Properties

Label 841.2.e.l.196.7
Level 841841
Weight 22
Character 841.196
Analytic conductor 6.7156.715
Analytic rank 00
Dimension 7272
Inner twists 1212

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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] = [841,2,Mod(63,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([11])) 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("841.63"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 841=292 841 = 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 841.e (of order 1414, degree 66, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [72,0,0,16,-4,-6,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.715418809996.71541880999
Analytic rank: 00
Dimension: 7272
Relative dimension: 1212 over Q(ζ14)\Q(\zeta_{14})
Twist minimal: yes
Sato-Tate group: SU(2)[C14]\mathrm{SU}(2)[C_{14}]

Embedding invariants

Embedding label 196.7
Character χ\chi == 841.196
Dual form 841.2.e.l.236.7

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+(0.4984370.113765i)q2+(1.168262.42591i)q3+(1.56644+0.754358i)q4+(0.490395+2.14856i)q5+(0.3063191.34207i)q6+(1.17312+0.564943i)q7+(1.49438+1.19173i)q8+(2.649753.32268i)q9+(0.488862+1.01513i)q10+(3.91583+3.12277i)q11+4.68133iq12+(1.95640+2.45325i)q13+(0.648996+0.148129i)q14+(5.78512+1.32042i)q15+(1.558741.95460i)q161.37659iq17+(1.698741.35470i)q18+(2.58255+5.36272i)q19+(2.388962.99566i)q20+(2.741002.18588i)q21+(2.30706+1.11102i)q22+(0.192554+0.843634i)q23+(1.14521+5.01749i)q24+(0.1290210.0621331i)q25+(0.696049+1.44536i)q26+(3.28098+0.748862i)q272.26379q28+3.03374q30+(2.675200.610597i)q31+(2.213214.59578i)q32+(12.15035.85126i)q33+(0.1566070.686142i)q34+(0.638524+2.79756i)q35+(6.65717+3.20593i)q36+(4.612803.67858i)q37+(1.89733+2.37918i)q38+(3.66578+7.61208i)q39+(3.293352.62636i)q40+1.90869iq41+(1.117541.40135i)q42+(10.73812.45090i)q43+(8.489601.93770i)q44+(5.839567.32258i)q45+0.442405iq46+(2.24903+1.79354i)q47+(2.920686.06485i)q48+(3.307394.14733i)q49+(0.05724010.0456475i)q50+(3.339481.60821i)q51+(1.213965.31869i)q52+(1.29129+5.65752i)q53+(1.55017+0.746522i)q54+(4.78915+9.94478i)q55+(2.42635+0.553798i)q56+16.0266q574.35304q59+(10.0581+2.29570i)q60+(2.35836+4.89717i)q61+(1.263960.608689i)q62+(1.231345.39485i)q63+(0.532309+2.33220i)q64+(6.230363.00038i)q65+(5.390474.29876i)q66+(1.47317+1.84730i)q67+(1.03844+2.15634i)q68+(1.82163+1.45270i)q69+1.46705iq70+(9.7200512.1886i)q71+(7.91950+1.80757i)q72+(3.31130+0.755782i)q73+(1.880702.35832i)q740.385580iq75+(8.090836.45222i)q76+(2.82954+5.87559i)q77+(2.69315+3.37711i)q78+(1.65445+1.31938i)q79+(4.96397+2.39052i)q80+(0.8207013.59573i)q81+(0.217143+0.951364i)q82+(5.72931+2.75909i)q83+(2.64468+5.49174i)q84+(2.957680.675070i)q855.63110q869.57325q88+(11.63362.65530i)q89+(2.077604.31419i)q90+(3.68103+1.77269i)q91+(0.3347781.46676i)q92+(1.644077.20313i)q93+(1.32504+0.638106i)q94+(10.2557+8.17862i)q95+(8.5633610.7381i)q96+(4.9565010.2923i)q97+(2.120351.69092i)q9821.2856iq99+O(q100)q+(0.498437 - 0.113765i) q^{2} +(1.16826 - 2.42591i) q^{3} +(-1.56644 + 0.754358i) q^{4} +(0.490395 + 2.14856i) q^{5} +(0.306319 - 1.34207i) q^{6} +(1.17312 + 0.564943i) q^{7} +(-1.49438 + 1.19173i) q^{8} +(-2.64975 - 3.32268i) q^{9} +(0.488862 + 1.01513i) q^{10} +(3.91583 + 3.12277i) q^{11} +4.68133i q^{12} +(-1.95640 + 2.45325i) q^{13} +(0.648996 + 0.148129i) q^{14} +(5.78512 + 1.32042i) q^{15} +(1.55874 - 1.95460i) q^{16} -1.37659i q^{17} +(-1.69874 - 1.35470i) q^{18} +(2.58255 + 5.36272i) q^{19} +(-2.38896 - 2.99566i) q^{20} +(2.74100 - 2.18588i) q^{21} +(2.30706 + 1.11102i) q^{22} +(-0.192554 + 0.843634i) q^{23} +(1.14521 + 5.01749i) q^{24} +(0.129021 - 0.0621331i) q^{25} +(-0.696049 + 1.44536i) q^{26} +(-3.28098 + 0.748862i) q^{27} -2.26379 q^{28} +3.03374 q^{30} +(2.67520 - 0.610597i) q^{31} +(2.21321 - 4.59578i) q^{32} +(12.1503 - 5.85126i) q^{33} +(-0.156607 - 0.686142i) q^{34} +(-0.638524 + 2.79756i) q^{35} +(6.65717 + 3.20593i) q^{36} +(4.61280 - 3.67858i) q^{37} +(1.89733 + 2.37918i) q^{38} +(3.66578 + 7.61208i) q^{39} +(-3.29335 - 2.62636i) q^{40} +1.90869i q^{41} +(1.11754 - 1.40135i) q^{42} +(-10.7381 - 2.45090i) q^{43} +(-8.48960 - 1.93770i) q^{44} +(5.83956 - 7.32258i) q^{45} +0.442405i q^{46} +(2.24903 + 1.79354i) q^{47} +(-2.92068 - 6.06485i) q^{48} +(-3.30739 - 4.14733i) q^{49} +(0.0572401 - 0.0456475i) q^{50} +(-3.33948 - 1.60821i) q^{51} +(1.21396 - 5.31869i) q^{52} +(1.29129 + 5.65752i) q^{53} +(-1.55017 + 0.746522i) q^{54} +(-4.78915 + 9.94478i) q^{55} +(-2.42635 + 0.553798i) q^{56} +16.0266 q^{57} -4.35304 q^{59} +(-10.0581 + 2.29570i) q^{60} +(-2.35836 + 4.89717i) q^{61} +(1.26396 - 0.608689i) q^{62} +(-1.23134 - 5.39485i) q^{63} +(-0.532309 + 2.33220i) q^{64} +(-6.23036 - 3.00038i) q^{65} +(5.39047 - 4.29876i) q^{66} +(1.47317 + 1.84730i) q^{67} +(1.03844 + 2.15634i) q^{68} +(1.82163 + 1.45270i) q^{69} +1.46705i q^{70} +(9.72005 - 12.1886i) q^{71} +(7.91950 + 1.80757i) q^{72} +(3.31130 + 0.755782i) q^{73} +(1.88070 - 2.35832i) q^{74} -0.385580i q^{75} +(-8.09083 - 6.45222i) q^{76} +(2.82954 + 5.87559i) q^{77} +(2.69315 + 3.37711i) q^{78} +(-1.65445 + 1.31938i) q^{79} +(4.96397 + 2.39052i) q^{80} +(0.820701 - 3.59573i) q^{81} +(0.217143 + 0.951364i) q^{82} +(-5.72931 + 2.75909i) q^{83} +(-2.64468 + 5.49174i) q^{84} +(2.95768 - 0.675070i) q^{85} -5.63110 q^{86} -9.57325 q^{88} +(11.6336 - 2.65530i) q^{89} +(2.07760 - 4.31419i) q^{90} +(-3.68103 + 1.77269i) q^{91} +(-0.334778 - 1.46676i) q^{92} +(1.64407 - 7.20313i) q^{93} +(1.32504 + 0.638106i) q^{94} +(-10.2557 + 8.17862i) q^{95} +(-8.56336 - 10.7381i) q^{96} +(-4.95650 - 10.2923i) q^{97} +(-2.12035 - 1.69092i) q^{98} -21.2856i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 72q+16q44q56q6+8q7+12q912q138q16+10q208q22+10q23+20q2412q25+60q28+312q30+54q338q35+42q36+82q38+74q96+O(q100) 72 q + 16 q^{4} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 12 q^{9} - 12 q^{13} - 8 q^{16} + 10 q^{20} - 8 q^{22} + 10 q^{23} + 20 q^{24} - 12 q^{25} + 60 q^{28} + 312 q^{30} + 54 q^{33} - 8 q^{35} + 42 q^{36} + 82 q^{38}+ \cdots - 74 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/841Z)×\left(\mathbb{Z}/841\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(1314)e\left(\frac{13}{14}\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 0.498437 0.113765i 0.352448 0.0804440i −0.0426314 0.999091i 0.513574π-0.513574\pi
0.395080 + 0.918647i 0.370717π0.370717\pi
33 1.16826 2.42591i 0.674494 1.40060i −0.229608 0.973283i 0.573744π-0.573744\pi
0.904102 0.427318i 0.140541π-0.140541\pi
44 −1.56644 + 0.754358i −0.783220 + 0.377179i
55 0.490395 + 2.14856i 0.219311 + 0.960865i 0.957989 + 0.286806i 0.0925936π0.0925936\pi
−0.738677 + 0.674059i 0.764549π0.764549\pi
66 0.306319 1.34207i 0.125054 0.547898i
77 1.17312 + 0.564943i 0.443396 + 0.213528i 0.642241 0.766503i 0.278005π-0.278005\pi
−0.198845 + 0.980031i 0.563719π0.563719\pi
88 −1.49438 + 1.19173i −0.528345 + 0.421341i
99 −2.64975 3.32268i −0.883251 1.10756i
1010 0.488862 + 1.01513i 0.154592 + 0.321013i
1111 3.91583 + 3.12277i 1.18067 + 0.941550i 0.999125 0.0418330i 0.0133197π-0.0133197\pi
0.181542 + 0.983383i 0.441891π0.441891\pi
1212 4.68133i 1.35138i
1313 −1.95640 + 2.45325i −0.542608 + 0.680409i −0.975237 0.221164i 0.929015π-0.929015\pi
0.432629 + 0.901572i 0.357586π0.357586\pi
1414 0.648996 + 0.148129i 0.173451 + 0.0395891i
1515 5.78512 + 1.32042i 1.49371 + 0.340930i
1616 1.55874 1.95460i 0.389685 0.488650i
1717 1.37659i 0.333871i −0.985968 0.166936i 0.946613π-0.946613\pi
0.985968 0.166936i 0.0533872π-0.0533872\pi
1818 −1.69874 1.35470i −0.400397 0.319306i
1919 2.58255 + 5.36272i 0.592478 + 1.23029i 0.954524 + 0.298133i 0.0963640π0.0963640\pi
−0.362046 + 0.932160i 0.617922π0.617922\pi
2020 −2.38896 2.99566i −0.534187 0.669850i
2121 2.74100 2.18588i 0.598136 0.476998i
2222 2.30706 + 1.11102i 0.491866 + 0.236870i
2323 −0.192554 + 0.843634i −0.0401503 + 0.175910i −0.991027 0.133659i 0.957327π-0.957327\pi
0.950877 + 0.309568i 0.100185π0.100185\pi
2424 1.14521 + 5.01749i 0.233765 + 1.02419i
2525 0.129021 0.0621331i 0.0258041 0.0124266i
2626 −0.696049 + 1.44536i −0.136506 + 0.283458i
2727 −3.28098 + 0.748862i −0.631425 + 0.144119i
2828 −2.26379 −0.427815
2929 0 0
3030 3.03374 0.553882
3131 2.67520 0.610597i 0.480480 0.109666i 0.0245809 0.999698i 0.492175π-0.492175\pi
0.455899 + 0.890031i 0.349318π0.349318\pi
3232 2.21321 4.59578i 0.391244 0.812427i
3333 12.1503 5.85126i 2.11509 1.01857i
3434 −0.156607 0.686142i −0.0268579 0.117672i
3535 −0.638524 + 2.79756i −0.107930 + 0.472873i
3636 6.65717 + 3.20593i 1.10953 + 0.534321i
3737 4.61280 3.67858i 0.758339 0.604755i −0.166089 0.986111i 0.553114π-0.553114\pi
0.924428 + 0.381356i 0.124543π0.124543\pi
3838 1.89733 + 2.37918i 0.307788 + 0.385954i
3939 3.66578 + 7.61208i 0.586995 + 1.21891i
4040 −3.29335 2.62636i −0.520724 0.415263i
4141 1.90869i 0.298088i 0.988831 + 0.149044i 0.0476196π0.0476196\pi
−0.988831 + 0.149044i 0.952380π0.952380\pi
4242 1.11754 1.40135i 0.172440 0.216233i
4343 −10.7381 2.45090i −1.63755 0.373759i −0.697978 0.716119i 0.745917π-0.745917\pi
−0.939569 + 0.342360i 0.888774π0.888774\pi
4444 −8.48960 1.93770i −1.27985 0.292119i
4545 5.83956 7.32258i 0.870511 1.09159i
4646 0.442405i 0.0652290i
4747 2.24903 + 1.79354i 0.328054 + 0.261615i 0.773641 0.633624i 0.218433π-0.218433\pi
−0.445587 + 0.895239i 0.647005π0.647005\pi
4848 −2.92068 6.06485i −0.421563 0.875385i
4949 −3.30739 4.14733i −0.472484 0.592476i
5050 0.0572401 0.0456475i 0.00809498 0.00645553i
5151 −3.33948 1.60821i −0.467620 0.225194i
5252 1.21396 5.31869i 0.168346 0.737570i
5353 1.29129 + 5.65752i 0.177373 + 0.777121i 0.982837 + 0.184476i 0.0590589π0.0590589\pi
−0.805464 + 0.592644i 0.798084π0.798084\pi
5454 −1.55017 + 0.746522i −0.210951 + 0.101589i
5555 −4.78915 + 9.94478i −0.645769 + 1.34095i
5656 −2.42635 + 0.553798i −0.324234 + 0.0740043i
5757 16.0266 2.12277
5858 0 0
5959 −4.35304 −0.566717 −0.283359 0.959014i 0.591449π-0.591449\pi
−0.283359 + 0.959014i 0.591449π0.591449\pi
6060 −10.0581 + 2.29570i −1.29850 + 0.296374i
6161 −2.35836 + 4.89717i −0.301956 + 0.627019i −0.995642 0.0932591i 0.970272π-0.970272\pi
0.693685 + 0.720278i 0.255986π0.255986\pi
6262 1.26396 0.608689i 0.160522 0.0773035i
6363 −1.23134 5.39485i −0.155134 0.679688i
6464 −0.532309 + 2.33220i −0.0665386 + 0.291525i
6565 −6.23036 3.00038i −0.772781 0.372152i
6666 5.39047 4.29876i 0.663521 0.529141i
6767 1.47317 + 1.84730i 0.179976 + 0.225683i 0.863634 0.504120i 0.168183π-0.168183\pi
−0.683657 + 0.729803i 0.739612π0.739612\pi
6868 1.03844 + 2.15634i 0.125929 + 0.261495i
6969 1.82163 + 1.45270i 0.219298 + 0.174885i
7070 1.46705i 0.175346i
7171 9.72005 12.1886i 1.15356 1.44651i 0.279863 0.960040i 0.409711π-0.409711\pi
0.873695 0.486475i 0.161718π-0.161718\pi
7272 7.91950 + 1.80757i 0.933322 + 0.213025i
7373 3.31130 + 0.755782i 0.387558 + 0.0884576i 0.411860 0.911247i 0.364879π-0.364879\pi
−0.0243021 + 0.999705i 0.507736π0.507736\pi
7474 1.88070 2.35832i 0.218626 0.274149i
7575 0.385580i 0.0445230i
7676 −8.09083 6.45222i −0.928082 0.740120i
7777 2.82954 + 5.87559i 0.322455 + 0.669586i
7878 2.69315 + 3.37711i 0.304939 + 0.382382i
7979 −1.65445 + 1.31938i −0.186141 + 0.148442i −0.712127 0.702051i 0.752268π-0.752268\pi
0.525986 + 0.850493i 0.323696π0.323696\pi
8080 4.96397 + 2.39052i 0.554989 + 0.267269i
8181 0.820701 3.59573i 0.0911890 0.399525i
8282 0.217143 + 0.951364i 0.0239794 + 0.105061i
8383 −5.72931 + 2.75909i −0.628874 + 0.302850i −0.721039 0.692894i 0.756335π-0.756335\pi
0.0921658 + 0.995744i 0.470621π0.470621\pi
8484 −2.64468 + 5.49174i −0.288559 + 0.599198i
8585 2.95768 0.675070i 0.320805 0.0732217i
8686 −5.63110 −0.607217
8787 0 0
8888 −9.57325 −1.02051
8989 11.6336 2.65530i 1.23316 0.281461i 0.444214 0.895921i 0.353483π-0.353483\pi
0.788949 + 0.614459i 0.210626π0.210626\pi
9090 2.07760 4.31419i 0.218998 0.454755i
9191 −3.68103 + 1.77269i −0.385877 + 0.185828i
9292 −0.334778 1.46676i −0.0349030 0.152920i
9393 1.64407 7.20313i 0.170482 0.746930i
9494 1.32504 + 0.638106i 0.136668 + 0.0658156i
9595 −10.2557 + 8.17862i −1.05221 + 0.839109i
9696 −8.56336 10.7381i −0.873994 1.09595i
9797 −4.95650 10.2923i −0.503256 1.04502i −0.985608 0.169045i 0.945932π-0.945932\pi
0.482352 0.875977i 0.339783π-0.339783\pi
9898 −2.12035 1.69092i −0.214187 0.170809i
9999 21.2856i 2.13929i
100100 −0.155233 + 0.194655i −0.0155233 + 0.0194655i
101101 0.950079 + 0.216849i 0.0945364 + 0.0215773i 0.269527 0.962993i 0.413133π-0.413133\pi
−0.174991 + 0.984570i 0.555990π0.555990\pi
102102 −1.84748 0.421674i −0.182927 0.0417520i
103103 −4.84899 + 6.08044i −0.477785 + 0.599124i −0.961058 0.276346i 0.910876π-0.910876\pi
0.483273 + 0.875470i 0.339448π0.339448\pi
104104 5.99760i 0.588113i
105105 6.04066 + 4.81727i 0.589508 + 0.470117i
106106 1.28726 + 2.67302i 0.125029 + 0.259626i
107107 −3.39760 4.26045i −0.328458 0.411874i 0.589993 0.807409i 0.299131π-0.299131\pi
−0.918451 + 0.395535i 0.870559π0.870559\pi
108108 4.57455 3.64808i 0.440186 0.351037i
109109 −7.11000 3.42400i −0.681015 0.327960i 0.0611961 0.998126i 0.480509π-0.480509\pi
−0.742211 + 0.670166i 0.766223π0.766223\pi
110110 −1.25572 + 5.50169i −0.119729 + 0.524565i
111111 −3.53498 15.4878i −0.335526 1.47003i
112112 2.93282 1.41237i 0.277126 0.133457i
113113 7.50659 15.5876i 0.706161 1.46636i −0.170555 0.985348i 0.554556π-0.554556\pi
0.876715 0.481009i 0.159730π-0.159730\pi
114114 7.98825 1.82326i 0.748168 0.170764i
115115 −1.90703 −0.177831
116116 0 0
117117 13.3353 1.23285
118118 −2.16972 + 0.495224i −0.199739 + 0.0455890i
119119 0.777692 1.61489i 0.0712909 0.148037i
120120 −10.2188 + 4.92111i −0.932843 + 0.449233i
121121 3.13430 + 13.7322i 0.284936 + 1.24839i
122122 −0.618365 + 2.70923i −0.0559841 + 0.245282i
123123 4.63032 + 2.22984i 0.417502 + 0.201058i
124124 −3.72993 + 2.97452i −0.334958 + 0.267120i
125125 7.06705 + 8.86180i 0.632096 + 0.792623i
126126 −1.22749 2.54891i −0.109354 0.227075i
127127 4.31272 + 3.43928i 0.382692 + 0.305187i 0.795875 0.605462i 0.207011π-0.207011\pi
−0.413183 + 0.910648i 0.635583π0.635583\pi
128128 11.4249i 1.00983i
129129 −18.4906 + 23.1864i −1.62800 + 2.04145i
130130 −3.44678 0.786705i −0.302303 0.0689986i
131131 −0.0275831 0.00629566i −0.00240995 0.000550054i 0.221316 0.975202i 0.428965π-0.428965\pi
−0.223726 + 0.974652i 0.571822π0.571822\pi
132132 −14.6187 + 18.3313i −1.27240 + 1.59553i
133133 7.75009i 0.672018i
134134 0.944440 + 0.753166i 0.0815872 + 0.0650636i
135135 −3.21795 6.68215i −0.276957 0.575108i
136136 1.64052 + 2.05715i 0.140673 + 0.176399i
137137 −4.81191 + 3.83737i −0.411109 + 0.327849i −0.807110 0.590402i 0.798969π-0.798969\pi
0.396000 + 0.918250i 0.370398π0.370398\pi
138138 1.07323 + 0.516843i 0.0913598 + 0.0439966i
139139 −2.76107 + 12.0971i −0.234191 + 1.02606i 0.711931 + 0.702249i 0.247821π0.247821\pi
−0.946122 + 0.323809i 0.895036π0.895036\pi
140140 −1.11015 4.86388i −0.0938247 0.411073i
141141 6.97841 3.36062i 0.587688 0.283016i
142142 3.45820 7.18103i 0.290206 0.602619i
143143 −15.3219 + 3.49711i −1.28128 + 0.292443i
144144 −10.6248 −0.885400
145145 0 0
146146 1.73646 0.143710
147147 −13.9249 + 3.17828i −1.14851 + 0.262140i
148148 −4.45070 + 9.24198i −0.365845 + 0.759686i
149149 −18.7471 + 9.02813i −1.53582 + 0.739614i −0.994844 0.101422i 0.967661π-0.967661\pi
−0.540980 + 0.841035i 0.681947π0.681947\pi
150150 −0.0438655 0.192187i −0.00358161 0.0156920i
151151 4.45672 19.5262i 0.362683 1.58902i −0.383672 0.923469i 0.625341π-0.625341\pi
0.746355 0.665548i 0.231802π-0.231802\pi
152152 −10.2503 4.93626i −0.831405 0.400384i
153153 −4.57396 + 3.64761i −0.369783 + 0.294892i
154154 2.07878 + 2.60671i 0.167513 + 0.210055i
155155 2.62381 + 5.44840i 0.210749 + 0.437626i
156156 −11.4845 9.15855i −0.919493 0.733271i
157157 11.7893i 0.940890i 0.882429 + 0.470445i 0.155907π0.155907\pi
−0.882429 + 0.470445i 0.844093π0.844093\pi
158158 −0.674542 + 0.845848i −0.0536636 + 0.0672921i
159159 15.2332 + 3.47688i 1.20807 + 0.275735i
160160 10.9597 + 2.50147i 0.866437 + 0.197759i
161161 −0.702494 + 0.880899i −0.0553643 + 0.0694246i
162162 1.88561i 0.148148i
163163 1.95975 + 1.56285i 0.153500 + 0.122412i 0.697228 0.716849i 0.254416π-0.254416\pi
−0.543728 + 0.839261i 0.682988π0.682988\pi
164164 −1.43984 2.98985i −0.112432 0.233468i
165165 18.5302 + 23.2361i 1.44257 + 1.80893i
166166 −2.54181 + 2.02703i −0.197283 + 0.157328i
167167 −2.40640 1.15886i −0.186213 0.0896754i 0.338454 0.940983i 0.390096π-0.390096\pi
−0.524667 + 0.851307i 0.675810π0.675810\pi
168168 −1.49113 + 6.53308i −0.115043 + 0.504038i
169169 0.701848 + 3.07500i 0.0539883 + 0.236538i
170170 1.39742 0.672961i 0.107177 0.0516137i
171171 10.9755 22.7909i 0.839319 1.74286i
172172 18.6695 4.26118i 1.42353 0.324912i
173173 −23.5982 −1.79414 −0.897071 0.441887i 0.854309π-0.854309\pi
−0.897071 + 0.441887i 0.854309π0.854309\pi
174174 0 0
175175 0.186458 0.0140949
176176 12.2075 2.78629i 0.920177 0.210024i
177177 −5.08547 + 10.5601i −0.382247 + 0.793745i
178178 5.49656 2.64700i 0.411984 0.198401i
179179 −4.66369 20.4329i −0.348580 1.52723i −0.780406 0.625273i 0.784988π-0.784988\pi
0.431826 0.901957i 0.357869π-0.357869\pi
180180 −3.62348 + 15.8755i −0.270078 + 1.18329i
181181 −8.19331 3.94569i −0.609004 0.293281i 0.103850 0.994593i 0.466884π-0.466884\pi
−0.712854 + 0.701312i 0.752598π0.752598\pi
182182 −1.63309 + 1.30235i −0.121053 + 0.0965364i
183183 9.12495 + 11.4423i 0.674536 + 0.845841i
184184 −0.717636 1.49019i −0.0529048 0.109858i
185185 10.1657 + 8.10691i 0.747401 + 0.596032i
186186 3.77735i 0.276969i
187187 4.29876 5.39047i 0.314356 0.394190i
188188 −4.87594 1.11290i −0.355614 0.0811666i
189189 −4.27204 0.975064i −0.310745 0.0709255i
190190 −4.18136 + 5.24327i −0.303348 + 0.380386i
191191 19.2700i 1.39433i 0.716912 + 0.697163i 0.245555π0.245555\pi
−0.716912 + 0.697163i 0.754445π0.754445\pi
192192 5.03583 + 4.01594i 0.363430 + 0.289826i
193193 −2.30742 4.79140i −0.166092 0.344893i 0.801266 0.598308i 0.204160π-0.204160\pi
−0.967357 + 0.253416i 0.918446π0.918446\pi
194194 −3.64140 4.56618i −0.261438 0.327832i
195195 −14.5573 + 11.6091i −1.04247 + 0.831344i
196196 8.30940 + 4.00160i 0.593529 + 0.285828i
197197 2.21912 9.72260i 0.158106 0.692706i −0.832278 0.554358i 0.812964π-0.812964\pi
0.990384 0.138348i 0.0441792π-0.0441792\pi
198198 −2.42156 10.6096i −0.172093 0.753988i
199199 19.9927 9.62796i 1.41724 0.682508i 0.440664 0.897672i 0.354743π-0.354743\pi
0.976578 + 0.215165i 0.0690288π0.0690288\pi
200200 −0.118760 + 0.246609i −0.00839763 + 0.0174379i
201201 6.20242 1.41566i 0.437485 0.0998531i
202202 0.498225 0.0350550
203203 0 0
204204 6.44425 0.451188
205205 −4.10094 + 0.936013i −0.286422 + 0.0653740i
206206 −1.72518 + 3.58236i −0.120199 + 0.249595i
207207 3.31335 1.59563i 0.230294 0.110904i
208208 1.74560 + 7.64796i 0.121035 + 0.530291i
209209 −6.63372 + 29.0642i −0.458864 + 2.01041i
210210 3.55893 + 1.71389i 0.245589 + 0.118270i
211211 5.71545 4.55792i 0.393468 0.313780i −0.406694 0.913565i 0.633318π-0.633318\pi
0.800162 + 0.599784i 0.204747π0.204747\pi
212212 −6.29053 7.88808i −0.432036 0.541755i
213213 −18.2128 37.8193i −1.24792 2.59134i
214214 −2.17818 1.73704i −0.148897 0.118742i
215215 24.2734i 1.65543i
216216 4.01060 5.02914i 0.272887 0.342189i
217217 3.48327 + 0.795034i 0.236460 + 0.0539705i
218218 −3.93342 0.897778i −0.266405 0.0608052i
219219 5.70191 7.14997i 0.385299 0.483150i
220220 19.1906i 1.29383i
221221 3.37711 + 2.69315i 0.227169 + 0.181161i
222222 −3.52393 7.31752i −0.236511 0.491120i
223223 3.42929 + 4.30020i 0.229642 + 0.287962i 0.883281 0.468845i 0.155330π-0.155330\pi
−0.653638 + 0.756807i 0.726758π0.726758\pi
224224 5.19271 4.14105i 0.346952 0.276685i
225225 −0.548321 0.264058i −0.0365548 0.0176038i
226226 1.96824 8.62343i 0.130925 0.573622i
227227 −3.50493 15.3561i −0.232630 1.01922i −0.947448 0.319910i 0.896347π-0.896347\pi
0.714818 0.699311i 0.246510π-0.246510\pi
228228 −25.1047 + 12.0898i −1.66260 + 0.800665i
229229 −6.43545 + 13.3634i −0.425267 + 0.883076i 0.572726 + 0.819747i 0.305886π0.305886\pi
−0.997993 + 0.0633287i 0.979828π0.979828\pi
230230 −0.950533 + 0.216953i −0.0626763 + 0.0143055i
231231 17.5593 1.15532
232232 0 0
233233 −15.8867 −1.04078 −0.520388 0.853930i 0.674213π-0.674213\pi
−0.520388 + 0.853930i 0.674213π0.674213\pi
234234 6.64683 1.51710i 0.434517 0.0991757i
235235 −2.75062 + 5.71171i −0.179430 + 0.372591i
236236 6.81877 3.28375i 0.443864 0.213754i
237237 1.26788 + 5.55494i 0.0823575 + 0.360832i
238238 0.203912 0.893398i 0.0132177 0.0579104i
239239 −8.46905 4.07848i −0.547818 0.263815i 0.139438 0.990231i 0.455470π-0.455470\pi
−0.687256 + 0.726416i 0.741185π0.741185\pi
240240 11.5984 9.24942i 0.748674 0.597047i
241241 6.50942 + 8.16255i 0.419308 + 0.525796i 0.945959 0.324286i 0.105124π-0.105124\pi
−0.526651 + 0.850082i 0.676552π0.676552\pi
242242 3.12450 + 6.48809i 0.200850 + 0.417070i
243243 −15.6576 12.4865i −1.00443 0.801008i
244244 9.45018i 0.604986i
245245 7.28887 9.13995i 0.465669 0.583930i
246246 2.56160 + 0.584669i 0.163322 + 0.0372771i
247247 −18.2086 4.15599i −1.15859 0.264440i
248248 −3.27011 + 4.10059i −0.207652 + 0.260388i
249249 17.1221i 1.08507i
250250 4.53064 + 3.61307i 0.286543 + 0.228510i
251251 −6.41374 13.3183i −0.404832 0.840642i −0.999332 0.0365464i 0.988364π-0.988364\pi
0.594500 0.804095i 0.297350π-0.297350\pi
252252 5.99847 + 7.52185i 0.377868 + 0.473832i
253253 −3.38848 + 2.70223i −0.213032 + 0.169887i
254254 2.54089 + 1.22363i 0.159430 + 0.0767772i
255255 1.81767 7.96372i 0.113827 0.498707i
256256 0.235133 + 1.03019i 0.0146958 + 0.0643866i
257257 −1.55916 + 0.750850i −0.0972575 + 0.0468368i −0.481880 0.876237i 0.660046π-0.660046\pi
0.384623 + 0.923074i 0.374332π0.374332\pi
258258 −6.57858 + 13.6606i −0.409564 + 0.850469i
259259 7.48953 1.70944i 0.465377 0.106219i
260260 12.0228 0.745625
261261 0 0
262262 −0.0144647 −0.000893630
263263 13.1918 3.01095i 0.813442 0.185663i 0.204489 0.978869i 0.434447π-0.434447\pi
0.608953 + 0.793206i 0.291590π0.291590\pi
264264 −11.1840 + 23.2239i −0.688329 + 1.42933i
265265 −11.5223 + 5.54884i −0.707808 + 0.340863i
266266 0.881690 + 3.86294i 0.0540599 + 0.236852i
267267 7.14955 31.3242i 0.437546 1.91701i
268268 −3.70115 1.78238i −0.226084 0.108876i
269269 23.3684 18.6357i 1.42480 1.13624i 0.455534 0.890218i 0.349448π-0.349448\pi
0.969265 0.246021i 0.0791231π-0.0791231\pi
270270 −2.36414 2.96454i −0.143877 0.180416i
271271 4.06287 + 8.43664i 0.246802 + 0.512490i 0.987162 0.159721i 0.0510594π-0.0510594\pi
−0.740360 + 0.672210i 0.765345π0.765345\pi
272272 −2.69067 2.14574i −0.163146 0.130105i
273273 11.0008i 0.665799i
274274 −1.96188 + 2.46012i −0.118521 + 0.148621i
275275 0.699250 + 0.159599i 0.0421663 + 0.00962419i
276276 −3.94933 0.901409i −0.237722 0.0542585i
277277 13.9800 17.5304i 0.839978 1.05330i −0.157852 0.987463i 0.550457π-0.550457\pi
0.997830 0.0658364i 0.0209715π-0.0209715\pi
278278 6.34374i 0.380472i
279279 −9.11744 7.27092i −0.545847 0.435298i
280280 −2.37974 4.94157i −0.142216 0.295315i
281281 −5.43187 6.81135i −0.324038 0.406331i 0.592954 0.805237i 0.297962π-0.297962\pi
−0.916992 + 0.398905i 0.869390π0.869390\pi
282282 3.09598 2.46896i 0.184363 0.147024i
283283 −13.0263 6.27313i −0.774332 0.372899i 0.00461408 0.999989i 0.498531π-0.498531\pi
−0.778946 + 0.627091i 0.784246π0.784246\pi
284284 −6.03134 + 26.4250i −0.357894 + 1.56804i
285285 7.85935 + 34.4341i 0.465548 + 2.03970i
286286 −7.23913 + 3.48618i −0.428059 + 0.206142i
287287 −1.07830 + 2.23912i −0.0636502 + 0.132171i
288288 −21.1348 + 4.82388i −1.24538 + 0.284250i
289289 15.1050 0.888530
290290 0 0
291291 −30.7586 −1.80310
292292 −5.75708 + 1.31402i −0.336908 + 0.0768970i
293293 14.2123 29.5121i 0.830291 1.72412i 0.153229 0.988191i 0.451033π-0.451033\pi
0.677062 0.735926i 0.263253π-0.263253\pi
294294 −6.57913 + 3.16834i −0.383703 + 0.184782i
295295 −2.13471 9.35276i −0.124287 0.544539i
296296 −2.50941 + 10.9944i −0.145856 + 0.639038i
297297 −15.1863 7.31333i −0.881197 0.424362i
298298 −8.31717 + 6.63273i −0.481801 + 0.384223i
299299 −1.69293 2.12287i −0.0979048 0.122769i
300300 0.290865 + 0.603988i 0.0167931 + 0.0348713i
301301 −11.2124 8.94161i −0.646274 0.515386i
302302 10.2396i 0.589222i
303303 1.63599 2.05147i 0.0939854 0.117854i
304304 14.5075 + 3.31125i 0.832063 + 0.189913i
305305 −11.6784 2.66552i −0.668703 0.152627i
306306 −1.86486 + 2.33846i −0.106607 + 0.133681i
307307 28.4921i 1.62613i −0.582173 0.813065i 0.697798π-0.697798\pi
0.582173 0.813065i 0.302202π-0.302202\pi
308308 −8.86460 7.06928i −0.505107 0.402810i
309309 9.08574 + 18.8667i 0.516870 + 1.07329i
310310 1.92764 + 2.41719i 0.109483 + 0.137287i
311311 17.0499 13.5968i 0.966810 0.771005i −0.00662321 0.999978i 0.502108π-0.502108\pi
0.973433 + 0.228973i 0.0735368π0.0735368\pi
312312 −14.5496 7.00674i −0.823711 0.396678i
313313 5.32440 23.3277i 0.300953 1.31856i −0.567740 0.823208i 0.692182π-0.692182\pi
0.868693 0.495352i 0.164961π-0.164961\pi
314314 1.34121 + 5.87623i 0.0756890 + 0.331615i
315315 10.9873 5.29122i 0.619066 0.298126i
316316 1.59632 3.31478i 0.0897998 0.186471i
317317 −9.11805 + 2.08114i −0.512121 + 0.116888i −0.470769 0.882256i 0.656024π-0.656024\pi
−0.0413517 + 0.999145i 0.513166π0.513166\pi
318318 7.98835 0.447964
319319 0 0
320320 −5.27191 −0.294709
321321 −14.3048 + 3.26497i −0.798414 + 0.182233i
322322 −0.249933 + 0.518992i −0.0139282 + 0.0289223i
323323 7.38225 3.55510i 0.410759 0.197811i
324324 1.42689 + 6.25159i 0.0792714 + 0.347311i
325325 −0.0999881 + 0.438077i −0.00554634 + 0.0243001i
326326 1.15461 + 0.556032i 0.0639480 + 0.0307957i
327327 −16.6126 + 13.2481i −0.918681 + 0.732623i
328328 −2.27465 2.85232i −0.125597 0.157493i
329329 1.62512 + 3.37460i 0.0895959 + 0.186048i
330330 11.8796 + 9.47367i 0.653951 + 0.521508i
331331 10.2474i 0.563247i 0.959525 + 0.281623i 0.0908729π0.0908729\pi
−0.959525 + 0.281623i 0.909127π0.909127\pi
332332 6.89328 8.64390i 0.378318 0.474396i
333333 −24.4455 5.57953i −1.33961 0.305757i
334334 −1.33128 0.303855i −0.0728443 0.0166262i
335335 −3.24659 + 4.07110i −0.177380 + 0.222428i
336336 8.76478i 0.478158i
337337 12.4652 + 9.94065i 0.679022 + 0.541502i 0.901146 0.433517i 0.142727π-0.142727\pi
−0.222124 + 0.975019i 0.571299π0.571299\pi
338338 0.699654 + 1.45285i 0.0380562 + 0.0790244i
339339 −29.0445 36.4206i −1.57748 1.97810i
340340 −4.12378 + 3.28860i −0.223643 + 0.178350i
341341 12.3824 + 5.96304i 0.670543 + 0.322917i
342342 2.87780 12.6085i 0.155614 0.681788i
343343 −3.56509 15.6197i −0.192497 0.843384i
344344 18.9677 9.13435i 1.02267 0.492491i
345345 −2.22790 + 4.62628i −0.119946 + 0.249070i
346346 −11.7622 + 2.68466i −0.632342 + 0.144328i
347347 −36.7925 −1.97513 −0.987563 0.157224i 0.949746π-0.949746\pi
−0.987563 + 0.157224i 0.949746π0.949746\pi
348348 0 0
349349 32.4894 1.73912 0.869558 0.493831i 0.164404π-0.164404\pi
0.869558 + 0.493831i 0.164404π0.164404\pi
350350 0.0929375 0.0212124i 0.00496772 0.00113385i
351351 4.58177 9.51413i 0.244557 0.507827i
352352 23.0181 11.0849i 1.22687 0.590829i
353353 −2.67405 11.7158i −0.142325 0.623568i −0.994892 0.100949i 0.967812π-0.967812\pi
0.852566 0.522619i 0.175045π-0.175045\pi
354354 −1.33342 + 5.84209i −0.0708704 + 0.310504i
355355 30.9545 + 14.9069i 1.64289 + 0.791176i
356356 −16.2203 + 12.9353i −0.859677 + 0.685569i
357357 −3.00905 3.77323i −0.159256 0.199700i
358358 −4.64911 9.65397i −0.245713 0.510228i
359359 3.05587 + 2.43698i 0.161283 + 0.128619i 0.700806 0.713352i 0.252824π-0.252824\pi
−0.539523 + 0.841971i 0.681395π0.681395\pi
360360 17.9019i 0.943515i
361361 −10.2429 + 12.8442i −0.539102 + 0.676012i
362362 −4.53273 1.03457i −0.238235 0.0543756i
363363 36.9749 + 8.43927i 1.94068 + 0.442947i
364364 4.42887 5.55363i 0.232136 0.291089i
365365 7.48515i 0.391791i
366366 5.84995 + 4.66518i 0.305782 + 0.243853i
367367 5.54823 + 11.5210i 0.289615 + 0.601392i 0.994117 0.108310i 0.0345439π-0.0345439\pi
−0.704502 + 0.709702i 0.748830π0.748830\pi
368368 1.34883 + 1.69137i 0.0703124 + 0.0881690i
369369 6.34199 5.05756i 0.330151 0.263286i
370370 5.98927 + 2.88428i 0.311367 + 0.149947i
371371 −1.68134 + 7.36644i −0.0872909 + 0.382446i
372372 2.85841 + 12.5235i 0.148201 + 0.649313i
373373 −22.5120 + 10.8412i −1.16563 + 0.561338i −0.913693 0.406406i 0.866782π-0.866782\pi
−0.251937 + 0.967744i 0.581068π0.581068\pi
374374 1.52941 3.17586i 0.0790841 0.164220i
375375 29.7541 6.79117i 1.53649 0.350695i
376376 −5.49833 −0.283555
377377 0 0
378378 −2.24027 −0.115227
379379 −12.7084 + 2.90061i −0.652786 + 0.148994i −0.536073 0.844172i 0.680093π-0.680093\pi
−0.116713 + 0.993166i 0.537236π0.537236\pi
380380 9.89528 20.5478i 0.507617 1.05408i
381381 13.3818 6.44431i 0.685568 0.330152i
382382 2.19225 + 9.60488i 0.112165 + 0.491428i
383383 5.34830 23.4324i 0.273285 1.19734i −0.632824 0.774296i 0.718104π-0.718104\pi
0.906109 0.423045i 0.139039π-0.139039\pi
384384 27.7157 + 13.3472i 1.41436 + 0.681121i
385385 −11.2365 + 8.96079i −0.572664 + 0.456684i
386386 −1.69520 2.12571i −0.0862833 0.108196i
387387 20.3098 + 42.1736i 1.03240 + 2.14381i
388388 15.5281 + 12.3833i 0.788321 + 0.628665i
389389 17.6717i 0.895991i −0.894036 0.447995i 0.852138π-0.852138\pi
0.894036 0.447995i 0.147862π-0.147862\pi
390390 −5.93521 + 7.44251i −0.300541 + 0.376866i
391391 1.16134 + 0.265067i 0.0587312 + 0.0134050i
392392 9.88501 + 2.25619i 0.499269 + 0.113955i
393393 −0.0474969 + 0.0595592i −0.00239590 + 0.00300436i
394394 5.09856i 0.256862i
395395 −3.64611 2.90767i −0.183456 0.146301i
396396 16.0570 + 33.3427i 0.806894 + 1.67553i
397397 18.8622 + 23.6524i 0.946665 + 1.18708i 0.982224 + 0.187713i 0.0601076π0.0601076\pi
−0.0355584 + 0.999368i 0.511321π0.511321\pi
398398 8.86976 7.07340i 0.444601 0.354557i
399399 18.8010 + 9.05410i 0.941229 + 0.453272i
400400 0.0796645 0.349033i 0.00398323 0.0174517i
401401 2.74975 + 12.0474i 0.137316 + 0.601620i 0.996019 + 0.0891461i 0.0284138π0.0284138\pi
−0.858703 + 0.512474i 0.828729π0.828729\pi
402402 2.93046 1.41124i 0.146158 0.0703861i
403403 −3.73582 + 7.75750i −0.186094 + 0.386429i
404404 −1.65182 + 0.377018i −0.0821813 + 0.0187574i
405405 8.12810 0.403889
406406 0 0
407407 29.5503 1.46475
408408 6.90701 1.57648i 0.341948 0.0780474i
409409 2.64972 5.50220i 0.131020 0.272066i −0.825130 0.564943i 0.808898π-0.808898\pi
0.956150 + 0.292877i 0.0946125π0.0946125\pi
410410 −1.93758 + 0.933088i −0.0956901 + 0.0460819i
411411 3.68757 + 16.1563i 0.181895 + 0.796932i
412412 3.00882 13.1825i 0.148234 0.649456i
413413 −5.10662 2.45922i −0.251280 0.121010i
414414 1.46997 1.17226i 0.0722452 0.0576136i
415415 −8.73770 10.9567i −0.428917 0.537845i
416416 6.94466 + 14.4207i 0.340490 + 0.707035i
417417 26.1207 + 20.8306i 1.27914 + 1.02008i
418418 15.2414i 0.745480i
419419 −7.23714 + 9.07508i −0.353557 + 0.443347i −0.926526 0.376230i 0.877220π-0.877220\pi
0.572969 + 0.819577i 0.305792π0.305792\pi
420420 −13.0963 2.98914i −0.639033 0.145855i
421421 19.7781 + 4.51422i 0.963925 + 0.220010i 0.675391 0.737460i 0.263975π-0.263975\pi
0.288534 + 0.957470i 0.406832π0.406832\pi
422422 2.33026 2.92206i 0.113435 0.142243i
423423 12.2252i 0.594412i
424424 −8.67194 6.91564i −0.421147 0.335853i
425425 −0.0855315 0.177608i −0.00414889 0.00861525i
426426 −13.3805 16.7786i −0.648286 0.812925i
427427 −5.53325 + 4.41262i −0.267773 + 0.213542i
428428 8.53604 + 4.11074i 0.412605 + 0.198700i
429429 −9.41618 + 41.2550i −0.454618 + 1.99181i
430430 −2.76146 12.0988i −0.133170 0.583454i
431431 −15.3018 + 7.36896i −0.737062 + 0.354950i −0.764457 0.644674i 0.776993π-0.776993\pi
0.0273954 + 0.999625i 0.491279π0.491279\pi
432432 −3.65047 + 7.58029i −0.175634 + 0.364707i
433433 −15.5357 + 3.54593i −0.746600 + 0.170407i −0.578862 0.815425i 0.696503π-0.696503\pi
−0.167737 + 0.985832i 0.553646π0.553646\pi
434434 1.82664 0.0876815
435435 0 0
436436 13.7203 0.657084
437437 −5.02146 + 1.14612i −0.240209 + 0.0548261i
438438 2.02863 4.21249i 0.0969316 0.201280i
439439 −4.86840 + 2.34450i −0.232356 + 0.111897i −0.546440 0.837499i 0.684017π-0.684017\pi
0.314083 + 0.949395i 0.398303π0.398303\pi
440440 −4.69467 20.5687i −0.223810 0.980575i
441441 −5.01652 + 21.9788i −0.238882 + 1.04661i
442442 1.98966 + 0.958171i 0.0946386 + 0.0455755i
443443 14.8950 11.8783i 0.707682 0.564357i −0.202140 0.979357i 0.564790π-0.564790\pi
0.909822 + 0.414999i 0.136218π0.136218\pi
444444 17.2207 + 21.5940i 0.817256 + 1.02481i
445445 11.4101 + 23.6934i 0.540893 + 1.12318i
446446 2.19850 + 1.75324i 0.104102 + 0.0830185i
447447 56.0260i 2.64994i
448448 −1.94202 + 2.43522i −0.0917518 + 0.115053i
449449 −17.2440 3.93582i −0.813793 0.185743i −0.204682 0.978828i 0.565616π-0.565616\pi
−0.609110 + 0.793086i 0.708473π0.708473\pi
450450 −0.303344 0.0692364i −0.0142998 0.00326383i
451451 −5.96041 + 7.47411i −0.280665 + 0.351942i
452452 30.0797i 1.41483i
453453 −42.1622 33.6232i −1.98095 1.57976i
454454 −3.49398 7.25532i −0.163980 0.340509i
455455 −5.61389 7.03959i −0.263183 0.330021i
456456 −23.9499 + 19.0994i −1.12156 + 0.894411i
457457 −13.6028 6.55078i −0.636314 0.306433i 0.0877740 0.996140i 0.472025π-0.472025\pi
−0.724088 + 0.689708i 0.757739π0.757739\pi
458458 −1.68739 + 7.39293i −0.0788464 + 0.345449i
459459 1.03087 + 4.51655i 0.0481170 + 0.210815i
460460 2.98724 1.43858i 0.139281 0.0670742i
461461 9.67638 20.0932i 0.450674 0.935834i −0.544597 0.838698i 0.683317π-0.683317\pi
0.995271 0.0971364i 0.0309683π-0.0309683\pi
462462 8.75220 1.99763i 0.407189 0.0929383i
463463 26.7391 1.24267 0.621335 0.783545i 0.286591π-0.286591\pi
0.621335 + 0.783545i 0.286591π0.286591\pi
464464 0 0
465465 16.2826 0.755088
466466 −7.91855 + 1.80736i −0.366820 + 0.0837242i
467467 5.01624 10.4163i 0.232124 0.482010i −0.752075 0.659078i 0.770947π-0.770947\pi
0.984199 + 0.177067i 0.0566611π0.0566611\pi
468468 −20.8890 + 10.0596i −0.965595 + 0.465006i
469469 0.684582 + 2.99935i 0.0316111 + 0.138497i
470470 −0.721216 + 3.15985i −0.0332672 + 0.145753i
471471 28.5998 + 13.7730i 1.31781 + 0.634624i
472472 6.50511 5.18765i 0.299422 0.238781i
473473 −34.3950 43.1300i −1.58148 1.98312i
474474 1.26392 + 2.62455i 0.0580535 + 0.120549i
475475 0.666405 + 0.531440i 0.0305768 + 0.0243841i
476476 3.11630i 0.142835i
477477 15.3766 19.2816i 0.704044 0.882844i
478478 −4.68528 1.06938i −0.214300 0.0489125i
479479 23.7181 + 5.41349i 1.08371 + 0.247349i 0.726840 0.686807i 0.240988π-0.240988\pi
0.356866 + 0.934156i 0.383845π0.383845\pi
480480 18.8720 23.6648i 0.861387 1.08015i
481481 18.5131i 0.844125i
482482 4.17315 + 3.32797i 0.190082 + 0.151585i
483483 1.31629 + 2.73330i 0.0598933 + 0.124370i
484484 −15.2687 19.1464i −0.694032 0.870289i
485485 19.6829 15.6966i 0.893756 0.712746i
486486 −9.22483 4.44245i −0.418447 0.201513i
487487 −0.286359 + 1.25462i −0.0129762 + 0.0568523i −0.981001 0.194000i 0.937854π-0.937854\pi
0.968025 + 0.250852i 0.0807109π0.0807109\pi
488488 −2.31183 10.1288i −0.104652 0.458509i
489489 6.08083 2.92838i 0.274985 0.132426i
490490 2.59324 5.38491i 0.117150 0.243265i
491491 −31.8396 + 7.26719i −1.43690 + 0.327963i −0.868869 0.495042i 0.835153π-0.835153\pi
−0.568033 + 0.823006i 0.692295π0.692295\pi
492492 −8.93522 −0.402831
493493 0 0
494494 −9.54865 −0.429614
495495 45.7335 10.4384i 2.05557 0.469169i
496496 2.97647 6.18071i 0.133648 0.277522i
497497 18.2886 8.80732i 0.820355 0.395062i
498498 1.94790 + 8.53431i 0.0872875 + 0.382432i
499499 −2.33273 + 10.2203i −0.104427 + 0.457525i 0.895495 + 0.445071i 0.146822π0.146822\pi
−0.999922 + 0.0124542i 0.996036π0.996036\pi
500500 −17.7551 8.55039i −0.794031 0.382385i
501501 −5.62259 + 4.48387i −0.251199 + 0.200324i
502502 −4.71200 5.90866i −0.210307 0.263717i
503503 −1.64458 3.41500i −0.0733280 0.152267i 0.861082 0.508465i 0.169787π-0.169787\pi
−0.934410 + 0.356198i 0.884073π0.884073\pi
504504 8.26931 + 6.59456i 0.368344 + 0.293745i
505505 2.14764i 0.0955689i
506506 −1.38153 + 1.73238i −0.0614164 + 0.0770137i
507507 8.27961 + 1.88977i 0.367710 + 0.0839275i
508508 −9.35006 2.13409i −0.414842 0.0946850i
509509 −4.99932 + 6.26895i −0.221591 + 0.277866i −0.880184 0.474633i 0.842581π-0.842581\pi
0.658593 + 0.752500i 0.271152π0.271152\pi
510510 4.17620i 0.184925i
511511 3.45756 + 2.75731i 0.152954 + 0.121976i
512512 −9.67974 20.1002i −0.427788 0.888311i
513513 −12.4892 15.6610i −0.551414 0.691451i
514514 −0.691721 + 0.551629i −0.0305105 + 0.0243313i
515515 −15.4421 7.43653i −0.680461 0.327693i
516516 11.4735 50.2686i 0.505092 2.21295i
517517 3.20599 + 14.0464i 0.140999 + 0.617759i
518518 3.53859 1.70409i 0.155477 0.0748736i
519519 −27.5688 + 57.2473i −1.21014 + 2.51288i
520520 12.8862 2.94119i 0.565097 0.128980i
521521 6.39024 0.279962 0.139981 0.990154i 0.455296π-0.455296\pi
0.139981 + 0.990154i 0.455296π0.455296\pi
522522 0 0
523523 −16.3261 −0.713891 −0.356946 0.934125i 0.616182π-0.616182\pi
−0.356946 + 0.934125i 0.616182π0.616182\pi
524524 0.0479564 0.0109457i 0.00209499 0.000478167i
525525 0.217831 0.452330i 0.00950691 0.0197413i
526526 6.23275 3.00154i 0.271761 0.130873i
527527 −0.840539 3.68264i −0.0366145 0.160418i
528528 7.50225 32.8695i 0.326493 1.43046i
529529 20.0476 + 9.65444i 0.871637 + 0.419758i
530530 −5.11187 + 4.07658i −0.222046 + 0.177075i
531531 11.5345 + 14.4638i 0.500554 + 0.627674i
532532 −5.84634 12.1401i −0.253471 0.526338i
533533 −4.68250 3.73417i −0.202821 0.161745i
534534 16.4265i 0.710846i
535535 7.48768 9.38925i 0.323721 0.405933i
536536 −4.40296 1.00495i −0.190179 0.0434071i
537537 −55.0169 12.5572i −2.37415 0.541885i
538538 9.52761 11.9472i 0.410764 0.515082i
539539 26.5684i 1.14438i
540540 10.0815 + 8.03970i 0.433837 + 0.345973i
541541 9.52857 + 19.7863i 0.409665 + 0.850678i 0.999082 + 0.0428490i 0.0136434π0.0136434\pi
−0.589416 + 0.807829i 0.700642π0.700642\pi
542542 2.98488 + 3.74292i 0.128212 + 0.160772i
543543 −19.1438 + 15.2667i −0.821539 + 0.655156i
544544 −6.32648 3.04667i −0.271246 0.130625i
545545 3.86996 16.9554i 0.165771 0.726289i
546546 1.25151 + 5.48321i 0.0535596 + 0.234660i
547547 −3.69865 + 1.78117i −0.158143 + 0.0761575i −0.511281 0.859414i 0.670829π-0.670829\pi
0.353138 + 0.935571i 0.385115π0.385115\pi
548548 4.64282 9.64092i 0.198332 0.411840i
549549 22.5208 5.14023i 0.961165 0.219380i
550550 0.366689 0.0156357
551551 0 0
552552 −4.45344 −0.189551
553553 −2.68624 + 0.613117i −0.114231 + 0.0260724i
554554 4.97382 10.3282i 0.211317 0.438805i
555555 31.5429 15.1902i 1.33892 0.644790i
556556 −4.80045 21.0322i −0.203584 0.891962i
557557 −5.53882 + 24.2671i −0.234687 + 1.02823i 0.711010 + 0.703182i 0.248238π0.248238\pi
−0.945697 + 0.325050i 0.894619π0.894619\pi
558558 −5.37165 2.58685i −0.227400 0.109510i
559559 27.0207 21.5483i 1.14285 0.911396i
560560 4.47281 + 5.60873i 0.189011 + 0.237012i
561561 −8.05475 16.7259i −0.340072 0.706167i
562562 −3.48234 2.77708i −0.146894 0.117144i
563563 22.6338i 0.953902i −0.878930 0.476951i 0.841742π-0.841742\pi
0.878930 0.476951i 0.158258π-0.158258\pi
564564 −8.39615 + 10.5284i −0.353542 + 0.443327i
565565 37.1721 + 8.48428i 1.56384 + 0.356936i
566566 −7.20645 1.64482i −0.302910 0.0691371i
567567 2.99416 3.75455i 0.125743 0.157676i
568568 29.7981i 1.25030i
569569 −8.12929 6.48290i −0.340798 0.271777i 0.438102 0.898925i 0.355651π-0.355651\pi
−0.778900 + 0.627148i 0.784222π0.784222\pi
570570 7.83479 + 16.2691i 0.328163 + 0.681438i
571571 22.2441 + 27.8932i 0.930887 + 1.16730i 0.985651 + 0.168796i 0.0539880π0.0539880\pi
−0.0547638 + 0.998499i 0.517441π0.517441\pi
572572 21.3627 17.0362i 0.893219 0.712318i
573573 46.7473 + 22.5123i 1.95290 + 0.940465i
574574 −0.282733 + 1.23873i −0.0118010 + 0.0517037i
575575 0.0275741 + 0.120810i 0.00114992 + 0.00503813i
576576 9.15965 4.41105i 0.381652 0.183794i
577577 −0.698030 + 1.44947i −0.0290594 + 0.0603424i −0.914993 0.403469i 0.867804π-0.867804\pi
0.885934 + 0.463812i 0.153519π0.153519\pi
578578 7.52890 1.71842i 0.313161 0.0714770i
579579 −14.3192 −0.595085
580580 0 0
581581 −8.27988 −0.343507
582582 −15.3312 + 3.49926i −0.635500 + 0.145049i
583583 −12.6107 + 26.1863i −0.522280 + 1.08453i
584584 −5.84904 + 2.81675i −0.242035 + 0.116558i
585585 6.53958 + 28.6518i 0.270379 + 1.18461i
586586 3.72649 16.3268i 0.153940 0.674454i
587587 −22.3028 10.7405i −0.920536 0.443307i −0.0872738 0.996184i 0.527815π-0.527815\pi
−0.833263 + 0.552877i 0.813530π0.813530\pi
588588 19.4150 15.4830i 0.800663 0.638507i
589589 10.1833 + 12.7695i 0.419596 + 0.526157i
590590 −2.12804 4.41891i −0.0876098 0.181924i
591591 −20.9937 16.7419i −0.863564 0.688669i
592592 14.7501i 0.606227i
593593 6.36426 7.98053i 0.261349 0.327721i −0.633793 0.773503i 0.718503π-0.718503\pi
0.895142 + 0.445782i 0.147074π0.147074\pi
594594 −8.40141 1.91757i −0.344714 0.0786787i
595595 3.85107 + 0.878983i 0.157879 + 0.0360348i
596596 22.5558 28.2841i 0.923921 1.15856i
597597 59.7483i 2.44534i
598598 −1.08533 0.865521i −0.0443824 0.0353938i
599599 −8.14582 16.9150i −0.332829 0.691127i 0.665650 0.746264i 0.268155π-0.268155\pi
−0.998479 + 0.0551377i 0.982440π0.982440\pi
600600 0.459508 + 0.576205i 0.0187593 + 0.0235235i
601601 31.9072 25.4451i 1.30152 1.03793i 0.305196 0.952290i 0.401278π-0.401278\pi
0.996326 0.0856397i 0.0272934π-0.0272934\pi
602602 −6.60594 3.18125i −0.269238 0.129658i
603603 2.23445 9.78975i 0.0909937 0.398670i
604604 7.74854 + 33.9486i 0.315283 + 1.38135i
605605 −27.9675 + 13.4684i −1.13704 + 0.547570i
606606 0.582055 1.20865i 0.0236444 0.0490980i
607607 −11.4104 + 2.60434i −0.463133 + 0.105707i −0.447719 0.894174i 0.647764π-0.647764\pi
−0.0154135 + 0.999881i 0.504906π0.504906\pi
608608 30.3616 1.23133
609609 0 0
610610 −6.12419 −0.247961
611611 −8.79999 + 2.00854i −0.356010 + 0.0812568i
612612 4.41323 9.16417i 0.178394 0.370440i
613613 12.4961 6.01779i 0.504711 0.243056i −0.164161 0.986434i 0.552492π-0.552492\pi
0.668872 + 0.743377i 0.266777π0.266777\pi
614614 −3.24140 14.2015i −0.130812 0.573127i
615615 −2.52027 + 11.0420i −0.101627 + 0.445258i
616616 −11.2305 5.40834i −0.452491 0.217908i
617617 −19.7258 + 15.7308i −0.794131 + 0.633298i −0.934162 0.356849i 0.883851π-0.883851\pi
0.140031 + 0.990147i 0.455280π0.455280\pi
618618 6.67505 + 8.37025i 0.268510 + 0.336701i
619619 −12.5407 26.0411i −0.504054 1.04668i −0.985417 0.170158i 0.945572π-0.945572\pi
0.481362 0.876522i 0.340142π-0.340142\pi
620620 −8.22008 6.55530i −0.330126 0.263267i
621621 2.91215i 0.116860i
622622 6.95145 8.71684i 0.278728 0.349513i
623623 15.1477 + 3.45736i 0.606880 + 0.138516i
624624 20.5926 + 4.70012i 0.824363 + 0.188155i
625625 −15.1280 + 18.9700i −0.605121 + 0.758798i
626626 12.2331i 0.488934i
627627 62.7573 + 50.0473i 2.50629 + 1.99870i
628628 −8.89336 18.4673i −0.354884 0.736924i
629629 −5.06388 6.34991i −0.201910 0.253187i
630630 4.87454 3.88731i 0.194206 0.154874i
631631 14.1425 + 6.81069i 0.563006 + 0.271129i 0.693665 0.720298i 0.255995π-0.255995\pi
−0.130659 + 0.991427i 0.541709π0.541709\pi
632632 0.900039 3.94333i 0.0358016 0.156857i
633633 −4.37999 19.1900i −0.174089 0.762734i
634634 −4.30802 + 2.07463i −0.171093 + 0.0823942i
635635 −5.27456 + 10.9527i −0.209315 + 0.434646i
636636 −26.4847 + 6.04497i −1.05019 + 0.239699i
637637 16.6450 0.659499
638638 0 0
639639 −66.2544 −2.62098
640640 −24.5470 + 5.60270i −0.970307 + 0.221466i
641641 −14.1210 + 29.3226i −0.557746 + 1.15817i 0.411348 + 0.911479i 0.365058π0.365058\pi
−0.969094 + 0.246693i 0.920656π0.920656\pi
642642 −6.75858 + 3.25476i −0.266740 + 0.128455i
643643 5.46633 + 23.9496i 0.215571 + 0.944479i 0.960707 + 0.277566i 0.0895276π0.0895276\pi
−0.745135 + 0.666913i 0.767615π0.767615\pi
644644 0.435901 1.90981i 0.0171769 0.0752570i
645645 −58.8851 28.3576i −2.31860 1.11658i
646646 3.27514 2.61184i 0.128859 0.102761i
647647 −8.11895 10.1808i −0.319189 0.400250i 0.596190 0.802843i 0.296680π-0.296680\pi
−0.915379 + 0.402593i 0.868109π0.868109\pi
648648 3.05870 + 6.35145i 0.120157 + 0.249509i
649649 −17.0457 13.5935i −0.669104 0.533593i
650650 0.229729i 0.00901071i
651651 5.99804 7.52131i 0.235082 0.294783i
652652 −4.24879 0.969758i −0.166395 0.0379786i
653653 −29.2080 6.66653i −1.14300 0.260882i −0.391219 0.920298i 0.627946π-0.627946\pi
−0.751778 + 0.659416i 0.770804π0.770804\pi
654654 −6.77318 + 8.49330i −0.264852 + 0.332114i
655655 0.0623513i 0.00243627i
656656 3.73073 + 2.97516i 0.145661 + 0.116160i
657657 −6.26289 13.0050i −0.244339 0.507375i
658658 1.19393 + 1.49714i 0.0465444 + 0.0583648i
659659 −11.1031 + 8.85440i −0.432514 + 0.344918i −0.815421 0.578869i 0.803494π-0.803494\pi
0.382907 + 0.923787i 0.374923π0.374923\pi
660660 −46.5548 22.4196i −1.81214 0.872682i
661661 −8.98572 + 39.3690i −0.349504 + 1.53128i 0.428806 + 0.903396i 0.358934π0.358934\pi
−0.778310 + 0.627880i 0.783923π0.783923\pi
662662 1.16579 + 5.10768i 0.0453099 + 0.198515i
663663 10.4787 5.04627i 0.406958 0.195981i
664664 5.27370 10.9509i 0.204659 0.424979i
665665 −16.6515 + 3.80061i −0.645719 + 0.147381i
666666 −12.8193 −0.496739
667667 0 0
668668 4.64368 0.179669
669669 14.4382 3.29542i 0.558213 0.127408i
670670 −1.15507 + 2.39854i −0.0446244 + 0.0926635i
671671 −24.5277 + 11.8119i −0.946880 + 0.455993i
672672 −3.97939 17.4349i −0.153508 0.672564i
673673 −9.07755 + 39.7713i −0.349914 + 1.53307i 0.427461 + 0.904034i 0.359408π0.359408\pi
−0.777374 + 0.629038i 0.783449π0.783449\pi
674674 7.34401 + 3.53669i 0.282881 + 0.136228i
675675 −0.376785 + 0.300476i −0.0145025 + 0.0115653i
676676 −3.41905 4.28735i −0.131502 0.164898i
677677 8.93310 + 18.5498i 0.343327 + 0.712926i 0.999117 0.0420177i 0.0133786π-0.0133786\pi
−0.655790 + 0.754943i 0.727664π0.727664\pi
678678 −18.6203 14.8492i −0.715107 0.570279i
679679 14.8742i 0.570818i
680680 −3.61540 + 4.53357i −0.138644 + 0.173855i
681681 −41.3472 9.43723i −1.58443 0.361636i
682682 6.85022 + 1.56352i 0.262309 + 0.0598702i
683683 7.87927 9.88029i 0.301492 0.378059i −0.607890 0.794021i 0.707984π-0.707984\pi
0.909382 + 0.415963i 0.136555π0.136555\pi
684684 43.9801i 1.68162i
685685 −10.6046 8.45686i −0.405179 0.323120i
686686 −3.55395 7.37986i −0.135690 0.281764i
687687 24.9001 + 31.2237i 0.949997 + 1.19126i
688688 −21.5285 + 17.1684i −0.820765 + 0.654539i
689689 −16.4056 7.90052i −0.625003 0.300986i
690690 −0.584159 + 2.55937i −0.0222385 + 0.0974334i
691691 4.92158 + 21.5628i 0.187226 + 0.820289i 0.978071 + 0.208273i 0.0667842π0.0667842\pi
−0.790845 + 0.612016i 0.790359π0.790359\pi
692692 36.9652 17.8015i 1.40521 0.676712i
693693 12.0252 24.9705i 0.456798 0.948551i
694694 −18.3388 + 4.18570i −0.696130 + 0.158887i
695695 −27.3453 −1.03726
696696 0 0
697697 2.62748 0.0995229
698698 16.1939 3.69615i 0.612948 0.139901i
699699 −18.5598 + 38.5398i −0.701996 + 1.45771i
700700 −0.292075 + 0.140656i −0.0110394 + 0.00531630i
701701 0.486817 + 2.13288i 0.0183868 + 0.0805579i 0.983289 0.182052i 0.0582739π-0.0582739\pi
−0.964902 + 0.262610i 0.915417π0.915417\pi
702702 1.20135 5.26344i 0.0453419 0.198656i
703703 31.6400 + 15.2370i 1.19333 + 0.574675i
704704 −9.36735 + 7.47021i −0.353045 + 0.281544i
705705 10.6427 + 13.3455i 0.400827 + 0.502621i
706706 −2.66569 5.53537i −0.100325 0.208326i
707707 0.992046 + 0.791130i 0.0373097 + 0.0297535i
708708 20.3780i 0.765852i
709709 −18.5787 + 23.2969i −0.697736 + 0.874934i −0.996852 0.0792830i 0.974737π-0.974737\pi
0.299116 + 0.954217i 0.403308π0.403308\pi
710710 17.1248 + 3.90861i 0.642681 + 0.146688i
711711 8.76778 + 2.00119i 0.328818 + 0.0750505i
712712 −14.2207 + 17.8322i −0.532944 + 0.668290i
713713 2.37446i 0.0889244i
714714 −1.92908 1.53839i −0.0721941 0.0575729i
715715 −15.0275 31.2050i −0.561997 1.16700i
716716 22.7191 + 28.4889i 0.849054 + 1.06468i
717717 −19.7881 + 15.7805i −0.738999 + 0.589332i
718718 1.80040 + 0.867029i 0.0671905 + 0.0323572i
719719 −1.80941 + 7.92753i −0.0674795 + 0.295647i −0.997396 0.0721247i 0.977022π-0.977022\pi
0.929916 + 0.367772i 0.119879π0.119879\pi
720720 −5.21035 22.8280i −0.194178 0.850750i
721721 −9.12353 + 4.39366i −0.339778 + 0.163628i
722722 −3.64423 + 7.56733i −0.135624 + 0.281627i
723723 27.4063 6.25531i 1.01925 0.232637i
724724 15.8108 0.587604
725725 0 0
726726 19.3898 0.719621
727727 9.94820 2.27061i 0.368958 0.0842123i −0.0340217 0.999421i 0.510832π-0.510832\pi
0.402980 + 0.915209i 0.367974π0.367974\pi
728728 3.38830 7.03588i 0.125579 0.260767i
729729 −38.6143 + 18.5957i −1.43016 + 0.688728i
730730 0.851549 + 3.73088i 0.0315172 + 0.138086i
731731 −3.37388 + 14.7819i −0.124787 + 0.546729i
732732 −22.9253 11.0402i −0.847343 0.408059i
733733 −19.2798 + 15.3751i −0.712115 + 0.567893i −0.911138 0.412102i 0.864795π-0.864795\pi
0.199023 + 0.979995i 0.436223π0.436223\pi
734734 4.07613 + 5.11131i 0.150453 + 0.188662i
735735 −13.6574 28.3600i −0.503762 1.04607i
736736 3.45100 + 2.75208i 0.127205 + 0.101443i
737737 11.8341i 0.435913i
738738 2.58571 3.24237i 0.0951812 0.119353i
739739 4.06706 + 0.928279i 0.149609 + 0.0341473i 0.296670 0.954980i 0.404124π-0.404124\pi
−0.147060 + 0.989128i 0.546981π0.546981\pi
740740 −22.0395 5.03038i −0.810190 0.184921i
741741 −31.3544 + 39.3172i −1.15183 + 1.44435i
742742 3.86299i 0.141815i
743743 2.18799 + 1.74486i 0.0802694 + 0.0640127i 0.662802 0.748794i 0.269367π-0.269367\pi
−0.582533 + 0.812807i 0.697938π0.697938\pi
744744 6.12733 + 12.7235i 0.224639 + 0.466468i
745745 −28.5910 35.8520i −1.04749 1.31351i
746746 −9.98749 + 7.96476i −0.365668 + 0.291610i
747747 24.3488 + 11.7258i 0.890878 + 0.429024i
748748 −2.66740 + 11.6867i −0.0975299 + 0.427307i
749749 −1.57886 6.91746i −0.0576905 0.252758i
750750 14.0579 6.76995i 0.513323 0.247203i
751751 6.37845 13.2450i 0.232753 0.483316i −0.751579 0.659643i 0.770707π-0.770707\pi
0.984332 + 0.176327i 0.0564216π0.0564216\pi
752752 7.01130 1.60028i 0.255676 0.0583564i
753753 −39.8019 −1.45046
754754 0 0
755755 44.1387 1.60637
756756 7.42744 1.69526i 0.270133 0.0616562i
757757 9.95155 20.6646i 0.361695 0.751068i −0.638127 0.769931i 0.720290π-0.720290\pi
0.999822 + 0.0188632i 0.00600469π0.00600469\pi
758758 −6.00435 + 2.89154i −0.218088 + 0.105026i
759759 2.59674 + 11.3771i 0.0942557 + 0.412961i
760760 5.57918 24.4440i 0.202378 0.886677i
761761 11.3722 + 5.47655i 0.412241 + 0.198525i 0.628497 0.777812i 0.283670π-0.283670\pi
−0.216256 + 0.976337i 0.569385π0.569385\pi
762762 5.93683 4.73446i 0.215069 0.171511i
763763 −6.40650 8.03349i −0.231931 0.290832i
764764 −14.5365 30.1853i −0.525911 1.09207i
765765 −10.0802 8.03866i −0.364449 0.290638i
766766 12.2880i 0.443985i
767767 8.51628 10.6791i 0.307505 0.385599i
768768 2.77384 + 0.633110i 0.100092 + 0.0228454i
769769 3.43897 + 0.784923i 0.124013 + 0.0283050i 0.284077 0.958802i 0.408313π-0.408313\pi
−0.160064 + 0.987107i 0.551170π0.551170\pi
770770 −4.58125 + 5.74471i −0.165097 + 0.207025i
771771 4.65956i 0.167810i
772772 7.22887 + 5.76483i 0.260173 + 0.207481i
773773 11.3711 + 23.6123i 0.408989 + 0.849274i 0.999119 + 0.0419657i 0.0133620π0.0133620\pi
−0.590130 + 0.807308i 0.700924π0.700924\pi
774774 14.9210 + 18.7104i 0.536325 + 0.672531i
775775 0.307218 0.244998i 0.0110356 0.00880059i
776776 19.6725 + 9.47380i 0.706203 + 0.340089i
777777 4.60276 20.1660i 0.165123 0.723452i
778778 −2.01042 8.80824i −0.0720771 0.315791i
779779 −10.2358 + 4.92930i −0.366735 + 0.176610i
780780 14.0458 29.1664i 0.502920 1.04432i
781781 76.1241 17.3748i 2.72393 0.621720i
782782 0.609008 0.0217781
783783 0 0
784784 −13.2617 −0.473634
785785 −25.3301 + 5.78142i −0.904068 + 0.206348i
786786 −0.0168985 + 0.0350900i −0.000602748 + 0.00125162i
787787 −16.2283 + 7.81515i −0.578477 + 0.278580i −0.700156 0.713989i 0.746886π-0.746886\pi
0.121679 + 0.992569i 0.461172π0.461172\pi
788788 3.85820 + 16.9039i 0.137443 + 0.602176i
789789 8.10715 35.5197i 0.288622 1.26454i
790790 −2.14815 1.03449i −0.0764277 0.0368056i
791791 17.6122 14.0453i 0.626218 0.499392i
792792 25.3668 + 31.8089i 0.901368 + 1.13028i
793793 −7.40010 15.3665i −0.262785 0.545679i
794794 12.0924 + 9.64339i 0.429144 + 0.342231i
795795 34.4345i 1.22127i
796796 −24.0544 + 30.1632i −0.852585 + 1.06911i
797797 34.0970 + 7.78241i 1.20778 + 0.275667i 0.778581 0.627544i 0.215940π-0.215940\pi
0.429196 + 0.903211i 0.358797π0.358797\pi
798798 10.4012 + 2.37400i 0.368198 + 0.0840387i
799799 2.46896 3.09598i 0.0873455 0.109528i
800800 0.730464i 0.0258258i
801801 −39.6490 31.6190i −1.40093 1.11720i
802802 2.74115 + 5.69207i 0.0967935 + 0.200994i
803803 10.6063 + 13.2999i 0.374290 + 0.469344i
804804 −8.64780 + 6.89639i −0.304985 + 0.243217i
805805 −2.23716 1.07736i −0.0788497 0.0379720i
806806 −0.979537 + 4.29163i −0.0345027 + 0.151166i
807807 −17.9082 78.4611i −0.630399 2.76196i
808808 −1.67821 + 0.808183i −0.0590392 + 0.0284318i
809809 16.6011 34.4725i 0.583663 1.21199i −0.374888 0.927070i 0.622319π-0.622319\pi
0.958551 0.284919i 0.0919668π-0.0919668\pi
810810 4.05135 0.924694i 0.142350 0.0324904i
811811 −31.7116 −1.11354 −0.556772 0.830665i 0.687960π-0.687960\pi
−0.556772 + 0.830665i 0.687960π0.687960\pi
812812 0 0
813813 25.2130 0.884260
814814 14.7290 3.36179i 0.516250 0.117831i
815815 −2.39683 + 4.97706i −0.0839572 + 0.174339i
816816 −8.34878 + 4.02056i −0.292266 + 0.140748i
817817 −14.5882 63.9151i −0.510377 2.23611i
818818 0.694761 3.04395i 0.0242917 0.106429i
819819 15.6439 + 7.53371i 0.546642 + 0.263249i
820820 5.71779 4.55979i 0.199674 0.159235i
821821 13.3976 + 16.8000i 0.467579 + 0.586325i 0.958576 0.284836i 0.0919391π-0.0919391\pi
−0.490998 + 0.871161i 0.663368π0.663368\pi
822822 3.67605 + 7.63339i 0.128217 + 0.266245i
823823 6.96053 + 5.55083i 0.242629 + 0.193490i 0.737253 0.675617i 0.236123π-0.236123\pi
−0.494624 + 0.869107i 0.664694π0.664694\pi
824824 14.8652i 0.517854i
825825 1.20408 1.50987i 0.0419206 0.0525668i
826826 −2.82510 0.644811i −0.0982979 0.0224358i
827827 26.7462 + 6.10465i 0.930058 + 0.212280i 0.660605 0.750734i 0.270300π-0.270300\pi
0.269453 + 0.963014i 0.413157π0.413157\pi
828828 −3.98650 + 4.99891i −0.138540 + 0.173724i
829829 40.4211i 1.40388i 0.712234 + 0.701942i 0.247683π0.247683\pi
−0.712234 + 0.701942i 0.752317π0.752317\pi
830830 −5.60169 4.46720i −0.194437 0.155059i
831831 −26.1949 54.3943i −0.908692 1.88692i
832832 −4.68005 5.86860i −0.162252 0.203457i
833833 −5.70916 + 4.55290i −0.197811 + 0.157749i
834834 15.3893 + 7.41112i 0.532889 + 0.256626i
835835 1.30980 5.73860i 0.0453274 0.198592i
836836 −11.5335 50.5316i −0.398894 1.74767i
837837 −8.32003 + 4.00671i −0.287582 + 0.138492i
838838 −2.57483 + 5.34669i −0.0889461 + 0.184698i
839839 7.90216 1.80362i 0.272813 0.0622677i −0.0839258 0.996472i 0.526746π-0.526746\pi
0.356738 + 0.934204i 0.383889π0.383889\pi
840840 −14.7680 −0.509543
841841 0 0
842842 10.3717 0.357432
843843 −22.8696 + 5.21983i −0.787670 + 0.179781i
844844 −5.51461 + 11.4512i −0.189821 + 0.394167i
845845 −6.26263 + 3.01592i −0.215441 + 0.103751i
846846 −1.39081 6.09352i −0.0478169 0.209499i
847847 −4.08104 + 17.8802i −0.140226 + 0.614371i
848848 13.0710 + 6.29466i 0.448860 + 0.216159i
849849 −30.4361 + 24.2720i −1.04456 + 0.833012i
850850 −0.0628377 0.0787959i −0.00215531 0.00270268i
851851 2.21517 + 4.59984i 0.0759349 + 0.157680i
852852 57.0586 + 45.5027i 1.95480 + 1.55890i
853853 12.7043i 0.434988i −0.976062 0.217494i 0.930212π-0.930212\pi
0.976062 0.217494i 0.0697883π-0.0697883\pi
854854 −2.25598 + 2.82890i −0.0771979 + 0.0968031i
855855 54.3500 + 12.4050i 1.85873 + 0.424243i
856856 10.1546 + 2.31773i 0.347078 + 0.0792184i
857857 −28.8170 + 36.1353i −0.984369 + 1.23436i −0.0122372 + 0.999925i 0.503895π0.503895\pi
−0.972132 + 0.234435i 0.924676π0.924676\pi
858858 21.6343i 0.738581i
859859 −4.73186 3.77354i −0.161449 0.128751i 0.539433 0.842029i 0.318639π-0.318639\pi
−0.700882 + 0.713277i 0.747210π0.747210\pi
860860 18.3108 + 38.0228i 0.624394 + 1.29657i
861861 4.17217 + 5.23173i 0.142187 + 0.178297i
862862 −6.78866 + 5.41377i −0.231223 + 0.184394i
863863 −11.8311 5.69757i −0.402736 0.193948i 0.221540 0.975151i 0.428892π-0.428892\pi
−0.624276 + 0.781204i 0.714606π0.714606\pi
864864 −3.81990 + 16.7361i −0.129955 + 0.569372i
865865 −11.5725 50.7022i −0.393475 1.72393i
866866 −7.34019 + 3.53485i −0.249430 + 0.120119i
867867 17.6465 36.6434i 0.599308 1.24448i
868868 −6.05608 + 1.38226i −0.205557 + 0.0469170i
869869 −10.5987 −0.359536
870870 0 0
871871 −7.41398 −0.251213
872872 14.7056 3.35645i 0.497993 0.113664i
873873 −21.0645 + 43.7409i −0.712925 + 1.48040i
874874 −2.37249 + 1.14253i −0.0802508 + 0.0386468i
875875 3.28406 + 14.3884i 0.111021 + 0.486417i
876876 −3.53807 + 15.5013i −0.119540 + 0.523740i
877877 −27.7280 13.3531i −0.936309 0.450903i −0.0974436 0.995241i 0.531067π-0.531067\pi
−0.838866 + 0.544338i 0.816781π0.816781\pi
878878 −2.15987 + 1.72244i −0.0728921 + 0.0581295i
879879 −54.9902 68.9555i −1.85477 2.32581i
880880 11.9730 + 24.8622i 0.403610 + 0.838106i
881881 23.0801 + 18.4058i 0.777589 + 0.620107i 0.929726 0.368253i 0.120044π-0.120044\pi
−0.152136 + 0.988360i 0.548615π0.548615\pi
882882 11.5258i 0.388093i
883883 −22.4589 + 28.1626i −0.755803 + 0.947747i −0.999757 0.0220394i 0.992984π-0.992984\pi
0.243954 + 0.969787i 0.421555π0.421555\pi
884884 −7.32164 1.67112i −0.246253 0.0562057i
885885 −25.1829 5.74782i −0.846513 0.193211i
886886 6.07287 7.61514i 0.204022 0.255836i
887887 14.2942i 0.479952i −0.970779 0.239976i 0.922860π-0.922860\pi
0.970779 0.239976i 0.0771396π-0.0771396\pi
888888 23.7399 + 18.9319i 0.796658 + 0.635314i
889889 3.11632 + 6.47111i 0.104518 + 0.217034i
890890 8.38273 + 10.5116i 0.280990 + 0.352350i
891891 14.4423 11.5174i 0.483837 0.385847i
892892 −8.61567 4.14909i −0.288474 0.138922i
893893 −3.81003 + 16.6928i −0.127498 + 0.558604i
894894 6.37380 + 27.9255i 0.213172 + 0.933967i
895895 41.6144 20.0404i 1.39101 0.669877i
896896 −6.45440 + 13.4027i −0.215626 + 0.447753i
897897 −7.12767 + 1.62684i −0.237986 + 0.0543188i
898898 −9.04279 −0.301762
899899 0 0
900900 1.05811 0.0352702
901901 7.78807 1.77758i 0.259458 0.0592196i
902902 −2.12060 + 4.40346i −0.0706081 + 0.146619i
903903 −34.7906 + 16.7543i −1.15776 + 0.557547i
904904 7.35850 + 32.2397i 0.244740 + 1.07228i
905905 4.45960 19.5388i 0.148242 0.649491i
906906 −24.8403 11.9625i −0.825265 0.397427i
907907 −15.7536 + 12.5631i −0.523089 + 0.417149i −0.849112 0.528212i 0.822863π-0.822863\pi
0.326024 + 0.945362i 0.394291π0.394291\pi
908908 17.0743 + 21.4105i 0.566629 + 0.710531i
909909 −1.79695 3.73141i −0.0596012 0.123763i
910910 −3.59903 2.87013i −0.119307 0.0951439i
911911 18.4045i 0.609769i 0.952389 + 0.304885i 0.0986179π0.0986179\pi
−0.952389 + 0.304885i 0.901382π0.901382\pi
912912 24.9813 31.3256i 0.827213 1.03729i
913913 −31.0510 7.08719i −1.02764 0.234552i
914914 −7.52541 1.71763i −0.248918 0.0568140i
915915 −20.1097 + 25.2168i −0.664806 + 0.833640i
916916 25.7875i 0.852044i
917917 −0.0288015 0.0229684i −0.000951109 0.000758484i
918918 1.02765 + 2.13394i 0.0339175 + 0.0704305i
919919 3.31549 + 4.15749i 0.109368 + 0.137143i 0.833503 0.552516i 0.186332π-0.186332\pi
−0.724135 + 0.689659i 0.757761π0.757761\pi
920920 2.84983 2.27266i 0.0939561 0.0749275i
921921 −69.1193 33.2861i −2.27756 1.09681i
922922 2.53716 11.1160i 0.0835570 0.366087i
923923 10.8852 + 47.6914i 0.358292 + 1.56978i
924924 −27.5056 + 13.2460i −0.904867 + 0.435761i
925925 0.366584 0.761220i 0.0120532 0.0250288i
926926 13.3277 3.04197i 0.437977 0.0999653i
927927 33.0520 1.08557
928928 0 0
929929 −1.90689 −0.0625630 −0.0312815 0.999511i 0.509959π-0.509959\pi
−0.0312815 + 0.999511i 0.509959π0.509959\pi
930930 8.11586 1.85239i 0.266130 0.0607423i
931931 13.6995 28.4473i 0.448983 0.932323i
932932 24.8856 11.9843i 0.815156 0.392559i
933933 −13.0660 57.2461i −0.427763 1.87415i
934934 1.31527 5.76256i 0.0430368 0.188557i
935935 13.6898 + 6.59268i 0.447706 + 0.215604i
936936 −19.9281 + 15.8922i −0.651371 + 0.519451i
937937 2.10308 + 2.63718i 0.0687047 + 0.0861530i 0.814996 0.579466i 0.196739π-0.196739\pi
−0.746292 + 0.665619i 0.768168π0.768168\pi
938938 0.682442 + 1.41711i 0.0222825 + 0.0462702i
939939 −50.3707 40.1693i −1.64378 1.31087i
940940 11.0220i 0.359498i
941941 12.3641 15.5041i 0.403059 0.505420i −0.538334 0.842731i 0.680946π-0.680946\pi
0.941393 + 0.337312i 0.109518π0.109518\pi
942942 15.8221 + 3.61129i 0.515512 + 0.117662i
943943 −1.61024 0.367527i −0.0524366 0.0119683i
944944 −6.78526 + 8.50845i −0.220841 + 0.276926i
945945 9.65689i 0.314139i
946946 −22.0504 17.5846i −0.716921 0.571726i
947947 −17.5787 36.5025i −0.571230 1.18617i −0.963844 0.266467i 0.914144π-0.914144\pi
0.392614 0.919703i 0.371571π-0.371571\pi
948948 −6.17647 7.74504i −0.200602 0.251547i
949949 −8.33234 + 6.64482i −0.270479 + 0.215700i
950950 0.392620 + 0.189076i 0.0127383 + 0.00613444i
951951 −5.60358 + 24.5509i −0.181709 + 0.796117i
952952 0.762350 + 3.34007i 0.0247079 + 0.108252i
953953 2.11000 1.01612i 0.0683497 0.0329155i −0.399397 0.916778i 0.630780π-0.630780\pi
0.467746 + 0.883863i 0.345066π0.345066\pi
954954 5.47068 11.3600i 0.177120 0.367793i
955955 −41.4027 + 9.44990i −1.33976 + 0.305792i
956956 16.3429 0.528567
957957 0 0
958958 12.4378 0.401848
959959 −7.81283 + 1.78323i −0.252289 + 0.0575834i
960960 −6.15895 + 12.7892i −0.198779 + 0.412769i
961961 −21.1462 + 10.1835i −0.682134 + 0.328499i
962962 2.10614 + 9.22762i 0.0679048 + 0.297511i
963963 −5.15335 + 22.5783i −0.166064 + 0.727576i
964964 −16.3541 7.87572i −0.526730 0.253660i
965965 9.16307 7.30730i 0.294970 0.235230i
966966 0.967043 + 1.21263i 0.0311141 + 0.0390158i
967967 5.73972 + 11.9187i 0.184577 + 0.383278i 0.972640 0.232316i 0.0746303π-0.0746303\pi
−0.788063 + 0.615594i 0.788916π0.788916\pi
968968 −21.0490 16.7860i −0.676540 0.539523i
969969 22.0620i 0.708732i
970970 8.02498 10.0630i 0.257667 0.323104i
971971 −20.1227 4.59287i −0.645767 0.147392i −0.112920 0.993604i 0.536021π-0.536021\pi
−0.532846 + 0.846212i 0.678878π0.678878\pi
972972 33.9459 + 7.74793i 1.08882 + 0.248515i
973973 −10.0732 + 12.6314i −0.322932 + 0.404944i
974974 0.657928i 0.0210814i
975975 0.945923 + 0.754349i 0.0302938 + 0.0241585i
976976 5.89595 + 12.2431i 0.188725 + 0.391891i
977977 −1.68503 2.11296i −0.0539088 0.0675995i 0.754146 0.656707i 0.228051π-0.228051\pi
−0.808055 + 0.589107i 0.799480π0.799480\pi
978978 2.69777 2.15140i 0.0862651 0.0687941i
979979 53.8472 + 25.9314i 1.72096 + 0.828773i
980980 −4.52278 + 19.8156i −0.144475 + 0.632986i
981981 7.46289 + 32.6971i 0.238272 + 1.04394i
982982 −15.0433 + 7.24447i −0.480051 + 0.231180i
983983 −6.32843 + 13.1411i −0.201846 + 0.419137i −0.977180 0.212415i 0.931867π-0.931867\pi
0.775334 + 0.631551i 0.217582π0.217582\pi
984984 −9.57685 + 2.18585i −0.305299 + 0.0696825i
985985 21.9778 0.700272
986986 0 0
987987 10.0850 0.321011
988988 31.6578 7.22568i 1.00717 0.229880i
989989 4.13533 8.58711i 0.131496 0.273054i
990990 21.6077 10.4057i 0.686739 0.330716i
991991 4.97316 + 21.7888i 0.157978 + 0.692146i 0.990426 + 0.138043i 0.0440813π0.0440813\pi
−0.832449 + 0.554102i 0.813062π0.813062\pi
992992 3.11461 13.6460i 0.0988891 0.433261i
993993 24.8592 + 11.9716i 0.788884 + 0.379907i
994994 8.11374 6.47050i 0.257352 0.205232i
995995 30.4905 + 38.2339i 0.966615 + 1.21210i
996996 −12.9162 26.8208i −0.409266 0.849850i
997997 −42.5456 33.9290i −1.34743 1.07454i −0.990070 0.140575i 0.955105π-0.955105\pi
−0.357362 0.933966i 0.616324π-0.616324\pi
998998 5.35958i 0.169655i
999999 −12.3797 + 15.5237i −0.391678 + 0.491148i
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 841.2.e.l.196.7 72
29.2 odd 28 841.2.a.h.1.3 yes 6
29.3 odd 28 841.2.d.n.778.3 36
29.4 even 14 inner 841.2.e.l.236.7 72
29.5 even 14 841.2.b.d.840.6 12
29.6 even 14 inner 841.2.e.l.270.7 72
29.7 even 7 inner 841.2.e.l.63.6 72
29.8 odd 28 841.2.d.o.190.3 36
29.9 even 14 inner 841.2.e.l.651.6 72
29.10 odd 28 841.2.d.o.605.3 36
29.11 odd 28 841.2.d.n.574.3 36
29.12 odd 4 841.2.d.o.645.3 36
29.13 even 14 inner 841.2.e.l.267.6 72
29.14 odd 28 841.2.d.n.571.4 36
29.15 odd 28 841.2.d.o.571.3 36
29.16 even 7 inner 841.2.e.l.267.7 72
29.17 odd 4 841.2.d.n.645.4 36
29.18 odd 28 841.2.d.o.574.4 36
29.19 odd 28 841.2.d.n.605.4 36
29.20 even 7 inner 841.2.e.l.651.7 72
29.21 odd 28 841.2.d.n.190.4 36
29.22 even 14 inner 841.2.e.l.63.7 72
29.23 even 7 inner 841.2.e.l.270.6 72
29.24 even 7 841.2.b.d.840.7 12
29.25 even 7 inner 841.2.e.l.236.6 72
29.26 odd 28 841.2.d.o.778.4 36
29.27 odd 28 841.2.a.g.1.4 6
29.28 even 2 inner 841.2.e.l.196.6 72
87.2 even 28 7569.2.a.y.1.4 6
87.56 even 28 7569.2.a.bc.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
841.2.a.g.1.4 6 29.27 odd 28
841.2.a.h.1.3 yes 6 29.2 odd 28
841.2.b.d.840.6 12 29.5 even 14
841.2.b.d.840.7 12 29.24 even 7
841.2.d.n.190.4 36 29.21 odd 28
841.2.d.n.571.4 36 29.14 odd 28
841.2.d.n.574.3 36 29.11 odd 28
841.2.d.n.605.4 36 29.19 odd 28
841.2.d.n.645.4 36 29.17 odd 4
841.2.d.n.778.3 36 29.3 odd 28
841.2.d.o.190.3 36 29.8 odd 28
841.2.d.o.571.3 36 29.15 odd 28
841.2.d.o.574.4 36 29.18 odd 28
841.2.d.o.605.3 36 29.10 odd 28
841.2.d.o.645.3 36 29.12 odd 4
841.2.d.o.778.4 36 29.26 odd 28
841.2.e.l.63.6 72 29.7 even 7 inner
841.2.e.l.63.7 72 29.22 even 14 inner
841.2.e.l.196.6 72 29.28 even 2 inner
841.2.e.l.196.7 72 1.1 even 1 trivial
841.2.e.l.236.6 72 29.25 even 7 inner
841.2.e.l.236.7 72 29.4 even 14 inner
841.2.e.l.267.6 72 29.13 even 14 inner
841.2.e.l.267.7 72 29.16 even 7 inner
841.2.e.l.270.6 72 29.23 even 7 inner
841.2.e.l.270.7 72 29.6 even 14 inner
841.2.e.l.651.6 72 29.9 even 14 inner
841.2.e.l.651.7 72 29.20 even 7 inner
7569.2.a.y.1.4 6 87.2 even 28
7569.2.a.bc.1.3 6 87.56 even 28