Properties

Label 845.2.t.g.188.3
Level 845845
Weight 22
Character 845.188
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(188,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.188");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.t (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: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6++1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 188.3
Root 0.131303i0.131303i of defining polynomial
Character χ\chi == 845.188
Dual form 845.2.t.g.427.3

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+(0.113711+0.0656513i)q2+(0.3321790.0890070i)q3+(0.9913801.71712i)q4+(2.08297+0.813169i)q5+(0.0436159+0.0116869i)q6+(1.390692.40874i)q70.522947iq8+(2.49566+1.44087i)q9+(0.2902430.0442830i)q10+(3.917061.04957i)q11+(0.4821510.482151i)q120.365201iq14+(0.619540+0.455516i)q15+(1.94843+3.37478i)q16+(0.627499+2.34186i)q170.378379q18+(0.491577+1.83459i)q19+(3.46132+2.77055i)q20+(0.6763510.676351i)q21+(0.514321+0.137812i)q22+(2.06467+7.70544i)q23+(0.04654590.173712i)q24+(3.677513.38761i)q25+(1.43027+1.43027i)q27+(2.75740+4.77595i)q28+(3.965652.28957i)q29+(0.100354+0.0111238i)q30+(3.87352+3.87352i)q31+(1.34889+0.778780i)q32+(1.207750.697292i)q33+(0.225100+0.225100i)q34+(4.85547+3.88646i)q35+(4.94829+2.85689i)q36+(3.50510+6.07101i)q37+(0.176341+0.176341i)q38+(0.425244+1.08928i)q40+(1.66178+6.20184i)q41+(0.03250550.121312i)q42+(6.243681.67299i)q43+(5.685545.68554i)q44+(4.026705.03067i)q45+(0.271096+1.01174i)q46+0.512375q47+(0.346847+1.29445i)q48+(0.368015+0.637420i)q49+(0.6405760.143776i)q50+0.833767iq51+(1.326621.32662i)q53+(0.256537+0.0687390i)q54+(7.30564+5.37147i)q55+(1.25964+0.727255i)q56+0.653165iq57+(0.3006260.520700i)q58+(2.536670.679700i)q59+(1.39638+0.612235i)q60+(0.641767+1.11157i)q61+(0.694764+0.186162i)q62+(6.94135+4.00759i)q63+7.58920q64+0.183113q66+(3.131801.80814i)q67+(4.643341.24418i)q68+(1.37168+2.37581i)q69+(0.296970+0.760703i)q70+(6.20800+1.66343i)q71+(0.753497+1.30509i)q729.93250iq73+(0.797139+0.460228i)q74+(0.9200701.45262i)q75+(3.637550.974678i)q76+(7.975567.97556i)q77+8.37577iq79+(1.314258.61395i)q80+(3.974806.88456i)q81+(0.218196+0.814318i)q823.17194q83+(0.490855+1.83190i)q84+(0.5972665.38828i)q85+(0.6001430.600143i)q86+(1.521090.407576i)q87+(0.5488712.04842i)q88+(1.612266.01705i)q89+(0.7881520.307686i)q90+(11.184311.1843i)q92+(0.941930+1.63147i)q93+(0.0582629+0.0336381i)q94+(0.4678924.22112i)q95+(0.378755+0.378755i)q96+(10.1931+5.88500i)q97+(0.0836950+0.0483213i)q98+(8.26335+8.26335i)q99+O(q100)q+(0.113711 + 0.0656513i) q^{2} +(0.332179 - 0.0890070i) q^{3} +(-0.991380 - 1.71712i) q^{4} +(-2.08297 + 0.813169i) q^{5} +(0.0436159 + 0.0116869i) q^{6} +(-1.39069 - 2.40874i) q^{7} -0.522947i q^{8} +(-2.49566 + 1.44087i) q^{9} +(-0.290243 - 0.0442830i) q^{10} +(3.91706 - 1.04957i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(-0.619540 + 0.455516i) q^{15} +(-1.94843 + 3.37478i) q^{16} +(-0.627499 + 2.34186i) q^{17} -0.378379 q^{18} +(-0.491577 + 1.83459i) q^{19} +(3.46132 + 2.77055i) q^{20} +(-0.676351 - 0.676351i) q^{21} +(0.514321 + 0.137812i) q^{22} +(2.06467 + 7.70544i) q^{23} +(-0.0465459 - 0.173712i) q^{24} +(3.67751 - 3.38761i) q^{25} +(-1.43027 + 1.43027i) q^{27} +(-2.75740 + 4.77595i) q^{28} +(-3.96565 - 2.28957i) q^{29} +(-0.100354 + 0.0111238i) q^{30} +(-3.87352 + 3.87352i) q^{31} +(-1.34889 + 0.778780i) q^{32} +(1.20775 - 0.697292i) q^{33} +(-0.225100 + 0.225100i) q^{34} +(4.85547 + 3.88646i) q^{35} +(4.94829 + 2.85689i) q^{36} +(-3.50510 + 6.07101i) q^{37} +(-0.176341 + 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(1.66178 + 6.20184i) q^{41} +(-0.0325055 - 0.121312i) q^{42} +(-6.24368 - 1.67299i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(4.02670 - 5.03067i) q^{45} +(-0.271096 + 1.01174i) q^{46} +0.512375 q^{47} +(-0.346847 + 1.29445i) q^{48} +(-0.368015 + 0.637420i) q^{49} +(0.640576 - 0.143776i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(-0.256537 + 0.0687390i) q^{54} +(-7.30564 + 5.37147i) q^{55} +(-1.25964 + 0.727255i) q^{56} +0.653165i q^{57} +(-0.300626 - 0.520700i) q^{58} +(-2.53667 - 0.679700i) q^{59} +(1.39638 + 0.612235i) q^{60} +(0.641767 + 1.11157i) q^{61} +(-0.694764 + 0.186162i) q^{62} +(6.94135 + 4.00759i) q^{63} +7.58920 q^{64} +0.183113 q^{66} +(-3.13180 - 1.80814i) q^{67} +(4.64334 - 1.24418i) q^{68} +(1.37168 + 2.37581i) q^{69} +(0.296970 + 0.760703i) q^{70} +(6.20800 + 1.66343i) q^{71} +(0.753497 + 1.30509i) q^{72} -9.93250i q^{73} +(-0.797139 + 0.460228i) q^{74} +(0.920070 - 1.45262i) q^{75} +(3.63755 - 0.974678i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(1.31425 - 8.61395i) q^{80} +(3.97480 - 6.88456i) q^{81} +(-0.218196 + 0.814318i) q^{82} -3.17194 q^{83} +(-0.490855 + 1.83190i) q^{84} +(-0.597266 - 5.38828i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(-1.52109 - 0.407576i) q^{87} +(-0.548871 - 2.04842i) q^{88} +(-1.61226 - 6.01705i) q^{89} +(0.788152 - 0.307686i) q^{90} +(11.1843 - 11.1843i) q^{92} +(-0.941930 + 1.63147i) q^{93} +(0.0582629 + 0.0336381i) q^{94} +(-0.467892 - 4.22112i) q^{95} +(-0.378755 + 0.378755i) q^{96} +(-10.1931 + 5.88500i) q^{97} +(-0.0836950 + 0.0483213i) q^{98} +(-8.26335 + 8.26335i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+6q22q3+6q4+8q6+2q7+12q92q10+16q1124q12+20q152q16+4q17+20q194q21+16q2210q2332q24+18q25+60q99+O(q100) 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/845Z)×\left(\mathbb{Z}/845\mathbb{Z}\right)^\times.

nn 171171 677677
χ(n)\chi(n) e(512)e\left(\frac{5}{12}\right) e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.113711 + 0.0656513i 0.0804061 + 0.0464225i 0.539664 0.841881i 0.318551π-0.318551\pi
−0.459258 + 0.888303i 0.651885π0.651885\pi
33 0.332179 0.0890070i 0.191783 0.0513882i −0.161649 0.986848i 0.551681π-0.551681\pi
0.353432 + 0.935460i 0.385015π0.385015\pi
44 −0.991380 1.71712i −0.495690 0.858560i
55 −2.08297 + 0.813169i −0.931532 + 0.363660i
66 0.0436159 + 0.0116869i 0.0178061 + 0.00477114i
77 −1.39069 2.40874i −0.525630 0.910418i −0.999554 0.0298522i 0.990496π-0.990496\pi
0.473924 0.880566i 0.342837π-0.342837\pi
88 0.522947i 0.184890i
99 −2.49566 + 1.44087i −0.831885 + 0.480289i
1010 −0.290243 0.0442830i −0.0917828 0.0140035i
1111 3.91706 1.04957i 1.18104 0.316459i 0.385701 0.922624i 0.373960π-0.373960\pi
0.795339 + 0.606165i 0.207293π0.207293\pi
1212 −0.482151 0.482151i −0.139185 0.139185i
1313 0 0
1414 0.365201i 0.0976042i
1515 −0.619540 + 0.455516i −0.159965 + 0.117614i
1616 −1.94843 + 3.37478i −0.487107 + 0.843694i
1717 −0.627499 + 2.34186i −0.152191 + 0.567984i 0.847139 + 0.531372i 0.178323π0.178323\pi
−0.999330 + 0.0366120i 0.988343π0.988343\pi
1818 −0.378379 −0.0891849
1919 −0.491577 + 1.83459i −0.112775 + 0.420883i −0.999111 0.0421602i 0.986576π-0.986576\pi
0.886335 + 0.463044i 0.153243π0.153243\pi
2020 3.46132 + 2.77055i 0.773975 + 0.619513i
2121 −0.676351 0.676351i −0.147592 0.147592i
2222 0.514321 + 0.137812i 0.109654 + 0.0293816i
2323 2.06467 + 7.70544i 0.430513 + 1.60670i 0.751582 + 0.659640i 0.229291π0.229291\pi
−0.321069 + 0.947056i 0.604042π0.604042\pi
2424 −0.0465459 0.173712i −0.00950115 0.0354588i
2525 3.67751 3.38761i 0.735502 0.677522i
2626 0 0
2727 −1.43027 + 1.43027i −0.275256 + 0.275256i
2828 −2.75740 + 4.77595i −0.521099 + 0.902570i
2929 −3.96565 2.28957i −0.736403 0.425162i 0.0843571 0.996436i 0.473116π-0.473116\pi
−0.820760 + 0.571273i 0.806450π0.806450\pi
3030 −0.100354 + 0.0111238i −0.0183220 + 0.00203092i
3131 −3.87352 + 3.87352i −0.695704 + 0.695704i −0.963481 0.267777i 0.913711π-0.913711\pi
0.267777 + 0.963481i 0.413711π0.413711\pi
3232 −1.34889 + 0.778780i −0.238452 + 0.137670i
3333 1.20775 0.697292i 0.210242 0.121383i
3434 −0.225100 + 0.225100i −0.0386043 + 0.0386043i
3535 4.85547 + 3.88646i 0.820724 + 0.656932i
3636 4.94829 + 2.85689i 0.824714 + 0.476149i
3737 −3.50510 + 6.07101i −0.576234 + 0.998067i 0.419672 + 0.907676i 0.362145π0.362145\pi
−0.995906 + 0.0903914i 0.971188π0.971188\pi
3838 −0.176341 + 0.176341i −0.0286063 + 0.0286063i
3939 0 0
4040 0.425244 + 1.08928i 0.0672370 + 0.172230i
4141 1.66178 + 6.20184i 0.259526 + 0.968565i 0.965516 + 0.260343i 0.0838357π0.0838357\pi
−0.705990 + 0.708222i 0.749498π0.749498\pi
4242 −0.0325055 0.121312i −0.00501570 0.0187189i
4343 −6.24368 1.67299i −0.952152 0.255128i −0.250877 0.968019i 0.580719π-0.580719\pi
−0.701275 + 0.712891i 0.747386π0.747386\pi
4444 −5.68554 5.68554i −0.857128 0.857128i
4545 4.02670 5.03067i 0.600265 0.749928i
4646 −0.271096 + 1.01174i −0.0399709 + 0.149174i
4747 0.512375 0.0747376 0.0373688 0.999302i 0.488102π-0.488102\pi
0.0373688 + 0.999302i 0.488102π0.488102\pi
4848 −0.346847 + 1.29445i −0.0500631 + 0.186838i
4949 −0.368015 + 0.637420i −0.0525736 + 0.0910601i
5050 0.640576 0.143776i 0.0905911 0.0203331i
5151 0.833767i 0.116751i
5252 0 0
5353 −1.32662 1.32662i −0.182225 0.182225i 0.610100 0.792325i 0.291129π-0.291129\pi
−0.792325 + 0.610100i 0.791129π0.791129\pi
5454 −0.256537 + 0.0687390i −0.0349103 + 0.00935419i
5555 −7.30564 + 5.37147i −0.985092 + 0.724288i
5656 −1.25964 + 0.727255i −0.168327 + 0.0971835i
5757 0.653165i 0.0865138i
5858 −0.300626 0.520700i −0.0394742 0.0683713i
5959 −2.53667 0.679700i −0.330247 0.0884894i 0.0898858 0.995952i 0.471350π-0.471350\pi
−0.420133 + 0.907463i 0.638016π0.638016\pi
6060 1.39638 + 0.612235i 0.180271 + 0.0790392i
6161 0.641767 + 1.11157i 0.0821698 + 0.142322i 0.904182 0.427148i 0.140482π-0.140482\pi
−0.822012 + 0.569470i 0.807148π0.807148\pi
6262 −0.694764 + 0.186162i −0.0882352 + 0.0236425i
6363 6.94135 + 4.00759i 0.874528 + 0.504909i
6464 7.58920 0.948650
6565 0 0
6666 0.183113 0.0225396
6767 −3.13180 1.80814i −0.382610 0.220900i 0.296343 0.955082i 0.404233π-0.404233\pi
−0.678953 + 0.734181i 0.737566π0.737566\pi
6868 4.64334 1.24418i 0.563088 0.150879i
6969 1.37168 + 2.37581i 0.165130 + 0.286014i
7070 0.296970 + 0.760703i 0.0354948 + 0.0909214i
7171 6.20800 + 1.66343i 0.736754 + 0.197413i 0.607635 0.794216i 0.292118π-0.292118\pi
0.129119 + 0.991629i 0.458785π0.458785\pi
7272 0.753497 + 1.30509i 0.0888005 + 0.153807i
7373 9.93250i 1.16251i −0.813721 0.581256i 0.802562π-0.802562\pi
0.813721 0.581256i 0.197438π-0.197438\pi
7474 −0.797139 + 0.460228i −0.0926655 + 0.0535005i
7575 0.920070 1.45262i 0.106241 0.167734i
7676 3.63755 0.974678i 0.417255 0.111803i
7777 −7.97556 7.97556i −0.908899 0.908899i
7878 0 0
7979 8.37577i 0.942347i 0.882040 + 0.471174i 0.156169π0.156169\pi
−0.882040 + 0.471174i 0.843831π0.843831\pi
8080 1.31425 8.61395i 0.146938 0.963069i
8181 3.97480 6.88456i 0.441645 0.764951i
8282 −0.218196 + 0.814318i −0.0240957 + 0.0899264i
8383 −3.17194 −0.348166 −0.174083 0.984731i 0.555696π-0.555696\pi
−0.174083 + 0.984731i 0.555696π0.555696\pi
8484 −0.490855 + 1.83190i −0.0535567 + 0.199876i
8585 −0.597266 5.38828i −0.0647826 0.584441i
8686 −0.600143 0.600143i −0.0647151 0.0647151i
8787 −1.52109 0.407576i −0.163078 0.0436967i
8888 −0.548871 2.04842i −0.0585099 0.218362i
8989 −1.61226 6.01705i −0.170900 0.637806i −0.997214 0.0745967i 0.976233π-0.976233\pi
0.826314 0.563210i 0.190434π-0.190434\pi
9090 0.788152 0.307686i 0.0830785 0.0324330i
9191 0 0
9292 11.1843 11.1843i 1.16604 1.16604i
9393 −0.941930 + 1.63147i −0.0976736 + 0.169176i
9494 0.0582629 + 0.0336381i 0.00600936 + 0.00346951i
9595 −0.467892 4.22112i −0.0480048 0.433078i
9696 −0.378755 + 0.378755i −0.0386565 + 0.0386565i
9797 −10.1931 + 5.88500i −1.03495 + 0.597531i −0.918400 0.395654i 0.870518π-0.870518\pi
−0.116554 + 0.993184i 0.537185π0.537185\pi
9898 −0.0836950 + 0.0483213i −0.00845447 + 0.00488119i
9999 −8.26335 + 8.26335i −0.830498 + 0.830498i
100100 −9.46275 2.95632i −0.946275 0.295632i
101101 0.873807 + 0.504493i 0.0869471 + 0.0501989i 0.542843 0.839834i 0.317348π-0.317348\pi
−0.455896 + 0.890033i 0.650681π0.650681\pi
102102 −0.0547379 + 0.0948088i −0.00541986 + 0.00938747i
103103 −6.00002 + 6.00002i −0.591200 + 0.591200i −0.937955 0.346756i 0.887283π-0.887283\pi
0.346756 + 0.937955i 0.387283π0.387283\pi
104104 0 0
105105 1.95880 + 0.858830i 0.191160 + 0.0838132i
106106 −0.0637574 0.237946i −0.00619267 0.0231113i
107107 1.28261 + 4.78678i 0.123995 + 0.462755i 0.999802 0.0199063i 0.00633678π-0.00633678\pi
−0.875807 + 0.482662i 0.839670π0.839670\pi
108108 3.87389 + 1.03801i 0.372765 + 0.0998821i
109109 6.51002 + 6.51002i 0.623546 + 0.623546i 0.946436 0.322890i 0.104654π-0.104654\pi
−0.322890 + 0.946436i 0.604654π0.604654\pi
110110 −1.18338 + 0.131172i −0.112831 + 0.0125068i
111111 −0.623956 + 2.32864i −0.0592233 + 0.221024i
112112 10.8386 1.02415
113113 1.94191 7.24731i 0.182680 0.681769i −0.812436 0.583051i 0.801859π-0.801859\pi
0.995115 0.0987188i 0.0314744π-0.0314744\pi
114114 −0.0428811 + 0.0742723i −0.00401619 + 0.00695624i
115115 −10.5665 14.3713i −0.985327 1.34013i
116116 9.07933i 0.842995i
117117 0 0
118118 −0.243826 0.243826i −0.0224460 0.0224460i
119119 6.51358 1.74531i 0.597099 0.159992i
120120 0.238211 + 0.323986i 0.0217456 + 0.0295758i
121121 4.71551 2.72250i 0.428683 0.247500i
122122 0.168531i 0.0152581i
123123 1.10402 + 1.91221i 0.0995457 + 0.172418i
124124 10.4914 + 2.81117i 0.942157 + 0.252450i
125125 −4.90544 + 10.0467i −0.438756 + 0.898606i
126126 0.526207 + 0.911417i 0.0468782 + 0.0811955i
127127 −15.9847 + 4.28310i −1.41842 + 0.380064i −0.884922 0.465739i 0.845788π-0.845788\pi
−0.533495 + 0.845803i 0.679122π0.679122\pi
128128 3.56075 + 2.05580i 0.314729 + 0.181709i
129129 −2.22292 −0.195718
130130 0 0
131131 −12.6880 −1.10856 −0.554278 0.832332i 0.687006π-0.687006\pi
−0.554278 + 0.832332i 0.687006π0.687006\pi
132132 −2.39467 1.38256i −0.208429 0.120337i
133133 5.10267 1.36726i 0.442458 0.118556i
134134 −0.237414 0.411213i −0.0205095 0.0355234i
135135 1.81616 4.14226i 0.156310 0.356509i
136136 1.22467 + 0.328148i 0.105014 + 0.0281385i
137137 −7.47254 12.9428i −0.638422 1.10578i −0.985779 0.168046i 0.946254π-0.946254\pi
0.347357 0.937733i 0.387079π-0.387079\pi
138138 0.360209i 0.0306631i
139139 7.42380 4.28613i 0.629679 0.363545i −0.150949 0.988542i 0.548233π-0.548233\pi
0.780628 + 0.624996i 0.214900π0.214900\pi
140140 1.85991 12.1904i 0.157191 1.03028i
141141 0.170200 0.0456050i 0.0143334 0.00384063i
142142 0.596714 + 0.596714i 0.0500751 + 0.0500751i
143143 0 0
144144 11.2297i 0.935809i
145145 10.1221 + 1.54436i 0.840597 + 0.128252i
146146 0.652082 1.12944i 0.0539666 0.0934730i
147147 −0.0655118 + 0.244493i −0.00540332 + 0.0201655i
148148 13.8995 1.14253
149149 3.14239 11.7276i 0.257435 0.960759i −0.709285 0.704922i 0.750982π-0.750982\pi
0.966720 0.255837i 0.0823511π-0.0823511\pi
150150 0.199989 0.104775i 0.0163290 0.00855486i
151151 −1.86999 1.86999i −0.152177 0.152177i 0.626912 0.779090i 0.284318π-0.284318\pi
−0.779090 + 0.626912i 0.784318π0.784318\pi
152152 0.959392 + 0.257068i 0.0778170 + 0.0208510i
153153 −1.80829 6.74861i −0.146191 0.545593i
154154 −0.383306 1.43052i −0.0308877 0.115274i
155155 4.91859 11.2182i 0.395071 0.901071i
156156 0 0
157157 −10.3194 + 10.3194i −0.823581 + 0.823581i −0.986620 0.163039i 0.947870π-0.947870\pi
0.163039 + 0.986620i 0.447870π0.447870\pi
158158 −0.549880 + 0.952420i −0.0437461 + 0.0757705i
159159 −0.558753 0.322596i −0.0443120 0.0255835i
160160 2.17641 2.71905i 0.172060 0.214960i
161161 15.6891 15.6891i 1.23647 1.23647i
162162 0.903960 0.521902i 0.0710218 0.0410045i
163163 −16.1907 + 9.34772i −1.26815 + 0.732170i −0.974639 0.223784i 0.928159π-0.928159\pi
−0.293516 + 0.955954i 0.594826π0.594826\pi
164164 9.00186 9.00186i 0.702927 0.702927i
165165 −1.94868 + 2.43454i −0.151704 + 0.189529i
166166 −0.360686 0.208242i −0.0279947 0.0161627i
167167 −10.3389 + 17.9075i −0.800049 + 1.38572i 0.119535 + 0.992830i 0.461860π0.461860\pi
−0.919583 + 0.392895i 0.871474π0.871474\pi
168168 −0.353695 + 0.353695i −0.0272882 + 0.0272882i
169169 0 0
170170 0.285831 0.651920i 0.0219223 0.0500000i
171171 −1.41659 5.28680i −0.108330 0.404292i
172172 3.31713 + 12.3797i 0.252929 + 0.943944i
173173 17.5278 + 4.69655i 1.33261 + 0.357072i 0.853688 0.520784i 0.174360π-0.174360\pi
0.478924 + 0.877856i 0.341027π0.341027\pi
174174 −0.146208 0.146208i −0.0110840 0.0110840i
175175 −13.2741 4.14706i −1.00343 0.313489i
176176 −4.09004 + 15.2642i −0.308298 + 1.15058i
177177 −0.903127 −0.0678832
178178 0.211694 0.790055i 0.0158672 0.0592171i
179179 8.68110 15.0361i 0.648856 1.12385i −0.334540 0.942382i 0.608581π-0.608581\pi
0.983396 0.181470i 0.0580857π-0.0580857\pi
180180 −12.6303 1.92703i −0.941404 0.143632i
181181 24.9284i 1.85291i 0.376406 + 0.926455i 0.377160π0.377160\pi
−0.376406 + 0.926455i 0.622840π0.622840\pi
182182 0 0
183183 0.312119 + 0.312119i 0.0230725 + 0.0230725i
184184 4.02953 1.07971i 0.297061 0.0795973i
185185 2.36425 15.4959i 0.173823 1.13928i
186186 −0.214216 + 0.123678i −0.0157071 + 0.00906850i
187187 9.83181i 0.718973i
188188 −0.507958 0.879810i −0.0370467 0.0641667i
189189 5.43421 + 1.45609i 0.395280 + 0.105915i
190190 0.223918 0.510708i 0.0162447 0.0370506i
191191 −3.39354 5.87779i −0.245548 0.425302i 0.716737 0.697343i 0.245635π-0.245635\pi
−0.962286 + 0.272041i 0.912301π0.912301\pi
192192 2.52097 0.675492i 0.181935 0.0487494i
193193 1.03504 + 0.597582i 0.0745040 + 0.0430149i 0.536789 0.843716i 0.319637π-0.319637\pi
−0.462285 + 0.886731i 0.652970π0.652970\pi
194194 −1.54543 −0.110955
195195 0 0
196196 1.45937 0.104241
197197 −17.4253 10.0605i −1.24150 0.716780i −0.272100 0.962269i 0.587718π-0.587718\pi
−0.969399 + 0.245489i 0.921051π0.921051\pi
198198 −1.48214 + 0.397137i −0.105331 + 0.0282233i
199199 −1.08885 1.88594i −0.0771862 0.133690i 0.824849 0.565354i 0.191260π-0.191260\pi
−0.902035 + 0.431663i 0.857927π0.857927\pi
200200 −1.77154 1.92314i −0.125267 0.135987i
201201 −1.20125 0.321875i −0.0847299 0.0227033i
202202 0.0662412 + 0.114733i 0.00466071 + 0.00807259i
203203 12.7363i 0.893912i
204204 1.43168 0.826580i 0.100237 0.0578721i
205205 −8.50458 11.5669i −0.593986 0.807870i
206206 −1.07618 + 0.288362i −0.0749810 + 0.0200911i
207207 −16.2552 16.2552i −1.12982 1.12982i
208208 0 0
209209 7.70215i 0.532769i
210210 0.166355 + 0.226257i 0.0114796 + 0.0156132i
211211 9.97642 17.2797i 0.686805 1.18958i −0.286061 0.958211i 0.592346π-0.592346\pi
0.972866 0.231370i 0.0743208π-0.0743208\pi
212212 −0.962781 + 3.59315i −0.0661240 + 0.246778i
213213 2.21022 0.151442
214214 −0.168410 + 0.628516i −0.0115123 + 0.0429645i
215215 14.3658 1.59238i 0.979740 0.108600i
216216 0.747956 + 0.747956i 0.0508919 + 0.0508919i
217217 14.7171 + 3.94345i 0.999064 + 0.267698i
218218 0.312872 + 1.16765i 0.0211904 + 0.0790835i
219219 −0.884062 3.29936i −0.0597394 0.222950i
220220 16.4661 + 7.21950i 1.11015 + 0.486738i
221221 0 0
222222 −0.223829 + 0.223829i −0.0150224 + 0.0150224i
223223 6.70672 11.6164i 0.449115 0.777891i −0.549213 0.835682i 0.685073π-0.685073\pi
0.998329 + 0.0577915i 0.0184059π0.0184059\pi
224224 3.75176 + 2.16608i 0.250675 + 0.144727i
225225 −4.29671 + 13.7531i −0.286447 + 0.916874i
226226 0.696612 0.696612i 0.0463380 0.0463380i
227227 12.7144 7.34064i 0.843882 0.487215i −0.0147000 0.999892i 0.504679π-0.504679\pi
0.858582 + 0.512677i 0.171346π0.171346\pi
228228 1.12156 0.647535i 0.0742773 0.0428840i
229229 −2.65280 + 2.65280i −0.175302 + 0.175302i −0.789304 0.614002i 0.789558π-0.789558\pi
0.614002 + 0.789304i 0.289558π0.289558\pi
230230 −0.258035 2.32788i −0.0170143 0.153496i
231231 −3.35919 1.93943i −0.221018 0.127605i
232232 −1.19732 + 2.07382i −0.0786081 + 0.136153i
233233 −13.9459 + 13.9459i −0.913629 + 0.913629i −0.996556 0.0829267i 0.973573π-0.973573\pi
0.0829267 + 0.996556i 0.473573π0.473573\pi
234234 0 0
235235 −1.06726 + 0.416648i −0.0696205 + 0.0271791i
236236 1.34768 + 5.02962i 0.0877266 + 0.327400i
237237 0.745502 + 2.78225i 0.0484256 + 0.180727i
238238 0.855249 + 0.229163i 0.0554376 + 0.0148545i
239239 10.1890 + 10.1890i 0.659074 + 0.659074i 0.955161 0.296087i 0.0956818π-0.0956818\pi
−0.296087 + 0.955161i 0.595682π0.595682\pi
240240 −0.330136 2.97835i −0.0213102 0.192252i
241241 2.09750 7.82799i 0.135112 0.504245i −0.864885 0.501970i 0.832609π-0.832609\pi
0.999997 0.00227574i 0.000724392π-0.000724392\pi
242242 0.714943 0.0459582
243243 2.27812 8.50205i 0.146141 0.545407i
244244 1.27247 2.20398i 0.0814615 0.141095i
245245 0.248233 1.62698i 0.0158590 0.103944i
246246 0.289920i 0.0184846i
247247 0 0
248248 2.02564 + 2.02564i 0.128628 + 0.128628i
249249 −1.05365 + 0.282325i −0.0667725 + 0.0178916i
250250 −1.21738 + 0.820378i −0.0769942 + 0.0518853i
251251 −4.04904 + 2.33771i −0.255573 + 0.147555i −0.622313 0.782768i 0.713807π-0.713807\pi
0.366740 + 0.930323i 0.380474π0.380474\pi
252252 15.8922i 1.00111i
253253 16.1749 + 28.0157i 1.01690 + 1.76133i
254254 −2.09884 0.562382i −0.131693 0.0352870i
255255 −0.677993 1.73671i −0.0424576 0.108757i
256256 −7.31927 12.6773i −0.457454 0.792334i
257257 −16.7639 + 4.49187i −1.04570 + 0.280195i −0.740474 0.672085i 0.765399π-0.765399\pi
−0.305227 + 0.952280i 0.598732π0.598732\pi
258258 −0.252772 0.145938i −0.0157369 0.00908569i
259259 19.4980 1.21154
260260 0 0
261261 13.1959 0.816804
262262 −1.44277 0.832984i −0.0891346 0.0514619i
263263 −2.33916 + 0.626777i −0.144239 + 0.0386487i −0.330216 0.943905i 0.607122π-0.607122\pi
0.185977 + 0.982554i 0.440455π0.440455\pi
264264 −0.364647 0.631587i −0.0224425 0.0388715i
265265 3.84207 + 1.68454i 0.236016 + 0.103480i
266266 0.669994 + 0.179524i 0.0410800 + 0.0110073i
267267 −1.07112 1.85523i −0.0655515 0.113538i
268268 7.17023i 0.437992i
269269 −8.42829 + 4.86608i −0.513882 + 0.296690i −0.734428 0.678687i 0.762549π-0.762549\pi
0.220546 + 0.975377i 0.429216π0.429216\pi
270270 0.478463 0.351789i 0.0291183 0.0214092i
271271 21.1708 5.67269i 1.28603 0.344591i 0.449880 0.893089i 0.351467π-0.351467\pi
0.836152 + 0.548498i 0.184800π0.184800\pi
272272 −6.68061 6.68061i −0.405071 0.405071i
273273 0 0
274274 1.96233i 0.118548i
275275 10.8495 17.1293i 0.654250 1.03294i
276276 2.71970 4.71067i 0.163707 0.283549i
277277 4.67325 17.4408i 0.280788 1.04792i −0.671074 0.741390i 0.734167π-0.734167\pi
0.951862 0.306526i 0.0991666π-0.0991666\pi
278278 1.12556 0.0675067
279279 4.08574 15.2482i 0.244607 0.912885i
280280 2.03241 2.53915i 0.121460 0.151743i
281281 −11.3739 11.3739i −0.678510 0.678510i 0.281153 0.959663i 0.409283π-0.409283\pi
−0.959663 + 0.281153i 0.909283π0.909283\pi
282282 0.0223477 + 0.00598805i 0.00133079 + 0.000356583i
283283 2.93892 + 10.9682i 0.174700 + 0.651991i 0.996602 + 0.0823620i 0.0262464π0.0262464\pi
−0.821902 + 0.569629i 0.807087π0.807087\pi
284284 −3.29818 12.3090i −0.195711 0.730403i
285285 −0.531134 1.36052i −0.0314616 0.0805904i
286286 0 0
287287 12.6276 12.6276i 0.745384 0.745384i
288288 2.24424 3.88713i 0.132243 0.229052i
289289 9.63189 + 5.56098i 0.566582 + 0.327116i
290290 1.04961 + 0.840142i 0.0616354 + 0.0493348i
291291 −2.86213 + 2.86213i −0.167781 + 0.167781i
292292 −17.0553 + 9.84688i −0.998086 + 0.576245i
293293 −0.605883 + 0.349807i −0.0353961 + 0.0204359i −0.517594 0.855627i 0.673172π-0.673172\pi
0.482198 + 0.876063i 0.339839π0.339839\pi
294294 −0.0235007 + 0.0235007i −0.00137059 + 0.00137059i
295295 5.83652 0.646952i 0.339815 0.0376670i
296296 3.17481 + 1.83298i 0.184532 + 0.106540i
297297 −4.10129 + 7.10364i −0.237981 + 0.412195i
298298 1.12725 1.12725i 0.0653001 0.0653001i
299299 0 0
300300 −3.40646 0.139776i −0.196672 0.00806999i
301301 4.65320 + 17.3660i 0.268206 + 1.00096i
302302 −0.0898718 0.335406i −0.00517154 0.0193004i
303303 0.335163 + 0.0898068i 0.0192546 + 0.00515926i
304304 −5.23352 5.23352i −0.300163 0.300163i
305305 −2.24068 1.79351i −0.128301 0.102696i
306306 0.237433 0.886110i 0.0135731 0.0506555i
307307 14.2048 0.810709 0.405355 0.914159i 0.367148π-0.367148\pi
0.405355 + 0.914159i 0.367148π0.367148\pi
308308 −5.78818 + 21.6018i −0.329812 + 1.23088i
309309 −1.45904 + 2.52712i −0.0830016 + 0.143763i
310310 1.29579 0.952730i 0.0735960 0.0541114i
311311 21.4961i 1.21893i −0.792812 0.609466i 0.791384π-0.791384\pi
0.792812 0.609466i 0.208616π-0.208616\pi
312312 0 0
313313 −9.36303 9.36303i −0.529230 0.529230i 0.391113 0.920343i 0.372090π-0.372090\pi
−0.920343 + 0.391113i 0.872090π0.872090\pi
314314 −1.85092 + 0.495953i −0.104454 + 0.0279882i
315315 −17.7175 2.70319i −0.998265 0.152308i
316316 14.3822 8.30357i 0.809062 0.467112i
317317 17.3024i 0.971798i 0.874015 + 0.485899i 0.161508π0.161508\pi
−0.874015 + 0.485899i 0.838492π0.838492\pi
318318 −0.0423577 0.0733657i −0.00237530 0.00411414i
319319 −17.9368 4.80615i −1.00427 0.269093i
320320 −15.8081 + 6.17130i −0.883697 + 0.344986i
321321 0.852114 + 1.47590i 0.0475603 + 0.0823769i
322322 2.81404 0.754019i 0.156820 0.0420198i
323323 −3.98788 2.30240i −0.221892 0.128109i
324324 −15.7622 −0.875675
325325 0 0
326326 −2.45476 −0.135957
327327 2.74193 + 1.58305i 0.151629 + 0.0875429i
328328 3.24323 0.869022i 0.179078 0.0479837i
329329 −0.712553 1.23418i −0.0392843 0.0680424i
330330 −0.381418 + 0.148901i −0.0209964 + 0.00819676i
331331 −17.3574 4.65090i −0.954049 0.255637i −0.251969 0.967735i 0.581078π-0.581078\pi
−0.702079 + 0.712099i 0.747745π0.747745\pi
332332 3.14460 + 5.44661i 0.172582 + 0.298921i
333333 20.2015i 1.10704i
334334 −2.35130 + 1.35753i −0.128658 + 0.0742805i
335335 7.99376 + 1.21963i 0.436746 + 0.0666353i
336336 3.60035 0.964712i 0.196415 0.0526293i
337337 4.83668 + 4.83668i 0.263471 + 0.263471i 0.826462 0.562992i 0.190350π-0.190350\pi
−0.562992 + 0.826462i 0.690350π0.690350\pi
338338 0 0
339339 2.58024i 0.140140i
340340 −8.66020 + 6.36741i −0.469665 + 0.345321i
341341 −11.1073 + 19.2384i −0.601493 + 1.04182i
342342 0.186002 0.694170i 0.0100579 0.0375364i
343343 −17.4224 −0.940723
344344 −0.874884 + 3.26511i −0.0471706 + 0.176043i
345345 −4.78910 3.83334i −0.257836 0.206380i
346346 1.68477 + 1.68477i 0.0905740 + 0.0905740i
347347 −17.9682 4.81456i −0.964582 0.258459i −0.258043 0.966133i 0.583078π-0.583078\pi
−0.706539 + 0.707674i 0.749744π0.749744\pi
348348 0.808124 + 3.01596i 0.0433200 + 0.161672i
349349 −0.651455 2.43126i −0.0348716 0.130143i 0.946296 0.323302i 0.104793π-0.104793\pi
−0.981167 + 0.193160i 0.938126π0.938126\pi
350350 −1.23716 1.34303i −0.0661290 0.0717881i
351351 0 0
352352 −4.46629 + 4.46629i −0.238054 + 0.238054i
353353 −16.3608 + 28.3377i −0.870795 + 1.50826i −0.00962005 + 0.999954i 0.503062π0.503062\pi
−0.861175 + 0.508308i 0.830271π0.830271\pi
354354 −0.102696 0.0592915i −0.00545822 0.00315131i
355355 −14.2837 + 1.58329i −0.758101 + 0.0840320i
356356 −8.73364 + 8.73364i −0.462882 + 0.462882i
357357 2.00833 1.15951i 0.106292 0.0613677i
358358 1.97428 1.13985i 0.104344 0.0602430i
359359 0.699684 0.699684i 0.0369279 0.0369279i −0.688402 0.725330i 0.741687π-0.741687\pi
0.725330 + 0.688402i 0.241687π0.241687\pi
360360 −2.63077 2.10575i −0.138654 0.110983i
361361 13.3304 + 7.69632i 0.701601 + 0.405069i
362362 −1.63658 + 2.83464i −0.0860167 + 0.148985i
363363 1.32407 1.32407i 0.0694956 0.0694956i
364364 0 0
365365 8.07680 + 20.6891i 0.422759 + 1.08292i
366366 0.0150005 + 0.0559825i 0.000784087 + 0.00292625i
367367 3.74601 + 13.9803i 0.195540 + 0.729767i 0.992126 + 0.125241i 0.0399705π0.0399705\pi
−0.796586 + 0.604525i 0.793363π0.793363\pi
368368 −30.0270 8.04571i −1.56526 0.419411i
369369 −13.0833 13.0833i −0.681087 0.681087i
370370 1.28617 1.60685i 0.0668649 0.0835361i
371371 −1.35057 + 5.04039i −0.0701180 + 0.261684i
372372 3.73524 0.193663
373373 −2.62454 + 9.79493i −0.135894 + 0.507162i 0.864099 + 0.503322i 0.167889π0.167889\pi
−0.999993 + 0.00384023i 0.998778π0.998778\pi
374374 −0.645471 + 1.11799i −0.0333765 + 0.0578098i
375375 −0.735254 + 3.77393i −0.0379683 + 0.194885i
376376 0.267945i 0.0138182i
377377 0 0
378378 0.522337 + 0.522337i 0.0268661 + 0.0268661i
379379 −1.01470 + 0.271887i −0.0521215 + 0.0139659i −0.284786 0.958591i 0.591922π-0.591922\pi
0.232664 + 0.972557i 0.425256π0.425256\pi
380380 −6.78432 + 4.98817i −0.348028 + 0.255887i
381381 −4.92857 + 2.84551i −0.252498 + 0.145780i
382382 0.891162i 0.0455958i
383383 −6.00353 10.3984i −0.306766 0.531334i 0.670887 0.741560i 0.265914π-0.265914\pi
−0.977653 + 0.210225i 0.932580π0.932580\pi
384384 1.36579 + 0.365961i 0.0696975 + 0.0186754i
385385 23.0983 + 10.1274i 1.17720 + 0.516138i
386386 0.0784640 + 0.135904i 0.00399371 + 0.00691732i
387387 17.9926 4.82111i 0.914616 0.245071i
388388 20.2105 + 11.6685i 1.02603 + 0.592380i
389389 7.37166 0.373758 0.186879 0.982383i 0.440163π-0.440163\pi
0.186879 + 0.982383i 0.440163π0.440163\pi
390390 0 0
391391 −19.3406 −0.978097
392392 0.333337 + 0.192452i 0.0168361 + 0.00972030i
393393 −4.21468 + 1.12932i −0.212603 + 0.0569667i
394394 −1.32097 2.28798i −0.0665494 0.115267i
395395 −6.81091 17.4465i −0.342694 0.877826i
396396 22.3813 + 5.99704i 1.12470 + 0.301363i
397397 3.02739 + 5.24359i 0.151940 + 0.263168i 0.931941 0.362611i 0.118115π-0.118115\pi
−0.780001 + 0.625779i 0.784781π0.784781\pi
398398 0.285937i 0.0143327i
399399 1.57330 0.908347i 0.0787637 0.0454742i
400400 4.26706 + 19.0113i 0.213353 + 0.950565i
401401 2.33226 0.624928i 0.116468 0.0312074i −0.200114 0.979773i 0.564131π-0.564131\pi
0.316582 + 0.948565i 0.397465π0.397465\pi
402402 −0.115465 0.115465i −0.00575886 0.00575886i
403403 0 0
404404 2.00058i 0.0995324i
405405 −2.68107 + 17.5725i −0.133224 + 0.873184i
406406 −0.836154 + 1.44826i −0.0414976 + 0.0718760i
407407 −7.35772 + 27.4594i −0.364709 + 1.36111i
408408 0.436016 0.0215860
409409 −5.21187 + 19.4510i −0.257710 + 0.961788i 0.708852 + 0.705357i 0.249213π0.249213\pi
−0.966563 + 0.256431i 0.917453π0.917453\pi
410410 −0.207683 1.87363i −0.0102567 0.0925319i
411411 −3.63422 3.63422i −0.179263 0.179263i
412412 16.2511 + 4.35446i 0.800632 + 0.214529i
413413 1.89050 + 7.05543i 0.0930253 + 0.347175i
414414 −0.781227 2.91558i −0.0383952 0.143293i
415415 6.60706 2.57933i 0.324328 0.126614i
416416 0 0
417417 2.08453 2.08453i 0.102080 0.102080i
418418 −0.505656 + 0.875822i −0.0247324 + 0.0428378i
419419 −26.0503 15.0401i −1.27264 0.734759i −0.297156 0.954829i 0.596038π-0.596038\pi
−0.975484 + 0.220070i 0.929371π0.929371\pi
420420 −0.467206 4.21493i −0.0227973 0.205668i
421421 −9.24685 + 9.24685i −0.450664 + 0.450664i −0.895575 0.444911i 0.853235π-0.853235\pi
0.444911 + 0.895575i 0.353235π0.353235\pi
422422 2.26887 1.30993i 0.110447 0.0637664i
423423 −1.27871 + 0.738265i −0.0621731 + 0.0358957i
424424 −0.693751 + 0.693751i −0.0336915 + 0.0336915i
425425 5.62567 + 10.7379i 0.272885 + 0.520866i
426426 0.251327 + 0.145104i 0.0121769 + 0.00703031i
427427 1.78499 3.09170i 0.0863818 0.149618i
428428 6.94792 6.94792i 0.335840 0.335840i
429429 0 0
430430 1.73810 + 0.762061i 0.0838185 + 0.0367499i
431431 1.63348 + 6.09624i 0.0786821 + 0.293646i 0.994043 0.108989i 0.0347613π-0.0347613\pi
−0.915361 + 0.402634i 0.868095π0.868095\pi
432432 −2.04006 7.61362i −0.0981527 0.366311i
433433 11.8706 + 3.18071i 0.570463 + 0.152855i 0.532509 0.846424i 0.321249π-0.321249\pi
0.0379543 + 0.999279i 0.487916π0.487916\pi
434434 1.41461 + 1.41461i 0.0679036 + 0.0679036i
435435 3.49982 0.387939i 0.167803 0.0186002i
436436 4.72458 17.6324i 0.226266 0.844438i
437437 −15.1513 −0.724783
438438 0.116080 0.433215i 0.00554650 0.0206998i
439439 −17.2223 + 29.8300i −0.821977 + 1.42371i 0.0822306 + 0.996613i 0.473796π0.473796\pi
−0.904208 + 0.427093i 0.859538π0.859538\pi
440440 2.80899 + 3.82046i 0.133913 + 0.182133i
441441 2.12104i 0.101002i
442442 0 0
443443 −5.39452 5.39452i −0.256301 0.256301i 0.567247 0.823548i 0.308009π-0.308009\pi
−0.823548 + 0.567247i 0.808009π0.808009\pi
444444 4.61713 1.23716i 0.219119 0.0587128i
445445 8.25118 + 11.2223i 0.391143 + 0.531987i
446446 1.52526 0.880610i 0.0722232 0.0416981i
447447 4.17534i 0.197487i
448448 −10.5542 18.2804i −0.498639 0.863668i
449449 30.0741 + 8.05832i 1.41928 + 0.380296i 0.885229 0.465155i 0.154002π-0.154002\pi
0.534053 + 0.845451i 0.320668π0.320668\pi
450450 −1.39149 + 1.28180i −0.0655957 + 0.0604247i
451451 13.0186 + 22.5489i 0.613021 + 1.06178i
452452 −14.3697 + 3.85034i −0.675892 + 0.181105i
453453 −0.787612 0.454728i −0.0370053 0.0213650i
454454 1.92769 0.0904710
455455 0 0
456456 0.341570 0.0159955
457457 2.69118 + 1.55375i 0.125888 + 0.0726814i 0.561622 0.827394i 0.310178π-0.310178\pi
−0.435734 + 0.900076i 0.643511π0.643511\pi
458458 −0.475812 + 0.127494i −0.0222333 + 0.00595738i
459459 −2.45200 4.24698i −0.114449 0.198232i
460460 −14.2018 + 32.3913i −0.662163 + 1.51025i
461461 16.1274 + 4.32132i 0.751126 + 0.201264i 0.614018 0.789292i 0.289552π-0.289552\pi
0.137109 + 0.990556i 0.456219π0.456219\pi
462462 −0.254652 0.441070i −0.0118475 0.0205205i
463463 15.6396i 0.726832i −0.931627 0.363416i 0.881610π-0.881610\pi
0.931627 0.363416i 0.118390π-0.118390\pi
464464 15.4536 8.92212i 0.717414 0.414199i
465465 0.635348 4.16425i 0.0294636 0.193112i
466466 −2.50138 + 0.670243i −0.115874 + 0.0310484i
467467 15.0821 + 15.0821i 0.697916 + 0.697916i 0.963961 0.266045i 0.0857169π-0.0857169\pi
−0.266045 + 0.963961i 0.585717π0.585717\pi
468468 0 0
469469 10.0582i 0.464447i
470470 −0.148713 0.0226895i −0.00685963 0.00104659i
471471 −2.50939 + 4.34640i −0.115627 + 0.200272i
472472 −0.355447 + 1.32655i −0.0163608 + 0.0610592i
473473 −26.2128 −1.20527
474474 −0.0978863 + 0.365317i −0.00449607 + 0.0167796i
475475 4.40709 + 8.41199i 0.202211 + 0.385969i
476476 −9.45433 9.45433i −0.433339 0.433339i
477477 5.22226 + 1.39930i 0.239111 + 0.0640696i
478478 0.489686 + 1.82753i 0.0223977 + 0.0835894i
479479 11.0386 + 41.1964i 0.504364 + 1.88231i 0.469522 + 0.882921i 0.344426π0.344426\pi
0.0348421 + 0.999393i 0.488907π0.488907\pi
480480 0.480942 1.09693i 0.0219519 0.0500676i
481481 0 0
482482 0.752428 0.752428i 0.0342722 0.0342722i
483483 3.81514 6.60802i 0.173595 0.300675i
484484 −9.34972 5.39806i −0.424987 0.245366i
485485 16.4464 20.5470i 0.746794 0.932990i
486486 0.817218 0.817218i 0.0370698 0.0370698i
487487 −13.1780 + 7.60834i −0.597154 + 0.344767i −0.767921 0.640545i 0.778709π-0.778709\pi
0.170767 + 0.985311i 0.445375π0.445375\pi
488488 0.581293 0.335610i 0.0263139 0.0151923i
489489 −4.54620 + 4.54620i −0.205586 + 0.205586i
490490 0.135041 0.168710i 0.00610051 0.00762154i
491491 24.2273 + 13.9876i 1.09336 + 0.631254i 0.934470 0.356042i 0.115874π-0.115874\pi
0.158894 + 0.987296i 0.449207π0.449207\pi
492492 2.18900 3.79145i 0.0986876 0.170932i
493493 7.85029 7.85029i 0.353559 0.353559i
494494 0 0
495495 10.4928 23.9318i 0.471616 1.07565i
496496 −5.52498 20.6195i −0.248079 0.925844i
497497 −4.62661 17.2668i −0.207532 0.774520i
498498 −0.138347 0.0370700i −0.00619949 0.00166115i
499499 1.67479 + 1.67479i 0.0749740 + 0.0749740i 0.743599 0.668625i 0.233117π-0.233117\pi
−0.668625 + 0.743599i 0.733117π0.733117\pi
500500 22.1146 1.53689i 0.988994 0.0687317i
501501 −1.84047 + 6.86873i −0.0822261 + 0.306872i
502502 −0.613896 −0.0273995
503503 5.99415 22.3705i 0.267266 0.997451i −0.693583 0.720377i 0.743969π-0.743969\pi
0.960849 0.277073i 0.0893645π-0.0893645\pi
504504 2.09575 3.62995i 0.0933523 0.161691i
505505 −2.23035 0.340289i −0.0992493 0.0151427i
506506 4.24760i 0.188829i
507507 0 0
508508 23.2016 + 23.2016i 1.02940 + 1.02940i
509509 −5.82068 + 1.55965i −0.257997 + 0.0691301i −0.385499 0.922708i 0.625971π-0.625971\pi
0.127502 + 0.991838i 0.459304π0.459304\pi
510510 0.0369217 0.241995i 0.00163492 0.0107157i
511511 −23.9248 + 13.8130i −1.05837 + 0.611051i
512512 10.1453i 0.448362i
513513 −1.92087 3.32705i −0.0848086 0.146893i
514514 −2.20114 0.589794i −0.0970881 0.0260147i
515515 7.61882 17.3769i 0.335725 0.765717i
516516 2.20376 + 3.81703i 0.0970152 + 0.168035i
517517 2.00701 0.537776i 0.0882681 0.0236514i
518518 2.21714 + 1.28007i 0.0974155 + 0.0562429i
519519 6.24038 0.273922
520520 0 0
521521 27.8183 1.21874 0.609371 0.792886i 0.291422π-0.291422\pi
0.609371 + 0.792886i 0.291422π0.291422\pi
522522 1.50052 + 0.866326i 0.0656760 + 0.0379180i
523523 0.529059 0.141761i 0.0231341 0.00619877i −0.247233 0.968956i 0.579521π-0.579521\pi
0.270368 + 0.962757i 0.412855π0.412855\pi
524524 12.5786 + 21.7868i 0.549500 + 0.951762i
525525 −4.77850 0.196075i −0.208551 0.00855742i
526526 −0.307138 0.0822974i −0.0133919 0.00358834i
527527 −6.64060 11.5019i −0.289269 0.501029i
528528 5.43449i 0.236506i
529529 −35.1924 + 20.3183i −1.53010 + 0.883406i
530530 0.326295 + 0.443788i 0.0141733 + 0.0192769i
531531 7.31002 1.95871i 0.317228 0.0850010i
532532 −7.40643 7.40643i −0.321110 0.321110i
533533 0 0
534534 0.281282i 0.0121722i
535535 −6.56410 8.92772i −0.283791 0.385979i
536536 −0.945563 + 1.63776i −0.0408421 + 0.0707406i
537537 1.54536 5.76736i 0.0666871 0.248880i
538538 −1.27786 −0.0550923
539539 −0.772518 + 2.88308i −0.0332747 + 0.124183i
540540 −8.91326 + 0.987995i −0.383566 + 0.0425165i
541541 29.7507 + 29.7507i 1.27908 + 1.27908i 0.941182 + 0.337899i 0.109716π0.109716\pi
0.337899 + 0.941182i 0.390284π0.390284\pi
542542 2.77978 + 0.744839i 0.119402 + 0.0319936i
543543 2.21880 + 8.28067i 0.0952177 + 0.355357i
544544 −0.977367 3.64758i −0.0419043 0.156389i
545545 −18.8539 8.26641i −0.807612 0.354094i
546546 0 0
547547 −14.2594 + 14.2594i −0.609688 + 0.609688i −0.942864 0.333176i 0.891880π-0.891880\pi
0.333176 + 0.942864i 0.391880π0.391880\pi
548548 −14.8162 + 25.6625i −0.632919 + 1.09625i
549549 −3.20326 1.84940i −0.136712 0.0789306i
550550 2.35827 1.23551i 0.100557 0.0526825i
551551 6.14984 6.14984i 0.261992 0.261992i
552552 1.24242 0.717314i 0.0528811 0.0305309i
553553 20.1750 11.6481i 0.857930 0.495326i
554554 1.67641 1.67641i 0.0712240 0.0712240i
555555 −0.593894 5.35786i −0.0252094 0.227428i
556556 −14.7196 8.49837i −0.624251 0.360411i
557557 17.5886 30.4644i 0.745254 1.29082i −0.204822 0.978799i 0.565662π-0.565662\pi
0.950076 0.312018i 0.101005π-0.101005\pi
558558 1.46566 1.46566i 0.0620463 0.0620463i
559559 0 0
560560 −22.5765 + 8.81362i −0.954030 + 0.372443i
561561 0.875100 + 3.26592i 0.0369468 + 0.137887i
562562 −0.546631 2.04005i −0.0230582 0.0860545i
563563 −40.5028 10.8527i −1.70699 0.457387i −0.732306 0.680975i 0.761556π-0.761556\pi
−0.974684 + 0.223589i 0.928223π0.928223\pi
564564 −0.247042 0.247042i −0.0104024 0.0104024i
565565 1.84835 + 16.6750i 0.0777607 + 0.701523i
566566 −0.385887 + 1.44015i −0.0162201 + 0.0605341i
567567 −22.1108 −0.928566
568568 0.869884 3.24645i 0.0364995 0.136218i
569569 13.7741 23.8575i 0.577441 1.00016i −0.418331 0.908295i 0.637385π-0.637385\pi
0.995772 0.0918621i 0.0292819π-0.0292819\pi
570570 0.0289241 0.189576i 0.00121150 0.00794048i
571571 4.72029i 0.197538i −0.995110 0.0987690i 0.968510π-0.968510\pi
0.995110 0.0987690i 0.0314905π-0.0314905\pi
572572 0 0
573573 −1.65043 1.65043i −0.0689476 0.0689476i
574574 2.26492 0.606884i 0.0945360 0.0253308i
575575 33.6959 + 21.3426i 1.40521 + 0.890046i
576576 −18.9400 + 10.9350i −0.789168 + 0.455626i
577577 6.73701i 0.280465i 0.990119 + 0.140233i 0.0447851π0.0447851\pi
−0.990119 + 0.140233i 0.955215π0.955215\pi
578578 0.730170 + 1.26469i 0.0303711 + 0.0526043i
579579 0.397008 + 0.106378i 0.0164991 + 0.00442092i
580580 −7.38303 18.9120i −0.306564 0.785276i
581581 4.41118 + 7.64038i 0.183006 + 0.316977i
582582 −0.513359 + 0.137554i −0.0212794 + 0.00570180i
583583 −6.58884 3.80407i −0.272882 0.157548i
584584 −5.19417 −0.214936
585585 0 0
586586 −0.0918611 −0.00379475
587587 4.49847 + 2.59719i 0.185672 + 0.107198i 0.589955 0.807436i 0.299146π-0.299146\pi
−0.404283 + 0.914634i 0.632479π0.632479\pi
588588 0.484772 0.129894i 0.0199916 0.00535674i
589589 −5.20218 9.01044i −0.214352 0.371269i
590590 0.706152 + 0.309609i 0.0290718 + 0.0127464i
591591 −6.68376 1.79091i −0.274933 0.0736681i
592592 −13.6589 23.6578i −0.561375 0.972331i
593593 12.9267i 0.530836i 0.964133 + 0.265418i 0.0855100π0.0855100\pi
−0.964133 + 0.265418i 0.914490π0.914490\pi
594594 −0.932726 + 0.538510i −0.0382702 + 0.0220953i
595595 −12.1483 + 8.93206i −0.498033 + 0.366179i
596596 −23.2529 + 6.23060i −0.952477 + 0.255215i
597597 −0.529553 0.529553i −0.0216732 0.0216732i
598598 0 0
599599 16.7523i 0.684481i −0.939612 0.342241i 0.888814π-0.888814\pi
0.939612 0.342241i 0.111186π-0.111186\pi
600600 −0.759641 0.481148i −0.0310122 0.0196428i
601601 −6.28803 + 10.8912i −0.256494 + 0.444261i −0.965300 0.261142i 0.915901π-0.915901\pi
0.708806 + 0.705403i 0.249234π0.249234\pi
602602 −0.610977 + 2.28020i −0.0249016 + 0.0929340i
603603 10.4212 0.424384
604604 −1.35713 + 5.06486i −0.0552207 + 0.206086i
605605 −7.60840 + 9.50539i −0.309325 + 0.386449i
606606 0.0322160 + 0.0322160i 0.00130868 + 0.00130868i
607607 −36.1909 9.69731i −1.46894 0.393602i −0.566374 0.824149i 0.691654π-0.691654\pi
−0.902568 + 0.430547i 0.858321π0.858321\pi
608608 −0.765660 2.85748i −0.0310516 0.115886i
609609 1.13362 + 4.23072i 0.0459366 + 0.171438i
610610 −0.137044 0.351045i −0.00554877 0.0142134i
611611 0 0
612612 −9.79548 + 9.79548i −0.395959 + 0.395959i
613613 8.64732 14.9776i 0.349262 0.604940i −0.636856 0.770982i 0.719766π-0.719766\pi
0.986119 + 0.166043i 0.0530990π0.0530990\pi
614614 1.61524 + 0.932562i 0.0651860 + 0.0376351i
615615 −3.85458 3.08532i −0.155432 0.124412i
616616 −4.17079 + 4.17079i −0.168046 + 0.168046i
617617 10.5136 6.07005i 0.423263 0.244371i −0.273210 0.961955i 0.588085π-0.588085\pi
0.696472 + 0.717584i 0.254752π0.254752\pi
618618 −0.331818 + 0.191575i −0.0133477 + 0.00770628i
619619 2.99993 2.99993i 0.120577 0.120577i −0.644243 0.764821i 0.722828π-0.722828\pi
0.764821 + 0.644243i 0.222828π0.222828\pi
620620 −24.1393 + 2.67573i −0.969456 + 0.107460i
621621 −13.9739 8.06784i −0.560753 0.323751i
622622 1.41125 2.44435i 0.0565858 0.0980095i
623623 −12.2514 + 12.2514i −0.490840 + 0.490840i
624624 0 0
625625 2.04819 24.9160i 0.0819276 0.996638i
626626 −0.449988 1.67938i −0.0179851 0.0671215i
627627 0.685545 + 2.55849i 0.0273780 + 0.102176i
628628 27.9502 + 7.48923i 1.11533 + 0.298853i
629629 −12.0180 12.0180i −0.479188 0.479188i
630630 −1.83721 1.47056i −0.0731961 0.0585884i
631631 −5.60031 + 20.9006i −0.222945 + 0.832041i 0.760273 + 0.649604i 0.225065π0.225065\pi
−0.983218 + 0.182437i 0.941601π0.941601\pi
632632 4.38008 0.174230
633633 1.77594 6.62791i 0.0705874 0.263436i
634634 −1.13592 + 1.96748i −0.0451133 + 0.0781385i
635635 29.8128 21.9199i 1.18309 0.869863i
636636 1.27926i 0.0507260i
637637 0 0
638638 −1.72409 1.72409i −0.0682572 0.0682572i
639639 −17.8898 + 4.79356i −0.707710 + 0.189630i
640640 −9.08865 1.38667i −0.359260 0.0548131i
641641 39.2467 22.6591i 1.55015 0.894980i 0.552022 0.833829i 0.313856π-0.313856\pi
0.998129 0.0611509i 0.0194771π-0.0194771\pi
642642 0.223769i 0.00883148i
643643 −15.8249 27.4095i −0.624072 1.08092i −0.988719 0.149779i 0.952144π-0.952144\pi
0.364647 0.931146i 0.381190π-0.381190\pi
644644 −42.4939 11.3862i −1.67449 0.448679i
645645 4.63028 1.80761i 0.182317 0.0711747i
646646 −0.302312 0.523619i −0.0118943 0.0206015i
647647 36.6924 9.83169i 1.44253 0.386524i 0.549109 0.835751i 0.314967π-0.314967\pi
0.893418 + 0.449227i 0.148301π0.148301\pi
648648 −3.60026 2.07861i −0.141431 0.0816555i
649649 −10.6497 −0.418038
650650 0 0
651651 5.23971 0.205361
652652 32.1023 + 18.5343i 1.25722 + 0.725858i
653653 −2.66385 + 0.713775i −0.104244 + 0.0279322i −0.310564 0.950552i 0.600518π-0.600518\pi
0.206320 + 0.978485i 0.433851π0.433851\pi
654654 0.207859 + 0.360022i 0.00812792 + 0.0140780i
655655 26.4287 10.3175i 1.03265 0.403138i
656656 −24.1677 6.47571i −0.943590 0.252834i
657657 14.3114 + 24.7881i 0.558342 + 0.967076i
658658 0.187120i 0.00729470i
659659 1.80219 1.04050i 0.0702034 0.0405320i −0.464487 0.885580i 0.653761π-0.653761\pi
0.534691 + 0.845048i 0.320428π0.320428\pi
660660 6.11228 + 0.932564i 0.237920 + 0.0363000i
661661 −36.3010 + 9.72683i −1.41195 + 0.378330i −0.882619 0.470089i 0.844222π-0.844222\pi
−0.529326 + 0.848418i 0.677555π0.677555\pi
662662 −1.66840 1.66840i −0.0648440 0.0648440i
663663 0 0
664664 1.65876i 0.0643723i
665665 −9.51689 + 6.99729i −0.369049 + 0.271343i
666666 1.32626 2.29714i 0.0513914 0.0890125i
667667 9.45440 35.2843i 0.366076 1.36621i
668668 40.9991 1.58630
669669 1.19389 4.45566i 0.0461585 0.172266i
670670 0.828912 + 0.663486i 0.0320237 + 0.0256327i
671671 3.68052 + 3.68052i 0.142085 + 0.142085i
672672 1.43905 + 0.385592i 0.0555125 + 0.0148745i
673673 −4.65984 17.3908i −0.179624 0.670364i −0.995718 0.0924454i 0.970532π-0.970532\pi
0.816094 0.577919i 0.196135π-0.196135\pi
674674 0.232451 + 0.867519i 0.00895368 + 0.0334156i
675675 −0.414638 + 10.1050i −0.0159594 + 0.388943i
676676 0 0
677677 15.4021 15.4021i 0.591952 0.591952i −0.346206 0.938158i 0.612530π-0.612530\pi
0.938158 + 0.346206i 0.112530π0.112530\pi
678678 0.169396 0.293403i 0.00650563 0.0112681i
679679 28.3508 + 16.3684i 1.08801 + 0.628160i
680680 −2.81778 + 0.312338i −0.108057 + 0.0119776i
681681 3.57007 3.57007i 0.136805 0.136805i
682682 −2.52605 + 1.45841i −0.0967273 + 0.0558455i
683683 5.34122 3.08376i 0.204376 0.117997i −0.394319 0.918974i 0.629019π-0.629019\pi
0.598695 + 0.800977i 0.295686π0.295686\pi
684684 −7.67369 + 7.67369i −0.293411 + 0.293411i
685685 26.0897 + 20.8830i 0.996838 + 0.797900i
686686 −1.98113 1.14381i −0.0756398 0.0436707i
687687 −0.645085 + 1.11732i −0.0246115 + 0.0426284i
688688 17.8113 17.8113i 0.679050 0.679050i
689689 0 0
690690 −0.292911 0.750304i −0.0111509 0.0285636i
691691 −3.39841 12.6830i −0.129282 0.482486i 0.870674 0.491860i 0.163683π-0.163683\pi
−0.999956 + 0.00937405i 0.997016π0.997016\pi
692692 −9.31214 34.7534i −0.353994 1.32112i
693693 31.3960 + 8.41252i 1.19263 + 0.319565i
694694 −1.72710 1.72710i −0.0655600 0.0655600i
695695 −11.9782 + 14.9647i −0.454359 + 0.567643i
696696 −0.213140 + 0.795450i −0.00807906 + 0.0301515i
697697 −15.5666 −0.589627
698698 0.0855377 0.319231i 0.00323765 0.0120831i
699699 −3.39126 + 5.87383i −0.128269 + 0.222169i
700700 6.03870 + 26.9046i 0.228241 + 1.01690i
701701 23.2292i 0.877354i −0.898645 0.438677i 0.855447π-0.855447\pi
0.898645 0.438677i 0.144553π-0.144553\pi
702702 0 0
703703 −9.41478 9.41478i −0.355085 0.355085i
704704 29.7274 7.96543i 1.12039 0.300208i
705705 −0.317437 + 0.233395i −0.0119554 + 0.00879017i
706706 −3.72081 + 2.14821i −0.140034 + 0.0808490i
707707 2.80636i 0.105544i
708708 0.895342 + 1.55078i 0.0336490 + 0.0582818i
709709 −2.00482 0.537189i −0.0752925 0.0201746i 0.220976 0.975279i 0.429076π-0.429076\pi
−0.296269 + 0.955105i 0.595742π0.595742\pi
710710 −1.72817 0.757707i −0.0648569 0.0284362i
711711 −12.0684 20.9030i −0.452599 0.783925i
712712 −3.14660 + 0.843128i −0.117924 + 0.0315976i
713713 −37.8447 21.8496i −1.41729 0.818275i
714714 0.304493 0.0113954
715715 0 0
716716 −34.4251 −1.28653
717717 4.29148 + 2.47769i 0.160268 + 0.0925309i
718718 0.125497 0.0336269i 0.00468351 0.00125494i
719719 3.36848 + 5.83438i 0.125623 + 0.217586i 0.921976 0.387246i 0.126574π-0.126574\pi
−0.796353 + 0.604832i 0.793240π0.793240\pi
720720 9.13165 + 23.3911i 0.340316 + 0.871735i
721721 22.7966 + 6.10834i 0.848991 + 0.227486i
722722 1.01055 + 1.75032i 0.0376086 + 0.0651401i
723723 2.78698i 0.103649i
724724 42.8050 24.7135i 1.59083 0.918469i
725725 −22.3399 + 5.01416i −0.829683 + 0.186221i
726726 0.237489 0.0636349i 0.00881403 0.00236171i
727727 34.4733 + 34.4733i 1.27854 + 1.27854i 0.941483 + 0.337062i 0.109433π0.109433\pi
0.337062 + 0.941483i 0.390567π0.390567\pi
728728 0 0
729729 20.8218i 0.771179i
730730 −0.439841 + 2.88284i −0.0162792 + 0.106699i
731731 7.83580 13.5720i 0.289817 0.501979i
732732 0.226517 0.845374i 0.00837232 0.0312459i
733733 28.7555 1.06211 0.531054 0.847338i 0.321796π-0.321796\pi
0.531054 + 0.847338i 0.321796π0.321796\pi
734734 −0.491861 + 1.83565i −0.0181549 + 0.0677551i
735735 −0.0623555 0.562544i −0.00230002 0.0207498i
736736 −8.78585 8.78585i −0.323851 0.323851i
737737 −14.1652 3.79556i −0.521783 0.139811i
738738 −0.628783 2.34665i −0.0231458 0.0863813i
739739 −7.94129 29.6373i −0.292125 1.09023i −0.943474 0.331447i 0.892463π-0.892463\pi
0.651349 0.758778i 0.274203π-0.274203\pi
740740 −28.9523 + 11.3027i −1.06431 + 0.415494i
741741 0 0
742742 −0.484483 + 0.484483i −0.0177859 + 0.0177859i
743743 26.4817 45.8676i 0.971519 1.68272i 0.280543 0.959841i 0.409485π-0.409485\pi
0.690976 0.722878i 0.257181π-0.257181\pi
744744 0.853172 + 0.492579i 0.0312788 + 0.0180588i
745745 2.99099 + 26.9834i 0.109581 + 0.988596i
746746 −0.941490 + 0.941490i −0.0344704 + 0.0344704i
747747 7.91608 4.57035i 0.289634 0.167220i
748748 16.8824 9.74706i 0.617282 0.356388i
749749 9.74639 9.74639i 0.356125 0.356125i
750750 −0.331370 + 0.380868i −0.0120999 + 0.0139073i
751751 −40.3780 23.3123i −1.47341 0.850676i −0.473862 0.880599i 0.657140π-0.657140\pi
−0.999552 + 0.0299230i 0.990474π0.990474\pi
752752 −0.998326 + 1.72915i −0.0364052 + 0.0630557i
753753 −1.13693 + 1.13693i −0.0414321 + 0.0414321i
754754 0 0
755755 5.41574 + 2.37451i 0.197099 + 0.0864172i
756756 −2.88708 10.7747i −0.105002 0.391873i
757757 −0.323327 1.20667i −0.0117515 0.0438572i 0.959801 0.280681i 0.0905603π-0.0905603\pi
−0.971553 + 0.236824i 0.923894π0.923894\pi
758758 −0.133232 0.0356995i −0.00483922 0.00129666i
759759 7.86654 + 7.86654i 0.285537 + 0.285537i
760760 −2.20742 + 0.244683i −0.0800716 + 0.00887558i
761761 5.28278 19.7156i 0.191501 0.714690i −0.801644 0.597801i 0.796041π-0.796041\pi
0.993145 0.116889i 0.0372921π-0.0372921\pi
762762 −0.747246 −0.0270698
763763 6.62754 24.7343i 0.239933 0.895442i
764764 −6.72858 + 11.6542i −0.243432 + 0.421636i
765765 9.25436 + 12.5867i 0.334592 + 0.455073i
766766 1.57656i 0.0569633i
767767 0 0
768768 −3.55968 3.55968i −0.128449 0.128449i
769769 −35.6638 + 9.55609i −1.28607 + 0.344602i −0.836167 0.548476i 0.815208π-0.815208\pi
−0.449904 + 0.893077i 0.648542π0.648542\pi
770770 1.96167 + 2.66803i 0.0706935 + 0.0961491i
771771 −5.16879 + 2.98420i −0.186150 + 0.107473i
772772 2.36972i 0.0852882i
773773 10.6918 + 18.5187i 0.384557 + 0.666072i 0.991708 0.128515i 0.0410209π-0.0410209\pi
−0.607151 + 0.794587i 0.707688π0.707688\pi
774774 2.36248 + 0.633024i 0.0849175 + 0.0227536i
775775 −1.12294 + 27.3669i −0.0403372 + 0.983047i
776776 3.07754 + 5.33045i 0.110477 + 0.191352i
777777 6.47681 1.73545i 0.232354 0.0622591i
778778 0.838242 + 0.483959i 0.0300524 + 0.0173508i
779779 −12.1947 −0.436921
780780 0 0
781781 26.0630 0.932608
782782 −2.19925 1.26974i −0.0786449 0.0454057i
783783 8.94666 2.39725i 0.319728 0.0856708i
784784 −1.43410 2.48393i −0.0512179 0.0887120i
785785 13.1036 29.8865i 0.467688 1.06670i
786786 −0.553399 0.148283i −0.0197391 0.00528907i
787787 19.6914 + 34.1065i 0.701923 + 1.21577i 0.967790 + 0.251757i 0.0810085π0.0810085\pi
−0.265867 + 0.964010i 0.585658π0.585658\pi
788788 39.8950i 1.42120i
789789 −0.721232 + 0.416404i −0.0256766 + 0.0148244i
790790 0.370904 2.43101i 0.0131962 0.0864913i
791791 −20.1575 + 5.40118i −0.716717 + 0.192044i
792792 4.32129 + 4.32129i 0.153550 + 0.153550i
793793 0 0
794794 0.795007i 0.0282138i
795795 1.42619 + 0.217597i 0.0505817 + 0.00771736i
796796 −2.15892 + 3.73936i −0.0765209 + 0.132538i
797797 −10.1370 + 37.8319i −0.359072 + 1.34007i 0.516210 + 0.856462i 0.327342π0.327342\pi
−0.875282 + 0.483612i 0.839324π0.839324\pi
798798 0.238537 0.00844411
799799 −0.321515 + 1.19991i −0.0113744 + 0.0424498i
800800 −2.32234 + 7.43348i −0.0821073 + 0.262813i
801801 12.6934 + 12.6934i 0.448500 + 0.448500i
802802 0.306232 + 0.0820546i 0.0108134 + 0.00289745i
803803 −10.4249 38.9062i −0.367887 1.37297i
804804 0.638201 + 2.38180i 0.0225076 + 0.0839996i
805805 −19.9220 + 45.4378i −0.702158 + 1.60147i
806806 0 0
807807 −2.36658 + 2.36658i −0.0833077 + 0.0833077i
808808 0.263823 0.456954i 0.00928125 0.0160756i
809809 23.1644 + 13.3740i 0.814416 + 0.470203i 0.848487 0.529216i 0.177514π-0.177514\pi
−0.0340712 + 0.999419i 0.510847π0.510847\pi
810810 −1.45853 + 1.82218i −0.0512474 + 0.0640248i
811811 7.93739 7.93739i 0.278720 0.278720i −0.553878 0.832598i 0.686853π-0.686853\pi
0.832598 + 0.553878i 0.186853π0.186853\pi
812812 21.8697 12.6265i 0.767477 0.443103i
813813 6.52757 3.76869i 0.228932 0.132174i
814814 −2.63940 + 2.63940i −0.0925109 + 0.0925109i
815815 26.1235 32.6368i 0.915065 1.14322i
816816 −2.81378 1.62453i −0.0985019 0.0568701i
817817 6.13849 10.6322i 0.214759 0.371973i
818818 −1.86963 + 1.86963i −0.0653700 + 0.0653700i
819819 0 0
820820 −11.4305 + 26.0706i −0.399172 + 0.910425i
821821 −6.99144 26.0924i −0.244003 0.910632i −0.973882 0.227055i 0.927090π-0.927090\pi
0.729879 0.683577i 0.239576π-0.239576\pi
822822 −0.174661 0.651843i −0.00609200 0.0227356i
823823 −9.05749 2.42695i −0.315724 0.0845980i 0.0974771 0.995238i 0.468923π-0.468923\pi
−0.413201 + 0.910640i 0.635589π0.635589\pi
824824 3.13769 + 3.13769i 0.109307 + 0.109307i
825825 2.07934 6.65567i 0.0723935 0.231721i
826826 −0.248227 + 0.926397i −0.00863693 + 0.0322335i
827827 45.0330 1.56595 0.782976 0.622052i 0.213701π-0.213701\pi
0.782976 + 0.622052i 0.213701π0.213701\pi
828828 −11.7971 + 44.0273i −0.409976 + 1.53005i
829829 21.0075 36.3861i 0.729622 1.26374i −0.227421 0.973796i 0.573029π-0.573029\pi
0.957043 0.289946i 0.0936372π-0.0936372\pi
830830 0.920634 + 0.140463i 0.0319557 + 0.00487555i
831831 6.20942i 0.215402i
832832 0 0
833833 −1.26182 1.26182i −0.0437194 0.0437194i
834834 0.373887 0.100183i 0.0129467 0.00346905i
835835 6.97378 45.7081i 0.241338 1.58179i
836836 13.2255 7.63575i 0.457414 0.264088i
837837 11.0804i 0.382993i
838838 −1.97481 3.42047i −0.0682186 0.118158i
839839 5.24673 + 1.40586i 0.181137 + 0.0485356i 0.348247 0.937403i 0.386777π-0.386777\pi
−0.167110 + 0.985938i 0.553444π0.553444\pi
840840 0.449122 1.02435i 0.0154962 0.0353434i
841841 −4.01574 6.95547i −0.138474 0.239844i
842842 −1.65854 + 0.444405i −0.0571571 + 0.0153152i
843843 −4.79053 2.76581i −0.164994 0.0952596i
844844 −39.5617 −1.36177
845845 0 0
846846 −0.193872 −0.00666546
847847 −13.1156 7.57228i −0.450657 0.260187i
848848 7.06186 1.89222i 0.242505 0.0649791i
849849 1.95249 + 3.38181i 0.0670093 + 0.116063i
850850 −0.0652568 + 1.59036i −0.00223829 + 0.0545488i
851851 −54.0166 14.4737i −1.85167 0.496152i
852852 −2.19117 3.79522i −0.0750682 0.130022i
853853 23.0805i 0.790260i −0.918625 0.395130i 0.870700π-0.870700\pi
0.918625 0.395130i 0.129300π-0.129300\pi
854854 0.405948 0.234374i 0.0138912 0.00802012i
855855 7.24978 + 9.86030i 0.247937 + 0.337215i
856856 2.50323 0.670738i 0.0855586 0.0229254i
857857 37.6679 + 37.6679i 1.28671 + 1.28671i 0.936772 + 0.349940i 0.113798π0.113798\pi
0.349940 + 0.936772i 0.386202π0.386202\pi
858858 0 0
859859 5.08674i 0.173557i −0.996228 0.0867787i 0.972343π-0.972343\pi
0.996228 0.0867787i 0.0276573π-0.0276573\pi
860860 −16.9763 23.0892i −0.578886 0.787333i
861861 3.07068 5.31857i 0.104648 0.181256i
862862 −0.214481 + 0.800452i −0.00730524 + 0.0272635i
863863 −45.1879 −1.53821 −0.769107 0.639120i 0.779299π-0.779299\pi
−0.769107 + 0.639120i 0.779299π0.779299\pi
864864 0.815407 3.04314i 0.0277407 0.103530i
865865 −40.3289 + 4.47028i −1.37122 + 0.151994i
866866 1.14100 + 1.14100i 0.0387728 + 0.0387728i
867867 3.69447 + 0.989932i 0.125471 + 0.0336198i
868868 −7.81890 29.1805i −0.265391 0.990452i
869869 8.79099 + 32.8084i 0.298214 + 1.11295i
870870 0.423437 + 0.185654i 0.0143559 + 0.00629427i
871871 0 0
872872 3.40439 3.40439i 0.115287 0.115287i
873873 16.9590 29.3738i 0.573975 0.994154i
874874 −1.72287 0.994699i −0.0582769 0.0336462i
875875 31.0219 2.15591i 1.04873 0.0728832i
876876 −4.78896 + 4.78896i −0.161804 + 0.161804i
877877 17.6048 10.1641i 0.594471 0.343218i −0.172392 0.985028i 0.555150π-0.555150\pi
0.766863 + 0.641810i 0.221816π0.221816\pi
878878 −3.91675 + 2.26134i −0.132184 + 0.0763164i
879879 −0.170126 + 0.170126i −0.00573821 + 0.00573821i
880880 −3.89298 35.1208i −0.131232 1.18392i
881881 −28.5961 16.5100i −0.963428 0.556236i −0.0662019 0.997806i 0.521088π-0.521088\pi
−0.897227 + 0.441571i 0.854421π0.854421\pi
882882 0.139249 0.241187i 0.00468876 0.00812118i
883883 15.9555 15.9555i 0.536944 0.536944i −0.385686 0.922630i 0.626035π-0.626035\pi
0.922630 + 0.385686i 0.126035π0.126035\pi
884884 0 0
885885 1.88119 0.734395i 0.0632353 0.0246864i
886886 −0.259261 0.967576i −0.00871005 0.0325063i
887887 −0.163391 0.609784i −0.00548614 0.0204745i 0.963129 0.269042i 0.0867070π-0.0867070\pi
−0.968615 + 0.248567i 0.920040π0.920040\pi
888888 1.21775 + 0.326296i 0.0408651 + 0.0109498i
889889 32.5466 + 32.5466i 1.09158 + 1.09158i
890890 0.201495 + 1.81780i 0.00675413 + 0.0609329i
891891 8.34370 31.1391i 0.279524 1.04320i
892892 −26.5956 −0.890488
893893 −0.251872 + 0.939998i −0.00842856 + 0.0314558i
894894 0.274116 0.474784i 0.00916782 0.0158791i
895895 −5.85556 + 38.3790i −0.195730 + 1.28287i
896896 11.4359i 0.382046i
897897 0 0
898898 2.89072 + 2.89072i 0.0964647 + 0.0964647i
899899 24.2297 6.49233i 0.808106 0.216531i
900900 27.8754 6.25660i 0.929181 0.208553i
901901 3.93920 2.27430i 0.131234 0.0757679i
902902 3.41875i 0.113832i
903903 3.09139 + 5.35444i 0.102875 + 0.178185i
904904 −3.78996 1.01552i −0.126052 0.0337755i
905905 −20.2710 51.9250i −0.673830 1.72604i
906906 −0.0597070 0.103416i −0.00198363 0.00343575i
907907 37.8383 10.1387i 1.25640 0.336651i 0.431594 0.902068i 0.357951π-0.357951\pi
0.824805 + 0.565417i 0.191285π0.191285\pi
908908 −25.2095 14.5547i −0.836607 0.483015i
909909 −2.90763 −0.0964400
910910 0 0
911911 6.21630 0.205955 0.102978 0.994684i 0.467163π-0.467163\pi
0.102978 + 0.994684i 0.467163π0.467163\pi
912912 −2.20429 1.27264i −0.0729912 0.0421415i
913913 −12.4247 + 3.32919i −0.411198 + 0.110180i
914914 0.204012 + 0.353358i 0.00674810 + 0.0116881i
915915 −0.903940 0.396328i −0.0298833 0.0131022i
916916 7.18510 + 1.92524i 0.237402 + 0.0636117i
917917 17.6450 + 30.5621i 0.582690 + 1.00925i
918918 0.643907i 0.0212521i
919919 −19.9013 + 11.4900i −0.656485 + 0.379022i −0.790936 0.611899i 0.790406π-0.790406\pi
0.134452 + 0.990920i 0.457073π0.457073\pi
920920 −7.51540 + 5.52569i −0.247776 + 0.182177i
921921 4.71852 1.26432i 0.155481 0.0416609i
922922 1.55017 + 1.55017i 0.0510520 + 0.0510520i
923923 0 0
924924 7.69084i 0.253010i
925925 7.67617 + 34.2001i 0.252391 + 1.12449i
926926 1.02676 1.77840i 0.0337413 0.0584417i
927927 6.32875 23.6192i 0.207863 0.775757i
928928 7.13229 0.234129
929929 −0.280692 + 1.04756i −0.00920921 + 0.0343692i −0.970378 0.241593i 0.922330π-0.922330\pi
0.961168 + 0.275963i 0.0889966π0.0889966\pi
930930 0.345635 0.431811i 0.0113338 0.0141596i
931931 −0.988497 0.988497i −0.0323967 0.0323967i
932932 37.7726 + 10.1211i 1.23728 + 0.331529i
933933 −1.91330 7.14054i −0.0626387 0.233771i
934934 0.724846 + 2.70516i 0.0237177 + 0.0885157i
935935 −7.99493 20.4794i −0.261462 0.669746i
936936 0 0
937937 −2.17699 + 2.17699i −0.0711191 + 0.0711191i −0.741772 0.670653i 0.766014π-0.766014\pi
0.670653 + 0.741772i 0.266014π0.266014\pi
938938 −0.660337 + 1.14374i −0.0215608 + 0.0373443i
939939 −3.94358 2.27682i −0.128694 0.0743014i
940940 1.77350 + 1.41956i 0.0578450 + 0.0463009i
941941 22.9413 22.9413i 0.747866 0.747866i −0.226212 0.974078i 0.572634π-0.572634\pi
0.974078 + 0.226212i 0.0726342π0.0726342\pi
942942 −0.570694 + 0.329490i −0.0185942 + 0.0107354i
943943 −44.3569 + 25.6095i −1.44446 + 0.833959i
944944 7.23636 7.23636i 0.235523 0.235523i
945945 −12.5033 + 1.38594i −0.406733 + 0.0450846i
946946 −2.98069 1.72090i −0.0969107 0.0559514i
947947 13.6493 23.6413i 0.443543 0.768239i −0.554406 0.832246i 0.687055π-0.687055\pi
0.997949 + 0.0640069i 0.0203880π0.0203880\pi
948948 4.03838 4.03838i 0.131161 0.131161i
949949 0 0
950950 −0.0511215 + 1.24587i −0.00165860 + 0.0404214i
951951 1.54003 + 5.74748i 0.0499390 + 0.186375i
952952 −0.912703 3.40625i −0.0295809 0.110397i
953953 6.17827 + 1.65546i 0.200134 + 0.0536257i 0.357493 0.933916i 0.383631π-0.383631\pi
−0.157360 + 0.987541i 0.550298π0.550298\pi
954954 0.501965 + 0.501965i 0.0162517 + 0.0162517i
955955 11.8483 + 9.48372i 0.383401 + 0.306886i
956956 7.39460 27.5970i 0.239158 0.892551i
957957 −6.38600 −0.206430
958958 −1.44939 + 5.40920i −0.0468277 + 0.174763i
959959 −20.7839 + 35.9988i −0.671147 + 1.16246i
960960 −4.70181 + 3.45700i −0.151750 + 0.111574i
961961 0.991728i 0.0319912i
962962 0 0
963963 −10.0981 10.0981i −0.325406 0.325406i
964964 −15.5210 + 4.15885i −0.499899 + 0.133947i
965965 −2.64189 0.403080i −0.0850456 0.0129756i
966966 0.867650 0.500938i 0.0279162 0.0161174i
967967 28.4424i 0.914647i −0.889300 0.457324i 0.848808π-0.848808\pi
0.889300 0.457324i 0.151192π-0.151192\pi
968968 −1.42372 2.46596i −0.0457602 0.0792589i
969969 −1.52962 0.409860i −0.0491384 0.0131666i
970970 3.21908 1.25670i 0.103358 0.0403501i
971971 0.619921 + 1.07374i 0.0198942 + 0.0344578i 0.875801 0.482672i 0.160334π-0.160334\pi
−0.855907 + 0.517130i 0.827000π0.827000\pi
972972 −16.8575 + 4.51696i −0.540705 + 0.144882i
973973 −20.6484 11.9213i −0.661956 0.382180i
974974 −1.99799 −0.0640197
975975 0 0
976976 −5.00174 −0.160102
977977 32.9480 + 19.0226i 1.05410 + 0.608586i 0.923795 0.382888i 0.125071π-0.125071\pi
0.130307 + 0.991474i 0.458404π0.458404\pi
978978 −0.815418 + 0.218491i −0.0260742 + 0.00698656i
979979 −12.6307 21.8770i −0.403678 0.699192i
980980 −3.03982 + 1.18671i −0.0971035 + 0.0379082i
981981 −25.6268 6.86669i −0.818202 0.219236i
982982 1.83661 + 3.18111i 0.0586087 + 0.101513i
983983 34.5934i 1.10336i 0.834056 + 0.551679i 0.186013π0.186013\pi
−0.834056 + 0.551679i 0.813987π0.813987\pi
984984 0.999984 0.577341i 0.0318783 0.0184050i
985985 44.4772 + 6.78598i 1.41716 + 0.216219i
986986 1.40805 0.377285i 0.0448414 0.0120152i
987987 −0.346545 0.346545i −0.0110307 0.0110307i
988988 0 0
989989 51.5644i 1.63965i
990990 2.76430 2.03245i 0.0878553 0.0645955i
991991 −19.7486 + 34.2056i −0.627335 + 1.08658i 0.360750 + 0.932663i 0.382521π0.382521\pi
−0.988084 + 0.153913i 0.950813π0.950813\pi
992992 2.20832 8.24156i 0.0701142 0.261670i
993993 −6.17972 −0.196107
994994 0.607486 2.26717i 0.0192683 0.0719103i
995995 3.80162 + 3.04293i 0.120519 + 0.0964673i
996996 1.52936 + 1.52936i 0.0484595 + 0.0484595i
997997 −7.10500 1.90378i −0.225018 0.0602933i 0.144549 0.989498i 0.453827π-0.453827\pi
−0.369566 + 0.929204i 0.620494π0.620494\pi
998998 0.0804906 + 0.300395i 0.00254789 + 0.00950884i
999999 −3.66995 13.6964i −0.116112 0.433336i
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 845.2.t.g.188.3 20
5.2 odd 4 845.2.o.g.357.3 20
13.2 odd 12 65.2.o.a.63.3 yes 20
13.3 even 3 845.2.t.e.418.3 20
13.4 even 6 845.2.f.e.408.7 20
13.5 odd 4 845.2.o.e.488.3 20
13.6 odd 12 845.2.k.e.268.4 20
13.7 odd 12 845.2.k.d.268.7 20
13.8 odd 4 845.2.o.f.488.3 20
13.9 even 3 845.2.f.d.408.4 20
13.10 even 6 845.2.t.f.418.3 20
13.11 odd 12 845.2.o.g.258.3 20
13.12 even 2 65.2.t.a.58.3 yes 20
39.2 even 12 585.2.cf.a.388.3 20
39.38 odd 2 585.2.dp.a.253.3 20
65.2 even 12 65.2.t.a.37.3 yes 20
65.7 even 12 845.2.f.d.437.7 20
65.12 odd 4 65.2.o.a.32.3 20
65.17 odd 12 845.2.k.e.577.4 20
65.22 odd 12 845.2.k.d.577.7 20
65.28 even 12 325.2.x.b.232.3 20
65.32 even 12 845.2.f.e.437.4 20
65.37 even 12 inner 845.2.t.g.427.3 20
65.38 odd 4 325.2.s.b.32.3 20
65.42 odd 12 845.2.o.f.587.3 20
65.47 even 4 845.2.t.e.657.3 20
65.54 odd 12 325.2.s.b.193.3 20
65.57 even 4 845.2.t.f.657.3 20
65.62 odd 12 845.2.o.e.587.3 20
65.64 even 2 325.2.x.b.318.3 20
195.2 odd 12 585.2.dp.a.37.3 20
195.77 even 4 585.2.cf.a.487.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.32.3 20 65.12 odd 4
65.2.o.a.63.3 yes 20 13.2 odd 12
65.2.t.a.37.3 yes 20 65.2 even 12
65.2.t.a.58.3 yes 20 13.12 even 2
325.2.s.b.32.3 20 65.38 odd 4
325.2.s.b.193.3 20 65.54 odd 12
325.2.x.b.232.3 20 65.28 even 12
325.2.x.b.318.3 20 65.64 even 2
585.2.cf.a.388.3 20 39.2 even 12
585.2.cf.a.487.3 20 195.77 even 4
585.2.dp.a.37.3 20 195.2 odd 12
585.2.dp.a.253.3 20 39.38 odd 2
845.2.f.d.408.4 20 13.9 even 3
845.2.f.d.437.7 20 65.7 even 12
845.2.f.e.408.7 20 13.4 even 6
845.2.f.e.437.4 20 65.32 even 12
845.2.k.d.268.7 20 13.7 odd 12
845.2.k.d.577.7 20 65.22 odd 12
845.2.k.e.268.4 20 13.6 odd 12
845.2.k.e.577.4 20 65.17 odd 12
845.2.o.e.488.3 20 13.5 odd 4
845.2.o.e.587.3 20 65.62 odd 12
845.2.o.f.488.3 20 13.8 odd 4
845.2.o.f.587.3 20 65.42 odd 12
845.2.o.g.258.3 20 13.11 odd 12
845.2.o.g.357.3 20 5.2 odd 4
845.2.t.e.418.3 20 13.3 even 3
845.2.t.e.657.3 20 65.47 even 4
845.2.t.f.418.3 20 13.10 even 6
845.2.t.f.657.3 20 65.57 even 4
845.2.t.g.188.3 20 1.1 even 1 trivial
845.2.t.g.427.3 20 65.37 even 12 inner