Properties

Label 845.2.o.f.488.1
Level 845845
Weight 22
Character 845.488
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); 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.o (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20,4,-2,-6,6,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content 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)
Copy content comment:defining polynomial
 
Copy content 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,a2,a3]\Z[a_1, a_2, a_3]
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 488.1
Root 2.25081i-2.25081i of defining polynomial
Character χ\chi == 845.488
Dual form 845.2.o.f.587.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.12540+1.94926i)q2+(1.91913+0.514229i)q3+(1.533072.65535i)q4+(2.222280.247944i)q5+(1.157434.31958i)q6+(1.10607+0.638592i)q7+2.39966q8+(0.8205420.473740i)q9+(2.01765+4.61083i)q10+(1.413735.27612i)q11+(4.30760+4.30760i)q122.87469iq14+(4.13734+1.61860i)q15+(0.3655510.633152i)q16+(0.833802+3.11179i)q17+2.13259iq18+(1.17707+0.315395i)q19+(4.065285.52081i)q20+(1.794311.79431i)q21+(11.8755+3.18204i)q22+(0.04287360.160006i)q23+(4.60524+1.23397i)q24+(4.877051.10200i)q25+(2.883582.88358i)q27+(3.39137+1.95801i)q28+(8.41068+4.85591i)q29+(1.501119.88630i)q30+(0.2333050.233305i)q31+(3.22244+5.58143i)q32+(5.42627+9.39857i)q33+(5.127325.12732i)q34+(2.29967+1.69337i)q35+(2.515891.45255i)q36+(1.144570.660816i)q37+(1.93947+1.93947i)q38+(5.332700.594981i)q40+(0.4835950.129579i)q41+(1.47825+5.51690i)q42+(6.43569+1.72444i)q43+(11.8426+11.8426i)q44+(1.706011.25623i)q45+(0.360144+0.0965002i)q46+3.20027iq47+(0.375953+1.40308i)q48+(2.68440+4.64952i)q49+(3.34056+10.7468i)q506.40069iq51+(4.49845+4.49845i)q53+(2.37565+8.86603i)q54+(4.4498911.3745i)q55+(2.65420+1.53240i)q562.42113q57+(18.9308+10.9297i)q58+(0.000595178+0.00222123i)q59+(10.6407+8.50465i)q60+(0.6959931.20550i)q61+(0.7173320.192209i)q62+(0.605053+1.04798i)q6313.0440q6424.4270q66+(3.037185.26055i)q67+(9.541172.55655i)q68+(0.164560+0.285026i)q69+(0.7127646.38837i)q70+(3.1464811.7428i)q71+(1.969021.13681i)q727.34614q73+(2.576201.48737i)q74+(8.79299+4.62280i)q75+(0.9670443.60906i)q76+(4.93298+4.93298i)q77+11.1774iq79+(0.6553691.49768i)q80+(5.47236+9.47841i)q81+(0.291657+1.08848i)q822.65539iq83+(7.515332.01373i)q84+(1.08139+7.12201i)q85+(10.6041+10.6041i)q86+(18.63824.99409i)q87+(3.3924712.6609i)q88+(6.965421.86638i)q89+(0.528764+4.73922i)q90+(0.359145+0.359145i)q92+(0.567713+0.327769i)q93+(6.238153.60160i)q94+(2.69398+0.409048i)q95+(9.054409.05440i)q96+(2.09035+3.62059i)q97+(6.0420710.4652i)q98+(3.659543.65954i)q99+O(q100)q+(-1.12540 + 1.94926i) q^{2} +(-1.91913 + 0.514229i) q^{3} +(-1.53307 - 2.65535i) q^{4} +(2.22228 - 0.247944i) q^{5} +(1.15743 - 4.31958i) q^{6} +(-1.10607 + 0.638592i) q^{7} +2.39966 q^{8} +(0.820542 - 0.473740i) q^{9} +(-2.01765 + 4.61083i) q^{10} +(-1.41373 - 5.27612i) q^{11} +(4.30760 + 4.30760i) q^{12} -2.87469i q^{14} +(-4.13734 + 1.61860i) q^{15} +(0.365551 - 0.633152i) q^{16} +(-0.833802 + 3.11179i) q^{17} +2.13259i q^{18} +(1.17707 + 0.315395i) q^{19} +(-4.06528 - 5.52081i) q^{20} +(1.79431 - 1.79431i) q^{21} +(11.8755 + 3.18204i) q^{22} +(-0.0428736 - 0.160006i) q^{23} +(-4.60524 + 1.23397i) q^{24} +(4.87705 - 1.10200i) q^{25} +(2.88358 - 2.88358i) q^{27} +(3.39137 + 1.95801i) q^{28} +(8.41068 + 4.85591i) q^{29} +(1.50111 - 9.88630i) q^{30} +(-0.233305 - 0.233305i) q^{31} +(3.22244 + 5.58143i) q^{32} +(5.42627 + 9.39857i) q^{33} +(-5.12732 - 5.12732i) q^{34} +(-2.29967 + 1.69337i) q^{35} +(-2.51589 - 1.45255i) q^{36} +(-1.14457 - 0.660816i) q^{37} +(-1.93947 + 1.93947i) q^{38} +(5.33270 - 0.594981i) q^{40} +(0.483595 - 0.129579i) q^{41} +(1.47825 + 5.51690i) q^{42} +(6.43569 + 1.72444i) q^{43} +(-11.8426 + 11.8426i) q^{44} +(1.70601 - 1.25623i) q^{45} +(0.360144 + 0.0965002i) q^{46} +3.20027i q^{47} +(-0.375953 + 1.40308i) q^{48} +(-2.68440 + 4.64952i) q^{49} +(-3.34056 + 10.7468i) q^{50} -6.40069i q^{51} +(4.49845 + 4.49845i) q^{53} +(2.37565 + 8.86603i) q^{54} +(-4.44989 - 11.3745i) q^{55} +(-2.65420 + 1.53240i) q^{56} -2.42113 q^{57} +(-18.9308 + 10.9297i) q^{58} +(-0.000595178 + 0.00222123i) q^{59} +(10.6407 + 8.50465i) q^{60} +(-0.695993 - 1.20550i) q^{61} +(0.717332 - 0.192209i) q^{62} +(-0.605053 + 1.04798i) q^{63} -13.0440 q^{64} -24.4270 q^{66} +(3.03718 - 5.26055i) q^{67} +(9.54117 - 2.55655i) q^{68} +(0.164560 + 0.285026i) q^{69} +(-0.712764 - 6.38837i) q^{70} +(3.14648 - 11.7428i) q^{71} +(1.96902 - 1.13681i) q^{72} -7.34614 q^{73} +(2.57620 - 1.48737i) q^{74} +(-8.79299 + 4.62280i) q^{75} +(-0.967044 - 3.60906i) q^{76} +(4.93298 + 4.93298i) q^{77} +11.1774i q^{79} +(0.655369 - 1.49768i) q^{80} +(-5.47236 + 9.47841i) q^{81} +(-0.291657 + 1.08848i) q^{82} -2.65539i q^{83} +(-7.51533 - 2.01373i) q^{84} +(-1.08139 + 7.12201i) q^{85} +(-10.6041 + 10.6041i) q^{86} +(-18.6382 - 4.99409i) q^{87} +(-3.39247 - 12.6609i) q^{88} +(6.96542 - 1.86638i) q^{89} +(0.528764 + 4.73922i) q^{90} +(-0.359145 + 0.359145i) q^{92} +(0.567713 + 0.327769i) q^{93} +(-6.23815 - 3.60160i) q^{94} +(2.69398 + 0.409048i) q^{95} +(-9.05440 - 9.05440i) q^{96} +(2.09035 + 3.62059i) q^{97} +(-6.04207 - 10.4652i) q^{98} +(-3.65954 - 3.65954i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q22q36q4+6q54q66q712q8+12q9+2q108q11+24q1212q152q164q17+16q198q204q21+16q22+10q23++60q99+O(q100) 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \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(1112)e\left(\frac{11}{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 −1.12540 + 1.94926i −0.795780 + 1.37833i 0.126562 + 0.991959i 0.459606π0.459606\pi
−0.922342 + 0.386373i 0.873728π0.873728\pi
33 −1.91913 + 0.514229i −1.10801 + 0.296890i −0.766022 0.642815i 0.777767π-0.777767\pi
−0.341987 + 0.939705i 0.611100π0.611100\pi
44 −1.53307 2.65535i −0.766533 1.32767i
55 2.22228 0.247944i 0.993833 0.110884i
66 1.15743 4.31958i 0.472518 1.76346i
77 −1.10607 + 0.638592i −0.418057 + 0.241365i −0.694245 0.719738i 0.744262π-0.744262\pi
0.276189 + 0.961103i 0.410928π0.410928\pi
88 2.39966 0.848406
99 0.820542 0.473740i 0.273514 0.157913i
1010 −2.01765 + 4.61083i −0.638038 + 1.45807i
1111 −1.41373 5.27612i −0.426257 1.59081i −0.761163 0.648560i 0.775371π-0.775371\pi
0.334907 0.942251i 0.391295π-0.391295\pi
1212 4.30760 + 4.30760i 1.24350 + 1.24350i
1313 0 0
1414 2.87469i 0.768294i
1515 −4.13734 + 1.61860i −1.06826 + 0.417920i
1616 0.365551 0.633152i 0.0913876 0.158288i
1717 −0.833802 + 3.11179i −0.202227 + 0.754721i 0.788050 + 0.615611i 0.211091π0.211091\pi
−0.990277 + 0.139110i 0.955576π0.955576\pi
1818 2.13259i 0.502657i
1919 1.17707 + 0.315395i 0.270039 + 0.0723567i 0.391297 0.920264i 0.372026π-0.372026\pi
−0.121259 + 0.992621i 0.538693π0.538693\pi
2020 −4.06528 5.52081i −0.909024 1.23449i
2121 1.79431 1.79431i 0.391551 0.391551i
2222 11.8755 + 3.18204i 2.53187 + 0.678413i
2323 −0.0428736 0.160006i −0.00893976 0.0333637i 0.961312 0.275462i 0.0888309π-0.0888309\pi
−0.970252 + 0.242099i 0.922164π0.922164\pi
2424 −4.60524 + 1.23397i −0.940042 + 0.251883i
2525 4.87705 1.10200i 0.975409 0.220401i
2626 0 0
2727 2.88358 2.88358i 0.554946 0.554946i
2828 3.39137 + 1.95801i 0.640908 + 0.370029i
2929 8.41068 + 4.85591i 1.56182 + 0.901719i 0.997073 + 0.0764575i 0.0243610π0.0243610\pi
0.564751 + 0.825262i 0.308972π0.308972\pi
3030 1.50111 9.88630i 0.274065 1.80498i
3131 −0.233305 0.233305i −0.0419027 0.0419027i 0.685845 0.727748i 0.259433π-0.259433\pi
−0.727748 + 0.685845i 0.759433π0.759433\pi
3232 3.22244 + 5.58143i 0.569652 + 0.986667i
3333 5.42627 + 9.39857i 0.944592 + 1.63608i
3434 −5.12732 5.12732i −0.879328 0.879328i
3535 −2.29967 + 1.69337i −0.388715 + 0.286232i
3636 −2.51589 1.45255i −0.419315 0.242091i
3737 −1.14457 0.660816i −0.188166 0.108638i 0.402958 0.915219i 0.367982π-0.367982\pi
−0.591124 + 0.806581i 0.701315π0.701315\pi
3838 −1.93947 + 1.93947i −0.314623 + 0.314623i
3939 0 0
4040 5.33270 0.594981i 0.843175 0.0940747i
4141 0.483595 0.129579i 0.0755249 0.0202368i −0.220859 0.975306i 0.570886π-0.570886\pi
0.296384 + 0.955069i 0.404219π0.404219\pi
4242 1.47825 + 5.51690i 0.228099 + 0.851277i
4343 6.43569 + 1.72444i 0.981434 + 0.262974i 0.713648 0.700504i 0.247041π-0.247041\pi
0.267786 + 0.963479i 0.413708π0.413708\pi
4444 −11.8426 + 11.8426i −1.78534 + 1.78534i
4545 1.70601 1.25623i 0.254317 0.187268i
4646 0.360144 + 0.0965002i 0.0531003 + 0.0142282i
4747 3.20027i 0.466808i 0.972380 + 0.233404i 0.0749864π0.0749864\pi
−0.972380 + 0.233404i 0.925014π0.925014\pi
4848 −0.375953 + 1.40308i −0.0542642 + 0.202517i
4949 −2.68440 + 4.64952i −0.383486 + 0.664217i
5050 −3.34056 + 10.7468i −0.472427 + 1.51983i
5151 6.40069i 0.896276i
5252 0 0
5353 4.49845 + 4.49845i 0.617909 + 0.617909i 0.944995 0.327086i 0.106067π-0.106067\pi
−0.327086 + 0.944995i 0.606067π0.606067\pi
5454 2.37565 + 8.86603i 0.323285 + 1.20651i
5555 −4.44989 11.3745i −0.600024 1.53374i
5656 −2.65420 + 1.53240i −0.354682 + 0.204776i
5757 −2.42113 −0.320687
5858 −18.9308 + 10.9297i −2.48574 + 1.43514i
5959 −0.000595178 0.00222123i −7.74855e−5 0.000289180i −0.965965 0.258674i 0.916714π-0.916714\pi
0.965887 + 0.258964i 0.0833810π0.0833810\pi
6060 10.6407 + 8.50465i 1.37371 + 1.09795i
6161 −0.695993 1.20550i −0.0891128 0.154348i 0.818024 0.575185i 0.195070π-0.195070\pi
−0.907136 + 0.420837i 0.861736π0.861736\pi
6262 0.717332 0.192209i 0.0911013 0.0244105i
6363 −0.605053 + 1.04798i −0.0762295 + 0.132033i
6464 −13.0440 −1.63050
6565 0 0
6666 −24.4270 −3.00675
6767 3.03718 5.26055i 0.371050 0.642678i −0.618677 0.785645i 0.712331π-0.712331\pi
0.989727 + 0.142967i 0.0456644π0.0456644\pi
6868 9.54117 2.55655i 1.15704 0.310027i
6969 0.164560 + 0.285026i 0.0198107 + 0.0343131i
7070 −0.712764 6.38837i −0.0851916 0.763557i
7171 3.14648 11.7428i 0.373418 1.39361i −0.482225 0.876048i 0.660171π-0.660171\pi
0.855643 0.517567i 0.173162π-0.173162\pi
7272 1.96902 1.13681i 0.232051 0.133975i
7373 −7.34614 −0.859801 −0.429901 0.902876i 0.641451π-0.641451\pi
−0.429901 + 0.902876i 0.641451π0.641451\pi
7474 2.57620 1.48737i 0.299477 0.172903i
7575 −8.79299 + 4.62280i −1.01533 + 0.533795i
7676 −0.967044 3.60906i −0.110928 0.413987i
7777 4.93298 + 4.93298i 0.562166 + 0.562166i
7878 0 0
7979 11.1774i 1.25756i 0.777584 + 0.628779i 0.216445π0.216445\pi
−0.777584 + 0.628779i 0.783555π0.783555\pi
8080 0.655369 1.49768i 0.0732725 0.167445i
8181 −5.47236 + 9.47841i −0.608040 + 1.05316i
8282 −0.291657 + 1.08848i −0.0322081 + 0.120202i
8383 2.65539i 0.291467i −0.989324 0.145733i 0.953446π-0.953446\pi
0.989324 0.145733i 0.0465542π-0.0465542\pi
8484 −7.51533 2.01373i −0.819990 0.219716i
8585 −1.08139 + 7.12201i −0.117293 + 0.772490i
8686 −10.6041 + 10.6041i −1.14347 + 1.14347i
8787 −18.6382 4.99409i −1.99823 0.535423i
8888 −3.39247 12.6609i −0.361639 1.34965i
8989 6.96542 1.86638i 0.738333 0.197836i 0.129996 0.991515i 0.458504π-0.458504\pi
0.608337 + 0.793679i 0.291837π0.291837\pi
9090 0.528764 + 4.73922i 0.0557367 + 0.499558i
9191 0 0
9292 −0.359145 + 0.359145i −0.0374434 + 0.0374434i
9393 0.567713 + 0.327769i 0.0588691 + 0.0339881i
9494 −6.23815 3.60160i −0.643416 0.371477i
9595 2.69398 + 0.409048i 0.276397 + 0.0419675i
9696 −9.05440 9.05440i −0.924111 0.924111i
9797 2.09035 + 3.62059i 0.212243 + 0.367616i 0.952416 0.304801i 0.0985899π-0.0985899\pi
−0.740173 + 0.672416i 0.765257π0.765257\pi
9898 −6.04207 10.4652i −0.610341 1.05714i
9999 −3.65954 3.65954i −0.367797 0.367797i
100100 −10.4030 11.2608i −1.04030 1.12608i
101101 7.47319 + 4.31465i 0.743610 + 0.429323i 0.823380 0.567490i 0.192085π-0.192085\pi
−0.0797704 + 0.996813i 0.525419π0.525419\pi
102102 12.4766 + 7.20336i 1.23537 + 0.713239i
103103 −1.07603 + 1.07603i −0.106025 + 0.106025i −0.758129 0.652104i 0.773886π-0.773886\pi
0.652104 + 0.758129i 0.273886π0.273886\pi
104104 0 0
105105 3.54258 4.43236i 0.345720 0.432554i
106106 −13.8312 + 3.70606i −1.34340 + 0.359964i
107107 3.75956 + 14.0309i 0.363451 + 1.35642i 0.869509 + 0.493917i 0.164435π0.164435\pi
−0.506058 + 0.862499i 0.668898π0.668898\pi
108108 −12.0776 3.23619i −1.16217 0.311403i
109109 −4.72405 + 4.72405i −0.452481 + 0.452481i −0.896177 0.443696i 0.853667π-0.853667\pi
0.443696 + 0.896177i 0.353667π0.353667\pi
110110 27.1797 + 4.12691i 2.59149 + 0.393486i
111111 2.53638 + 0.679621i 0.240743 + 0.0645068i
112112 0.933751i 0.0882311i
113113 2.94919 11.0065i 0.277437 1.03541i −0.676754 0.736209i 0.736614π-0.736614\pi
0.954191 0.299199i 0.0967193π-0.0967193\pi
114114 2.72475 4.71941i 0.255197 0.442013i
115115 −0.134950 0.344949i −0.0125841 0.0321666i
116116 29.7777i 2.76479i
117117 0 0
118118 −0.00365994 0.00365994i −0.000336925 0.000336925i
119119 −1.06492 3.97433i −0.0976210 0.364326i
120120 −9.92818 + 3.88407i −0.906315 + 0.354566i
121121 −16.3126 + 9.41807i −1.48296 + 0.856188i
122122 3.13309 0.283657
123123 −0.861447 + 0.497357i −0.0776741 + 0.0448452i
124124 −0.261833 + 0.977176i −0.0235133 + 0.0877530i
125125 10.5649 3.65819i 0.944956 0.327199i
126126 −1.36186 2.35881i −0.121324 0.210139i
127127 0.506651 0.135757i 0.0449580 0.0120465i −0.236270 0.971687i 0.575925π-0.575925\pi
0.281228 + 0.959641i 0.409258π0.409258\pi
128128 8.23486 14.2632i 0.727865 1.26070i
129129 −13.2377 −1.16551
130130 0 0
131131 5.09883 0.445486 0.222743 0.974877i 0.428499π-0.428499\pi
0.222743 + 0.974877i 0.428499π0.428499\pi
132132 16.6377 28.8173i 1.44812 2.50822i
133133 −1.50334 + 0.402818i −0.130356 + 0.0349287i
134134 6.83610 + 11.8405i 0.590549 + 1.02286i
135135 5.69316 7.12309i 0.489989 0.613058i
136136 −2.00084 + 7.46723i −0.171571 + 0.640310i
137137 3.29390 1.90173i 0.281417 0.162476i −0.352648 0.935756i 0.614719π-0.614719\pi
0.634065 + 0.773280i 0.281385π0.281385\pi
138138 −0.740785 −0.0630598
139139 −1.28017 + 0.739106i −0.108583 + 0.0626902i −0.553308 0.832977i 0.686635π-0.686635\pi
0.444725 + 0.895667i 0.353301π0.353301\pi
140140 8.02204 + 3.51037i 0.677986 + 0.296680i
141141 −1.64567 6.14173i −0.138591 0.517227i
142142 19.3487 + 19.3487i 1.62371 + 1.62371i
143143 0 0
144144 0.692704i 0.0577253i
145145 19.8949 + 8.70580i 1.65218 + 0.722977i
146146 8.26737 14.3195i 0.684213 1.18509i
147147 2.76079 10.3034i 0.227706 0.849811i
148148 4.05230i 0.333097i
149149 16.6295 + 4.45586i 1.36234 + 0.365038i 0.864675 0.502331i 0.167524π-0.167524\pi
0.497665 + 0.867369i 0.334191π0.334191\pi
150150 0.884644 22.3423i 0.0722308 1.82424i
151151 10.0539 10.0539i 0.818178 0.818178i −0.167666 0.985844i 0.553623π-0.553623\pi
0.985844 + 0.167666i 0.0536230π0.0536230\pi
152152 2.82457 + 0.756840i 0.229103 + 0.0613879i
153153 0.790011 + 2.94836i 0.0638686 + 0.238361i
154154 −15.1672 + 4.06405i −1.22221 + 0.327491i
155155 −0.576314 0.460621i −0.0462907 0.0369980i
156156 0 0
157157 3.07230 3.07230i 0.245196 0.245196i −0.573799 0.818996i 0.694531π-0.694531\pi
0.818996 + 0.573799i 0.194531π0.194531\pi
158158 −21.7876 12.5791i −1.73333 1.00074i
159159 −10.9463 6.31986i −0.868100 0.501198i
160160 8.54504 + 11.6045i 0.675545 + 0.917417i
161161 0.149600 + 0.149600i 0.0117902 + 0.0117902i
162162 −12.3172 21.3341i −0.967733 1.67616i
163163 4.60251 + 7.97177i 0.360496 + 0.624398i 0.988043 0.154182i 0.0492741π-0.0492741\pi
−0.627546 + 0.778579i 0.715941π0.715941\pi
164164 −1.08546 1.08546i −0.0847602 0.0847602i
165165 14.3890 + 19.5408i 1.12018 + 1.52125i
166166 5.17603 + 2.98838i 0.401738 + 0.231944i
167167 10.9455 + 6.31936i 0.846985 + 0.489007i 0.859632 0.510913i 0.170693π-0.170693\pi
−0.0126474 + 0.999920i 0.504026π0.504026\pi
168168 4.30574 4.30574i 0.332195 0.332195i
169169 0 0
170170 −12.6656 10.1230i −0.971409 0.776402i
171171 1.11525 0.298831i 0.0852854 0.0228522i
172172 −5.28736 19.7327i −0.403157 1.50460i
173173 13.2481 + 3.54983i 1.00724 + 0.269888i 0.724474 0.689302i 0.242083π-0.242083\pi
0.282762 + 0.959190i 0.408749π0.408749\pi
174174 30.7103 30.7103i 2.32814 2.32814i
175175 −4.69064 + 4.33334i −0.354579 + 0.327570i
176176 −3.85738 1.03358i −0.290761 0.0779092i
177177 0.00456889i 0.000343419i
178178 −4.20086 + 15.6778i −0.314867 + 1.17510i
179179 6.32126 10.9487i 0.472473 0.818347i −0.527031 0.849846i 0.676695π-0.676695\pi
0.999504 + 0.0314989i 0.0100281π0.0100281\pi
180180 −5.95116 2.60417i −0.443573 0.194103i
181181 8.16619i 0.606988i −0.952833 0.303494i 0.901847π-0.901847\pi
0.952833 0.303494i 0.0981533π-0.0981533\pi
182182 0 0
183183 1.95560 + 1.95560i 0.144562 + 0.144562i
184184 −0.102882 0.383960i −0.00758455 0.0283059i
185185 −2.70739 1.18473i −0.199052 0.0871030i
186186 −1.27781 + 0.737745i −0.0936937 + 0.0540941i
187187 17.5970 1.28682
188188 8.49784 4.90623i 0.619769 0.357824i
189189 −1.34802 + 5.03089i −0.0980542 + 0.365943i
190190 −3.82916 + 4.79091i −0.277796 + 0.347569i
191191 7.37692 + 12.7772i 0.533775 + 0.924526i 0.999222 + 0.0394498i 0.0125605π0.0125605\pi
−0.465446 + 0.885076i 0.654106π0.654106\pi
192192 25.0330 6.70758i 1.80660 0.484078i
193193 −7.54845 + 13.0743i −0.543349 + 0.941109i 0.455359 + 0.890308i 0.349511π0.349511\pi
−0.998709 + 0.0508011i 0.983823π0.983823\pi
194194 −9.40995 −0.675595
195195 0 0
196196 16.4614 1.17582
197197 −7.68576 + 13.3121i −0.547588 + 0.948450i 0.450851 + 0.892599i 0.351121π0.351121\pi
−0.998439 + 0.0558510i 0.982213π0.982213\pi
198198 11.2518 3.01492i 0.799633 0.214261i
199199 −5.72810 9.92136i −0.406054 0.703307i 0.588389 0.808578i 0.299762π-0.299762\pi
−0.994444 + 0.105271i 0.966429π0.966429\pi
200200 11.7032 2.64443i 0.827544 0.186989i
201201 −3.12361 + 11.6575i −0.220322 + 0.822254i
202202 −16.8207 + 9.71144i −1.18350 + 0.683294i
203203 −12.4038 −0.870574
204204 −16.9961 + 9.81268i −1.18996 + 0.687025i
205205 1.04255 0.407865i 0.0728152 0.0284865i
206206 −0.886492 3.30843i −0.0617648 0.230509i
207207 −0.110981 0.110981i −0.00771372 0.00771372i
208208 0 0
209209 6.65626i 0.460423i
210210 4.65297 + 11.8936i 0.321085 + 0.820735i
211211 −1.59195 + 2.75735i −0.109595 + 0.189823i −0.915606 0.402076i 0.868289π-0.868289\pi
0.806011 + 0.591900i 0.201622π0.201622\pi
212212 5.04852 18.8414i 0.346734 1.29403i
213213 24.1539i 1.65500i
214214 −31.5808 8.46205i −2.15882 0.578454i
215215 14.7295 + 2.23649i 1.00454 + 0.152527i
216216 6.91961 6.91961i 0.470820 0.470820i
217217 0.407038 + 0.109066i 0.0276316 + 0.00740386i
218218 −3.89192 14.5248i −0.263594 0.983746i
219219 14.0982 3.77760i 0.952667 0.255266i
220220 −23.3813 + 29.2539i −1.57636 + 1.97230i
221221 0 0
222222 −4.17921 + 4.17921i −0.280490 + 0.280490i
223223 −10.2862 5.93874i −0.688815 0.397688i 0.114353 0.993440i 0.463521π-0.463521\pi
−0.803168 + 0.595753i 0.796854π0.796854\pi
224224 −7.12851 4.11565i −0.476294 0.274988i
225225 3.47976 3.21469i 0.231984 0.214313i
226226 18.1355 + 18.1355i 1.20636 + 1.20636i
227227 −13.8333 23.9600i −0.918149 1.59028i −0.802225 0.597022i 0.796350π-0.796350\pi
−0.115924 0.993258i 0.536983π-0.536983\pi
228228 3.71176 + 6.42896i 0.245817 + 0.425768i
229229 12.9000 + 12.9000i 0.852455 + 0.852455i 0.990435 0.137980i 0.0440610π-0.0440610\pi
−0.137980 + 0.990435i 0.544061π0.544061\pi
230230 0.824266 + 0.125155i 0.0543505 + 0.00825246i
231231 −12.0037 6.93034i −0.789786 0.455983i
232232 20.1827 + 11.6525i 1.32506 + 0.765024i
233233 16.3545 16.3545i 1.07142 1.07142i 0.0741712 0.997246i 0.476369π-0.476369\pi
0.997246 0.0741712i 0.0236311π-0.0236311\pi
234234 0 0
235235 0.793489 + 7.11190i 0.0517615 + 0.463929i
236236 0.00681059 0.00182489i 0.000443332 0.000118790i
237237 −5.74774 21.4509i −0.373356 1.39338i
238238 8.94546 + 2.39693i 0.579848 + 0.155370i
239239 −2.61794 + 2.61794i −0.169341 + 0.169341i −0.786690 0.617349i 0.788207π-0.788207\pi
0.617349 + 0.786690i 0.288207π0.288207\pi
240240 −0.487588 + 3.21124i −0.0314737 + 0.207285i
241241 20.1013 + 5.38613i 1.29484 + 0.346951i 0.839496 0.543365i 0.182850π-0.182850\pi
0.455343 + 0.890316i 0.349517π0.349517\pi
242242 42.3965i 2.72535i
243243 2.46169 9.18717i 0.157918 0.589357i
244244 −2.13401 + 3.69621i −0.136616 + 0.236625i
245245 −4.81267 + 10.9981i −0.307470 + 0.702643i
246246 2.23891i 0.142748i
247247 0 0
248248 −0.559851 0.559851i −0.0355505 0.0355505i
249249 1.36548 + 5.09603i 0.0865336 + 0.322948i
250250 −4.75905 + 24.7107i −0.300989 + 1.56284i
251251 2.05050 1.18386i 0.129427 0.0747245i −0.433889 0.900966i 0.642859π-0.642859\pi
0.563315 + 0.826242i 0.309526π0.309526\pi
252252 3.71034 0.233730
253253 −0.783602 + 0.452413i −0.0492647 + 0.0284430i
254254 −0.305562 + 1.14037i −0.0191727 + 0.0715533i
255255 −1.58701 14.2241i −0.0993827 0.890749i
256256 5.49109 + 9.51085i 0.343193 + 0.594428i
257257 −0.840391 + 0.225182i −0.0524221 + 0.0140465i −0.284935 0.958547i 0.591972π-0.591972\pi
0.232513 + 0.972593i 0.425305π0.425305\pi
258258 14.8977 25.8036i 0.927492 1.60646i
259259 1.68797 0.104885
260260 0 0
261261 9.20175 0.569574
262262 −5.73824 + 9.93892i −0.354509 + 0.614028i
263263 14.6707 3.93099i 0.904632 0.242395i 0.223627 0.974675i 0.428210π-0.428210\pi
0.681004 + 0.732279i 0.261543π0.261543\pi
264264 13.0212 + 22.5533i 0.801398 + 1.38806i
265265 11.1122 + 8.88144i 0.682615 + 0.545582i
266266 0.906665 3.38372i 0.0555912 0.207469i
267267 −12.4078 + 7.16363i −0.759343 + 0.438407i
268268 −18.6248 −1.13769
269269 21.1150 12.1908i 1.28741 0.743285i 0.309216 0.950992i 0.399933π-0.399933\pi
0.978191 + 0.207707i 0.0666000π0.0666000\pi
270270 7.47763 + 19.1138i 0.455074 + 1.16323i
271271 −3.39484 12.6697i −0.206222 0.769630i −0.989074 0.147422i 0.952903π-0.952903\pi
0.782852 0.622208i 0.213764π-0.213764\pi
272272 1.66544 + 1.66544i 0.100982 + 0.100982i
273273 0 0
274274 8.56086i 0.517181i
275275 −12.7091 24.1740i −0.766390 1.45775i
276276 0.504562 0.873927i 0.0303711 0.0526042i
277277 −3.16472 + 11.8109i −0.190149 + 0.709647i 0.803320 + 0.595548i 0.203065π0.203065\pi
−0.993469 + 0.114099i 0.963602π0.963602\pi
278278 3.32717i 0.199550i
279279 −0.301962 0.0809104i −0.0180780 0.00484398i
280280 −5.51841 + 4.06352i −0.329788 + 0.242841i
281281 6.43529 6.43529i 0.383897 0.383897i −0.488607 0.872504i 0.662495π-0.662495\pi
0.872504 + 0.488607i 0.162495π0.162495\pi
282282 13.8239 + 3.70409i 0.823198 + 0.220575i
283283 −7.07953 26.4212i −0.420834 1.57057i −0.772855 0.634583i 0.781172π-0.781172\pi
0.352021 0.935992i 0.385495π-0.385495\pi
284284 −36.0050 + 9.64751i −2.13650 + 0.572474i
285285 −5.38044 + 0.600307i −0.318710 + 0.0355591i
286286 0 0
287287 −0.452144 + 0.452144i −0.0266892 + 0.0266892i
288288 5.28829 + 3.05320i 0.311616 + 0.179911i
289289 5.73440 + 3.31076i 0.337318 + 0.194750i
290290 −39.3596 + 28.9826i −2.31127 + 1.70192i
291291 −5.87346 5.87346i −0.344308 0.344308i
292292 11.2621 + 19.5066i 0.659066 + 1.14154i
293293 −13.0620 22.6241i −0.763092 1.32171i −0.941249 0.337713i 0.890347π-0.890347\pi
0.178157 0.984002i 0.442987π-0.442987\pi
294294 16.9770 + 16.9770i 0.990118 + 0.990118i
295295 −0.000771909 0.00508377i −4.49423e−5 0.000295989i
296296 −2.74657 1.58573i −0.159641 0.0921688i
297297 −19.2908 11.1375i −1.11936 0.646265i
298298 −27.4005 + 27.4005i −1.58727 + 1.58727i
299299 0 0
300300 25.7554 + 16.2614i 1.48699 + 0.938852i
301301 −8.21957 + 2.20243i −0.473768 + 0.126946i
302302 8.28296 + 30.9124i 0.476631 + 1.77881i
303303 −16.5607 4.43743i −0.951388 0.254924i
304304 0.629972 0.629972i 0.0361314 0.0361314i
305305 −1.84559 2.50638i −0.105678 0.143515i
306306 −6.63619 1.77816i −0.379366 0.101651i
307307 14.7038i 0.839189i 0.907712 + 0.419595i 0.137828π0.137828\pi
−0.907712 + 0.419595i 0.862172π0.862172\pi
308308 5.53620 20.6614i 0.315454 1.17729i
309309 1.51172 2.61837i 0.0859985 0.148954i
310310 1.54645 0.604999i 0.0878327 0.0343617i
311311 31.8525i 1.80619i 0.429440 + 0.903095i 0.358711π0.358711\pi
−0.429440 + 0.903095i 0.641289π0.641289\pi
312312 0 0
313313 −11.9865 11.9865i −0.677519 0.677519i 0.281919 0.959438i 0.409029π-0.409029\pi
−0.959438 + 0.281919i 0.909029π0.909029\pi
314314 2.53112 + 9.44628i 0.142840 + 0.533084i
315315 −1.08476 + 2.47893i −0.0611190 + 0.139672i
316316 29.6799 17.1357i 1.66963 0.963959i
317317 −15.5627 −0.874088 −0.437044 0.899440i 0.643975π-0.643975\pi
−0.437044 + 0.899440i 0.643975π0.643975\pi
318318 24.6380 14.2248i 1.38163 0.797686i
319319 13.7299 51.2407i 0.768728 2.86893i
320320 −28.9874 + 3.23418i −1.62044 + 0.180796i
321321 −14.4302 24.9938i −0.805413 1.39502i
322322 −0.459970 + 0.123249i −0.0256331 + 0.00686837i
323323 −1.96289 + 3.39983i −0.109218 + 0.189171i
324324 33.5580 1.86433
325325 0 0
326326 −20.7187 −1.14750
327327 6.63680 11.4953i 0.367016 0.635691i
328328 1.16046 0.310945i 0.0640758 0.0171691i
329329 −2.04367 3.53974i −0.112671 0.195152i
330330 −54.2835 + 6.05653i −2.98821 + 0.333401i
331331 −4.41633 + 16.4820i −0.242743 + 0.905930i 0.731761 + 0.681561i 0.238699π0.238699\pi
−0.974504 + 0.224369i 0.927968π0.927968\pi
332332 −7.05098 + 4.07089i −0.386973 + 0.223419i
333333 −1.25222 −0.0686212
334334 −24.6361 + 14.2237i −1.34803 + 0.778284i
335335 5.44513 12.4435i 0.297499 0.679858i
336336 −0.480161 1.79199i −0.0261949 0.0977609i
337337 −25.0560 25.0560i −1.36489 1.36489i −0.867568 0.497319i 0.834318π-0.834318\pi
−0.497319 0.867568i 0.665682π-0.665682\pi
338338 0 0
339339 22.6395i 1.22961i
340340 20.5693 8.04704i 1.11552 0.436412i
341341 −0.901114 + 1.56077i −0.0487980 + 0.0845207i
342342 −0.672610 + 2.51022i −0.0363706 + 0.135737i
343343 15.7972i 0.852971i
344344 15.4435 + 4.13806i 0.832655 + 0.223109i
345345 0.436368 + 0.592605i 0.0234933 + 0.0319048i
346346 −21.8290 + 21.8290i −1.17354 + 1.17354i
347347 −12.4604 3.33874i −0.668907 0.179233i −0.0916446 0.995792i 0.529212π-0.529212\pi
−0.577262 + 0.816559i 0.695879π0.695879\pi
348348 15.3125 + 57.1472i 0.820838 + 3.06341i
349349 25.9362 6.94957i 1.38833 0.372002i 0.514191 0.857676i 0.328092π-0.328092\pi
0.874140 + 0.485674i 0.161426π0.161426\pi
350350 −3.16792 14.0200i −0.169332 0.749402i
351351 0 0
352352 24.8926 24.8926i 1.32678 1.32678i
353353 20.1885 + 11.6558i 1.07453 + 0.620378i 0.929414 0.369038i 0.120313π-0.120313\pi
0.145111 + 0.989415i 0.453646π0.453646\pi
354354 0.00890593 + 0.00514184i 0.000473345 + 0.000273286i
355355 4.08078 26.8759i 0.216586 1.42643i
356356 −15.6343 15.6343i −0.828617 0.828617i
357357 4.08743 + 7.07964i 0.216330 + 0.374694i
358358 14.2279 + 24.6435i 0.751970 + 1.30245i
359359 9.17222 + 9.17222i 0.484091 + 0.484091i 0.906435 0.422344i 0.138793π-0.138793\pi
−0.422344 + 0.906435i 0.638793π0.638793\pi
360360 4.09384 3.01452i 0.215764 0.158879i
361361 −15.1685 8.75751i −0.798340 0.460922i
362362 15.9180 + 9.19026i 0.836631 + 0.483029i
363363 26.4629 26.4629i 1.38894 1.38894i
364364 0 0
365365 −16.3252 + 1.82143i −0.854499 + 0.0953382i
366366 −6.01280 + 1.61113i −0.314294 + 0.0842149i
367367 3.84780 + 14.3602i 0.200853 + 0.749595i 0.990674 + 0.136256i 0.0435071π0.0435071\pi
−0.789820 + 0.613338i 0.789826π0.789826\pi
368368 −0.116981 0.0313449i −0.00609805 0.00163397i
369369 0.335423 0.335423i 0.0174614 0.0174614i
370370 5.35625 3.94410i 0.278458 0.205044i
371371 −7.84829 2.10294i −0.407463 0.109179i
372372 2.00997i 0.104212i
373373 1.59980 5.97055i 0.0828348 0.309144i −0.912061 0.410055i 0.865509π-0.865509\pi
0.994895 + 0.100912i 0.0321760π0.0321760\pi
374374 −19.8037 + 34.3010i −1.02403 + 1.77366i
375375 −18.3943 + 12.4533i −0.949877 + 0.643087i
376376 7.67955i 0.396043i
377377 0 0
378378 −8.28942 8.28942i −0.426362 0.426362i
379379 −4.72834 17.6464i −0.242878 0.906435i −0.974438 0.224657i 0.927874π-0.927874\pi
0.731559 0.681778i 0.238793π-0.238793\pi
380380 −3.04389 7.78056i −0.156148 0.399134i
381381 −0.902517 + 0.521068i −0.0462373 + 0.0266951i
382382 −33.2081 −1.69907
383383 −8.87106 + 5.12171i −0.453290 + 0.261707i −0.709219 0.704989i 0.750952π-0.750952\pi
0.255929 + 0.966696i 0.417619π0.417619\pi
384384 −8.46920 + 31.6075i −0.432192 + 1.61296i
385385 12.1856 + 9.73936i 0.621034 + 0.496364i
386386 −16.9901 29.4277i −0.864774 1.49783i
387387 6.09769 1.63387i 0.309963 0.0830543i
388388 6.40929 11.1012i 0.325382 0.563579i
389389 3.41200 0.172995 0.0864977 0.996252i 0.472432π-0.472432\pi
0.0864977 + 0.996252i 0.472432π0.472432\pi
390390 0 0
391391 0.533655 0.0269881
392392 −6.44164 + 11.1572i −0.325352 + 0.563526i
393393 −9.78529 + 2.62196i −0.493603 + 0.132260i
394394 −17.2992 29.9630i −0.871519 1.50952i
395395 2.77138 + 24.8393i 0.139443 + 1.24980i
396396 −4.10703 + 15.3277i −0.206386 + 0.770244i
397397 −10.3335 + 5.96603i −0.518622 + 0.299426i −0.736371 0.676578i 0.763462π-0.763462\pi
0.217749 + 0.976005i 0.430129π0.430129\pi
398398 25.7857 1.29252
399399 2.67795 1.54612i 0.134065 0.0774027i
400400 1.08507 3.49075i 0.0542536 0.174538i
401401 1.05497 + 3.93721i 0.0526828 + 0.196615i 0.987252 0.159168i 0.0508811π-0.0508811\pi
−0.934569 + 0.355783i 0.884214π0.884214\pi
402402 −19.2081 19.2081i −0.958011 0.958011i
403403 0 0
404404 26.4586i 1.31636i
405405 −9.81100 + 22.4205i −0.487512 + 1.11408i
406406 13.9592 24.1781i 0.692786 1.19994i
407407 −1.86844 + 6.97310i −0.0926149 + 0.345644i
408408 15.3595i 0.760406i
409409 6.70266 + 1.79597i 0.331425 + 0.0888051i 0.420694 0.907202i 0.361786π-0.361786\pi
−0.0892692 + 0.996008i 0.528453π0.528453\pi
410410 −0.378261 + 2.49122i −0.0186810 + 0.123033i
411411 −5.34348 + 5.34348i −0.263574 + 0.263574i
412412 4.50687 + 1.20761i 0.222037 + 0.0594948i
413413 −0.000760151 0.00283692i −3.74046e−5 0.000139596i
414414 0.341229 0.0914320i 0.0167705 0.00449364i
415415 −0.658389 5.90102i −0.0323190 0.289670i
416416 0 0
417417 2.07674 2.07674i 0.101698 0.101698i
418418 12.9748 + 7.49098i 0.634616 + 0.366396i
419419 −18.3846 10.6144i −0.898147 0.518546i −0.0215487 0.999768i 0.506860π-0.506860\pi
−0.876599 + 0.481222i 0.840193π0.840193\pi
420420 −17.2004 2.61168i −0.839296 0.127437i
421421 3.15727 + 3.15727i 0.153876 + 0.153876i 0.779847 0.625971i 0.215297π-0.215297\pi
−0.625971 + 0.779847i 0.715297π0.715297\pi
422422 −3.58318 6.20625i −0.174427 0.302116i
423423 1.51610 + 2.62596i 0.0737152 + 0.127678i
424424 10.7947 + 10.7947i 0.524238 + 0.524238i
425425 −0.637290 + 16.0952i −0.0309131 + 0.780733i
426426 −47.0822 27.1829i −2.28114 1.31702i
427427 1.53964 + 0.888911i 0.0745084 + 0.0430174i
428428 31.4932 31.4932i 1.52228 1.52228i
429429 0 0
430430 −20.9361 + 26.1946i −1.00963 + 1.26321i
431431 34.6226 9.27711i 1.66771 0.446863i 0.703221 0.710971i 0.251744π-0.251744\pi
0.964493 + 0.264109i 0.0850777π0.0850777\pi
432432 −0.771651 2.87984i −0.0371261 0.138556i
433433 −7.81733 2.09465i −0.375677 0.100662i 0.0660397 0.997817i 0.478964π-0.478964\pi
−0.441716 + 0.897155i 0.645630π0.645630\pi
434434 −0.670679 + 0.670679i −0.0321936 + 0.0321936i
435435 −42.6575 6.47703i −2.04527 0.310550i
436436 19.7863 + 5.30171i 0.947590 + 0.253906i
437437 0.201861i 0.00965633i
438438 −8.50264 + 31.7323i −0.406272 + 1.51623i
439439 −14.3336 + 24.8265i −0.684104 + 1.18490i 0.289613 + 0.957144i 0.406473π0.406473\pi
−0.973717 + 0.227759i 0.926860π0.926860\pi
440440 −10.6782 27.2949i −0.509064 1.30123i
441441 5.08683i 0.242230i
442442 0 0
443443 −17.1586 17.1586i −0.815229 0.815229i 0.170184 0.985412i 0.445564π-0.445564\pi
−0.985412 + 0.170184i 0.945564π0.945564\pi
444444 −2.08381 7.77688i −0.0988931 0.369074i
445445 15.0163 5.87465i 0.711843 0.278485i
446446 23.1523 13.3670i 1.09629 0.632944i
447447 −34.2054 −1.61786
448448 14.4276 8.32978i 0.681640 0.393545i
449449 −2.37239 + 8.85389i −0.111960 + 0.417841i −0.999042 0.0437720i 0.986062π-0.986062\pi
0.887081 + 0.461613i 0.152729π0.152729\pi
450450 2.35012 + 10.4008i 0.110786 + 0.490297i
451451 −1.36735 2.36832i −0.0643860 0.111520i
452452 −33.7475 + 9.04261i −1.58735 + 0.425329i
453453 −14.1248 + 24.4648i −0.663639 + 1.14946i
454454 62.2722 2.92258
455455 0 0
456456 −5.80989 −0.272073
457457 −10.7399 + 18.6021i −0.502391 + 0.870167i 0.497605 + 0.867404i 0.334213π0.334213\pi
−0.999996 + 0.00276341i 0.999120π0.999120\pi
458458 −39.6631 + 10.6277i −1.85333 + 0.496599i
459459 6.56877 + 11.3775i 0.306604 + 0.531054i
460460 −0.709072 + 0.887168i −0.0330607 + 0.0413644i
461461 −1.31453 + 4.90591i −0.0612240 + 0.228491i −0.989758 0.142757i 0.954403π-0.954403\pi
0.928534 + 0.371248i 0.121070π0.121070\pi
462462 27.0180 15.5989i 1.25699 0.725725i
463463 20.0793 0.933163 0.466581 0.884478i 0.345485π-0.345485\pi
0.466581 + 0.884478i 0.345485π0.345485\pi
464464 6.14905 3.55016i 0.285463 0.164812i
465465 1.34289 + 0.587633i 0.0622748 + 0.0272508i
466466 13.4737 + 50.2844i 0.624156 + 2.32938i
467467 21.4507 + 21.4507i 0.992618 + 0.992618i 0.999973 0.00735447i 0.00234102π-0.00234102\pi
−0.00735447 + 0.999973i 0.502341π0.502341\pi
468468 0 0
469469 7.75807i 0.358234i
470470 −14.7559 6.45704i −0.680639 0.297841i
471471 −4.31627 + 7.47600i −0.198883 + 0.344476i
472472 −0.00142822 + 0.00533020i −6.57392e−5 + 0.000245342i
473473 36.3934i 1.67337i
474474 48.2818 + 12.9371i 2.21766 + 0.594219i
475475 6.08820 + 0.241062i 0.279346 + 0.0110607i
476476 −8.92064 + 8.92064i −0.408877 + 0.408877i
477477 5.82226 + 1.56007i 0.266583 + 0.0714306i
478478 −2.15680 8.04928i −0.0986497 0.368166i
479479 −30.0497 + 8.05179i −1.37300 + 0.367896i −0.868575 0.495557i 0.834964π-0.834964\pi
−0.504430 + 0.863453i 0.668297π0.668297\pi
480480 −22.3664 17.8764i −1.02088 0.815943i
481481 0 0
482482 −33.1210 + 33.1210i −1.50862 + 1.50862i
483483 −0.364031 0.210173i −0.0165640 0.00956321i
484484 50.0165 + 28.8770i 2.27348 + 1.31259i
485485 5.54305 + 7.52768i 0.251697 + 0.341814i
486486 15.1377 + 15.1377i 0.686662 + 0.686662i
487487 9.71579 + 16.8282i 0.440264 + 0.762560i 0.997709 0.0676540i 0.0215514π-0.0215514\pi
−0.557445 + 0.830214i 0.688218π0.688218\pi
488488 −1.67014 2.89277i −0.0756039 0.130950i
489489 −12.9321 12.9321i −0.584810 0.584810i
490490 −16.0219 21.7584i −0.723797 0.982945i
491491 30.5824 + 17.6568i 1.38017 + 0.796839i 0.992179 0.124825i 0.0398371π-0.0398371\pi
0.387987 + 0.921665i 0.373170π0.373170\pi
492492 2.64131 + 1.52496i 0.119079 + 0.0687506i
493493 −22.1234 + 22.1234i −0.996389 + 0.996389i
494494 0 0
495495 −9.03988 7.22515i −0.406312 0.324746i
496496 −0.233002 + 0.0624327i −0.0104621 + 0.00280331i
497497 4.01863 + 14.9977i 0.180260 + 0.672740i
498498 −11.4702 3.07343i −0.513991 0.137723i
499499 −9.44430 + 9.44430i −0.422785 + 0.422785i −0.886161 0.463377i 0.846638π-0.846638\pi
0.463377 + 0.886161i 0.346638π0.346638\pi
500500 −25.9105 22.4453i −1.15875 1.00378i
501501 −24.2553 6.49919i −1.08365 0.290363i
502502 5.32928i 0.237857i
503503 −6.24460 + 23.3052i −0.278433 + 1.03913i 0.675073 + 0.737751i 0.264112π0.264112\pi
−0.953506 + 0.301375i 0.902554π0.902554\pi
504504 −1.45192 + 2.51480i −0.0646736 + 0.112018i
505505 17.6773 + 7.73542i 0.786630 + 0.344221i
506506 2.03659i 0.0905374i
507507 0 0
508508 −1.13721 1.13721i −0.0504555 0.0504555i
509509 −0.963376 3.59537i −0.0427009 0.159362i 0.941283 0.337618i 0.109621π-0.109621\pi
−0.983984 + 0.178256i 0.942954π0.942954\pi
510510 29.5125 + 12.9144i 1.30683 + 0.571858i
511511 8.12538 4.69119i 0.359446 0.207526i
512512 8.22064 0.363304
513513 4.30365 2.48471i 0.190011 0.109703i
514514 0.506841 1.89156i 0.0223558 0.0834330i
515515 −2.12445 + 2.65804i −0.0936144 + 0.117127i
516516 20.2942 + 35.1506i 0.893403 + 1.54742i
517517 16.8850 4.52433i 0.742603 0.198980i
518518 −1.89964 + 3.29028i −0.0834656 + 0.144567i
519519 −27.2503 −1.19615
520520 0 0
521521 45.2323 1.98166 0.990832 0.135103i 0.0431364π-0.0431364\pi
0.990832 + 0.135103i 0.0431364π0.0431364\pi
522522 −10.3557 + 17.9366i −0.453256 + 0.785062i
523523 −1.10259 + 0.295439i −0.0482131 + 0.0129187i −0.282845 0.959166i 0.591278π-0.591278\pi
0.234632 + 0.972084i 0.424612π0.424612\pi
524524 −7.81683 13.5392i −0.341480 0.591461i
525525 6.77362 10.7283i 0.295625 0.468221i
526526 −8.84790 + 33.0208i −0.385787 + 1.43978i
527527 0.920525 0.531466i 0.0400987 0.0231510i
528528 7.93430 0.345296
529529 19.8948 11.4863i 0.864992 0.499403i
530530 −29.8179 + 11.6653i −1.29521 + 0.506706i
531531 0.000563919 0.00210457i 2.44720e−5 9.13307e-5i
532532 3.37434 + 3.37434i 0.146296 + 0.146296i
533533 0 0
534534 32.2479i 1.39550i
535535 11.8337 + 30.2484i 0.511614 + 1.30775i
536536 7.28818 12.6235i 0.314801 0.545252i
537537 −6.50114 + 24.2626i −0.280545 + 1.04701i
538538 54.8782i 2.36597i
539539 28.3265 + 7.59005i 1.22011 + 0.326927i
540540 −27.6423 4.19714i −1.18953 0.180616i
541541 −22.3573 + 22.3573i −0.961218 + 0.961218i −0.999276 0.0380580i 0.987883π-0.987883\pi
0.0380580 + 0.999276i 0.487883π0.487883\pi
542542 28.5171 + 7.64112i 1.22491 + 0.328214i
543543 4.19929 + 15.6720i 0.180209 + 0.672548i
544544 −20.0551 + 5.37376i −0.859857 + 0.230398i
545545 −9.32685 + 11.6694i −0.399518 + 0.499864i
546546 0 0
547547 −5.20384 + 5.20384i −0.222500 + 0.222500i −0.809550 0.587050i 0.800289π-0.800289\pi
0.587050 + 0.809550i 0.300289π0.300289\pi
548548 −10.0995 5.83096i −0.431430 0.249086i
549549 −1.14218 0.659440i −0.0487472 0.0281442i
550550 61.4242 + 2.43209i 2.61914 + 0.103705i
551551 8.36844 + 8.36844i 0.356507 + 0.356507i
552552 0.394887 + 0.683964i 0.0168075 + 0.0291114i
553553 −7.13781 12.3630i −0.303530 0.525730i
554554 −19.4608 19.4608i −0.826812 0.826812i
555555 5.80505 + 0.881427i 0.246411 + 0.0374145i
556556 3.92517 + 2.26620i 0.166464 + 0.0961081i
557557 −5.70401 3.29321i −0.241687 0.139538i 0.374265 0.927322i 0.377895π-0.377895\pi
−0.615952 + 0.787784i 0.711228π0.711228\pi
558558 0.497544 0.497544i 0.0210627 0.0210627i
559559 0 0
560560 0.231518 + 2.07505i 0.00978343 + 0.0876871i
561561 −33.7709 + 9.04887i −1.42581 + 0.382044i
562562 5.30173 + 19.7863i 0.223640 + 0.834636i
563563 −28.3543 7.59751i −1.19499 0.320197i −0.394134 0.919053i 0.628955π-0.628955\pi
−0.800856 + 0.598856i 0.795622π0.795622\pi
564564 −13.7855 + 13.7855i −0.580475 + 0.580475i
565565 3.82492 25.1908i 0.160916 1.05979i
566566 59.4689 + 15.9347i 2.49967 + 0.669783i
567567 13.9784i 0.587039i
568568 7.55046 28.1787i 0.316810 1.18235i
569569 16.9543 29.3658i 0.710763 1.23108i −0.253808 0.967255i 0.581683π-0.581683\pi
0.964571 0.263823i 0.0849835π-0.0849835\pi
570570 4.88501 11.1634i 0.204611 0.467585i
571571 33.5525i 1.40413i 0.712113 + 0.702065i 0.247738π0.247738\pi
−0.712113 + 0.702065i 0.752262π0.752262\pi
572572 0 0
573573 −20.7277 20.7277i −0.865910 0.865910i
574574 −0.372500 1.39019i −0.0155478 0.0580253i
575575 −0.385424 0.733112i −0.0160733 0.0305729i
576576 −10.7031 + 6.17945i −0.445964 + 0.257477i
577577 −11.0413 −0.459654 −0.229827 0.973232i 0.573816π-0.573816\pi
−0.229827 + 0.973232i 0.573816π0.573816\pi
578578 −12.9070 + 7.45188i −0.536862 + 0.309957i
579579 7.76326 28.9729i 0.322630 1.20407i
580580 −7.38321 66.1743i −0.306571 2.74774i
581581 1.69571 + 2.93706i 0.0703499 + 0.121850i
582582 18.0589 4.83886i 0.748565 0.200577i
583583 17.3748 30.0940i 0.719589 1.24636i
584584 −17.6282 −0.729461
585585 0 0
586586 58.8002 2.42902
587587 11.7529 20.3567i 0.485095 0.840209i −0.514758 0.857335i 0.672118π-0.672118\pi
0.999853 + 0.0171260i 0.00545165π0.00545165\pi
588588 −31.5916 + 8.46495i −1.30282 + 0.349089i
589589 −0.201033 0.348199i −0.00828342 0.0143473i
590590 −0.00904086 0.00722594i −0.000372206 0.000297487i
591591 7.90448 29.4999i 0.325147 1.21346i
592592 −0.836794 + 0.483123i −0.0343920 + 0.0198563i
593593 30.6582 1.25898 0.629491 0.777007i 0.283263π-0.283263\pi
0.629491 + 0.777007i 0.283263π0.283263\pi
594594 43.4198 25.0684i 1.78153 1.02857i
595595 −3.35196 8.56804i −0.137417 0.351255i
596596 −13.6622 50.9882i −0.559627 2.08856i
597597 16.0948 + 16.0948i 0.658717 + 0.658717i
598598 0 0
599599 7.49378i 0.306188i −0.988212 0.153094i 0.951076π-0.951076\pi
0.988212 0.153094i 0.0489237π-0.0489237\pi
600600 −21.1002 + 11.0931i −0.861410 + 0.452875i
601601 7.04653 12.2049i 0.287434 0.497850i −0.685763 0.727825i 0.740531π-0.740531\pi
0.973196 + 0.229975i 0.0738645π0.0738645\pi
602602 4.95724 18.5007i 0.202042 0.754030i
603603 5.75533i 0.234375i
604604 −42.1101 11.2834i −1.71343 0.459113i
605605 −33.9159 + 24.9742i −1.37888 + 1.01534i
606606 27.2872 27.2872i 1.10847 1.10847i
607607 −14.5660 3.90296i −0.591218 0.158416i −0.0492080 0.998789i 0.515670π-0.515670\pi
−0.542010 + 0.840372i 0.682336π0.682336\pi
608608 2.03268 + 7.58608i 0.0824363 + 0.307656i
609609 23.8044 6.37837i 0.964604 0.258465i
610610 6.96260 0.776832i 0.281908 0.0314530i
611611 0 0
612612 6.61779 6.61779i 0.267508 0.267508i
613613 10.3197 + 5.95807i 0.416808 + 0.240644i 0.693711 0.720254i 0.255975π-0.255975\pi
−0.276903 + 0.960898i 0.589308π0.589308\pi
614614 −28.6614 16.5477i −1.15668 0.667810i
615615 −1.79106 + 1.31886i −0.0722225 + 0.0531814i
616616 11.8375 + 11.8375i 0.476945 + 0.476945i
617617 −19.4158 33.6292i −0.781652 1.35386i −0.930979 0.365074i 0.881044π-0.881044\pi
0.149326 0.988788i 0.452290π-0.452290\pi
618618 3.40258 + 5.89344i 0.136872 + 0.237069i
619619 −14.9567 14.9567i −0.601159 0.601159i 0.339461 0.940620i 0.389755π-0.389755\pi
−0.940620 + 0.339461i 0.889755π0.889755\pi
620620 −0.339582 + 2.23648i −0.0136379 + 0.0898191i
621621 −0.585021 0.337762i −0.0234761 0.0135539i
622622 −62.0887 35.8469i −2.48953 1.43733i
623623 −6.51241 + 6.51241i −0.260914 + 0.260914i
624624 0 0
625625 22.5712 10.7490i 0.902847 0.429961i
626626 36.8545 9.87514i 1.47300 0.394690i
627627 3.42284 + 12.7742i 0.136695 + 0.510153i
628628 −12.8681 3.44799i −0.513492 0.137590i
629629 3.01067 3.01067i 0.120043 0.120043i
630630 −3.61128 4.90426i −0.143877 0.195390i
631631 −37.7256 10.1085i −1.50183 0.402415i −0.588119 0.808775i 0.700131π-0.700131\pi
−0.913713 + 0.406360i 0.866798π0.866798\pi
632632 26.8219i 1.06692i
633633 1.63726 6.11032i 0.0650751 0.242864i
634634 17.5143 30.3357i 0.695582 1.20478i
635635 1.09226 0.427310i 0.0433450 0.0169573i
636636 38.7550i 1.53674i
637637 0 0
638638 84.4296 + 84.4296i 3.34260 + 3.34260i
639639 −2.98122 11.1261i −0.117935 0.440141i
640640 14.7637 33.7386i 0.583585 1.33363i
641641 7.55607 4.36250i 0.298447 0.172308i −0.343298 0.939226i 0.611544π-0.611544\pi
0.641745 + 0.766918i 0.278211π0.278211\pi
642642 64.9590 2.56373
643643 −12.8146 + 7.39852i −0.505359 + 0.291769i −0.730924 0.682459i 0.760911π-0.760911\pi
0.225565 + 0.974228i 0.427577π0.427577\pi
644644 0.167894 0.626588i 0.00661594 0.0246910i
645645 −29.4178 + 3.28220i −1.15832 + 0.129237i
646646 −4.41809 7.65235i −0.173827 0.301078i
647647 −32.7213 + 8.76765i −1.28641 + 0.344692i −0.836295 0.548280i 0.815283π-0.815283\pi
−0.450113 + 0.892972i 0.648616π0.648616\pi
648648 −13.1318 + 22.7449i −0.515865 + 0.893505i
649649 0.0125609 0.000493060
650650 0 0
651651 −0.837243 −0.0328141
652652 14.1119 24.4425i 0.552664 0.957242i
653653 19.5581 5.24059i 0.765369 0.205080i 0.145044 0.989425i 0.453667π-0.453667\pi
0.620325 + 0.784345i 0.287001π0.287001\pi
654654 14.9382 + 25.8737i 0.584128 + 1.01174i
655655 11.3310 1.26422i 0.442739 0.0493973i
656656 0.0947353 0.353557i 0.00369879 0.0138041i
657657 −6.02782 + 3.48016i −0.235168 + 0.135774i
658658 9.19981 0.358646
659659 −26.2317 + 15.1449i −1.02184 + 0.589961i −0.914637 0.404276i 0.867523π-0.867523\pi
−0.107205 + 0.994237i 0.534190π0.534190\pi
660660 29.8284 68.1652i 1.16107 2.65333i
661661 −5.66280 21.1339i −0.220257 0.822012i −0.984249 0.176786i 0.943430π-0.943430\pi
0.763992 0.645226i 0.223237π-0.223237\pi
662662 −27.1574 27.1574i −1.05550 1.05550i
663663 0 0
664664 6.37202i 0.247282i
665665 −3.24096 + 1.26792i −0.125679 + 0.0491677i
666666 1.40925 2.44090i 0.0546074 0.0945829i
667667 0.416380 1.55395i 0.0161223 0.0601693i
668668 38.7520i 1.49936i
669669 22.7944 + 6.10774i 0.881282 + 0.236139i
670670 18.1275 + 24.6179i 0.700326 + 0.951071i
671671 −5.37640 + 5.37640i −0.207553 + 0.207553i
672672 15.7969 + 4.23277i 0.609379 + 0.163283i
673673 −0.148622 0.554664i −0.00572895 0.0213807i 0.963002 0.269494i 0.0868563π-0.0868563\pi
−0.968731 + 0.248113i 0.920190π0.920190\pi
674674 77.0386 20.6424i 2.96742 0.795117i
675675 10.8857 17.2411i 0.418989 0.663610i
676676 0 0
677677 −11.5229 + 11.5229i −0.442862 + 0.442862i −0.892973 0.450111i 0.851385π-0.851385\pi
0.450111 + 0.892973i 0.351385π0.351385\pi
678678 −44.1302 25.4786i −1.69481 0.978498i
679679 −4.62416 2.66976i −0.177459 0.102456i
680680 −2.59496 + 17.0904i −0.0995124 + 0.655386i
681681 38.8688 + 38.8688i 1.48946 + 1.48946i
682682 −2.02823 3.51300i −0.0776650 0.134520i
683683 10.0529 + 17.4121i 0.384663 + 0.666256i 0.991722 0.128400i 0.0409843π-0.0409843\pi
−0.607059 + 0.794657i 0.707651π0.707651\pi
684684 −2.50325 2.50325i −0.0957143 0.0957143i
685685 6.84843 5.04288i 0.261665 0.192679i
686686 30.7929 + 17.7783i 1.17568 + 0.678777i
687687 −31.3902 18.1232i −1.19761 0.691442i
688688 3.44440 3.44440i 0.131317 0.131317i
689689 0 0
690690 −1.64623 + 0.183673i −0.0626709 + 0.00699232i
691691 −41.8571 + 11.2156i −1.59232 + 0.426661i −0.942712 0.333608i 0.891734π-0.891734\pi
−0.649608 + 0.760269i 0.725067π0.725067\pi
692692 −10.8842 40.6205i −0.413756 1.54416i
693693 6.38467 + 1.71077i 0.242534 + 0.0649867i
694694 20.5310 20.5310i 0.779346 0.779346i
695695 −2.66164 + 1.95991i −0.100962 + 0.0743436i
696696 −44.7253 11.9841i −1.69531 0.454256i
697697 1.61289i 0.0610926i
698698 −15.6421 + 58.3773i −0.592064 + 2.20961i
699699 −22.9764 + 39.7962i −0.869046 + 1.50523i
700700 18.6976 + 5.81200i 0.706702 + 0.219673i
701701 8.03468i 0.303466i 0.988422 + 0.151733i 0.0484853π0.0484853\pi
−0.988422 + 0.151733i 0.951515π0.951515\pi
702702 0 0
703703 −1.13882 1.13882i −0.0429514 0.0429514i
704704 18.4407 + 68.8216i 0.695010 + 2.59381i
705705 −5.17995 13.2406i −0.195088 0.498670i
706706 −45.4404 + 26.2350i −1.71017 + 0.987369i
707707 −11.0212 −0.414495
708708 −0.0121320 + 0.00700440i −0.000455948 + 0.000263242i
709709 −5.88217 + 21.9526i −0.220910 + 0.824446i 0.763092 + 0.646289i 0.223680π0.223680\pi
−0.984002 + 0.178157i 0.942987π0.942987\pi
710710 47.7956 + 38.2008i 1.79374 + 1.43365i
711711 5.29519 + 9.17153i 0.198585 + 0.343959i
712712 16.7146 4.47866i 0.626406 0.167845i
713713 −0.0273276 + 0.0473328i −0.00102343 + 0.00177263i
714714 −18.4000 −0.688604
715715 0 0
716716 −38.7636 −1.44866
717717 3.67794 6.37039i 0.137355 0.237906i
718718 −28.2014 + 7.55655i −1.05247 + 0.282008i
719719 −21.4786 37.2021i −0.801018 1.38740i −0.918946 0.394382i 0.870959π-0.870959\pi
0.117928 0.993022i 0.462375π-0.462375\pi
720720 −0.171752 1.53938i −0.00640081 0.0573693i
721721 0.503026 1.87732i 0.0187336 0.0699149i
722722 34.1413 19.7115i 1.27061 0.733585i
723723 −41.3467 −1.53770
724724 −21.6841 + 12.5193i −0.805882 + 0.465276i
725725 46.3705 + 14.4139i 1.72216 + 0.535319i
726726 21.8015 + 81.3643i 0.809129 + 3.01971i
727727 1.42786 + 1.42786i 0.0529563 + 0.0529563i 0.733089 0.680133i 0.238078π-0.238078\pi
−0.680133 + 0.733089i 0.738078π0.738078\pi
728728 0 0
729729 13.9369i 0.516183i
730730 14.8220 33.8718i 0.548586 1.25365i
731731 −10.7322 + 18.5887i −0.396945 + 0.687528i
732732 2.19473 8.19086i 0.0811197 0.302743i
733733 32.1064i 1.18588i −0.805247 0.592939i 0.797967π-0.797967\pi
0.805247 0.592939i 0.202033π-0.202033\pi
734734 −32.3220 8.66065i −1.19303 0.319670i
735735 3.58058 23.5816i 0.132072 0.869820i
736736 0.754907 0.754907i 0.0278262 0.0278262i
737737 −32.0491 8.58752i −1.18054 0.316325i
738738 0.276339 + 1.03131i 0.0101722 + 0.0379631i
739739 −19.8460 + 5.31771i −0.730046 + 0.195615i −0.604650 0.796492i 0.706687π-0.706687\pi
−0.125396 + 0.992107i 0.540020π0.540020\pi
740740 1.00474 + 9.00534i 0.0369351 + 0.331043i
741741 0 0
742742 12.9317 12.9317i 0.474736 0.474736i
743743 19.4891 + 11.2520i 0.714985 + 0.412797i 0.812904 0.582398i 0.197885π-0.197885\pi
−0.0979193 + 0.995194i 0.531219π0.531219\pi
744744 1.36232 + 0.786533i 0.0499449 + 0.0288357i
745745 38.0601 + 5.77897i 1.39442 + 0.211725i
746746 9.83771 + 9.83771i 0.360184 + 0.360184i
747747 −1.25796 2.17886i −0.0460265 0.0797202i
748748 −26.9773 46.7261i −0.986389 1.70848i
749749 −13.1184 13.1184i −0.479334 0.479334i
750750 −3.57372 49.8702i −0.130494 1.82100i
751751 −1.44204 0.832560i −0.0526207 0.0303806i 0.473459 0.880816i 0.343005π-0.343005\pi
−0.526080 + 0.850435i 0.676339π0.676339\pi
752752 2.02626 + 1.16986i 0.0738901 + 0.0426605i
753753 −3.32640 + 3.32640i −0.121221 + 0.121221i
754754 0 0
755755 19.8498 24.8355i 0.722410 0.903855i
756756 15.4254 4.13321i 0.561015 0.150324i
757757 −10.1014 37.6990i −0.367143 1.37019i −0.864493 0.502645i 0.832360π-0.832360\pi
0.497350 0.867550i 0.334306π-0.334306\pi
758758 39.7186 + 10.6426i 1.44265 + 0.386556i
759759 1.27119 1.27119i 0.0461412 0.0461412i
760760 6.46463 + 0.981575i 0.234497 + 0.0356055i
761761 −15.7109 4.20973i −0.569521 0.152603i −0.0374441 0.999299i 0.511922π-0.511922\pi
−0.532077 + 0.846696i 0.678588π0.678588\pi
762762 2.34565i 0.0849739i
763763 2.20841 8.24188i 0.0799496 0.298376i
764764 22.6186 39.1766i 0.818313 1.41736i
765765 2.48665 + 6.35620i 0.0899052 + 0.229809i
766766 23.0560i 0.833045i
767767 0 0
768768 −15.4289 15.4289i −0.556741 0.556741i
769769 −10.3296 38.5504i −0.372493 1.39016i −0.856973 0.515362i 0.827658π-0.827658\pi
0.484479 0.874803i 0.339009π-0.339009\pi
770770 −32.6982 + 12.7921i −1.17836 + 0.460995i
771771 1.49702 0.864306i 0.0539139 0.0311272i
772772 46.2891 1.66598
773773 −17.8304 + 10.2944i −0.641313 + 0.370262i −0.785120 0.619343i 0.787399π-0.787399\pi
0.143807 + 0.989606i 0.454066π0.454066\pi
774774 −3.67753 + 13.7247i −0.132186 + 0.493325i
775775 −1.39494 0.880735i −0.0501077 0.0316369i
776776 5.01612 + 8.68818i 0.180068 + 0.311887i
777777 −3.23942 + 0.868001i −0.116214 + 0.0311394i
778778 −3.83988 + 6.65087i −0.137666 + 0.238445i
779779 0.610095 0.0218589
780780 0 0
781781 −66.4048 −2.37615
782782 −0.600577 + 1.04023i −0.0214766 + 0.0371986i
783783 38.2553 10.2505i 1.36713 0.366322i
784784 1.96257 + 3.39927i 0.0700917 + 0.121402i
785785 6.06575 7.58927i 0.216496 0.270873i
786786 5.90153 22.0248i 0.210501 0.785599i
787787 24.8106 14.3244i 0.884404 0.510611i 0.0122960 0.999924i 0.496086π-0.496086\pi
0.872108 + 0.489314i 0.162753π0.162753\pi
788788 47.1311 1.67898
789789 −26.1334 + 15.0881i −0.930375 + 0.537152i
790790 −51.5371 22.5521i −1.83361 0.802369i
791791 3.76666 + 14.0574i 0.133927 + 0.499822i
792792 −8.78163 8.78163i −0.312042 0.312042i
793793 0 0
794794 26.8568i 0.953111i
795795 −25.8927 11.3304i −0.918321 0.401848i
796796 −17.5631 + 30.4202i −0.622508 + 1.07822i
797797 2.27363 8.48530i 0.0805361 0.300565i −0.913895 0.405950i 0.866941π-0.866941\pi
0.994432 + 0.105385i 0.0336075π0.0336075\pi
798798 6.96002i 0.246382i
799799 −9.95859 2.66840i −0.352310 0.0944011i
800800 21.8667 + 23.6698i 0.773106 + 0.836852i
801801 4.83124 4.83124i 0.170703 0.170703i
802802 −8.86190 2.37454i −0.312924 0.0838479i
803803 10.3855 + 38.7592i 0.366496 + 1.36778i
804804 35.7433 9.57739i 1.26057 0.337768i
805805 0.369546 + 0.295361i 0.0130248 + 0.0104101i
806806 0 0
807807 −34.2536 + 34.2536i −1.20578 + 1.20578i
808808 17.9331 + 10.3537i 0.630884 + 0.364241i
809809 −0.820571 0.473757i −0.0288497 0.0166564i 0.485506 0.874233i 0.338635π-0.338635\pi
−0.514356 + 0.857577i 0.671969π0.671969\pi
810810 −32.6620 44.3563i −1.14762 1.55852i
811811 −28.8041 28.8041i −1.01145 1.01145i −0.999934 0.0115151i 0.996335π-0.996335\pi
−0.0115151 0.999934i 0.503665π-0.503665\pi
812812 19.0158 + 32.9363i 0.667324 + 1.15584i
813813 13.0302 + 22.5690i 0.456991 + 0.791531i
814814 −11.4896 11.4896i −0.402711 0.402711i
815815 12.2046 + 16.5743i 0.427509 + 0.580574i
816816 −4.05261 2.33978i −0.141870 0.0819086i
817817 7.03139 + 4.05958i 0.245997 + 0.142027i
818818 −11.0440 + 11.0440i −0.386145 + 0.386145i
819819 0 0
820820 −2.68133 2.14306i −0.0936361 0.0748390i
821821 1.29968 0.348249i 0.0453592 0.0121540i −0.236068 0.971737i 0.575859π-0.575859\pi
0.281427 + 0.959583i 0.409192π0.409192\pi
822822 −4.40224 16.4294i −0.153546 0.573041i
823823 31.9429 + 8.55907i 1.11346 + 0.298350i 0.768234 0.640169i 0.221136π-0.221136\pi
0.345225 + 0.938520i 0.387803π0.387803\pi
824824 −2.58211 + 2.58211i −0.0899520 + 0.0899520i
825825 36.8214 + 39.8575i 1.28196 + 1.38766i
826826 0.00638537 + 0.00171095i 0.000222175 + 5.95317e-5i
827827 26.4195i 0.918697i −0.888256 0.459349i 0.848083π-0.848083\pi
0.888256 0.459349i 0.151917π-0.151917\pi
828828 −0.124552 + 0.464834i −0.00432848 + 0.0161541i
829829 −1.23034 + 2.13101i −0.0427314 + 0.0740130i −0.886600 0.462537i 0.846939π-0.846939\pi
0.843869 + 0.536550i 0.180273π0.180273\pi
830830 12.2435 + 5.35766i 0.424980 + 0.185967i
831831 24.2940i 0.842748i
832832 0 0
833833 −12.2301 12.2301i −0.423747 0.423747i
834834 1.71093 + 6.38526i 0.0592445 + 0.221104i
835835 25.8907 + 11.3295i 0.895985 + 0.392074i
836836 −17.6747 + 10.2045i −0.611292 + 0.352929i
837837 −1.34551 −0.0465075
838838 41.3802 23.8909i 1.42946 0.825297i
839839 −13.0306 + 48.6308i −0.449866 + 1.67892i 0.252893 + 0.967494i 0.418618π0.418618\pi
−0.702759 + 0.711428i 0.748049π0.748049\pi
840840 8.50096 10.6361i 0.293311 0.366981i
841841 32.6597 + 56.5682i 1.12619 + 1.95063i
842842 −9.70754 + 2.60113i −0.334544 + 0.0896408i
843843 −9.04093 + 15.6594i −0.311386 + 0.539337i
844844 9.76228 0.336032
845845 0 0
846846 −6.82488 −0.234644
847847 12.0286 20.8342i 0.413308 0.715870i
848848 4.49261 1.20379i 0.154277 0.0413384i
849849 27.1730 + 47.0651i 0.932576 + 1.61527i
850850 −30.6565 19.3559i −1.05151 0.663900i
851851 −0.0566632 + 0.211470i −0.00194239 + 0.00724909i
852852 64.1371 37.0296i 2.19730 1.26861i
853853 −42.9612 −1.47096 −0.735481 0.677545i 0.763044π-0.763044\pi
−0.735481 + 0.677545i 0.763044π0.763044\pi
854854 −3.46543 + 2.00077i −0.118585 + 0.0684649i
855855 2.40431 0.940605i 0.0822255 0.0321680i
856856 9.02166 + 33.6693i 0.308354 + 1.15079i
857857 −29.0789 29.0789i −0.993316 0.993316i 0.00666151 0.999978i 0.497880π-0.497880\pi
−0.999978 + 0.00666151i 0.997880π0.997880\pi
858858 0 0
859859 42.1283i 1.43740i 0.695321 + 0.718700i 0.255262π0.255262\pi
−0.695321 + 0.718700i 0.744738π0.744738\pi
860860 −16.6426 42.5406i −0.567508 1.45062i
861861 0.635216 1.10023i 0.0216481 0.0374956i
862862 −20.8810 + 77.9289i −0.711209 + 2.65427i
863863 6.80768i 0.231736i −0.993265 0.115868i 0.963035π-0.963035\pi
0.993265 0.115868i 0.0369650π-0.0369650\pi
864864 25.3867 + 6.80234i 0.863672 + 0.231420i
865865 30.3212 + 4.60391i 1.03095 + 0.156537i
866866 12.8806 12.8806i 0.437702 0.437702i
867867 −12.7075 3.40497i −0.431570 0.115639i
868868 −0.334410 1.24803i −0.0113506 0.0423610i
869869 58.9734 15.8019i 2.00054 0.536042i
870870 60.6323 75.8612i 2.05563 2.57194i
871871 0 0
872872 −11.3361 + 11.3361i −0.383888 + 0.383888i
873873 3.43044 + 1.98056i 0.116103 + 0.0670320i
874874 0.393479 + 0.227175i 0.0133096 + 0.00768432i
875875 −9.34949 + 10.7929i −0.316071 + 0.364867i
876876 −31.6443 31.6443i −1.06916 1.06916i
877877 23.8407 + 41.2933i 0.805043 + 1.39437i 0.916262 + 0.400579i 0.131191π0.131191\pi
−0.111219 + 0.993796i 0.535476π0.535476\pi
878878 −32.2621 55.8796i −1.08879 1.88585i
879879 36.7017 + 36.7017i 1.23792 + 1.23792i
880880 −8.82845 1.34049i −0.297607 0.0451880i
881881 −4.43737 2.56192i −0.149499 0.0863133i 0.423385 0.905950i 0.360842π-0.360842\pi
−0.572884 + 0.819637i 0.694175π0.694175\pi
882882 −9.91554 5.72474i −0.333873 0.192762i
883883 14.8283 14.8283i 0.499014 0.499014i −0.412117 0.911131i 0.635211π-0.635211\pi
0.911131 + 0.412117i 0.135211π0.135211\pi
884884 0 0
885885 −0.00113283 0.0101533i −3.80796e−5 0.000341301i
886886 52.7568 14.1361i 1.77240 0.474913i
887887 −2.72597 10.1735i −0.0915293 0.341592i 0.904941 0.425537i 0.139915π-0.139915\pi
−0.996470 + 0.0839449i 0.973248π0.973248\pi
888888 6.08644 + 1.63086i 0.204248 + 0.0547280i
889889 −0.473700 + 0.473700i −0.0158874 + 0.0158874i
890890 −5.44825 + 35.8820i −0.182626 + 1.20277i
891891 57.7457 + 15.4729i 1.93455 + 0.518362i
892892 36.4179i 1.21936i
893893 −1.00935 + 3.76695i −0.0337767 + 0.126056i
894894 38.4949 66.6751i 1.28746 2.22995i
895895 11.3329 25.8985i 0.378818 0.865691i
896896 21.0349i 0.702725i
897897 0 0
898898 −14.5886 14.5886i −0.486828 0.486828i
899899 −0.829344 3.09515i −0.0276602 0.103229i
900900 −13.8708 4.31163i −0.462361 0.143721i
901901 −17.7490 + 10.2474i −0.591307 + 0.341391i
902902 6.15528 0.204948
903903 14.6418 8.45347i 0.487250 0.281314i
904904 7.07704 26.4119i 0.235379 0.878446i
905905 −2.02476 18.1476i −0.0673053 0.603245i
906906 −31.7921 55.0656i −1.05622 1.82943i
907907 −20.8031 + 5.57417i −0.690755 + 0.185087i −0.587086 0.809525i 0.699725π-0.699725\pi
−0.103669 + 0.994612i 0.533058π0.533058\pi
908908 −42.4147 + 73.4645i −1.40758 + 2.43800i
909909 8.17608 0.271184
910910 0 0
911911 −16.6400 −0.551309 −0.275654 0.961257i 0.588895π-0.588895\pi
−0.275654 + 0.961257i 0.588895π0.588895\pi
912912 −0.885047 + 1.53295i −0.0293068 + 0.0507609i
913913 −14.0102 + 3.75401i −0.463669 + 0.124240i
914914 −24.1734 41.8696i −0.799586 1.38492i
915915 4.83077 + 3.86101i 0.159700 + 0.127641i
916916 14.4774 54.0305i 0.478347 1.78522i
917917 −5.63968 + 3.25607i −0.186239 + 0.107525i
918918 −29.5701 −0.975958
919919 5.95358 3.43730i 0.196390 0.113386i −0.398580 0.917133i 0.630497π-0.630497\pi
0.594971 + 0.803747i 0.297164π0.297164\pi
920920 −0.323833 0.827758i −0.0106765 0.0272904i
921921 −7.56111 28.2184i −0.249147 0.929829i
922922 −8.08349 8.08349i −0.266216 0.266216i
923923 0 0
924924 42.4987i 1.39810i
925925 −6.31033 1.96152i −0.207482 0.0644942i
926926 −22.5973 + 39.1396i −0.742593 + 1.28621i
927927 −0.373170 + 1.39269i −0.0122565 + 0.0457419i
928928 62.5915i 2.05467i
929929 −42.9399 11.5057i −1.40881 0.377490i −0.527312 0.849672i 0.676800π-0.676800\pi
−0.881501 + 0.472182i 0.843467π0.843467\pi
930930 −2.65674 + 1.95630i −0.0871178 + 0.0641497i
931931 −4.62617 + 4.62617i −0.151617 + 0.151617i
932932 −68.4993 18.3543i −2.24377 0.601216i
933933 −16.3795 61.1290i −0.536240 2.00127i
934934 −65.9535 + 17.6722i −2.15806 + 0.578252i
935935 39.1054 4.36307i 1.27888 0.142688i
936936 0 0
937937 13.1724 13.1724i 0.430323 0.430323i −0.458415 0.888738i 0.651583π-0.651583\pi
0.888738 + 0.458415i 0.151583π0.151583\pi
938938 −15.1225 8.73096i −0.493766 0.285076i
939939 29.1675 + 16.8399i 0.951846 + 0.549548i
940940 17.6681 13.0100i 0.576270 0.424339i
941941 −40.0251 40.0251i −1.30478 1.30478i −0.925130 0.379650i 0.876045π-0.876045\pi
−0.379650 0.925130i 0.623955π-0.623955\pi
942942 −9.71510 16.8270i −0.316535 0.548255i
943943 −0.0414669 0.0718228i −0.00135035 0.00233887i
944944 0.00118881 + 0.00118881i 3.86925e−5 + 3.86925e-5i
945945 −1.74830 + 11.5143i −0.0568723 + 0.374559i
946946 70.9401 + 40.9573i 2.30646 + 1.33164i
947947 51.0040 + 29.4472i 1.65741 + 0.956904i 0.973905 + 0.226955i 0.0728770π0.0728770\pi
0.683501 + 0.729949i 0.260456π0.260456\pi
948948 −48.1479 + 48.1479i −1.56377 + 1.56377i
949949 0 0
950950 −7.32157 + 11.5962i −0.237543 + 0.376229i
951951 29.8668 8.00278i 0.968497 0.259508i
952952 −2.55544 9.53703i −0.0828223 0.309097i
953953 17.2456 + 4.62094i 0.558640 + 0.149687i 0.527081 0.849815i 0.323286π-0.323286\pi
0.0315583 + 0.999502i 0.489953π0.489953\pi
954954 −9.59336 + 9.59336i −0.310596 + 0.310596i
955955 19.5616 + 26.5654i 0.632999 + 0.859638i
956956 10.9650 + 2.93807i 0.354634 + 0.0950240i
957957 105.398i 3.40703i
958958 18.1230 67.6360i 0.585528 2.18522i
959959 −2.42886 + 4.20691i −0.0784320 + 0.135848i
960960 53.9673 21.1129i 1.74179 0.681417i
961961 30.8911i 0.996488i
962962 0 0
963963 9.73187 + 9.73187i 0.313605 + 0.313605i
964964 −16.5146 61.6333i −0.531899 1.98507i
965965 −13.5331 + 30.9263i −0.435645 + 0.995554i
966966 0.819363 0.473059i 0.0263626 0.0152204i
967967 23.2093 0.746360 0.373180 0.927759i 0.378267π-0.378267\pi
0.373180 + 0.927759i 0.378267π0.378267\pi
968968 −39.1446 + 22.6001i −1.25815 + 0.726395i
969969 2.01875 7.53407i 0.0648515 0.242029i
970970 −20.9115 + 2.33314i −0.671429 + 0.0749127i
971971 −21.1932 36.7078i −0.680123 1.17801i −0.974943 0.222455i 0.928593π-0.928593\pi
0.294820 0.955553i 0.404740π-0.404740\pi
972972 −28.1691 + 7.54788i −0.903523 + 0.242098i
973973 0.943975 1.63501i 0.0302624 0.0524161i
974974 −43.7367 −1.40141
975975 0 0
976976 −1.01768 −0.0325752
977977 −12.2049 + 21.1395i −0.390469 + 0.676312i −0.992511 0.122152i 0.961020π-0.961020\pi
0.602043 + 0.798464i 0.294354π0.294354\pi
978978 39.7618 10.6541i 1.27144 0.340682i
979979 −19.6945 34.1118i −0.629438 1.09022i
980980 36.5819 4.08152i 1.16857 0.130379i
981981 −1.63831 + 6.11424i −0.0523071 + 0.195213i
982982 −68.8352 + 39.7420i −2.19662 + 1.26822i
983983 4.47004 0.142572 0.0712860 0.997456i 0.477290π-0.477290\pi
0.0712860 + 0.997456i 0.477290π0.477290\pi
984984 −2.06718 + 1.19349i −0.0658992 + 0.0380469i
985985 −13.7792 + 31.4889i −0.439043 + 1.00332i
986986 −18.2264 68.0220i −0.580448 2.16626i
987987 5.74230 + 5.74230i 0.182779 + 0.182779i
988988 0 0
989989 1.10369i 0.0350952i
990990 24.2572 9.48982i 0.770944 0.301606i
991991 24.7675 42.8986i 0.786766 1.36272i −0.141172 0.989985i 0.545087π-0.545087\pi
0.927938 0.372734i 0.121580π-0.121580\pi
992992 0.550363 2.05398i 0.0174740 0.0652140i
993993 33.9020i 1.07585i
994994 −33.7570 9.04516i −1.07071 0.286895i
995995 −15.1894 20.6278i −0.481536 0.653945i
996996 11.4384 11.4384i 0.362439 0.362439i
997997 33.8485 + 9.06967i 1.07199 + 0.287239i 0.751311 0.659948i 0.229422π-0.229422\pi
0.320681 + 0.947187i 0.396088π0.396088\pi
998998 −7.78071 29.0380i −0.246294 0.919182i
999999 −5.20597 + 1.39494i −0.164710 + 0.0441338i
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.o.f.488.1 20
5.2 odd 4 845.2.t.e.657.1 20
13.2 odd 12 845.2.t.e.418.1 20
13.3 even 3 845.2.o.g.258.1 20
13.4 even 6 845.2.k.e.268.1 20
13.5 odd 4 845.2.t.g.188.5 20
13.6 odd 12 845.2.f.d.408.1 20
13.7 odd 12 845.2.f.e.408.10 20
13.8 odd 4 65.2.t.a.58.1 yes 20
13.9 even 3 845.2.k.d.268.10 20
13.10 even 6 65.2.o.a.63.5 yes 20
13.11 odd 12 845.2.t.f.418.5 20
13.12 even 2 845.2.o.e.488.5 20
39.8 even 4 585.2.dp.a.253.5 20
39.23 odd 6 585.2.cf.a.388.1 20
65.2 even 12 inner 845.2.o.f.587.1 20
65.7 even 12 845.2.k.e.577.1 20
65.8 even 4 325.2.s.b.32.1 20
65.12 odd 4 845.2.t.f.657.5 20
65.17 odd 12 845.2.f.e.437.1 20
65.22 odd 12 845.2.f.d.437.10 20
65.23 odd 12 325.2.x.b.232.5 20
65.32 even 12 845.2.k.d.577.10 20
65.34 odd 4 325.2.x.b.318.5 20
65.37 even 12 845.2.o.e.587.5 20
65.42 odd 12 845.2.t.g.427.5 20
65.47 even 4 65.2.o.a.32.5 20
65.49 even 6 325.2.s.b.193.1 20
65.57 even 4 845.2.o.g.357.1 20
65.62 odd 12 65.2.t.a.37.1 yes 20
195.47 odd 4 585.2.cf.a.487.1 20
195.62 even 12 585.2.dp.a.37.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.32.5 20 65.47 even 4
65.2.o.a.63.5 yes 20 13.10 even 6
65.2.t.a.37.1 yes 20 65.62 odd 12
65.2.t.a.58.1 yes 20 13.8 odd 4
325.2.s.b.32.1 20 65.8 even 4
325.2.s.b.193.1 20 65.49 even 6
325.2.x.b.232.5 20 65.23 odd 12
325.2.x.b.318.5 20 65.34 odd 4
585.2.cf.a.388.1 20 39.23 odd 6
585.2.cf.a.487.1 20 195.47 odd 4
585.2.dp.a.37.5 20 195.62 even 12
585.2.dp.a.253.5 20 39.8 even 4
845.2.f.d.408.1 20 13.6 odd 12
845.2.f.d.437.10 20 65.22 odd 12
845.2.f.e.408.10 20 13.7 odd 12
845.2.f.e.437.1 20 65.17 odd 12
845.2.k.d.268.10 20 13.9 even 3
845.2.k.d.577.10 20 65.32 even 12
845.2.k.e.268.1 20 13.4 even 6
845.2.k.e.577.1 20 65.7 even 12
845.2.o.e.488.5 20 13.12 even 2
845.2.o.e.587.5 20 65.37 even 12
845.2.o.f.488.1 20 1.1 even 1 trivial
845.2.o.f.587.1 20 65.2 even 12 inner
845.2.o.g.258.1 20 13.3 even 3
845.2.o.g.357.1 20 65.57 even 4
845.2.t.e.418.1 20 13.2 odd 12
845.2.t.e.657.1 20 5.2 odd 4
845.2.t.f.418.5 20 13.11 odd 12
845.2.t.f.657.5 20 65.12 odd 4
845.2.t.g.188.5 20 13.5 odd 4
845.2.t.g.427.5 20 65.42 odd 12