.0778349i −0.962905 0.269841i 0.913029π-0.913029\pi
0.937615 + 0.347676i 0.113029π0.113029\pi
164164 −0.771183 0.856485i −0.0602193 0.0668803i
165165 12.5791 5.60056i 0.979279 0.436003i
166166 9.51460 + 2.02239i 0.738477 + 0.156968i
167167 −1.18006 + 11.2276i −0.0913161 + 0.868815i 0.848973 + 0.528437i 0.177222π0.177222\pi
−0.940289 + 0.340378i 0.889445π0.889445\pi
168168 −0.174994 1.66495i −0.0135011 0.128454i
169169 4.43428 0.942536i 0.341099 0.0725028i
170170 −2.70615 + 1.96613i −0.207552 + 0.150796i
171171 −6.71853 + 4.88129i −0.513778 + 0.373282i
172172 10.6730 2.26861i 0.813805 0.172980i
173173 2.15879 + 20.5395i 0.164130 + 1.56159i 0.698045 + 0.716054i 0.254054π0.254054\pi
−0.533915 + 0.845538i 0.679280π0.679280\pi
174174 −0.318400 + 3.02937i −0.0241378 + 0.229656i
175175 −6.53050 1.38810i −0.493660 0.104931i
176176 5.16449 2.29938i 0.389288 0.173322i
177177 0.559908 + 0.621841i 0.0420853 + 0.0467404i
178178 −0.944903 + 2.90811i −0.0708235 + 0.217972i
179179 0.0880993 0.0978442i 0.00658485 0.00731322i −0.739843 0.672779i 0.765100π-0.765100\pi
0.746428 + 0.665466i 0.231767π0.231767\pi
180180 −6.17723 10.6993i −0.460424 0.797477i
181181 3.86599 6.69610i 0.287357 0.497717i −0.685821 0.727770i 0.740557π-0.740557\pi
0.973178 + 0.230053i 0.0738901π0.0738901\pi
182182 −0.473278 1.45660i −0.0350817 0.107970i
183183 −1.91013 0.850445i −0.141201 0.0628667i
184184 −6.45450 4.68947i −0.475832 0.345712i
185185 38.6056 2.83834
186186 0 0
187187 −5.38539 −0.393819
188188 −1.08056 0.785076i −0.0788083 0.0572576i
189189 −3.26350 1.45300i −0.237385 0.105690i
190190 3.00142 + 9.23741i 0.217746 + 0.670152i
191191 10.5513 18.2755i 0.763468 1.32237i −0.177585 0.984106i 0.556828π-0.556828\pi
0.941053 0.338260i 0.109838π-0.109838\pi
192192 −0.567157 0.982344i −0.0409310 0.0708946i
193193 3.78944 4.20860i 0.272770 0.302942i −0.591159 0.806555i 0.701330π-0.701330\pi
0.863929 + 0.503613i 0.167996π0.167996\pi
194194 1.12448 3.46079i 0.0807330 0.248471i
195195 6.51402 + 7.23456i 0.466479 + 0.518077i
196196 8.93786 3.97939i 0.638419 0.284242i
197197 15.5670 + 3.30887i 1.10910 + 0.235747i 0.725821 0.687883i 0.241460π-0.241460\pi
0.383283 + 0.923631i 0.374793π0.374793\pi
198198 −0.648313 + 6.16829i −0.0460736 + 0.438361i
199199 −0.445443 4.23811i −0.0315766 0.300432i −0.998900 0.0468866i 0.985070π-0.985070\pi
0.967324 0.253545i 0.0815966π-0.0815966\pi
200200 −20.7892 + 4.41888i −1.47002 + 0.312462i
201201 1.52356 1.10693i 0.107463 0.0780767i
202202 2.12383 1.54305i 0.149432 0.108569i
203203 3.65563 0.777027i 0.256575 0.0545366i
204204 −0.188179 1.79041i −0.0131752 0.125353i
205205 −0.292960 + 2.78733i −0.0204612 + 0.194675i
206206 −4.21226 0.895343i −0.293482 0.0623815i
207207 −6.55512 + 2.91853i −0.455612 + 0.202852i
208208 2.67441 + 2.97024i 0.185437 + 0.205949i
209209 −4.83225 + 14.8721i −0.334254 + 1.02873i
210210 −1.17834 + 1.30868i −0.0813134 + 0.0903077i
211211 5.75414 + 9.96646i 0.396131 + 0.686120i 0.993245 0.116037i 0.0370191π-0.0370191\pi
−0.597113 + 0.802157i 0.703686π0.703686\pi
212212 −2.72576 + 4.72115i −0.187206 + 0.324250i
213213 −2.15726 6.63937i −0.147813 0.454922i
214214 −1.46598 0.652696i −0.100212 0.0446174i
215215 −21.4667 15.5965i −1.46402 1.06367i
216216 −11.3722 −0.773780
217217 0 0
218218 −1.01826 −0.0689654
219219 −4.13028 3.00083i −0.279099 0.202777i
220220 −21.2522 9.46211i −1.43283 0.637935i
221221 −1.17658 3.62113i −0.0791450 0.243583i
222222 3.23941 5.61082i 0.217415 0.376574i
223223 4.71196 + 8.16135i 0.315536 + 0.546524i 0.979551 0.201195i 0.0644824π-0.0644824\pi
−0.664015 + 0.747719i 0.731149π0.731149\pi
224224 −2.96651 + 3.29464i −0.198208 + 0.220133i
225225 −5.90692 + 18.1796i −0.393795 + 1.21197i
226226 −2.94373 3.26935i −0.195814 0.217474i
227227 19.8815 8.85182i 1.31958 0.587516i 0.378471 0.925613i 0.376450π-0.376450\pi
0.941111 + 0.338097i 0.109783π0.109783\pi
228228 −5.11318 1.08684i −0.338629 0.0719777i
229229 1.77237 16.8630i 0.117122 1.11434i −0.765233 0.643754i 0.777376π-0.777376\pi
0.882355 0.470585i 0.155957π-0.155957\pi
230230 0.877228 + 8.34627i 0.0578427 + 0.550337i
231231 −2.77324 + 0.589471i −0.182466 + 0.0387844i
232232 9.62511 6.99305i 0.631920 0.459117i
233233 7.95758 5.78152i 0.521318 0.378760i −0.295782 0.955255i 0.595580π-0.595580\pi
0.817100 + 0.576496i 0.195580π0.195580\pi
234234 −4.28919 + 0.911695i −0.280393 + 0.0595994i
235235 0.339512 + 3.23024i 0.0221473 + 0.210718i
236236 0.147774 1.40597i 0.00961924 0.0915209i
237237 −12.4411 2.64445i −0.808139 0.171775i
238238 0.629202 0.280139i 0.0407851 0.0181587i
239239 −0.395212 0.438927i −0.0255641 0.0283919i 0.730227 0.683204i 0.239414π-0.239414\pi
−0.755791 + 0.654813i 0.772748π0.772748\pi
240240 1.42012 4.37069i 0.0916687 0.282127i
241241 −10.2848 + 11.4225i −0.662504 + 0.735786i −0.976945 0.213491i 0.931516π-0.931516\pi
0.314440 + 0.949277i 0.398183π0.398183\pi
242242 2.04722 + 3.54590i 0.131601 + 0.227939i
243243 −8.07252 + 13.9820i −0.517852 + 0.896946i
244244 1.09162 + 3.35966i 0.0698838 + 0.215080i
245245 −21.7351 9.67707i −1.38860 0.618245i
246246 0.380520 + 0.276464i 0.0242611 + 0.0176267i
247247 −11.0557 −0.703459
248248 0 0
249249 12.7308 0.806783
250250 7.74642 + 5.62810i 0.489926 + 0.355952i
251251 5.52832 + 2.46137i 0.348945 + 0.155360i 0.573722 0.819050i 0.305499π-0.305499\pi
−0.224778 + 0.974410i 0.572166π0.572166\pi
252252 0.786090 + 2.41933i 0.0495190 + 0.152404i
253253 −6.75571 + 11.7012i −0.424728 + 0.735650i
254254 0.493682 + 0.855082i 0.0309763 + 0.0536526i
255255 −2.92938 + 3.25340i −0.183445 + 0.203736i
256256 −3.06694 + 9.43906i −0.191684 + 0.589942i
257257 −3.02972 3.36484i −0.188988 0.209893i 0.641203 0.767371i 0.278436π-0.278436\pi
−0.830192 + 0.557478i 0.811769π0.811769\pi
258258 −4.06803 + 1.81120i −0.253264 + 0.112760i
259259 −7.77535 1.65270i −0.483137 0.102694i
260260 1.71921 16.3572i 0.106621 1.01443i
261261 −1.11848 10.6416i −0.0692322 0.658700i
262262 4.24409 0.902110i 0.262201 0.0557325i
263263 −2.02971 + 1.47467i −0.125157 + 0.0909322i −0.648603 0.761127i 0.724646π-0.724646\pi
0.523445 + 0.852059i 0.324646π0.324646\pi
264264 −7.30184 + 5.30510i −0.449397 + 0.326506i
265265 12.9673 2.75628i 0.796574 0.169317i
266266 −0.209047 1.98895i −0.0128175 0.121950i
267267 −0.418321 + 3.98005i −0.0256008 + 0.243575i
268268 −3.11216 0.661509i −0.190105 0.0404081i
269269 −12.1865 + 5.42577i −0.743023 + 0.330815i −0.743096 0.669185i 0.766643π-0.766643\pi
7.27860e−5 1.00000i 0.499977π0.499977\pi
270270 8.00439 + 8.88978i 0.487132 + 0.541015i
271271 −4.27190 + 13.1476i −0.259500 + 0.798658i 0.733410 + 0.679787i 0.237928π0.237928\pi
−0.992910 + 0.118871i 0.962072π0.962072\pi
272272 −1.20269 + 1.33572i −0.0729239 + 0.0809902i
273273 −1.00225 1.73594i −0.0606586 0.105064i
274274 −4.39548 + 7.61320i −0.265541 + 0.459930i
275275 11.1227 + 34.2322i 0.670726 + 2.06428i
276276 −4.12621 1.83711i −0.248368 0.110581i
277277 9.36093 + 6.80111i 0.562444 + 0.408639i 0.832353 0.554247i 0.186994π-0.186994\pi
−0.269909 + 0.962886i 0.586994π0.586994\pi
278278 12.9030 0.773870
279279 0 0
280280 6.87814 0.411048
281281 12.4583 + 9.05151i 0.743202 + 0.539968i 0.893712 0.448641i 0.148092π-0.148092\pi
−0.150510 + 0.988608i 0.548092π0.548092\pi
282282 0.497962 + 0.221707i 0.0296532 + 0.0132025i
283283 −7.01336 21.5849i −0.416901 1.28309i −0.910539 0.413422i 0.864333π-0.864333\pi
0.493638 0.869667i 0.335667π-0.335667\pi
284284 −5.89722 + 10.2143i −0.349935 + 0.606106i
285285 6.35600 + 11.0089i 0.376497 + 0.652112i
286286 −5.52500 + 6.13613i −0.326700 + 0.362837i
287287 0.178329 0.548840i 0.0105264 0.0323970i
288288 8.49342 + 9.43289i 0.500479 + 0.555839i
289289 −13.9661 + 6.21809i −0.821533 + 0.365770i
290290 −12.2413 2.60196i −0.718831 0.152792i
291291 0.497822 4.73646i 0.0291828 0.277656i
292292 0.901599 + 8.57814i 0.0527621 + 0.501998i
293293 −12.1299 + 2.57828i −0.708635 + 0.150625i −0.548109 0.836407i 0.684652π-0.684652\pi
−0.160525 + 0.987032i 0.551319π0.551319\pi
294294 −3.23024 + 2.34690i −0.188391 + 0.136874i
295295 −2.78129 + 2.02073i −0.161933 + 0.117651i
296296 −24.7520 + 5.26121i −1.43868 + 0.305801i
297297 2.01314 + 19.1538i 0.116814 + 1.11142i
298298 −1.45118 + 13.8071i −0.0840649 + 0.799824i
299299 −9.34384 1.98610i −0.540368 0.114859i
300300 −10.9921 + 4.89398i −0.634627 + 0.282554i
301301 3.65581 + 4.06019i 0.210718 + 0.234026i
302302 3.27533 10.0804i 0.188474 0.580064i
303303 2.29902 2.55332i 0.132075 0.146684i
304304 2.60953 + 4.51984i 0.149667 + 0.259231i
305305 4.29523 7.43956i 0.245944 0.425988i
306306 −0.609367 1.87544i −0.0348352 0.107212i
307307 28.0641 + 12.4949i 1.60170 + 0.713124i 0.996551 0.0829855i 0.0264455π-0.0264455\pi
0.605152 + 0.796110i 0.293112π0.293112\pi
308308 3.87523 + 2.81552i 0.220812 + 0.160429i
309309 −5.63612 −0.320628
310310 0 0
311311 2.38141 0.135037 0.0675187 0.997718i 0.478492π-0.478492\pi
0.0675187 + 0.997718i 0.478492π0.478492\pi
312312 −5.16241 3.75071i −0.292264 0.212342i
313313 −9.81659 4.37063i −0.554866 0.247042i 0.110094 0.993921i 0.464885π-0.464885\pi
−0.664960 + 0.746879i 0.731551π0.731551\pi
314314 −3.22735 9.93277i −0.182130 0.560539i
315315 3.09305 5.35732i 0.174274 0.301851i
316316 10.7444 + 18.6098i 0.604420 + 1.04689i
317317 5.85245 6.49980i 0.328706 0.365065i −0.556026 0.831165i 0.687674π-0.687674\pi
0.884732 + 0.466100i 0.154341π0.154341\pi
318318 0.687501 2.11591i 0.0385531 0.118654i
319319 −13.4820 14.9733i −0.754849 0.838344i
320320 4.25742 1.89553i 0.237997 0.105963i
321321 −2.05434 0.436663i −0.114662 0.0243722i
322322 0.180625 1.71853i 0.0100658 0.0957701i
323323 −0.519694 4.94456i −0.0289165 0.275122i
324324 3.48093 0.739894i 0.193385 0.0411052i
325325 −20.5877 + 14.9578i −1.14200 + 0.829710i
326326 −0.582840 + 0.423458i −0.0322805 + 0.0234532i
327327 −1.30357 + 0.277082i −0.0720874 + 0.0153227i
328328 −0.192028 1.82703i −0.0106030 0.100881i
329329 0.0699070 0.665120i 0.00385410 0.0366693i
330330 9.28650 + 1.97391i 0.511205 + 0.108660i
331331 29.5706 13.1657i 1.62535 0.723652i 0.626889 0.779109i 0.284328π-0.284328\pi
0.998461 + 0.0554567i 0.0176615π0.0176615\pi
332332 −14.3921 15.9840i −0.789868 0.877237i
333333 −7.03290 + 21.6450i −0.385400 + 1.18614i
334334 −5.20849 + 5.78461i −0.284996 + 0.316520i
335335 3.86860 + 6.70062i 0.211364 + 0.366094i
336336 −0.473129 + 0.819484i −0.0258113 + 0.0447065i
337337 −8.57021 26.3764i −0.466849 1.43681i −0.856642 0.515912i 0.827453π-0.827453\pi
0.389792 0.920903i 0.372547π-0.372547\pi
338338 2.85548 + 1.27134i 0.155318 + 0.0691518i
339339 −4.65817 3.38436i −0.252997 0.183813i
340340 7.39640 0.401126
341341 0 0
342342 −5.72593 −0.309623
343343 8.28646 + 6.02047i 0.447427 + 0.325075i
344344 15.8889 + 7.07420i 0.856672 + 0.381415i
345345 3.39414 + 10.4461i 0.182735 + 0.562399i
346346 −7.11994 + 12.3321i −0.382770 + 0.662977i
347347 −12.9580 22.4440i −0.695624 1.20486i −0.969970 0.243224i 0.921795π-0.921795\pi
0.274347 0.961631i 0.411538π-0.411538\pi
348348 4.50687 5.00539i 0.241594 0.268317i
349349 1.72862 5.32015i 0.0925309 0.284781i −0.894071 0.447924i 0.852163π-0.852163\pi
0.986602 + 0.163144i 0.0521634π0.0521634\pi
350350 −3.08023 3.42094i −0.164645 0.182857i
351351 −12.4391 + 5.53827i −0.663953 + 0.295611i
352352 23.3790 + 4.96936i 1.24611 + 0.264868i
353353 1.21974 11.6051i 0.0649202 0.617675i −0.912893 0.408198i 0.866157π-0.866157\pi
0.977814 0.209477i 0.0671760π-0.0671760\pi
354354 0.0603073 + 0.573786i 0.00320530 + 0.0304964i
355355 28.0549 5.96325i 1.48900 0.316497i
356356 5.47002 3.97420i 0.289910 0.210632i
357357 0.729269 0.529845i 0.0385970 0.0280424i
358358 0.0887965 0.0188743i 0.00469304 0.000997537i
359359 −2.73863 26.0563i −0.144539 1.37520i −0.790796 0.612080i 0.790333π-0.790333\pi
0.646257 0.763120i 0.276334π-0.276334\pi
360360 2.05846 19.5849i 0.108490 1.03222i
361361 4.46376 + 0.948801i 0.234935 + 0.0499369i
362362 4.87025 2.16837i 0.255974 0.113967i
363363 3.58572 + 3.98234i 0.188201 + 0.209019i
364364 −1.04651 + 3.22082i −0.0548519 + 0.168817i
365365 14.0351 15.5876i 0.734633 0.815893i
366366 −0.720830 1.24851i −0.0376784 0.0652608i
367367 13.5073 23.3953i 0.705076 1.22123i −0.261589 0.965179i 0.584246π-0.584246\pi
0.966664 0.256047i 0.0824203π-0.0824203\pi
368368 1.39351 + 4.28877i 0.0726416 + 0.223568i
369369 −1.50941 0.672031i −0.0785765 0.0349845i
370370 21.5346 + 15.6458i 1.11953 + 0.813387i
371371 −2.72967 −0.141717
372372 0 0
373373 −12.4058 −0.642351 −0.321175 0.947020i 0.604078π-0.604078\pi
−0.321175 + 0.947020i 0.604078π0.604078\pi
374374 −3.00403 2.18256i −0.155335 0.112857i
375375 11.4484 + 5.09714i 0.591191 + 0.263215i
376376 −0.657899 2.02480i −0.0339285 0.104421i
377377 7.12253 12.3366i 0.366829 0.635367i
378378 −1.23155 2.13311i −0.0633442 0.109715i
379379 −3.10411 + 3.44746i −0.159447 + 0.177084i −0.817575 0.575822i 0.804682π-0.804682\pi
0.658128 + 0.752906i 0.271349π0.271349\pi
380380 6.63670 20.4257i 0.340456 1.04782i
381381 0.864685 + 0.960330i 0.0442991 + 0.0491992i
382382 13.2922 5.91808i 0.680089 0.302795i
383383 −4.91161 1.04399i −0.250971 0.0533456i 0.0807080 0.996738i 0.474282π-0.474282\pi
−0.331679 + 0.943392i 0.607615π0.607615\pi
384384 −1.01384 + 9.64608i −0.0517375 + 0.492250i
385385 −1.21759 11.5846i −0.0620542 0.590407i
386386 3.81943 0.811845i 0.194404 0.0413218i
387387 12.6551 9.19450i 0.643297 0.467383i
388388 −6.50958 + 4.72949i −0.330474 + 0.240103i
389389 18.1953 3.86754i 0.922540 0.196092i 0.277928 0.960602i 0.410352π-0.410352\pi
0.644612 + 0.764510i 0.277019π0.277019\pi
390390 0.701621 + 6.67548i 0.0355280 + 0.338026i
391391 0.449036 4.27230i 0.0227087 0.216059i
392392 15.2543 + 3.24240i 0.770457 + 0.163766i
393393 5.18777 2.30974i 0.261688 0.116511i
394394 7.34246 + 8.15463i 0.369908 + 0.410824i
395395 16.1481 49.6988i 0.812500 2.50062i
396396 9.17672 10.1918i 0.461147 0.512156i
397397 −16.2794 28.1968i −0.817040 1.41515i −0.907854 0.419287i 0.862280π-0.862280\pi
0.0908142 0.995868i 0.471053π-0.471053\pi
398398 1.46912 2.54459i 0.0736404 0.127549i
399399 −0.808838 2.48935i −0.0404926 0.124623i
400400 10.9745 + 4.88617i 0.548725 + 0.244308i
401401 −10.0239 7.28282i −0.500572 0.363687i 0.308664 0.951171i 0.400118π-0.400118\pi
−0.809235 + 0.587485i 0.800118π0.800118\pi
402402 1.29847 0.0647616
403403 0 0
404404 −5.80481 −0.288800
405405 −7.00125 5.08671i −0.347895 0.252760i
406406 2.35406 + 1.04809i 0.116830 + 0.0520161i
407407 13.2429 + 40.7576i 0.656429 + 2.02028i
408408 1.43480 2.48514i 0.0710331 0.123033i
409409 −1.72404 2.98613i −0.0852484 0.147654i 0.820249 0.572007i 0.193835π-0.193835\pi
−0.905497 + 0.424353i 0.860502π0.860502\pi
410410 −1.29305 + 1.43607i −0.0638590 + 0.0709227i
411411 −3.55540 + 10.9424i −0.175375 + 0.539749i
412412 6.37158 + 7.07636i 0.313905 + 0.348627i
413413 0.646673 0.287918i 0.0318207 0.0141675i
414414 −4.83932 1.02863i −0.237840 0.0505544i
415415 −5.46732 + 52.0180i −0.268380 + 2.55347i
416416 1.76635 + 16.8057i 0.0866024 + 0.823967i
417417 16.5183 3.51107i 0.808903 0.171938i
418418 −8.72276 + 6.33746i −0.426644 + 0.309975i
419419 32.3988 23.5391i 1.58279 1.14996i 0.669374 0.742926i 0.266563π-0.266563\pi
0.913412 0.407035i 0.133437π-0.133437\pi
420420 3.80883 0.809592i 0.185852 0.0395040i
421421 −2.26664 21.5656i −0.110469 1.05104i −0.899569 0.436779i 0.856119π-0.856119\pi
0.789100 0.614265i 0.210548π-0.210548\pi
422422 −0.829421 + 7.89141i −0.0403756 + 0.384148i
423423 −1.87295 0.398108i −0.0910660 0.0193567i
424424 −7.93837 + 3.53439i −0.385521 + 0.171645i
425425 −7.65748 8.50450i −0.371442 0.412529i
426426 1.48742 4.57780i 0.0720656 0.221795i
427427 −1.18357 + 1.31448i −0.0572768 + 0.0636124i
428428 1.77417 + 3.07294i 0.0857575 + 0.148536i
429429 −5.40332 + 9.35883i −0.260875 + 0.451849i
430430 −5.65353 17.3998i −0.272637 0.839091i
431431 −10.6160 4.72655i −0.511355 0.227670i 0.134805 0.990872i 0.456959π-0.456959\pi
−0.646160 + 0.763202i 0.723626π0.723626\pi
432432 5.20024 + 3.77820i 0.250197 + 0.181779i
433433 −24.5964 −1.18203 −0.591015 0.806661i 0.701272π-0.701272\pi
−0.591015 + 0.806661i 0.701272π0.701272\pi
434434 0 0
435435 −16.3791 −0.785320
436436 1.82156 + 1.32344i 0.0872368 + 0.0633813i
437437 −11.3953 5.07353i −0.545112 0.242700i
438438 −1.08776 3.34779i −0.0519753 0.159964i
439439 −9.09662 + 15.7558i −0.434158 + 0.751984i −0.997227 0.0744265i 0.976287π-0.976287\pi
0.563068 + 0.826410i 0.309621π0.309621\pi
440440 −18.5408 32.1136i −0.883897 1.53096i
441441 9.38520 10.4233i 0.446914 0.496349i
442442 0.811240 2.49674i 0.0385868 0.118758i
443443 11.8840 + 13.1985i 0.564625 + 0.627080i 0.956076 0.293119i 0.0946933π-0.0946933\pi
−0.391451 + 0.920199i 0.628027π0.628027\pi
444444 −13.0874 + 5.82687i −0.621099 + 0.276531i
445445 −16.0828 3.41851i −0.762400 0.162053i
446446 −0.679196 + 6.46212i −0.0321609 + 0.305990i
447447 1.89929 + 18.0706i 0.0898336 + 0.854709i
448448 −0.938613 + 0.199508i −0.0443453 + 0.00942588i
449449 −7.44180 + 5.40679i −0.351200 + 0.255162i −0.749372 0.662149i 0.769645π-0.769645\pi
0.398172 + 0.917311i 0.369645π0.369645\pi
450450 −10.6627 + 7.74688i −0.502643 + 0.365192i
451451 −3.04320 + 0.646852i −0.143299 + 0.0304591i
452452 1.01683 + 9.67449i 0.0478277 + 0.455050i
453453 1.45003 13.7961i 0.0681284 0.648199i
454454 14.6775 + 3.11981i 0.688851 + 0.146420i
455455 7.52346 3.34966i 0.352705 0.157035i
456456 −5.57547 6.19218i −0.261095 0.289975i
457457 9.64130 29.6729i 0.451001 1.38804i −0.424766 0.905303i 0.639644π-0.639644\pi
0.875767 0.482735i 0.160356π-0.160356\pi
458458 7.82278 8.68808i 0.365535 0.405967i
459459 −3.06166 5.30294i −0.142906 0.247520i
460460 9.27842 16.0707i 0.432609 0.749300i
461461 2.06067 + 6.34209i 0.0959750 + 0.295381i 0.987507 0.157578i 0.0503685π-0.0503685\pi
−0.891532 + 0.452959i 0.850369π0.850369\pi
462462 −1.78584 0.795109i −0.0830850 0.0369918i
463463 28.5732 + 20.7597i 1.32791 + 0.964784i 0.999797 + 0.0201457i 0.00641301π0.00641301\pi
0.328114 + 0.944638i 0.393587π0.393587\pi
464464 −6.72466 −0.312184
465465 0 0
466466 6.78192 0.314167
467467 −29.0789 21.1270i −1.34561 0.977642i −0.999218 0.0395520i 0.987407π-0.987407\pi
−0.346391 0.938090i 0.612593π-0.612593\pi
468468 8.85782 + 3.94376i 0.409453 + 0.182300i
469469 −0.492303 1.51515i −0.0227324 0.0699632i
470470 −1.11975 + 1.93946i −0.0516501 + 0.0894606i
471471 −6.83446 11.8376i −0.314915 0.545449i
472472 1.50784 1.67463i 0.0694042 0.0770811i
473473 9.10211 28.0134i 0.418516 1.28806i
474474 −5.86809 6.51717i −0.269530 0.299344i
475475 −30.3567 + 13.5157i −1.39286 + 0.620142i
476476 −1.48967 0.316640i −0.0682790 0.0145131i
477477 −0.816923 + 7.77251i −0.0374043 + 0.355879i
478478 −0.0425680 0.405008i −0.00194702 0.0185246i
479479 −32.5179 + 6.91190i −1.48578 + 0.315813i −0.878142 0.478400i 0.841217π-0.841217\pi
−0.607640 + 0.794212i 0.707884π0.707884\pi
480480 15.7191 11.4206i 0.717474 0.521275i
481481 −24.5121 + 17.8091i −1.11765 + 0.812024i
482482 −10.3662 + 2.20341i −0.472168 + 0.100363i
483483 −0.236400 2.24920i −0.0107566 0.102342i
484484 0.946360 9.00401i 0.0430163 0.409273i
485485 19.1393 + 4.06819i 0.869073 + 0.184727i
486486 −10.1695 + 4.52775i −0.461297 + 0.205383i
487487 −19.0805 21.1910i −0.864620 0.960258i 0.134912 0.990858i 0.456925π-0.456925\pi
−0.999532 + 0.0305999i 0.990258π0.990258\pi
488488 −1.74002 + 5.35524i −0.0787672 + 0.242420i
489489 −0.630917 + 0.700705i −0.0285311 + 0.0316870i
490490 −8.20220 14.2066i −0.370538 0.641790i
491491 −13.9818 + 24.2172i −0.630991 + 1.09291i 0.356359 + 0.934349i 0.384018π0.384018\pi
−0.987350 + 0.158559i 0.949315π0.949315\pi
492492 −0.321387 0.989128i −0.0144892 0.0445933i
493493 5.85222 + 2.60558i 0.263571 + 0.117349i
494494 −6.16701 4.48059i −0.277467 0.201591i
495495 −33.3506 −1.49900
496496 0 0
497497 −5.90568 −0.264906
498498 7.10139 + 5.15946i 0.318221 + 0.231201i
499499 37.7340 + 16.8002i 1.68920 + 0.752082i 0.999611 + 0.0278849i 0.00887720π0.00887720\pi
0.689593 + 0.724197i 0.257789π0.257789\pi
500500 −6.54262 20.1361i −0.292595 0.900514i
501501 −5.09378 + 8.82269i −0.227573 + 0.394169i
502502 2.08623 + 3.61346i 0.0931132 + 0.161277i
503503 −17.1204 + 19.0141i −0.763361 + 0.847798i −0.992069 0.125697i 0.959883π-0.959883\pi
0.228708 + 0.973495i 0.426550π0.426550\pi
504504 −1.25301 + 3.85638i −0.0558136 + 0.171777i
505505 9.44552 + 10.4903i 0.420320 + 0.466813i
506506 −8.51061 + 3.78917i −0.378343 + 0.168449i
507507 4.00150 + 0.850545i 0.177713 + 0.0377741i
508508 0.228212 2.17129i 0.0101253 0.0963353i
509509 −2.55758 24.3337i −0.113363 1.07857i −0.892291 0.451461i 0.850903π-0.850903\pi
0.778928 0.627113i 0.215764π-0.215764\pi
510510 −2.95256 + 0.627585i −0.130741 + 0.0277900i
511511 −3.49405 + 2.53858i −0.154568 + 0.112300i
512512 11.8548 8.61304i 0.523915 0.380646i
513513 −17.3916 + 3.69670i −0.767859 + 0.163213i
514514 −0.326329 3.10481i −0.0143937 0.136947i
515515 2.42046 23.0292i 0.106658 1.01479i
516516 9.63128 + 2.04719i 0.423994 + 0.0901226i
517517 −3.29384 + 1.46651i −0.144863 + 0.0644972i
518518 −3.66738 4.07304i −0.161135 0.178959i
519519 −5.75915 + 17.7248i −0.252799 + 0.778034i
520520 17.5424 19.4828i 0.769286 0.854378i
521521 −7.48279 12.9606i −0.327827 0.567813i 0.654253 0.756275i 0.272983π-0.272983\pi
−0.982080 + 0.188462i 0.939650π0.939650\pi
522522 3.68887 6.38931i 0.161458 0.279653i
523523 6.47873 + 19.9395i 0.283295 + 0.871893i 0.986904 + 0.161306i 0.0515706π0.0515706\pi
−0.703609 + 0.710587i 0.748429π0.748429\pi
524524 −8.76470 3.90229i −0.382887 0.170472i
525525 −4.87415 3.54128i −0.212726 0.154554i
526526 −1.72984 −0.0754247
527527 0 0
528528 5.10148 0.222014
529529 9.88796 + 7.18402i 0.429911 + 0.312349i
530530 8.35035 + 3.71781i 0.362716 + 0.161492i
531531 −0.626287 1.92751i −0.0271786 0.0836470i
532532 −2.21109 + 3.82971i −0.0958628 + 0.166039i
533533 −1.09981 1.90492i −0.0476379 0.0825113i
534534 −1.84636 + 2.05059i −0.0798996 + 0.0887375i
535535 2.66645 8.20649i 0.115281 0.354798i
536536 −3.39353 3.76890i −0.146578 0.162791i
537537 0.108540 0.0483253i 0.00468386 0.00208539i
538538 −8.99669 1.91230i −0.387875 0.0824453i
539539 2.76069 26.2662i 0.118911 1.13137i
540540 −2.76489 26.3062i −0.118982 1.13204i
541541 −1.69347 + 0.359958i −0.0728079 + 0.0154758i −0.244172 0.969732i 0.578516π-0.578516\pi
0.171364 + 0.985208i 0.445183π0.445183\pi
542542 −7.71128 + 5.60257i −0.331228 + 0.240651i
543543 5.64480 4.10118i 0.242241 0.175999i
544544 −7.43314 + 1.57996i −0.318693 + 0.0677404i
545545 −0.572331 5.44536i −0.0245160 0.233254i
546546 0.144467 1.37451i 0.00618261 0.0588236i
547547 12.8347 + 2.72810i 0.548772 + 0.116645i 0.473950 0.880552i 0.342828π-0.342828\pi
0.0748220 + 0.997197i 0.476161π0.476161\pi
548548 17.7580 7.90635i 0.758582 0.337743i
549549 3.38867 + 3.76350i 0.144625 + 0.160622i
550550 −7.66904 + 23.6029i −0.327009 + 1.00643i
551551 12.4466 13.8234i 0.530243 0.588895i
552552 −3.59977 6.23498i −0.153216 0.265378i
553553 −5.37991 + 9.31828i −0.228777 + 0.396254i
554554 2.46532 + 7.58748i 0.104741 + 0.322361i
555555 31.8258 + 14.1698i 1.35093 + 0.601473i
556556 −23.0820 16.7701i −0.978897 0.711210i
557557 28.0246 1.18744 0.593721 0.804671i 0.297658π-0.297658\pi
0.593721 + 0.804671i 0.297658π0.297658\pi
558558 0 0
559559 20.8248 0.880794
560560 −3.14522 2.28514i −0.132910 0.0965646i
561561 −4.43963 1.97665i −0.187441 0.0834543i
562562 3.28106 + 10.0981i 0.138403 + 0.425961i
563563 −11.3259 + 19.6171i −0.477331 + 0.826762i −0.999662 0.0259808i 0.991729π-0.991729\pi
0.522331 + 0.852743i 0.325062π0.325062\pi
564564 −0.602646 1.04381i −0.0253760 0.0439525i
565565 15.8289 17.5798i 0.665928 0.739589i
566566 4.83566 14.8826i 0.203258 0.625564i
567567 1.19232 + 1.32421i 0.0500729 + 0.0556116i
568568 −17.1748 + 7.64670i −0.720637 + 0.320848i
569569 −45.4271 9.65584i −1.90441 0.404794i −0.904634 0.426189i 0.859856π-0.859856\pi
−0.999771 + 0.0213953i 0.993189π0.993189\pi
570570 −0.916174 + 8.71682i −0.0383743 + 0.365107i
571571 −1.30643 12.4299i −0.0546726 0.520175i −0.987247 0.159197i 0.949110π-0.949110\pi
0.932574 0.360978i 0.117557π-0.117557\pi
572572 17.8588 3.79600i 0.746713 0.158719i
573573 15.4062 11.1932i 0.643602 0.467604i
574574 0.321904 0.233877i 0.0134360 0.00976184i
575575 −28.0843 + 5.96950i −1.17120 + 0.248945i
576576 0.287179 + 2.73233i 0.0119658 + 0.113847i
577577 3.18648 30.3173i 0.132655 1.26213i −0.702330 0.711852i 0.747857π-0.747857\pi
0.834984 0.550274i 0.185477π-0.185477\pi
578578 −10.3105 2.19156i −0.428859 0.0911567i
579579 4.66868 2.07863i 0.194024 0.0863850i
580580 18.5165 + 20.5646i 0.768855 + 0.853900i
581581 3.32803 10.2426i 0.138070 0.424936i
582582 2.19725 2.44030i 0.0910790 0.101153i
583583 7.35812 + 12.7446i 0.304742 + 0.527829i
584584 −6.87436 + 11.9067i −0.284463 + 0.492705i
585585 −7.28629 22.4249i −0.301251 0.927155i
586586 −7.81109 3.47772i −0.322673 0.143663i
587587 27.2300 + 19.7837i 1.12390 + 0.816562i 0.984796 0.173716i 0.0555774π-0.0555774\pi
0.139105 + 0.990278i 0.455577π0.455577\pi
588588 8.82883 0.364095
589589 0 0
590590 −2.37039 −0.0975872
591591 11.6187 + 8.44150i 0.477930 + 0.347237i
592592 13.0665 + 5.81757i 0.537029 + 0.239101i
593593 −13.8711 42.6909i −0.569619 1.75311i −0.653812 0.756657i 0.726831π-0.726831\pi
0.0841933 0.996449i 0.473169π-0.473169\pi
594594 −6.63957 + 11.5001i −0.272425 + 0.471854i
595595 1.85175 + 3.20733i 0.0759145 + 0.131488i
596596 20.5412 22.8133i 0.841399 0.934468i
597597 1.18834 3.65733i 0.0486354 0.149684i
598598 −4.40719 4.89468i −0.180223 0.200158i
599599 −17.8914 + 7.96578i −0.731024 + 0.325473i −0.738274 0.674501i 0.764359π-0.764359\pi
0.00724987 + 0.999974i 0.497692π0.497692\pi
600600 −18.7602 3.98760i −0.765881 0.162793i
601601 3.18388 30.2926i 0.129873 1.23566i −0.714396 0.699742i 0.753298π-0.753298\pi
0.844269 0.535919i 0.180035π-0.180035\pi
602602 0.393765 + 3.74642i 0.0160487 + 0.152693i
603603 −4.46160 + 0.948342i −0.181690 + 0.0386195i
604604 −18.9608 + 13.7758i −0.771504 + 0.560531i
605605 −17.8117 + 12.9410i −0.724150 + 0.526126i
606606 2.31721 0.492538i 0.0941302 0.0200080i
607607 1.39802 + 13.3013i 0.0567440 + 0.539883i 0.985558 + 0.169337i 0.0541627π0.0541627\pi
−0.928814 + 0.370546i 0.879171π0.879171\pi
608608 −2.30649 + 21.9448i −0.0935406 + 0.889980i
609609 3.29884 + 0.701190i 0.133676 + 0.0284137i
610610 5.41099 2.40913i 0.219084 0.0975427i
611611 −1.70570 1.89438i −0.0690054 0.0766383i
612612 −1.34743 + 4.14695i −0.0544665 + 0.167631i
613613 3.47627 3.86079i 0.140405 0.155936i −0.668841 0.743406i 0.733209π-0.733209\pi
0.809246 + 0.587470i 0.199876π0.199876\pi
614614 10.5906 + 18.3435i 0.427402 + 0.740282i
615615 −1.26457 + 2.19030i −0.0509924 + 0.0883215i
616616 2.35942 + 7.26156i 0.0950639 + 0.292577i
617617 −27.4183 12.2074i −1.10382 0.491452i −0.227790 0.973710i 0.573150π-0.573150\pi
−0.876029 + 0.482258i 0.839817π0.839817\pi
618618 −3.14389 2.28417i −0.126466 0.0918828i
619619 −18.3260 −0.736584 −0.368292 0.929710i 0.620057π-0.620057\pi
−0.368292 + 0.929710i 0.620057π0.620057\pi
620620 0 0
621621 −15.3628 −0.616487
622622 1.32838 + 0.965124i 0.0532631 + 0.0386979i
623623 3.09282 + 1.37701i 0.123911 + 0.0551687i
624624 1.11455 + 3.43023i 0.0446177 + 0.137319i
625625 −3.87924 + 6.71905i −0.155170 + 0.268762i
626626 −3.70450 6.41639i −0.148062 0.256450i
627627 −9.44229 + 10.4867i −0.377089 + 0.418799i
628628 −7.13629 + 21.9632i −0.284769 + 0.876429i
629629 −9.11716 10.1256i −0.363525 0.403735i
630630 3.89652 1.73484i 0.155241 0.0691178i
631631 10.1094 + 2.14881i 0.402447 + 0.0855428i 0.404688 0.914455i 0.367380π-0.367380\pi
−0.00224100 + 0.999997i 0.500713π0.500713\pi
632632 −3.58039 + 34.0651i −0.142420 + 1.35504i
633633 1.08554 + 10.3282i 0.0431462 + 0.410509i
634634 5.89876 1.25382i 0.234270 0.0497956i
635635 −4.29525 + 3.12068i −0.170452 + 0.123840i
636636 −3.97992 + 2.89158i −0.157814 + 0.114659i
637637 18.2645 3.88224i 0.723666 0.153820i
638638 −1.45214 13.8162i −0.0574908 0.546988i
639639 −1.76742 + 16.8159i −0.0699182 + 0.665228i
640640 −38.9785 8.28513i −1.54076 0.327498i
641641 −0.0924983 + 0.0411829i −0.00365346 + 0.00162663i −0.408563 0.912730i 0.633970π-0.633970\pi
0.404909 + 0.914357i 0.367303π0.367303\pi
642642 −0.968965 1.07615i −0.0382420 0.0424721i
643643 4.23719 13.0407i 0.167098 0.514276i −0.832086 0.554646i 0.812854π-0.812854\pi
0.999185 + 0.0403701i 0.0128537π0.0128537\pi
644644 −2.55671 + 2.83951i −0.100748 + 0.111892i
645645 −11.9723 20.7366i −0.471408 0.816503i
646646 1.71401 2.96875i 0.0674367 0.116804i
647647 3.34800 + 10.3041i 0.131624 + 0.405096i 0.995050 0.0993798i 0.0316859π-0.0316859\pi
−0.863426 + 0.504476i 0.831686π0.831686\pi
648648 5.18208 + 2.30721i 0.203572 + 0.0906359i
649649 −3.08745 2.24316i −0.121193 0.0880518i
650650 −17.5460 −0.688212
651651 0 0
652652 1.59301 0.0623870
653653 19.6204 + 14.2551i 0.767807 + 0.557844i 0.901295 0.433206i 0.142618π-0.142618\pi
−0.133488 + 0.991050i 0.542618π0.542618\pi
654654 −0.839439 0.373742i −0.0328246 0.0146145i
655655 7.20968 + 22.1891i 0.281706 + 0.867001i
656656 −0.519185 + 0.899255i −0.0202708 + 0.0351100i
657657 6.18270 + 10.7087i 0.241210 + 0.417788i
658658 0.308551 0.342680i 0.0120286 0.0133591i
659659 −2.63699 + 8.11583i −0.102723 + 0.316148i −0.989189 0.146645i 0.953153π-0.953153\pi
0.886467 + 0.462793i 0.153153π0.153153\pi
660660 −14.0470 15.6008i −0.546780 0.607261i
661661 34.6089 15.4089i 1.34613 0.599337i 0.398050 0.917364i 0.369687π-0.369687\pi
0.948082 + 0.318027i 0.103020π0.103020\pi
662662 21.8306 + 4.64023i 0.848469 + 0.180348i
663663 0.359146 3.41705i 0.0139481 0.132707i
664664 −3.58369 34.0966i −0.139074 1.32320i
665665 10.5188 2.23585i 0.407903 0.0867024i
666666 −12.6952 + 9.22360i −0.491929 + 0.357407i
667667 13.0026 9.44697i 0.503464 0.365788i
668668 16.8357 3.57854i 0.651393 0.138458i
669669 0.888925 + 8.45756i 0.0343678 + 0.326988i
670670 −0.557633 + 5.30552i −0.0215432 + 0.204970i
671671 9.32767 + 1.98266i 0.360091 + 0.0765397i
672672 −3.65481 + 1.62723i −0.140987 + 0.0627716i
673673 −4.76428 5.29127i −0.183650 0.203963i 0.644289 0.764782i 0.277153π-0.277153\pi
−0.827939 + 0.560818i 0.810487π0.810487\pi
674674 5.90910 18.1863i 0.227610 0.700512i
675675 −27.3848 + 30.4139i −1.05404 + 1.17063i
676676 −3.45577 5.98557i −0.132914 0.230214i
677677 24.0305 41.6220i 0.923567 1.59966i 0.129716 0.991551i 0.458593π-0.458593\pi
0.793850 0.608113i 0.208073π-0.208073\pi
678678 −1.22679 3.77566i −0.0471145 0.145004i
679679 −3.68060 1.63871i −0.141248 0.0628879i
680680 9.53810 + 6.92984i 0.365769 + 0.265747i
681681 19.6390 0.752567
682682 0 0
683683 32.5731 1.24638 0.623188 0.782072i 0.285837π-0.285837\pi
0.623188 + 0.782072i 0.285837π0.285837\pi
684684 10.2431 + 7.44202i 0.391653 + 0.284553i
685685 −43.1837 19.2266i −1.64997 0.734612i
686686 2.18235 + 6.71657i 0.0833224 + 0.256440i
687687 7.65051 13.2511i 0.291885 0.505560i
688688 −4.91537 8.51366i −0.187397 0.324580i
689689 −6.96191 + 7.73198i −0.265228 + 0.294565i
690690 −2.34024 + 7.20251i −0.0890913 + 0.274195i
691691 18.2359 + 20.2530i 0.693725 + 0.770460i 0.982364 0.186978i 0.0598693π-0.0598693\pi
−0.288639 + 0.957438i 0.593203π0.593203\pi
692692 28.7649 12.8069i 1.09348 0.486847i
693693 6.71698 + 1.42774i 0.255157 + 0.0542353i
694694 1.86781 17.7710i 0.0709012 0.674580i
695695 7.25234 + 69.0014i 0.275097 + 2.61737i
696696 10.5015 2.23217i 0.398059 0.0846101i
697697 0.800258 0.581421i 0.0303119 0.0220229i
698698 3.12036 2.26707i 0.118107 0.0858100i
699699 8.68215 1.84545i 0.328389 0.0698012i
700700 1.06398 + 10.1231i 0.0402146 + 0.382616i
701701 −0.887358 + 8.44265i −0.0335150 + 0.318874i 0.964901 + 0.262614i 0.0845845π0.0845845\pi
−0.998416 + 0.0562607i 0.982082π0.982082\pi
702702 −9.18321 1.95195i −0.346598 0.0736717i
703703 −36.1433 + 16.0920i −1.36317 + 0.606923i
704704 3.46162 + 3.84452i 0.130465 + 0.144896i
705705 −0.905737 + 2.78757i −0.0341120 + 0.104986i
706706 5.38361 5.97910i 0.202615 0.225026i
707707 −1.45328 2.51716i −0.0546564 0.0946676i
708708 0.637869 1.10482i 0.0239726 0.0415217i
709709 7.22670 + 22.2415i 0.271404 + 0.835297i 0.990148 + 0.140022i 0.0447174π0.0447174\pi
−0.718744 + 0.695275i 0.755283π0.755283\pi
710710 18.0661 + 8.04354i 0.678008 + 0.301869i
711711 24.9229 + 18.1076i 0.934683 + 0.679087i
712712 10.7774 0.403901
713713 0 0
714714 0.621526 0.0232600
715715 −35.9197 26.0972i −1.34332 0.975978i
716716 −0.183378 0.0816452i −0.00685317 0.00305123i
717717 −0.164703 0.506903i −0.00615094 0.0189306i
718718 9.03230 15.6444i 0.337083 0.583844i
719719 6.48843 + 11.2383i 0.241978 + 0.419118i 0.961278 0.275582i 0.0888706π-0.0888706\pi
−0.719300 + 0.694700i 0.755537π0.755537\pi
720720 −7.44802 + 8.27186i −0.277571 + 0.308274i
721721 −1.47337 + 4.53457i −0.0548712 + 0.168876i
722722 2.10541 + 2.33830i 0.0783553 + 0.0870224i
723723 −12.6712 + 5.64156i −0.471245 + 0.209812i
724724 −11.5306 2.45090i −0.428531 0.0910870i
725725 4.47545 42.5811i 0.166214 1.58142i
726726 0.386215 + 3.67459i 0.0143338 + 0.136377i
727727 12.1515 2.58289i 0.450676 0.0957941i 0.0230186 0.999735i 0.492672π-0.492672\pi
0.427657 + 0.903941i 0.359339π0.359339\pi
728728 −4.36719 + 3.17295i −0.161859 + 0.117597i
729729 −6.12163 + 4.44762i −0.226727 + 0.164727i
730730 14.1462 3.00687i 0.523575 0.111289i
731731 0.978905 + 9.31366i 0.0362061 + 0.344478i
732732 −0.333214 + 3.17032i −0.0123159 + 0.117178i
733733 33.4109 + 7.10171i 1.23406 + 0.262308i 0.778356 0.627823i 0.216054π-0.216054\pi
0.455705 + 0.890131i 0.349387π0.349387\pi
734734 17.0160 7.57603i 0.628074 0.279636i
735735 −14.3662 15.9553i −0.529904 0.588518i
736736 −5.89161 + 18.1325i −0.217168 + 0.668373i
737737 −5.74708 + 6.38278i −0.211697 + 0.235113i
738738 −0.569607 0.986589i −0.0209675 0.0363168i
739739 −6.18747 + 10.7170i −0.227610 + 0.394231i −0.957099 0.289761i 0.906424π-0.906424\pi
0.729490 + 0.683992i 0.239758π0.239758\pi
740740 −18.1881 55.9773i −0.668609 2.05777i
741741 −9.11416 4.05789i −0.334817 0.149070i
742742 −1.52264 1.10626i −0.0558979 0.0406122i
743743 16.2455 0.595990 0.297995 0.954567i 0.403682π-0.403682\pi
0.297995 + 0.954567i 0.403682π0.403682\pi
744744 0 0
745745 −74.6520 −2.73504
746746 −6.92012 5.02776i −0.253364 0.184080i
747747 −28.1690 12.5417i −1.03065 0.458875i
748748 2.53720 + 7.80871i 0.0927694 + 0.285515i
749749 −0.888356 + 1.53868i −0.0324598 + 0.0562220i
750750 4.32029 + 7.48296i 0.157755 + 0.273239i
751751 −7.21876 + 8.01725i −0.263416 + 0.292554i −0.860315 0.509763i 0.829733π-0.829733\pi
0.596898 + 0.802317i 0.296400π0.296400\pi
752752 −0.371861 + 1.14447i −0.0135604 + 0.0417346i
753753 3.65404 + 4.05823i 0.133161 + 0.147890i
754754 8.97273 3.99492i 0.326767 0.145486i
755755 55.7482 + 11.8496i 2.02888 + 0.431253i
756756 −0.569303 + 5.41656i −0.0207054 + 0.196998i
757757 4.29629 + 40.8765i 0.156151 + 1.48568i 0.739333 + 0.673340i 0.235141π0.235141\pi
−0.583181 + 0.812342i 0.698192π0.698192\pi
758758 −3.12867 + 0.665019i −0.113638 + 0.0241546i
759759 −9.86411 + 7.16670i −0.358045 + 0.260135i
760760 27.6956 20.1221i 1.00463 0.729904i
761761 19.2309 4.08765i 0.697119 0.148177i 0.154296 0.988025i 0.450689π-0.450689\pi
0.542823 + 0.839847i 0.317356π0.317356\pi
762762 0.0931346 + 0.886117i 0.00337391 + 0.0321006i
763763 −0.117845 + 1.12122i −0.00426629 + 0.0405911i
764764 −31.4701 6.68917i −1.13855 0.242006i
765765 9.68679 4.31284i 0.350227 0.155931i
766766 −2.31665 2.57290i −0.0837038 0.0929625i
767767 0.833766 2.56607i 0.0301056 0.0926554i
768768 −5.99284 + 6.65573i −0.216248 + 0.240168i
769769 −1.89417 3.28080i −0.0683055 0.118309i 0.829850 0.557986i 0.188426π-0.188426\pi
−0.898155 + 0.439678i 0.855093π0.855093\pi
770770 4.01575 6.95549i 0.144718 0.250658i
771771 −1.26262 3.88595i −0.0454722 0.139949i
772772 −7.88770 3.51183i −0.283885 0.126394i
773773 −20.5244 14.9119i −0.738212 0.536342i 0.153939 0.988080i 0.450804π-0.450804\pi
−0.892151 + 0.451738i 0.850804π0.850804\pi
774774 10.7855 0.387676
775775 0 0
776776 −12.8256 −0.460414
777777 −5.80327 4.21632i −0.208191 0.151260i
778778 11.7170 + 5.21674i 0.420074 + 0.187029i
779779 −0.887573 2.73167i −0.0318006 0.0978722i
780780 7.42103 12.8536i 0.265716 0.460233i
781781 15.9194 + 27.5732i 0.569641 + 0.986647i
782782 1.98193 2.20115i 0.0708736 0.0787131i
783783 7.07939 21.7881i 0.252997 0.778644i
784784 −5.89821 6.55062i −0.210650 0.233951i
785785 51.3036 22.8418i 1.83110 0.815260i
786786 3.82987 + 0.814065i 0.136607 + 0.0290367i
787787 −2.71216 + 25.8045i −0.0966780 + 0.919829i 0.833450 + 0.552594i 0.186362π0.186362\pi
−0.930128 + 0.367235i 0.880305π0.880305\pi
788788 −2.53625 24.1308i −0.0903501 0.859623i
789789 −2.21453 + 0.470712i −0.0788392 + 0.0167578i
790790 29.1492 21.1781i 1.03708 0.753484i
791791 −3.94062 + 2.86303i −0.140112 + 0.101797i
792792 21.3828 4.54505i 0.759805 0.161501i
793793 0.704732 + 6.70507i 0.0250258 + 0.238104i
794794 2.34657 22.3261i 0.0832765 0.792323i
795795 11.7017 + 2.48727i 0.415016 + 0.0882144i
796796 −5.93532 + 2.64257i −0.210372 + 0.0936635i
797797 12.3807 + 13.7501i 0.438546 + 0.487054i 0.921383 0.388656i 0.127060π-0.127060\pi
−0.482837 + 0.875710i 0.660394π0.660394\pi
798798 0.557688 1.71639i 0.0197419 0.0607595i
799799 0.767061 0.851907i 0.0271367 0.0301383i
800800 25.3951 + 43.9856i 0.897852 + 1.55513i
801801 4.84652 8.39442i 0.171243 0.296602i
802802 −2.63993 8.12488i −0.0932192 0.286899i
803803 21.2710 + 9.47047i 0.750638 + 0.334206i
804804 −2.32281 1.68762i −0.0819193 0.0595178i
805805 9.29174 0.327491
806806 0 0
807807 −12.0378 −0.423751
808808 −7.48564 5.43864i −0.263344 0.191331i
809809 −33.5708 14.9467i −1.18029 0.525498i −0.279664 0.960098i 0.590223π-0.590223\pi
−0.900623 + 0.434600i 0.856890π0.856890\pi
810810 −1.84387 5.67484i −0.0647869 0.199394i
811811 19.7151 34.1475i 0.692289 1.19908i −0.278797 0.960350i 0.589936π-0.589936\pi
0.971086 0.238730i 0.0767310π-0.0767310\pi
812812 −2.84894 4.93451i −0.0999782 0.173167i
813813 −8.34737 + 9.27069i −0.292755 + 0.325137i
814814 −9.13092 + 28.1021i −0.320039 + 0.984977i
815815 −2.59213 2.87885i −0.0907982 0.100842i
816816 −1.48174 + 0.659715i −0.0518714 + 0.0230946i
817817 26.5987 + 5.65372i 0.930570 + 0.197799i
818818 0.248509 2.36440i 0.00868891 0.0826694i
819819 0.507486 + 4.82841i 0.0177330 + 0.168718i
820820 4.17959 0.888400i 0.145958 0.0310243i
821821 1.19782 0.870264i 0.0418041 0.0303724i −0.566687 0.823933i 0.691775π-0.691775\pi
0.608491 + 0.793561i 0.291775π0.291775\pi
822822 −6.41791 + 4.66289i −0.223850 + 0.162637i
823823 −38.0159 + 8.08053i −1.32515 + 0.281670i −0.815523 0.578725i 0.803551π-0.803551\pi
−0.509629 + 0.860394i 0.670217π0.670217\pi
824824 1.58655 + 15.0950i 0.0552702 + 0.525861i
825825 −3.39518 + 32.3030i −0.118205 + 1.12465i
826826 0.477407 + 0.101476i 0.0166111 + 0.00353080i
827827 −31.0023 + 13.8031i −1.07806 + 0.479982i −0.867417 0.497582i 0.834221π-0.834221\pi
−0.210640 + 0.977564i 0.567555π0.567555\pi
828828 7.32010 + 8.12980i 0.254391 + 0.282530i
829829 −5.10827 + 15.7216i −0.177417 + 0.546035i −0.999736 0.0229933i 0.992680π-0.992680\pi
0.822318 + 0.569028i 0.192680π0.192680\pi
830830 −24.1313 + 26.8005i −0.837609 + 0.930259i
831831 5.22073 + 9.04256i 0.181105 + 0.313683i
832832 −1.82877 + 3.16752i −0.0634012 + 0.109814i
833833 2.59485 + 7.98612i 0.0899061 + 0.276703i
834834 10.6370 + 4.73591i 0.368330 + 0.163991i
835835 −33.8619 24.6021i −1.17184 0.851392i
836836 23.8409 0.824555
837837 0 0
838838 27.6122 0.953848
839839 43.7501 + 31.7863i 1.51042 + 1.09738i 0.965990 + 0.258579i 0.0832542π0.0832542\pi
0.544430 + 0.838806i 0.316746π0.316746\pi
840840 5.67023 + 2.52455i 0.195642 + 0.0871053i
841841 −1.55522 4.78647i −0.0536282 0.165051i
842842 7.47562 12.9482i 0.257627 0.446223i
843843 6.94819 + 12.0346i 0.239308 + 0.414494i
844844 11.7402 13.0389i 0.404116 0.448816i
845845 −5.19379 + 15.9848i −0.178672 + 0.549896i
846846 −0.883411 0.981127i −0.0303723 0.0337319i
847847 4.14138 1.84386i 0.142299 0.0633558i
848848 4.80427 + 1.02118i 0.164979 + 0.0350674i
849849 2.14081 20.3684i 0.0734724 0.699043i
850850 −0.824782 7.84728i −0.0282898 0.269160i
851851 −33.4377 + 7.10741i −1.14623 + 0.243639i
852852 −8.61062 + 6.25598i −0.294995 + 0.214326i
853853 −32.0178 + 23.2623i −1.09627 + 0.796487i −0.980447 0.196783i 0.936950π-0.936950\pi
−0.115823 + 0.993270i 0.536950π0.536950\pi
854854 −1.19293 + 0.253566i −0.0408213 + 0.00867684i
855855 −3.21836 30.6206i −0.110065 1.04720i
856856 −0.591211 + 5.62499i −0.0202072 + 0.192258i
857857 −12.4470 2.64569i −0.425180 0.0903749i −0.00964843 0.999953i 0.503071π-0.503071\pi
−0.415532 + 0.909579i 0.636405π0.636405\pi
858858 −6.80692 + 3.03064i −0.232384 + 0.103464i
859859 14.1550 + 15.7207i 0.482963 + 0.536385i 0.934545 0.355845i 0.115807π-0.115807\pi
−0.451582 + 0.892230i 0.649140π0.649140\pi
860860 −12.5010 + 38.4742i −0.426281 + 1.31196i
861861 0.348457 0.387001i 0.0118754 0.0131890i
862862 −4.00618 6.93891i −0.136451 0.236340i
863863 4.66987 8.08845i 0.158964 0.275334i −0.775531 0.631309i 0.782518π-0.782518\pi
0.934495 + 0.355975i 0.115851π0.115851\pi
864864 8.39795 + 25.8462i 0.285704 + 0.879307i
865865 −69.9503 31.1439i −2.37838 1.05892i
866866 −13.7202 9.96829i −0.466230 0.338736i
867867 −13.7957 −0.468526
868868 0 0
869869 58.0085 1.96780
870870 −9.13647 6.63804i −0.309755 0.225051i
871871 −5.54737 2.46985i −0.187965 0.0836876i
872872 1.10905 + 3.41331i 0.0375572 + 0.115589i
873873 −5.76760 + 9.98977i −0.195204 + 0.338102i
874874 −4.30028 7.44830i −0.145459 0.251942i
875875 7.09370 7.87836i 0.239811 0.266337i
876876 −2.40525 + 7.40260i −0.0812659 + 0.250111i
877877 15.0121 + 16.6726i 0.506923 + 0.562995i 0.941228 0.337771i 0.109673π-0.109673\pi
−0.434305 + 0.900766i 0.643006π0.643006\pi
878878 −11.4596 + 5.10215i −0.386743 + 0.172189i
879879 −10.9460 2.32665i −0.369200 0.0784758i
880880 −2.19086 + 20.8446i −0.0738539 + 0.702673i
881881 −4.85341 46.1771i −0.163516 1.55575i −0.701425 0.712744i 0.747452π-0.747452\pi
0.537909 0.843003i 0.319214π-0.319214\pi
882882 9.45947 2.01067i 0.318517 0.0677029i
883883 29.5611 21.4774i 0.994811 0.722773i 0.0338419 0.999427i 0.489226π-0.489226\pi
0.960969 + 0.276654i 0.0892257π0.0892257\pi
884884 −4.69625 + 3.41202i −0.157952 + 0.114759i
885885 −3.03454 + 0.645012i −0.102005 + 0.0216818i
886886 1.28002 + 12.1785i 0.0430030 + 0.409146i
887887 −2.99840 + 28.5279i −0.100677 + 0.957873i 0.821266 + 0.570546i 0.193268π0.193268\pi
−0.921942 + 0.387327i 0.873398π0.873398\pi
888888 −22.3362 4.74772i −0.749555 0.159323i
889889 0.998680 0.444641i 0.0334946 0.0149128i
890890 −7.58576 8.42484i −0.254275 0.282401i
891891 2.96861 9.13643i 0.0994521 0.306082i
892892 9.61386 10.6773i 0.321896 0.357502i
893893 −1.66433 2.88270i −0.0556945 0.0964658i
894894 −6.26408 + 10.8497i −0.209502 + 0.362869i
895895 0.150844 + 0.464249i 0.00504215 + 0.0155181i
896896 7.49577 + 3.33733i 0.250416 + 0.111492i
897897 −6.97394 5.06687i −0.232853 0.169178i
898898 −6.34235 −0.211647
899899 0 0
900900 29.1430 0.971434
901901 −3.78531 2.75019i −0.126107 0.0916220i
902902 −1.95968 0.872508i −0.0652503 0.0290513i
903903 1.52354 + 4.68898i 0.0507004 + 0.156040i
904904 −7.75296 + 13.4285i −0.257860 + 0.446626i
905905 14.3332 + 24.8259i 0.476453 + 0.825240i
906906 6.40005 7.10798i 0.212627 0.236147i
907907 −6.85697 + 21.1036i −0.227682 + 0.700733i 0.770326 + 0.637650i 0.220093π0.220093\pi
−0.998008 + 0.0630831i 0.979907π0.979907\pi
908908 −22.2017 24.6575i −0.736789 0.818287i
909909 −7.60234 + 3.38478i −0.252154 + 0.112266i
910910 5.55420 + 1.18058i 0.184120 + 0.0391359i
911911 −3.01381 + 28.6745i −0.0998520 + 0.950028i 0.823822 + 0.566849i 0.191838π0.191838\pi
−0.923674 + 0.383179i 0.874829π0.874829\pi
912912 0.492297 + 4.68389i 0.0163016 + 0.155099i
913913 −56.7932 + 12.0718i −1.87958 + 0.399517i
914914 17.4037 12.6445i 0.575662 0.418243i
915915 6.27153 4.55653i 0.207330 0.150634i
916916 −25.2860 + 5.37471i −0.835474 + 0.177586i
917917 −0.502151 4.77764i −0.0165825 0.157772i
918918 0.441317 4.19885i 0.0145656 0.138583i
919919 −47.0121 9.99272i −1.55078 0.329629i −0.648651 0.761086i 0.724667π-0.724667\pi
−0.902134 + 0.431456i 0.858000π0.858000\pi
920920 27.0220 12.0310i 0.890890 0.396650i
921921 18.5495 + 20.6013i 0.611226 + 0.678835i
922922 −1.42082 + 4.37283i −0.0467921 + 0.144011i
923923 −15.0622 + 16.7282i −0.495778 + 0.550617i
924924 2.16127 + 3.74343i 0.0711007 + 0.123150i
925925 −45.5334 + 78.8662i −1.49713 + 2.59310i
926926 7.52513 + 23.1600i 0.247291 + 0.761084i
927927 12.4708 + 5.55238i 0.409596 + 0.182364i
928928 −23.0013 16.7114i −0.755055 0.548580i
929929 −7.01617 −0.230193 −0.115097 0.993354i 0.536718π-0.536718\pi
−0.115097 + 0.993354i 0.536718π0.536718\pi
930930 0 0
931931 24.3825 0.799105
932932 −12.1321 8.81450i −0.397401 0.288729i
933933 1.96320 + 0.874072i 0.0642722 + 0.0286158i
934934 −7.65829 23.5698i −0.250587 0.771227i
935935 9.98321 17.2914i 0.326486 0.565490i
936936 7.72770 + 13.3848i 0.252588 + 0.437495i
937937 −8.61884 + 9.57219i −0.281565 + 0.312710i −0.867293 0.497798i 0.834142π-0.834142\pi
0.585728 + 0.810508i 0.300809π0.300809\pi
938938 0.339439 1.04469i 0.0110831 0.0341102i
939939 −6.48845 7.20615i −0.211742 0.235164i
940940 4.52383 2.01414i 0.147551 0.0656940i
941941 −48.9458 10.4037i −1.59559 0.339152i −0.677497 0.735526i 0.736935π-0.736935\pi
−0.918089 + 0.396373i 0.870269π0.870269\pi
942942 0.985141 9.37299i 0.0320976 0.305388i
943943 −0.259412 2.46814i −0.00844763 0.0803738i
944944 −1.24587 + 0.264817i −0.0405496 + 0.00861907i
945945 10.7150 7.78494i 0.348560 0.253244i
946946 16.4304 11.9374i 0.534197 0.388117i
947947 50.7345 10.7840i 1.64865 0.350431i 0.712402 0.701772i 0.247607π-0.247607\pi
0.936248 + 0.351340i 0.114274π0.114274\pi
948948 2.02697 + 19.2853i 0.0658328 + 0.626357i
949949 −1.72073 + 16.3717i −0.0558573 + 0.531447i
950950 −22.4109 4.76358i −0.727105 0.154551i
951951 7.21035 3.21026i 0.233812 0.104100i
952952 −1.62435 1.80403i −0.0526456 0.0584689i
953953 −5.78950 + 17.8183i −0.187540 + 0.577190i −0.999983 0.00585146i 0.998137π-0.998137\pi
0.812443 + 0.583041i 0.198137π0.198137\pi
954954 −3.60568 + 4.00451i −0.116738 + 0.129651i
955955 39.1193 + 67.7565i 1.26587 + 2.19255i
956956 −0.450241 + 0.779840i −0.0145618 + 0.0252218i
957957 −5.61857 17.2922i −0.181623 0.558977i
958958 −20.9401 9.32313i −0.676543 0.301217i
959959 7.87432 + 5.72103i 0.254275 + 0.184742i
960960 4.20549 0.135731
961961 0 0
962962 −20.8907 −0.673542
963963 4.11539 + 2.99001i 0.132617 + 0.0963516i
964964 21.4078 + 9.53138i 0.689499 + 0.306985i
965965 6.48829 + 19.9689i 0.208865 + 0.642821i
966966 0.779674 1.35044i 0.0250856 0.0434496i
967967 −23.8923 41.3827i −0.768324 1.33078i −0.938471 0.345358i 0.887757π-0.887757\pi
0.170146 0.985419i 0.445576π-0.445576\pi
968968 9.65642 10.7245i 0.310369 0.344700i
969969 1.38642 4.26696i 0.0445382 0.137075i
970970 9.02741 + 10.0260i 0.289853 + 0.321914i
971971 −28.4119 + 12.6498i −0.911780 + 0.405951i −0.808361 0.588687i 0.799645π-0.799645\pi
−0.103419 + 0.994638i 0.532978π0.532978\pi
972972 24.0768 + 5.11769i 0.772265 + 0.164150i
973973 1.49329 14.2077i 0.0478727 0.455478i
974974 −2.05515 19.5534i −0.0658512 0.626532i
975975 −22.4622 + 4.77450i −0.719368 + 0.152906i
976976 2.57485 1.87074i 0.0824191 0.0598810i
977977 17.8624 12.9778i 0.571469 0.415197i −0.264170 0.964476i 0.585098π-0.585098\pi
0.835639 + 0.549280i 0.185098π0.185098\pi
978978 −0.635910 + 0.135167i −0.0203342 + 0.00432216i
979979 −1.90785 18.1520i −0.0609753 0.580141i
980980 −3.79159 + 36.0745i −0.121118 + 1.15236i
981981 3.15732 + 0.671110i 0.100806 + 0.0214269i
982982 −17.6138 + 7.84218i −0.562080 + 0.250254i
983983 25.1438 + 27.9251i 0.801964 + 0.890671i 0.995911 0.0903411i 0.0287957π-0.0287957\pi
−0.193947 + 0.981012i 0.562129π0.562129\pi
984984 0.512285 1.57665i 0.0163311 0.0502618i
985985 −39.4816 + 43.8488i −1.25799 + 1.39714i
986986 2.20846 + 3.82517i 0.0703318 + 0.121818i
987987 0.301756 0.522656i 0.00960499 0.0166363i
988988 5.20865 + 16.0306i 0.165709 + 0.510001i
989989 21.4645 + 9.55659i 0.682530 + 0.303882i
990990 −18.6033 13.5161i −0.591253 0.429571i
991991 6.77397 0.215182 0.107591 0.994195i 0.465686π-0.465686\pi
0.107591 + 0.994195i 0.465686π0.465686\pi
992992 0 0
993993 29.2099 0.926948
994994 −3.29426 2.39342i −0.104487 0.0759146i
995995 14.4335 + 6.42620i 0.457572 + 0.203724i
996996 −5.99783 18.4594i −0.190049 0.584909i
997997 14.7866 25.6112i 0.468298 0.811115i −0.531046 0.847343i 0.678201π-0.678201\pi
0.999344 + 0.0362278i 0.0115342π0.0115342\pi
998998 14.2397 + 24.6639i 0.450751 + 0.780724i
999999 −32.6049 + 36.2114i −1.03157 + 1.14568i
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 961.2.g.l.732.2 16
31.2 even 5 961.2.g.n.448.1 16
31.3 odd 30 961.2.d.o.388.4 16
31.4 even 5 961.2.c.i.521.3 16
31.5 even 3 961.2.g.j.816.2 16
31.6 odd 6 961.2.d.o.374.4 16
31.7 even 15 961.2.a.j.1.3 8
31.8 even 5 961.2.g.m.844.1 16
31.9 even 15 961.2.g.n.547.1 16
31.10 even 15 961.2.g.m.846.1 16
31.11 odd 30 961.2.c.j.439.3 16
31.12 odd 30 961.2.d.p.628.1 16
31.13 odd 30 31.2.g.a.18.2 16
31.14 even 15 961.2.d.q.531.1 16
31.15 odd 10 961.2.g.k.338.2 16
31.16 even 5 961.2.g.j.338.2 16
31.17 odd 30 961.2.d.p.531.1 16
31.18 even 15 inner 961.2.g.l.235.2 16
31.19 even 15 961.2.d.q.628.1 16
31.20 even 15 961.2.c.i.439.3 16
31.21 odd 30 961.2.g.s.846.1 16
31.22 odd 30 961.2.g.t.547.1 16
31.23 odd 10 961.2.g.s.844.1 16
31.24 odd 30 961.2.a.i.1.3 8
31.25 even 3 961.2.d.n.374.4 16
31.26 odd 6 961.2.g.k.816.2 16
31.27 odd 10 961.2.c.j.521.3 16
31.28 even 15 961.2.d.n.388.4 16
31.29 odd 10 961.2.g.t.448.1 16
31.30 odd 2 31.2.g.a.19.2 yes 16
93.38 odd 30 8649.2.a.be.1.6 8
93.44 even 30 279.2.y.c.235.1 16
93.86 even 30 8649.2.a.bf.1.6 8
93.92 even 2 279.2.y.c.19.1 16
124.75 even 30 496.2.bg.c.49.1 16
124.123 even 2 496.2.bg.c.81.1 16
155.13 even 60 775.2.ck.a.49.2 32
155.44 odd 30 775.2.bl.a.576.1 16
155.92 even 4 775.2.ck.a.174.2 32
155.123 even 4 775.2.ck.a.174.3 32
155.137 even 60 775.2.ck.a.49.3 32
155.154 odd 2 775.2.bl.a.701.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.2.g.a.18.2 16 31.13 odd 30
31.2.g.a.19.2 yes 16 31.30 odd 2
279.2.y.c.19.1 16 93.92 even 2
279.2.y.c.235.1 16 93.44 even 30
496.2.bg.c.49.1 16 124.75 even 30
496.2.bg.c.81.1 16 124.123 even 2
775.2.bl.a.576.1 16 155.44 odd 30
775.2.bl.a.701.1 16 155.154 odd 2
775.2.ck.a.49.2 32 155.13 even 60
775.2.ck.a.49.3 32 155.137 even 60
775.2.ck.a.174.2 32 155.92 even 4
775.2.ck.a.174.3 32 155.123 even 4
961.2.a.i.1.3 8 31.24 odd 30
961.2.a.j.1.3 8 31.7 even 15
961.2.c.i.439.3 16 31.20 even 15
961.2.c.i.521.3 16 31.4 even 5
961.2.c.j.439.3 16 31.11 odd 30
961.2.c.j.521.3 16 31.27 odd 10
961.2.d.n.374.4 16 31.25 even 3
961.2.d.n.388.4 16 31.28 even 15
961.2.d.o.374.4 16 31.6 odd 6
961.2.d.o.388.4 16 31.3 odd 30
961.2.d.p.531.1 16 31.17 odd 30
961.2.d.p.628.1 16 31.12 odd 30
961.2.d.q.531.1 16 31.14 even 15
961.2.d.q.628.1 16 31.19 even 15
961.2.g.j.338.2 16 31.16 even 5
961.2.g.j.816.2 16 31.5 even 3
961.2.g.k.338.2 16 31.15 odd 10
961.2.g.k.816.2 16 31.26 odd 6
961.2.g.l.235.2 16 31.18 even 15 inner
961.2.g.l.732.2 16 1.1 even 1 trivial
961.2.g.m.844.1 16 31.8 even 5
961.2.g.m.846.1 16 31.10 even 15
961.2.g.n.448.1 16 31.2 even 5
961.2.g.n.547.1 16 31.9 even 15
961.2.g.s.844.1 16 31.23 odd 10
961.2.g.s.846.1 16 31.21 odd 30
961.2.g.t.448.1 16 31.29 odd 10
961.2.g.t.547.1 16 31.22 odd 30
8649.2.a.be.1.6 8 93.38 odd 30
8649.2.a.bf.1.6 8 93.86 even 30