Properties

Label 85.2.m.a.9.1
Level 8585
Weight 22
Character 85.9
Analytic conductor 0.6790.679
Analytic rank 00
Dimension 2424
Inner twists 44

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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] = [85,2,Mod(9,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 1])) 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("85.9"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 85=517 85 = 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 85.m (of order 88, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.6787284171810.678728417181
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 9.1
Character χ\chi == 85.9
Dual form 85.2.m.a.19.1

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+(1.488431.48843i)q2+(0.690961+1.66813i)q3+2.43082iq4+(1.70647+1.44498i)q5+(3.511331.45444i)q6+(2.479121.02689i)q7+(0.6412410.641241i)q8+(0.1839010.183901i)q9+(0.3892104.69069i)q10+(0.901470+0.373401i)q11+(4.054911.67960i)q12+2.65240q13+(5.218432.16155i)q14+(3.58951+1.84818i)q15+2.95276q16+(3.25539+2.53030i)q17+0.547447iq18+(0.478059+0.478059i)q19+(3.51248+4.14812i)q20+4.84503iq21+(1.89755+0.785991i)q22+(1.543973.72748i)q23+(0.626599+1.51274i)q24+(0.824076+4.93162i)q25+(3.947903.94790i)q26+(4.57054+1.89318i)q27+(2.49617+6.02630i)q28+(3.839589.26957i)q29+(8.09360+2.59183i)q30+(9.104973.77140i)q31+(5.677445.67744i)q321.76177iq33+(8.61157+1.07924i)q34+(5.71438+1.82993i)q35+(0.4470310.447031i)q36+(2.616466.31669i)q37+1.42311q38+(1.83270+4.42454i)q39+(2.020840.167679i)q40+(2.80190+6.76439i)q41+(7.211477.21147i)q42+(6.296286.29628i)q43+(0.9076702.19131i)q44+(0.04808860.579556i)q45+(3.24999+7.84616i)q460.874497q47+(2.04024+4.92558i)q48+(0.1418090.141809i)q49+(6.113778.56693i)q50+(1.971527.17875i)q51+6.44750iq52+(2.00842+2.00842i)q53+(9.62077+3.98505i)q54+(2.077890.665407i)q55+(0.9312342.24820i)q56+(0.4671441.12778i)q57+(19.5120+8.08213i)q58+(7.590057.59005i)q59+(4.492608.72545i)q60+(0.793008+1.91449i)q61+(7.93862+19.1655i)q62+(0.6447600.267068i)q63+10.9954iq64+(4.52624+3.83266i)q65+(2.62227+2.62227i)q66+5.73990iq67+(6.150707.91327i)q68+7.28473q69+(5.7817111.2291i)q70+(1.03955+0.430595i)q710.235850q72+(2.770271.14748i)q73+(13.2963+5.50752i)q74+(8.795982.03289i)q75+(1.162081.16208i)q76+(1.85141+1.85141i)q77+(9.313433.85775i)q78+(0.377872+0.156520i)q79+(5.03879+4.26667i)q809.71259iq81+(5.8978614.2387i)q82+(4.64846+4.64846i)q8311.7774q84+(9.211460.386088i)q8518.7431q86+(12.8098+12.8098i)q87+(0.338619+0.817499i)q885.62649iq89+(0.791049+0.934201i)q90+(6.575622.72371i)q91+(9.060823.75312i)q92+(12.582412.5824i)q93+(1.30162+1.30162i)q94+(1.50658+0.125008i)q95+(13.39365.54781i)q96+(14.24055.89862i)q970.422145q98+(0.234451+0.0971126i)q99+O(q100)q+(-1.48843 - 1.48843i) q^{2} +(-0.690961 + 1.66813i) q^{3} +2.43082i q^{4} +(1.70647 + 1.44498i) q^{5} +(3.51133 - 1.45444i) q^{6} +(2.47912 - 1.02689i) q^{7} +(0.641241 - 0.641241i) q^{8} +(-0.183901 - 0.183901i) q^{9} +(-0.389210 - 4.69069i) q^{10} +(-0.901470 + 0.373401i) q^{11} +(-4.05491 - 1.67960i) q^{12} +2.65240 q^{13} +(-5.21843 - 2.16155i) q^{14} +(-3.58951 + 1.84818i) q^{15} +2.95276 q^{16} +(-3.25539 + 2.53030i) q^{17} +0.547447i q^{18} +(-0.478059 + 0.478059i) q^{19} +(-3.51248 + 4.14812i) q^{20} +4.84503i q^{21} +(1.89755 + 0.785991i) q^{22} +(-1.54397 - 3.72748i) q^{23} +(0.626599 + 1.51274i) q^{24} +(0.824076 + 4.93162i) q^{25} +(-3.94790 - 3.94790i) q^{26} +(-4.57054 + 1.89318i) q^{27} +(2.49617 + 6.02630i) q^{28} +(3.83958 - 9.26957i) q^{29} +(8.09360 + 2.59183i) q^{30} +(-9.10497 - 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} -1.76177i q^{33} +(8.61157 + 1.07924i) q^{34} +(5.71438 + 1.82993i) q^{35} +(0.447031 - 0.447031i) q^{36} +(2.61646 - 6.31669i) q^{37} +1.42311 q^{38} +(-1.83270 + 4.42454i) q^{39} +(2.02084 - 0.167679i) q^{40} +(2.80190 + 6.76439i) q^{41} +(7.21147 - 7.21147i) q^{42} +(6.29628 - 6.29628i) q^{43} +(-0.907670 - 2.19131i) q^{44} +(-0.0480886 - 0.579556i) q^{45} +(-3.24999 + 7.84616i) q^{46} -0.874497 q^{47} +(-2.04024 + 4.92558i) q^{48} +(0.141809 - 0.141809i) q^{49} +(6.11377 - 8.56693i) q^{50} +(-1.97152 - 7.17875i) q^{51} +6.44750i q^{52} +(2.00842 + 2.00842i) q^{53} +(9.62077 + 3.98505i) q^{54} +(-2.07789 - 0.665407i) q^{55} +(0.931234 - 2.24820i) q^{56} +(-0.467144 - 1.12778i) q^{57} +(-19.5120 + 8.08213i) q^{58} +(-7.59005 - 7.59005i) q^{59} +(-4.49260 - 8.72545i) q^{60} +(0.793008 + 1.91449i) q^{61} +(7.93862 + 19.1655i) q^{62} +(-0.644760 - 0.267068i) q^{63} +10.9954i q^{64} +(4.52624 + 3.83266i) q^{65} +(-2.62227 + 2.62227i) q^{66} +5.73990i q^{67} +(-6.15070 - 7.91327i) q^{68} +7.28473 q^{69} +(-5.78171 - 11.2291i) q^{70} +(1.03955 + 0.430595i) q^{71} -0.235850 q^{72} +(-2.77027 - 1.14748i) q^{73} +(-13.2963 + 5.50752i) q^{74} +(-8.79598 - 2.03289i) q^{75} +(-1.16208 - 1.16208i) q^{76} +(-1.85141 + 1.85141i) q^{77} +(9.31343 - 3.85775i) q^{78} +(-0.377872 + 0.156520i) q^{79} +(5.03879 + 4.26667i) q^{80} -9.71259i q^{81} +(5.89786 - 14.2387i) q^{82} +(4.64846 + 4.64846i) q^{83} -11.7774 q^{84} +(-9.21146 - 0.386088i) q^{85} -18.7431 q^{86} +(12.8098 + 12.8098i) q^{87} +(-0.338619 + 0.817499i) q^{88} -5.62649i q^{89} +(-0.791049 + 0.934201i) q^{90} +(6.57562 - 2.72371i) q^{91} +(9.06082 - 3.75312i) q^{92} +(12.5824 - 12.5824i) q^{93} +(1.30162 + 1.30162i) q^{94} +(-1.50658 + 0.125008i) q^{95} +(13.3936 - 5.54781i) q^{96} +(-14.2405 - 5.89862i) q^{97} -0.422145 q^{98} +(0.234451 + 0.0971126i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q8q916q1024q1416q15+8q1624q198q20+32q24+16q2516q26+24q2924q31+8q34+8q35+8q3624q39+16q40+80q99+O(q100) 24 q - 8 q^{9} - 16 q^{10} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 24 q^{19} - 8 q^{20} + 32 q^{24} + 16 q^{25} - 16 q^{26} + 24 q^{29} - 24 q^{31} + 8 q^{34} + 8 q^{35} + 8 q^{36} - 24 q^{39} + 16 q^{40}+ \cdots - 80 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/85Z)×\left(\mathbb{Z}/85\mathbb{Z}\right)^\times.

nn 5252 7171
χ(n)\chi(n) 1-1 e(18)e\left(\frac{1}{8}\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 −1.48843 1.48843i −1.05248 1.05248i −0.998545 0.0539308i 0.982825π-0.982825\pi
−0.0539308 0.998545i 0.517175π-0.517175\pi
33 −0.690961 + 1.66813i −0.398926 + 0.963094i 0.588995 + 0.808137i 0.299524π0.299524\pi
−0.987921 + 0.154957i 0.950476π0.950476\pi
44 2.43082i 1.21541i
55 1.70647 + 1.44498i 0.763156 + 0.646214i
66 3.51133 1.45444i 1.43349 0.593772i
77 2.47912 1.02689i 0.937021 0.388127i 0.138683 0.990337i 0.455713π-0.455713\pi
0.798338 + 0.602210i 0.205713π0.205713\pi
88 0.641241 0.641241i 0.226713 0.226713i
99 −0.183901 0.183901i −0.0613005 0.0613005i
1010 −0.389210 4.69069i −0.123079 1.48333i
1111 −0.901470 + 0.373401i −0.271803 + 0.112585i −0.514422 0.857537i 0.671994π-0.671994\pi
0.242619 + 0.970122i 0.421994π0.421994\pi
1212 −4.05491 1.67960i −1.17055 0.484859i
1313 2.65240 0.735643 0.367821 0.929896i 0.380104π-0.380104\pi
0.367821 + 0.929896i 0.380104π0.380104\pi
1414 −5.21843 2.16155i −1.39468 0.577697i
1515 −3.58951 + 1.84818i −0.926808 + 0.477199i
1616 2.95276 0.738190
1717 −3.25539 + 2.53030i −0.789548 + 0.613688i
1818 0.547447i 0.129034i
1919 −0.478059 + 0.478059i −0.109674 + 0.109674i −0.759814 0.650140i 0.774710π-0.774710\pi
0.650140 + 0.759814i 0.274710π0.274710\pi
2020 −3.51248 + 4.14812i −0.785414 + 0.927547i
2121 4.84503i 1.05727i
2222 1.89755 + 0.785991i 0.404559 + 0.167574i
2323 −1.54397 3.72748i −0.321940 0.777233i −0.999141 0.0414347i 0.986807π-0.986807\pi
0.677201 0.735798i 0.263193π-0.263193\pi
2424 0.626599 + 1.51274i 0.127904 + 0.308788i
2525 0.824076 + 4.93162i 0.164815 + 0.986324i
2626 −3.94790 3.94790i −0.774246 0.774246i
2727 −4.57054 + 1.89318i −0.879601 + 0.364343i
2828 2.49617 + 6.02630i 0.471733 + 1.13886i
2929 3.83958 9.26957i 0.712992 1.72132i 0.0206072 0.999788i 0.493440π-0.493440\pi
0.692385 0.721528i 0.256560π-0.256560\pi
3030 8.09360 + 2.59183i 1.47768 + 0.473202i
3131 −9.10497 3.77140i −1.63530 0.677364i −0.639490 0.768800i 0.720854π-0.720854\pi
−0.995811 + 0.0914357i 0.970854π0.970854\pi
3232 −5.67744 5.67744i −1.00364 1.00364i
3333 1.76177i 0.306685i
3434 8.61157 + 1.07924i 1.47687 + 0.185089i
3535 5.71438 + 1.82993i 0.965906 + 0.309314i
3636 0.447031 0.447031i 0.0745052 0.0745052i
3737 2.61646 6.31669i 0.430143 1.03846i −0.549098 0.835758i 0.685029π-0.685029\pi
0.979241 0.202699i 0.0649714π-0.0649714\pi
3838 1.42311 0.230859
3939 −1.83270 + 4.42454i −0.293467 + 0.708493i
4040 2.02084 0.167679i 0.319522 0.0265124i
4141 2.80190 + 6.76439i 0.437583 + 1.05642i 0.976781 + 0.214240i 0.0687276π0.0687276\pi
−0.539198 + 0.842179i 0.681272π0.681272\pi
4242 7.21147 7.21147i 1.11275 1.11275i
4343 6.29628 6.29628i 0.960173 0.960173i −0.0390633 0.999237i 0.512437π-0.512437\pi
0.999237 + 0.0390633i 0.0124374π0.0124374\pi
4444 −0.907670 2.19131i −0.136836 0.330352i
4545 −0.0480886 0.579556i −0.00716863 0.0863951i
4646 −3.24999 + 7.84616i −0.479184 + 1.15685i
4747 −0.874497 −0.127558 −0.0637792 0.997964i 0.520315π-0.520315\pi
−0.0637792 + 0.997964i 0.520315π0.520315\pi
4848 −2.04024 + 4.92558i −0.294483 + 0.710946i
4949 0.141809 0.141809i 0.0202585 0.0202585i
5050 6.11377 8.56693i 0.864618 1.21155i
5151 −1.97152 7.17875i −0.276067 1.00523i
5252 6.44750i 0.894107i
5353 2.00842 + 2.00842i 0.275878 + 0.275878i 0.831461 0.555583i 0.187505π-0.187505\pi
−0.555583 + 0.831461i 0.687505π0.687505\pi
5454 9.62077 + 3.98505i 1.30922 + 0.542297i
5555 −2.07789 0.665407i −0.280182 0.0897234i
5656 0.931234 2.24820i 0.124441 0.300428i
5757 −0.467144 1.12778i −0.0618747 0.149379i
5858 −19.5120 + 8.08213i −2.56205 + 1.06124i
5959 −7.59005 7.59005i −0.988140 0.988140i 0.0117908 0.999930i 0.496247π-0.496247\pi
−0.999930 + 0.0117908i 0.996247π0.996247\pi
6060 −4.49260 8.72545i −0.579992 1.12645i
6161 0.793008 + 1.91449i 0.101534 + 0.245125i 0.966481 0.256738i 0.0826479π-0.0826479\pi
−0.864947 + 0.501864i 0.832648π0.832648\pi
6262 7.93862 + 19.1655i 1.00821 + 2.43402i
6363 −0.644760 0.267068i −0.0812321 0.0336475i
6464 10.9954i 1.37442i
6565 4.52624 + 3.83266i 0.561410 + 0.475383i
6666 −2.62227 + 2.62227i −0.322779 + 0.322779i
6767 5.73990i 0.701240i 0.936518 + 0.350620i 0.114029π0.114029\pi
−0.936518 + 0.350620i 0.885971π0.885971\pi
6868 −6.15070 7.91327i −0.745882 0.959624i
6969 7.28473 0.876979
7070 −5.78171 11.2291i −0.691047 1.34214i
7171 1.03955 + 0.430595i 0.123372 + 0.0511022i 0.443515 0.896267i 0.353731π-0.353731\pi
−0.320144 + 0.947369i 0.603731π0.603731\pi
7272 −0.235850 −0.0277952
7373 −2.77027 1.14748i −0.324236 0.134303i 0.214628 0.976696i 0.431146π-0.431146\pi
−0.538864 + 0.842393i 0.681146π0.681146\pi
7474 −13.2963 + 5.50752i −1.54567 + 0.640236i
7575 −8.79598 2.03289i −1.01567 0.234738i
7676 −1.16208 1.16208i −0.133299 0.133299i
7777 −1.85141 + 1.85141i −0.210988 + 0.210988i
7878 9.31343 3.85775i 1.05454 0.436804i
7979 −0.377872 + 0.156520i −0.0425139 + 0.0176099i −0.403839 0.914830i 0.632324π-0.632324\pi
0.361325 + 0.932440i 0.382324π0.382324\pi
8080 5.03879 + 4.26667i 0.563354 + 0.477028i
8181 9.71259i 1.07918i
8282 5.89786 14.2387i 0.651310 1.57240i
8383 4.64846 + 4.64846i 0.510235 + 0.510235i 0.914598 0.404363i 0.132507π-0.132507\pi
−0.404363 + 0.914598i 0.632507π0.632507\pi
8484 −11.7774 −1.28502
8585 −9.21146 0.386088i −0.999123 0.0418771i
8686 −18.7431 −2.02112
8787 12.8098 + 12.8098i 1.37336 + 1.37336i
8888 −0.338619 + 0.817499i −0.0360969 + 0.0871457i
8989 5.62649i 0.596407i −0.954502 0.298204i 0.903613π-0.903613\pi
0.954502 0.298204i 0.0963874π-0.0963874\pi
9090 −0.791049 + 0.934201i −0.0833839 + 0.0984735i
9191 6.57562 2.72371i 0.689312 0.285523i
9292 9.06082 3.75312i 0.944656 0.391289i
9393 12.5824 12.5824i 1.30473 1.30473i
9494 1.30162 + 1.30162i 0.134252 + 0.134252i
9595 −1.50658 + 0.125008i −0.154572 + 0.0128256i
9696 13.3936 5.54781i 1.36698 0.566221i
9797 −14.2405 5.89862i −1.44591 0.598915i −0.484685 0.874689i 0.661066π-0.661066\pi
−0.961222 + 0.275774i 0.911066π0.911066\pi
9898 −0.422145 −0.0426430
9999 0.234451 + 0.0971126i 0.0235632 + 0.00976018i
100100 −11.9879 + 2.00318i −1.19879 + 0.200318i
101101 14.6242 1.45516 0.727582 0.686021i 0.240644π-0.240644\pi
0.727582 + 0.686021i 0.240644π0.240644\pi
102102 −7.75057 + 13.6195i −0.767421 + 1.34853i
103103 1.63280i 0.160884i 0.996759 + 0.0804421i 0.0256332π0.0256332\pi
−0.996759 + 0.0804421i 0.974367π0.974367\pi
104104 1.70083 1.70083i 0.166780 0.166780i
105105 −7.00097 + 8.26790i −0.683224 + 0.806864i
106106 5.97877i 0.580710i
107107 5.14591 + 2.13151i 0.497474 + 0.206060i 0.617290 0.786736i 0.288231π-0.288231\pi
−0.119816 + 0.992796i 0.538231π0.538231\pi
108108 −4.60198 11.1102i −0.442826 1.06908i
109109 −1.00965 2.43750i −0.0967066 0.233470i 0.868122 0.496351i 0.165327π-0.165327\pi
−0.964828 + 0.262881i 0.915327π0.915327\pi
110110 2.10237 + 4.08319i 0.200453 + 0.389317i
111111 8.72917 + 8.72917i 0.828536 + 0.828536i
112112 7.32025 3.03215i 0.691699 0.286511i
113113 −2.22293 5.36662i −0.209115 0.504849i 0.784169 0.620547i 0.213090π-0.213090\pi
−0.993284 + 0.115698i 0.963090π0.963090\pi
114114 −0.983314 + 2.37393i −0.0920958 + 0.222339i
115115 2.75138 8.59183i 0.256568 0.801193i
116116 22.5326 + 9.33332i 2.09210 + 0.866577i
117117 −0.487780 0.487780i −0.0450952 0.0450952i
118118 22.5944i 2.07999i
119119 −5.47219 + 9.61585i −0.501634 + 0.881483i
120120 −1.11661 + 3.48687i −0.101932 + 0.318306i
121121 −7.10496 + 7.10496i −0.645905 + 0.645905i
122122 1.66924 4.02991i 0.151126 0.364851i
123123 −13.2199 −1.19199
124124 9.16759 22.1325i 0.823274 1.98756i
125125 −5.71983 + 9.60644i −0.511597 + 0.859226i
126126 0.562166 + 1.35719i 0.0500817 + 0.120908i
127127 −7.53018 + 7.53018i −0.668195 + 0.668195i −0.957298 0.289103i 0.906643π-0.906643\pi
0.289103 + 0.957298i 0.406643π0.406643\pi
128128 5.01091 5.01091i 0.442906 0.442906i
129129 6.15251 + 14.8535i 0.541698 + 1.30778i
130130 −1.03234 12.4416i −0.0905422 1.09120i
131131 −0.619360 + 1.49527i −0.0541137 + 0.130642i −0.948624 0.316405i 0.897524π-0.897524\pi
0.894511 + 0.447047i 0.147524π0.147524\pi
132132 4.28255 0.372748
133133 −0.694256 + 1.67608i −0.0601996 + 0.145335i
134134 8.54341 8.54341i 0.738038 0.738038i
135135 −10.5351 3.37368i −0.906717 0.290360i
136136 −0.464958 + 3.71002i −0.0398698 + 0.318132i
137137 4.70326i 0.401826i −0.979609 0.200913i 0.935609π-0.935609\pi
0.979609 0.200913i 0.0643909π-0.0643909\pi
138138 −10.8428 10.8428i −0.922999 0.922999i
139139 0.761078 + 0.315249i 0.0645538 + 0.0267391i 0.414727 0.909946i 0.363877π-0.363877\pi
−0.350173 + 0.936685i 0.613877π0.613877\pi
140140 −4.44822 + 13.8906i −0.375944 + 1.17397i
141141 0.604243 1.45877i 0.0508865 0.122851i
142142 −0.906381 2.18820i −0.0760618 0.183629i
143143 −2.39106 + 0.990408i −0.199950 + 0.0828221i
144144 −0.543017 0.543017i −0.0452514 0.0452514i
145145 19.9465 10.2701i 1.65646 0.852888i
146146 2.41540 + 5.83129i 0.199900 + 0.482601i
147147 0.138571 + 0.334540i 0.0114292 + 0.0275924i
148148 15.3547 + 6.36014i 1.26215 + 0.522800i
149149 9.60320i 0.786725i −0.919383 0.393362i 0.871312π-0.871312\pi
0.919383 0.393362i 0.128688π-0.128688\pi
150150 10.0663 + 16.1180i 0.821914 + 1.31603i
151151 −1.00179 + 1.00179i −0.0815244 + 0.0815244i −0.746693 0.665169i 0.768360π-0.768360\pi
0.665169 + 0.746693i 0.268360π0.268360\pi
152152 0.613103i 0.0497292i
153153 1.06400 + 0.133345i 0.0860191 + 0.0107803i
154154 5.51138 0.444120
155155 −10.0878 19.5923i −0.810268 1.57369i
156156 −10.7552 4.45497i −0.861109 0.356683i
157157 4.81882 0.384584 0.192292 0.981338i 0.438408π-0.438408\pi
0.192292 + 0.981338i 0.438408π0.438408\pi
158158 0.795403 + 0.329467i 0.0632788 + 0.0262109i
159159 −4.73804 + 1.96256i −0.375751 + 0.155641i
160160 −1.48460 17.8922i −0.117368 1.41450i
161161 −7.65539 7.65539i −0.603330 0.603330i
162162 −14.4565 + 14.4565i −1.13581 + 1.13581i
163163 1.49578 0.619572i 0.117158 0.0485286i −0.323334 0.946285i 0.604804π-0.604804\pi
0.440493 + 0.897756i 0.354804π0.354804\pi
164164 −16.4430 + 6.81091i −1.28398 + 0.531843i
165165 2.54572 3.00641i 0.198184 0.234049i
166166 13.8378i 1.07402i
167167 8.47025 20.4490i 0.655447 1.58239i −0.149313 0.988790i 0.547706π-0.547706\pi
0.804760 0.593600i 0.202294π-0.202294\pi
168168 3.10683 + 3.10683i 0.239697 + 0.239697i
169169 −5.96479 −0.458830
170170 13.1359 + 14.2852i 1.00748 + 1.09563i
171171 0.175832 0.0134462
172172 15.3051 + 15.3051i 1.16700 + 1.16700i
173173 −3.97100 + 9.58685i −0.301910 + 0.728875i 0.698008 + 0.716089i 0.254070π0.254070\pi
−0.999918 + 0.0127852i 0.995930π0.995930\pi
174174 38.1329i 2.89085i
175175 7.10720 + 11.3799i 0.537254 + 0.860237i
176176 −2.66182 + 1.10256i −0.200642 + 0.0831088i
177177 17.9056 7.41674i 1.34587 0.557476i
178178 −8.37461 + 8.37461i −0.627704 + 0.627704i
179179 13.2428 + 13.2428i 0.989813 + 0.989813i 0.999949 0.0101361i 0.00322646π-0.00322646\pi
−0.0101361 + 0.999949i 0.503226π0.503226\pi
180180 1.40879 0.116895i 0.105005 0.00871282i
181181 −2.26809 + 0.939472i −0.168585 + 0.0698304i −0.465380 0.885111i 0.654082π-0.654082\pi
0.296795 + 0.954941i 0.404082π0.404082\pi
182182 −13.8414 5.73328i −1.02599 0.424979i
183183 −3.74155 −0.276584
184184 −3.38027 1.40015i −0.249197 0.103221i
185185 13.5924 6.99851i 0.999332 0.514541i
186186 −37.4558 −2.74639
187187 1.98982 3.49656i 0.145510 0.255694i
188188 2.12574i 0.155036i
189189 −9.38686 + 9.38686i −0.682793 + 0.682793i
190190 2.42850 + 2.05636i 0.176182 + 0.149184i
191191 10.9126i 0.789607i 0.918766 + 0.394803i 0.129187π0.129187\pi
−0.918766 + 0.394803i 0.870813π0.870813\pi
192192 −18.3417 7.59738i −1.32370 0.548293i
193193 7.03202 + 16.9768i 0.506176 + 1.22202i 0.946069 + 0.323966i 0.105016π0.105016\pi
−0.439893 + 0.898050i 0.644984π0.644984\pi
194194 12.4163 + 29.9756i 0.891439 + 2.15213i
195195 −9.52081 + 4.90212i −0.681800 + 0.351048i
196196 0.344712 + 0.344712i 0.0246223 + 0.0246223i
197197 −18.0071 + 7.45879i −1.28295 + 0.531417i −0.916878 0.399168i 0.869299π-0.869299\pi
−0.366076 + 0.930585i 0.619299π0.619299\pi
198198 −0.204417 0.493507i −0.0145273 0.0350720i
199199 −8.92336 + 21.5429i −0.632560 + 1.52713i 0.203834 + 0.979005i 0.434660π0.434660\pi
−0.836394 + 0.548129i 0.815340π0.815340\pi
200200 3.69079 + 2.63393i 0.260978 + 0.186247i
201201 −9.57488 3.96605i −0.675360 0.279743i
202202 −21.7670 21.7670i −1.53152 1.53152i
203203 26.9232i 1.88964i
204204 17.4502 4.79240i 1.22176 0.335535i
205205 −4.99303 + 15.5919i −0.348729 + 1.08899i
206206 2.43029 2.43029i 0.169327 0.169327i
207207 −0.401550 + 0.969427i −0.0279096 + 0.0673798i
208208 7.83189 0.543044
209209 0.252448 0.609464i 0.0174622 0.0421575i
210210 22.7266 1.88574i 1.56828 0.130128i
211211 −8.77140 21.1760i −0.603848 1.45782i −0.869590 0.493774i 0.835617π-0.835617\pi
0.265742 0.964044i 0.414383π-0.414383\pi
212212 −4.88211 + 4.88211i −0.335305 + 0.335305i
213213 −1.43657 + 1.43657i −0.0984324 + 0.0984324i
214214 −4.48671 10.8319i −0.306706 0.740453i
215215 19.8424 1.64642i 1.35324 0.112285i
216216 −1.71683 + 4.14480i −0.116816 + 0.282018i
217217 −26.4451 −1.79521
218218 −2.12526 + 5.13082i −0.143940 + 0.347503i
219219 3.82830 3.82830i 0.258692 0.258692i
220220 1.61748 5.05097i 0.109051 0.340536i
221221 −8.63459 + 6.71137i −0.580826 + 0.451455i
222222 25.9854i 1.74403i
223223 9.23194 + 9.23194i 0.618217 + 0.618217i 0.945074 0.326857i 0.105990π-0.105990\pi
−0.326857 + 0.945074i 0.605990π0.605990\pi
224224 −19.9052 8.24499i −1.32997 0.550892i
225225 0.755383 1.05848i 0.0503589 0.0705654i
226226 −4.67915 + 11.2965i −0.311253 + 0.751430i
227227 4.09453 + 9.88506i 0.271763 + 0.656095i 0.999559 0.0296996i 0.00945506π-0.00945506\pi
−0.727796 + 0.685794i 0.759455π0.759455\pi
228228 2.74144 1.13554i 0.181556 0.0752031i
229229 13.3171 + 13.3171i 0.880020 + 0.880020i 0.993536 0.113516i 0.0362113π-0.0362113\pi
−0.113516 + 0.993536i 0.536211π0.536211\pi
230230 −16.8835 + 8.69307i −1.11327 + 0.573204i
231231 −1.80914 4.36765i −0.119033 0.287370i
232232 −3.48193 8.40612i −0.228600 0.551889i
233233 2.07494 + 0.859469i 0.135934 + 0.0563057i 0.449613 0.893223i 0.351562π-0.351562\pi
−0.313679 + 0.949529i 0.601562π0.601562\pi
234234 1.45205i 0.0949233i
235235 −1.49230 1.26363i −0.0973471 0.0824301i
236236 18.4500 18.4500i 1.20099 1.20099i
237237 0.738488i 0.0479700i
238238 22.4574 6.16753i 1.45570 0.399782i
239239 16.7293 1.08213 0.541063 0.840982i 0.318022π-0.318022\pi
0.541063 + 0.840982i 0.318022π0.318022\pi
240240 −10.5990 + 5.45724i −0.684160 + 0.352264i
241241 10.8767 + 4.50526i 0.700627 + 0.290209i 0.704420 0.709784i 0.251207π-0.251207\pi
−0.00379273 + 0.999993i 0.501207π0.501207\pi
242242 21.1504 1.35960
243243 2.49021 + 1.03148i 0.159747 + 0.0661693i
244244 −4.65378 + 1.92766i −0.297928 + 0.123406i
245245 0.446904 0.0370819i 0.0285517 0.00236907i
246246 19.6768 + 19.6768i 1.25455 + 1.25455i
247247 −1.26800 + 1.26800i −0.0806812 + 0.0806812i
248248 −8.25686 + 3.42010i −0.524311 + 0.217177i
249249 −10.9661 + 4.54232i −0.694950 + 0.287858i
250250 22.8120 5.78493i 1.44276 0.365871i
251251 17.7019i 1.11733i 0.829392 + 0.558666i 0.188687π0.188687\pi
−0.829392 + 0.558666i 0.811313π0.811313\pi
252252 0.649195 1.56729i 0.0408954 0.0987303i
253253 2.78369 + 2.78369i 0.175009 + 0.175009i
254254 22.4162 1.40652
255255 7.00880 15.0991i 0.438908 0.945543i
256256 7.07403 0.442127
257257 5.44763 + 5.44763i 0.339814 + 0.339814i 0.856297 0.516483i 0.172759π-0.172759\pi
−0.516483 + 0.856297i 0.672759π0.672759\pi
258258 12.9507 31.2658i 0.806278 1.94653i
259259 18.3467i 1.14001i
260260 −9.31649 + 11.0025i −0.577784 + 0.682343i
261261 −2.41079 + 0.998582i −0.149224 + 0.0618107i
262262 3.14746 1.30372i 0.194451 0.0805442i
263263 4.45259 4.45259i 0.274558 0.274558i −0.556374 0.830932i 0.687808π-0.687808\pi
0.830932 + 0.556374i 0.187808π0.187808\pi
264264 −1.12972 1.12972i −0.0695295 0.0695295i
265265 0.525185 + 6.32944i 0.0322619 + 0.388814i
266266 3.52807 1.46137i 0.216320 0.0896026i
267267 9.38571 + 3.88769i 0.574396 + 0.237923i
268268 −13.9527 −0.852294
269269 −8.55428 3.54330i −0.521563 0.216039i 0.106340 0.994330i 0.466087π-0.466087\pi
−0.627904 + 0.778291i 0.716087π0.716087\pi
270270 10.6592 + 20.7022i 0.648700 + 1.25989i
271271 16.7791 1.01926 0.509628 0.860395i 0.329783π-0.329783\pi
0.509628 + 0.860395i 0.329783π0.329783\pi
272272 −9.61239 + 7.47137i −0.582837 + 0.453018i
273273 12.8510i 0.777775i
274274 −7.00044 + 7.00044i −0.422912 + 0.422912i
275275 −2.58435 4.13800i −0.155842 0.249531i
276276 17.7079i 1.06589i
277277 −11.0923 4.59456i −0.666469 0.276061i 0.0236887 0.999719i 0.492459π-0.492459\pi
−0.690158 + 0.723659i 0.742459π0.742459\pi
278278 −0.663584 1.60203i −0.0397991 0.0960835i
279279 0.980851 + 2.36798i 0.0587220 + 0.141767i
280280 4.83772 2.49087i 0.289109 0.148858i
281281 −19.9411 19.9411i −1.18959 1.18959i −0.977182 0.212403i 0.931871π-0.931871\pi
−0.212403 0.977182i 0.568129π-0.568129\pi
282282 −3.07064 + 1.27190i −0.182854 + 0.0757407i
283283 −6.53556 15.7782i −0.388499 0.937919i −0.990258 0.139242i 0.955534π-0.955534\pi
0.601760 0.798677i 0.294466π-0.294466\pi
284284 −1.04670 + 2.52695i −0.0621101 + 0.149947i
285285 0.832458 2.59954i 0.0493105 0.153984i
286286 5.03306 + 2.08476i 0.297611 + 0.123274i
287287 13.8925 + 13.8925i 0.820049 + 0.820049i
288288 2.08818i 0.123047i
289289 4.19515 16.4742i 0.246774 0.969073i
290290 −44.9751 14.4025i −2.64103 0.845743i
291291 19.6793 19.6793i 1.15362 1.15362i
292292 2.78933 6.73403i 0.163233 0.394079i
293293 −6.82563 −0.398758 −0.199379 0.979922i 0.563892π-0.563892\pi
−0.199379 + 0.979922i 0.563892π0.563892\pi
294294 0.291685 0.704191i 0.0170114 0.0410693i
295295 −1.98473 23.9196i −0.115556 1.39265i
296296 −2.37274 5.72830i −0.137913 0.332951i
297297 3.41329 3.41329i 0.198059 0.198059i
298298 −14.2936 + 14.2936i −0.828009 + 0.828009i
299299 −4.09523 9.88676i −0.236833 0.571766i
300300 4.94160 21.3814i 0.285303 1.23446i
301301 9.14369 22.0748i 0.527033 1.27237i
302302 2.98218 0.171605
303303 −10.1048 + 24.3950i −0.580503 + 1.40146i
304304 −1.41159 + 1.41159i −0.0809605 + 0.0809605i
305305 −1.41315 + 4.41290i −0.0809169 + 0.252682i
306306 −1.38521 1.78215i −0.0791869 0.101879i
307307 0.746287i 0.0425929i −0.999773 0.0212964i 0.993221π-0.993221\pi
0.999773 0.0212964i 0.00677938π-0.00677938\pi
308308 −4.50045 4.50045i −0.256437 0.256437i
309309 −2.72371 1.12820i −0.154947 0.0641810i
310310 −14.1467 + 44.1765i −0.803481 + 2.50906i
311311 −6.96494 + 16.8149i −0.394946 + 0.953483i 0.593900 + 0.804539i 0.297587π0.297587\pi
−0.988846 + 0.148944i 0.952413π0.952413\pi
312312 1.66199 + 4.01240i 0.0940916 + 0.227157i
313313 −9.16854 + 3.79773i −0.518236 + 0.214661i −0.626442 0.779468i 0.715490π-0.715490\pi
0.108206 + 0.994129i 0.465490π0.465490\pi
314314 −7.17245 7.17245i −0.404765 0.404765i
315315 −0.714356 1.38741i −0.0402494 0.0781716i
316316 −0.380471 0.918539i −0.0214032 0.0516718i
317317 −9.30367 22.4610i −0.522546 1.26154i −0.936317 0.351157i 0.885788π-0.885788\pi
0.413770 0.910381i 0.364212π-0.364212\pi
318318 9.97335 + 4.13110i 0.559278 + 0.231660i
319319 9.78994i 0.548131i
320320 −15.8881 + 18.7633i −0.888171 + 1.04890i
321321 −7.11125 + 7.11125i −0.396911 + 0.396911i
322322 22.7890i 1.26998i
323323 0.346636 2.76591i 0.0192874 0.153899i
324324 23.6095 1.31164
325325 2.18578 + 13.0806i 0.121245 + 0.725582i
326326 −3.14854 1.30417i −0.174381 0.0722312i
327327 4.76369 0.263433
328328 6.13429 + 2.54091i 0.338710 + 0.140298i
329329 −2.16799 + 0.898009i −0.119525 + 0.0495088i
330330 −8.26393 + 0.685700i −0.454915 + 0.0377465i
331331 −0.346315 0.346315i −0.0190352 0.0190352i 0.697525 0.716560i 0.254285π-0.254285\pi
−0.716560 + 0.697525i 0.754285π0.754285\pi
332332 −11.2996 + 11.2996i −0.620144 + 0.620144i
333333 −1.64282 + 0.680478i −0.0900259 + 0.0372899i
334334 −43.0441 + 17.8295i −2.35527 + 0.975584i
335335 −8.29403 + 9.79496i −0.453151 + 0.535156i
336336 14.3062i 0.780468i
337337 −2.30186 + 5.55719i −0.125390 + 0.302719i −0.974092 0.226153i 0.927385π-0.927385\pi
0.848701 + 0.528872i 0.177385π0.177385\pi
338338 8.87814 + 8.87814i 0.482907 + 0.482907i
339339 10.4882 0.569639
340340 0.938510 22.3914i 0.0508979 1.21434i
341341 9.61610 0.520741
342342 −0.261712 0.261712i −0.0141518 0.0141518i
343343 −6.98227 + 16.8567i −0.377007 + 0.910175i
344344 8.07486i 0.435367i
345345 12.4312 + 10.5263i 0.669272 + 0.566716i
346346 20.1798 8.35877i 1.08488 0.449370i
347347 7.29831 3.02306i 0.391794 0.162286i −0.178085 0.984015i 0.556990π-0.556990\pi
0.569879 + 0.821729i 0.306990π0.306990\pi
348348 −31.1383 + 31.1383i −1.66919 + 1.66919i
349349 −13.5417 13.5417i −0.724868 0.724868i 0.244725 0.969593i 0.421302π-0.421302\pi
−0.969593 + 0.244725i 0.921302π0.921302\pi
350350 6.35954 27.5166i 0.339932 1.47083i
351351 −12.1229 + 5.02147i −0.647072 + 0.268026i
352352 7.23801 + 2.99808i 0.385787 + 0.159798i
353353 13.7165 0.730055 0.365027 0.930997i 0.381060π-0.381060\pi
0.365027 + 0.930997i 0.381060π0.381060\pi
354354 −37.6904 15.6119i −2.00322 0.829761i
355355 1.15176 + 2.23692i 0.0611289 + 0.118723i
356356 13.6770 0.724879
357357 −12.2594 15.7725i −0.648836 0.834768i
358358 39.4218i 2.08351i
359359 17.6460 17.6460i 0.931322 0.931322i −0.0664662 0.997789i 0.521172π-0.521172\pi
0.997789 + 0.0664662i 0.0211725π0.0211725\pi
360360 −0.402471 0.340798i −0.0212121 0.0179617i
361361 18.5429i 0.975943i
362362 4.77421 + 1.97754i 0.250927 + 0.103937i
363363 −6.94272 16.7612i −0.364398 0.879736i
364364 6.62085 + 15.9841i 0.347027 + 0.837797i
365365 −3.06929 5.96113i −0.160654 0.312020i
366366 5.56902 + 5.56902i 0.291097 + 0.291097i
367367 7.87910 3.26363i 0.411286 0.170360i −0.167440 0.985882i 0.553550π-0.553550\pi
0.578726 + 0.815522i 0.303550π0.303550\pi
368368 −4.55898 11.0063i −0.237653 0.573745i
369369 0.728707 1.75925i 0.0379350 0.0915831i
370370 −30.6480 9.81449i −1.59331 0.510231i
371371 7.04155 + 2.91670i 0.365579 + 0.151428i
372372 30.5854 + 30.5854i 1.58578 + 1.58578i
373373 11.5593i 0.598519i 0.954172 + 0.299260i 0.0967397π0.0967397\pi
−0.954172 + 0.299260i 0.903260π0.903260\pi
374374 −8.16606 + 2.24266i −0.422257 + 0.115965i
375375 −12.0726 16.1791i −0.623425 0.835484i
376376 −0.560763 + 0.560763i −0.0289192 + 0.0289192i
377377 10.1841 24.5866i 0.524508 1.26627i
378378 27.9433 1.43725
379379 4.70807 11.3663i 0.241837 0.583847i −0.755628 0.655001i 0.772668π-0.772668\pi
0.997465 + 0.0711543i 0.0226683π0.0226683\pi
380380 −0.303873 3.66222i −0.0155883 0.187868i
381381 −7.35824 17.7644i −0.376974 0.910096i
382382 16.2426 16.2426i 0.831042 0.831042i
383383 −4.00295 + 4.00295i −0.204541 + 0.204541i −0.801942 0.597401i 0.796200π-0.796200\pi
0.597401 + 0.801942i 0.296200π0.296200\pi
384384 4.89649 + 11.8212i 0.249873 + 0.603247i
385385 −5.83464 + 0.484129i −0.297361 + 0.0246735i
386386 14.8020 35.7353i 0.753404 1.81888i
387387 −2.31579 −0.117718
388388 14.3385 34.6162i 0.727926 1.75737i
389389 1.15168 1.15168i 0.0583927 0.0583927i −0.677307 0.735700i 0.736853π-0.736853\pi
0.735700 + 0.677307i 0.236853π0.236853\pi
390390 21.4675 + 6.87457i 1.08705 + 0.348108i
391391 14.4579 + 8.22769i 0.731166 + 0.416092i
392392 0.181868i 0.00918570i
393393 −2.06634 2.06634i −0.104233 0.104233i
394394 37.9041 + 15.7004i 1.90958 + 0.790975i
395395 −0.870995 0.278921i −0.0438245 0.0140340i
396396 −0.236063 + 0.569907i −0.0118626 + 0.0286389i
397397 4.91819 + 11.8736i 0.246837 + 0.595917i 0.997932 0.0642772i 0.0204742π-0.0204742\pi
−0.751095 + 0.660194i 0.770474π0.770474\pi
398398 45.3467 18.7832i 2.27303 0.941518i
399399 −2.31621 2.31621i −0.115956 0.115956i
400400 2.43330 + 14.5619i 0.121665 + 0.728095i
401401 −11.0222 26.6099i −0.550422 1.32884i −0.917163 0.398512i 0.869527π-0.869527\pi
0.366741 0.930323i 0.380473π-0.380473\pi
402402 8.34833 + 20.1547i 0.416377 + 1.00522i
403403 −24.1500 10.0033i −1.20300 0.498298i
404404 35.5488i 1.76862i
405405 14.0345 16.5742i 0.697379 0.823580i
406406 −40.0732 + 40.0732i −1.98880 + 1.98880i
407407 6.67129i 0.330684i
408408 −5.86752 3.33909i −0.290486 0.165310i
409409 −13.6197 −0.673451 −0.336725 0.941603i 0.609319π-0.609319\pi
−0.336725 + 0.941603i 0.609319π0.609319\pi
410410 30.6391 15.7756i 1.51316 0.779103i
411411 7.84563 + 3.24977i 0.386996 + 0.160299i
412412 −3.96903 −0.195540
413413 −26.6108 11.0225i −1.30943 0.542384i
414414 2.04060 0.845243i 0.100290 0.0415414i
415415 1.21553 + 14.6494i 0.0596682 + 0.719110i
416416 −15.0588 15.0588i −0.738320 0.738320i
417417 −1.05175 + 1.05175i −0.0515045 + 0.0515045i
418418 −1.28289 + 0.531391i −0.0627483 + 0.0259912i
419419 13.1802 5.45940i 0.643893 0.266709i −0.0367500 0.999324i 0.511701π-0.511701\pi
0.680643 + 0.732615i 0.261701π0.261701\pi
420420 −20.0978 17.0181i −0.980670 0.830397i
421421 28.9349i 1.41020i 0.709107 + 0.705101i 0.249098π0.249098\pi
−0.709107 + 0.705101i 0.750902π0.750902\pi
422422 −18.4634 + 44.5745i −0.898783 + 2.16985i
423423 0.160821 + 0.160821i 0.00781940 + 0.00781940i
424424 2.57576 0.125090
425425 −15.1612 13.9692i −0.735425 0.677606i
426426 4.27646 0.207195
427427 3.93193 + 3.93193i 0.190279 + 0.190279i
428428 −5.18130 + 12.5088i −0.250448 + 0.604634i
429429 4.67292i 0.225611i
430430 −31.9845 27.0833i −1.54243 1.30607i
431431 −18.9908 + 7.86623i −0.914753 + 0.378903i −0.789874 0.613269i 0.789854π-0.789854\pi
−0.124879 + 0.992172i 0.539854π0.539854\pi
432432 −13.4957 + 5.59011i −0.649313 + 0.268954i
433433 17.0995 17.0995i 0.821748 0.821748i −0.164611 0.986359i 0.552637π-0.552637\pi
0.986359 + 0.164611i 0.0526368π0.0526368\pi
434434 39.3616 + 39.3616i 1.88942 + 1.88942i
435435 3.34966 + 40.3695i 0.160604 + 1.93557i
436436 5.92512 2.45427i 0.283762 0.117538i
437437 2.52007 + 1.04385i 0.120551 + 0.0499339i
438438 −11.3963 −0.544535
439439 −20.3668 8.43621i −0.972055 0.402638i −0.160578 0.987023i 0.551336π-0.551336\pi
−0.811477 + 0.584385i 0.801336π0.801336\pi
440440 −1.75911 + 0.905740i −0.0838624 + 0.0431795i
441441 −0.0521578 −0.00248371
442442 22.8413 + 2.86258i 1.08645 + 0.136159i
443443 32.3324i 1.53616i 0.640356 + 0.768079i 0.278787π0.278787\pi
−0.640356 + 0.768079i 0.721213π0.721213\pi
444444 −21.2190 + 21.2190i −1.00701 + 1.00701i
445445 8.13016 9.60144i 0.385407 0.455152i
446446 27.4821i 1.30132i
447447 16.0194 + 6.63544i 0.757690 + 0.313845i
448448 11.2910 + 27.2589i 0.533450 + 1.28786i
449449 12.0051 + 28.9829i 0.566556 + 1.36779i 0.904441 + 0.426599i 0.140288π0.140288\pi
−0.337885 + 0.941187i 0.609712π0.609712\pi
450450 −2.69980 + 0.451138i −0.127270 + 0.0212668i
451451 −5.05166 5.05166i −0.237873 0.237873i
452452 13.0453 5.40353i 0.613598 0.254161i
453453 −0.978914 2.36331i −0.0459934 0.111038i
454454 8.61878 20.8076i 0.404499 0.976548i
455455 15.1568 + 4.85370i 0.710562 + 0.227545i
456456 −1.02273 0.423630i −0.0478939 0.0198383i
457457 9.01432 + 9.01432i 0.421672 + 0.421672i 0.885779 0.464107i 0.153625π-0.153625\pi
−0.464107 + 0.885779i 0.653625π0.653625\pi
458458 39.6431i 1.85240i
459459 10.0886 17.7279i 0.470895 0.827467i
460460 20.8852 + 6.68811i 0.973777 + 0.311835i
461461 −12.3023 + 12.3023i −0.572974 + 0.572974i −0.932958 0.359984i 0.882782π-0.882782\pi
0.359984 + 0.932958i 0.382782π0.382782\pi
462462 −3.80815 + 9.19369i −0.177171 + 0.427729i
463463 −29.5747 −1.37445 −0.687227 0.726443i 0.741172π-0.741172\pi
−0.687227 + 0.726443i 0.741172π0.741172\pi
464464 11.3374 27.3708i 0.526324 1.27066i
465465 39.6526 3.29018i 1.83885 0.152578i
466466 −1.80914 4.36765i −0.0838068 0.202327i
467467 −23.2530 + 23.2530i −1.07602 + 1.07602i −0.0791599 + 0.996862i 0.525224π0.525224\pi
−0.996862 + 0.0791599i 0.974776π0.974776\pi
468468 1.18570 1.18570i 0.0548092 0.0548092i
469469 5.89422 + 14.2299i 0.272170 + 0.657076i
470470 0.340363 + 4.10200i 0.0156998 + 0.189211i
471471 −3.32962 + 8.03840i −0.153421 + 0.370390i
472472 −9.73409 −0.448048
473473 −3.32487 + 8.02694i −0.152878 + 0.369079i
474474 −1.09918 + 1.09918i −0.0504872 + 0.0504872i
475475 −2.75157 1.96365i −0.126251 0.0900985i
476476 −23.3744 13.3019i −1.07136 0.609691i
477477 0.738703i 0.0338229i
478478 −24.9003 24.9003i −1.13891 1.13891i
479479 0.548605 + 0.227240i 0.0250664 + 0.0103828i 0.395181 0.918603i 0.370682π-0.370682\pi
−0.370115 + 0.928986i 0.620682π0.620682\pi
480480 30.8722 + 9.88628i 1.40912 + 0.451245i
481481 6.93989 16.7544i 0.316432 0.763934i
482482 −9.48335 22.8948i −0.431955 1.04283i
483483 18.0598 7.48059i 0.821747 0.340379i
484484 −17.2709 17.2709i −0.785039 0.785039i
485485 −15.7777 30.6431i −0.716427 1.39143i
486486 −2.17121 5.24176i −0.0984881 0.237771i
487487 −0.862103 2.08130i −0.0390656 0.0943127i 0.903142 0.429341i 0.141254π-0.141254\pi
−0.942208 + 0.335028i 0.891254π0.891254\pi
488488 1.73616 + 0.719141i 0.0785922 + 0.0325540i
489489 2.92325i 0.132194i
490490 −0.720377 0.609990i −0.0325433 0.0275565i
491491 −5.16155 + 5.16155i −0.232937 + 0.232937i −0.813918 0.580980i 0.802669π-0.802669\pi
0.580980 + 0.813918i 0.302669π0.302669\pi
492492 32.1351i 1.44876i
493493 10.9555 + 39.8914i 0.493409 + 1.79662i
494494 3.77466 0.169830
495495 0.259757 + 0.504496i 0.0116752 + 0.0226754i
496496 −26.8848 11.1360i −1.20716 0.500023i
497497 3.01934 0.135436
498498 23.0832 + 9.56136i 1.03438 + 0.428455i
499499 −7.02196 + 2.90859i −0.314346 + 0.130206i −0.534278 0.845309i 0.679416π-0.679416\pi
0.219932 + 0.975515i 0.429416π0.429416\pi
500500 −23.3515 13.9039i −1.04431 0.621799i
501501 28.2589 + 28.2589i 1.26251 + 1.26251i
502502 26.3479 26.3479i 1.17597 1.17597i
503503 −14.3260 + 5.93402i −0.638764 + 0.264585i −0.678472 0.734627i 0.737357π-0.737357\pi
0.0397075 + 0.999211i 0.487357π0.487357\pi
504504 −0.584702 + 0.242191i −0.0260447 + 0.0107881i
505505 24.9558 + 21.1317i 1.11052 + 0.940347i
506506 8.28662i 0.368385i
507507 4.12143 9.95002i 0.183039 0.441896i
508508 −18.3045 18.3045i −0.812131 0.812131i
509509 −29.3375 −1.30036 −0.650182 0.759779i 0.725307π-0.725307\pi
−0.650182 + 0.759779i 0.725307π0.725307\pi
510510 −32.9060 + 12.0418i −1.45710 + 0.533221i
511511 −8.04618 −0.355942
512512 −20.5510 20.5510i −0.908233 0.908233i
513513 1.27994 3.09004i 0.0565107 0.136429i
514514 16.2168i 0.715292i
515515 −2.35935 + 2.78632i −0.103966 + 0.122780i
516516 −36.1061 + 14.9556i −1.58948 + 0.658385i
517517 0.788333 0.326538i 0.0346708 0.0143611i
518518 −27.3076 + 27.3076i −1.19983 + 1.19983i
519519 −13.2483 13.2483i −0.581535 0.581535i
520520 5.36006 0.444751i 0.235054 0.0195036i
521521 −14.0288 + 5.81093i −0.614614 + 0.254581i −0.668200 0.743982i 0.732935π-0.732935\pi
0.0535860 + 0.998563i 0.482935π0.482935\pi
522522 5.07460 + 2.10197i 0.222109 + 0.0920006i
523523 35.8569 1.56791 0.783957 0.620815i 0.213198π-0.213198\pi
0.783957 + 0.620815i 0.213198π0.213198\pi
524524 −3.63472 1.50555i −0.158784 0.0657703i
525525 −23.8939 + 3.99268i −1.04281 + 0.174255i
526526 −13.2547 −0.577932
527527 39.1830 10.7609i 1.70684 0.468753i
528528 5.20209i 0.226392i
529529 4.75321 4.75321i 0.206661 0.206661i
530530 8.63919 10.2026i 0.375263 0.443172i
531531 2.79164i 0.121147i
532532 −4.07425 1.68761i −0.176641 0.0731671i
533533 7.43175 + 17.9418i 0.321905 + 0.777148i
534534 −8.18339 19.7565i −0.354130 0.854945i
535535 5.70136 + 11.0731i 0.246491 + 0.478731i
536536 3.68066 + 3.68066i 0.158980 + 0.158980i
537537 −31.2409 + 12.9404i −1.34814 + 0.558420i
538538 7.45847 + 18.0063i 0.321557 + 0.776308i
539539 −0.0748850 + 0.180788i −0.00322553 + 0.00778711i
540540 8.20080 25.6089i 0.352906 1.10203i
541541 24.6831 + 10.2241i 1.06121 + 0.439568i 0.843881 0.536531i 0.180266π-0.180266\pi
0.217329 + 0.976098i 0.430266π0.430266\pi
542542 −24.9744 24.9744i −1.07274 1.07274i
543543 4.43259i 0.190221i
544544 32.8479 + 4.11666i 1.40834 + 0.176500i
545545 1.79921 5.61844i 0.0770695 0.240667i
546546 19.1277 19.1277i 0.818589 0.818589i
547547 −5.16946 + 12.4802i −0.221030 + 0.533614i −0.995030 0.0995712i 0.968253π-0.968253\pi
0.774000 + 0.633185i 0.218253π0.218253\pi
548548 11.4328 0.488383
549549 0.206242 0.497913i 0.00880221 0.0212504i
550550 −2.31248 + 10.0057i −0.0986047 + 0.426645i
551551 2.59586 + 6.26695i 0.110587 + 0.266981i
552552 4.67127 4.67127i 0.198822 0.198822i
553553 −0.776064 + 0.776064i −0.0330016 + 0.0330016i
554554 9.67133 + 23.3487i 0.410895 + 0.991989i
555555 2.28260 + 27.5095i 0.0968911 + 1.16771i
556556 −0.766313 + 1.85004i −0.0324989 + 0.0784593i
557557 16.9198 0.716915 0.358458 0.933546i 0.383303π-0.383303\pi
0.358458 + 0.933546i 0.383303π0.383303\pi
558558 2.06464 4.98449i 0.0874033 0.211010i
559559 16.7002 16.7002i 0.706345 0.706345i
560560 16.8732 + 5.40334i 0.713022 + 0.228333i
561561 4.45781 + 5.73526i 0.188209 + 0.242143i
562562 59.3616i 2.50402i
563563 26.6224 + 26.6224i 1.12200 + 1.12200i 0.991441 + 0.130558i 0.0416768π0.0416768\pi
0.130558 + 0.991441i 0.458323π0.458323\pi
564564 3.54601 + 1.46881i 0.149314 + 0.0618479i
565565 3.96129 12.3701i 0.166653 0.520412i
566566 −13.7570 + 33.2124i −0.578251 + 1.39602i
567567 −9.97373 24.0787i −0.418857 1.01121i
568568 0.942715 0.390485i 0.0395555 0.0163844i
569569 −21.0557 21.0557i −0.882701 0.882701i 0.111108 0.993808i 0.464560π-0.464560\pi
−0.993808 + 0.111108i 0.964560π0.964560\pi
570570 −5.10827 + 2.63017i −0.213962 + 0.110166i
571571 −3.82363 9.23107i −0.160014 0.386308i 0.823456 0.567381i 0.192043π-0.192043\pi
−0.983470 + 0.181072i 0.942043π0.942043\pi
572572 −2.40750 5.81222i −0.100663 0.243021i
573573 −18.2036 7.54017i −0.760465 0.314995i
574574 41.3559i 1.72616i
575575 17.1102 10.6860i 0.713543 0.445638i
576576 2.02207 2.02207i 0.0842527 0.0842527i
577577 17.5104i 0.728968i −0.931210 0.364484i 0.881245π-0.881245\pi
0.931210 0.364484i 0.118755π-0.118755\pi
578578 −30.7648 + 18.2765i −1.27965 + 0.760203i
579579 −33.1783 −1.37884
580580 24.9648 + 48.4862i 1.03661 + 2.01328i
581581 16.2976 + 6.75067i 0.676137 + 0.280065i
582582 −58.5824 −2.42832
583583 −2.56048 1.06058i −0.106044 0.0439249i
584584 −2.51222 + 1.04060i −0.103957 + 0.0430602i
585585 −0.127550 1.53721i −0.00527355 0.0635559i
586586 10.1594 + 10.1594i 0.419683 + 0.419683i
587587 −11.3396 + 11.3396i −0.468036 + 0.468036i −0.901278 0.433242i 0.857370π-0.857370\pi
0.433242 + 0.901278i 0.357370π0.357370\pi
588588 −0.813207 + 0.336841i −0.0335361 + 0.0138911i
589589 6.15567 2.54976i 0.253640 0.105061i
590590 −32.6485 + 38.5567i −1.34412 + 1.58735i
591591 35.1919i 1.44760i
592592 7.72577 18.6517i 0.317527 0.766579i
593593 −27.1563 27.1563i −1.11517 1.11517i −0.992439 0.122735i 0.960833π-0.960833\pi
−0.122735 0.992439i 0.539167π-0.539167\pi
594594 −10.1609 −0.416905
595595 −23.2328 + 8.50196i −0.952452 + 0.348546i
596596 23.3436 0.956193
597597 −29.7706 29.7706i −1.21843 1.21843i
598598 −8.62025 + 20.8111i −0.352508 + 0.851031i
599599 23.5261i 0.961251i 0.876926 + 0.480625i 0.159590π0.159590\pi
−0.876926 + 0.480625i 0.840410π0.840410\pi
600600 −6.94392 + 4.33677i −0.283484 + 0.177048i
601601 23.1362 9.58331i 0.943744 0.390911i 0.142868 0.989742i 0.454368π-0.454368\pi
0.800876 + 0.598830i 0.204368π0.204368\pi
602602 −46.4664 + 19.2470i −1.89383 + 0.784450i
603603 1.05558 1.05558i 0.0429864 0.0429864i
604604 −2.43517 2.43517i −0.0990855 0.0990855i
605605 −22.3909 + 1.85788i −0.910319 + 0.0755337i
606606 51.3504 21.2700i 2.08597 0.864036i
607607 29.8946 + 12.3827i 1.21338 + 0.502600i 0.895300 0.445463i 0.146961π-0.146961\pi
0.318083 + 0.948063i 0.396961π0.396961\pi
608608 5.42831 0.220147
609609 44.9114 + 18.6029i 1.81990 + 0.753827i
610610 8.67164 4.46490i 0.351105 0.180778i
611611 −2.31951 −0.0938375
612612 −0.324138 + 2.58638i −0.0131025 + 0.104548i
613613 25.0386i 1.01130i −0.862739 0.505650i 0.831253π-0.831253\pi
0.862739 0.505650i 0.168747π-0.168747\pi
614614 −1.11079 + 1.11079i −0.0448280 + 0.0448280i
615615 −22.5593 19.1024i −0.909678 0.770284i
616616 2.37441i 0.0956675i
617617 9.00101 + 3.72834i 0.362367 + 0.150097i 0.556436 0.830891i 0.312169π-0.312169\pi
−0.194069 + 0.980988i 0.562169π0.562169\pi
618618 2.37480 + 5.73328i 0.0955285 + 0.230626i
619619 −2.82897 6.82973i −0.113706 0.274510i 0.856774 0.515692i 0.172465π-0.172465\pi
−0.970480 + 0.241182i 0.922465π0.922465\pi
620620 47.6252 24.5215i 1.91268 0.984808i
621621 14.1136 + 14.1136i 0.566358 + 0.566358i
622622 35.3944 14.6609i 1.41919 0.587847i
623623 −5.77777 13.9488i −0.231481 0.558846i
624624 −5.41153 + 13.0646i −0.216635 + 0.523002i
625625 −23.6418 + 8.12807i −0.945672 + 0.325123i
626626 19.2993 + 7.99404i 0.771356 + 0.319506i
627627 0.842232 + 0.842232i 0.0336355 + 0.0336355i
628628 11.7137i 0.467426i
629629 7.46553 + 27.1837i 0.297670 + 1.08389i
630630 −1.00179 + 3.12832i −0.0399122 + 0.124635i
631631 −6.09529 + 6.09529i −0.242650 + 0.242650i −0.817945 0.575296i 0.804887π-0.804887\pi
0.575296 + 0.817945i 0.304887π0.304887\pi
632632 −0.141940 + 0.342674i −0.00564608 + 0.0136308i
633633 41.3850 1.64491
634634 −19.5838 + 47.2794i −0.777771 + 1.87770i
635635 −23.7310 + 1.96908i −0.941735 + 0.0781404i
636636 −4.77063 11.5173i −0.189168 0.456692i
637637 0.376134 0.376134i 0.0149030 0.0149030i
638638 14.5716 14.5716i 0.576895 0.576895i
639639 −0.111987 0.270361i −0.00443015 0.0106953i
640640 15.7916 1.31031i 0.624219 0.0517945i
641641 −14.9873 + 36.1825i −0.591963 + 1.42912i 0.289641 + 0.957135i 0.406464π0.406464\pi
−0.881604 + 0.471989i 0.843536π0.843536\pi
642642 21.1691 0.835478
643643 17.4803 42.2011i 0.689355 1.66425i −0.0567210 0.998390i 0.518065π-0.518065\pi
0.746076 0.665861i 0.231935π-0.231935\pi
644644 18.6089 18.6089i 0.733292 0.733292i
645645 −10.9639 + 34.2372i −0.431702 + 1.34809i
646646 −4.63279 + 3.60090i −0.182275 + 0.141676i
647647 9.17577i 0.360737i −0.983599 0.180368i 0.942271π-0.942271\pi
0.983599 0.180368i 0.0577290π-0.0577290\pi
648648 −6.22811 6.22811i −0.244663 0.244663i
649649 9.67633 + 4.00807i 0.379829 + 0.157330i
650650 16.2162 22.7229i 0.636050 0.891265i
651651 18.2726 44.1139i 0.716158 1.72896i
652652 1.50607 + 3.63596i 0.0589821 + 0.142395i
653653 15.3604 6.36250i 0.601100 0.248984i −0.0613178 0.998118i 0.519530π-0.519530\pi
0.662418 + 0.749134i 0.269530π0.269530\pi
654654 −7.09039 7.09039i −0.277256 0.277256i
655655 −3.21755 + 1.65667i −0.125720 + 0.0647313i
656656 8.27334 + 19.9736i 0.323020 + 0.779838i
657657 0.298433 + 0.720481i 0.0116430 + 0.0281086i
658658 4.56350 + 1.89027i 0.177904 + 0.0736902i
659659 5.95839i 0.232106i 0.993243 + 0.116053i 0.0370242π0.0370242\pi
−0.993243 + 0.116053i 0.962976π0.962976\pi
660660 7.30804 + 6.18819i 0.284465 + 0.240875i
661661 30.3724 30.3724i 1.18135 1.18135i 0.201955 0.979395i 0.435270π-0.435270\pi
0.979395 0.201955i 0.0647296π-0.0647296\pi
662662 1.03093i 0.0400681i
663663 −5.22924 19.0409i −0.203087 0.739487i
664664 5.96157 0.231354
665665 −3.60663 + 1.85700i −0.139859 + 0.0720113i
666666 3.45805 + 1.43237i 0.133997 + 0.0555033i
667667 −40.4803 −1.56740
668668 49.7078 + 20.5896i 1.92325 + 0.796637i
669669 −21.7790 + 9.02114i −0.842024 + 0.348778i
670670 26.9241 2.23403i 1.04017 0.0863080i
671671 −1.42975 1.42975i −0.0551947 0.0551947i
672672 27.5074 27.5074i 1.06112 1.06112i
673673 16.0256 6.63803i 0.617743 0.255877i −0.0517924 0.998658i 0.516493π-0.516493\pi
0.669535 + 0.742781i 0.266493π0.266493\pi
674674 11.6976 4.84531i 0.450575 0.186634i
675675 −13.1029 20.9801i −0.504332 0.807523i
676676 14.4993i 0.557666i
677677 −9.79369 + 23.6441i −0.376402 + 0.908715i 0.616232 + 0.787565i 0.288658π0.288658\pi
−0.992634 + 0.121150i 0.961342π0.961342\pi
678678 −15.6108 15.6108i −0.599531 0.599531i
679679 −41.3613 −1.58730
680680 −6.15434 + 5.65919i −0.236008 + 0.217020i
681681 −19.3187 −0.740294
682682 −14.3128 14.3128i −0.548067 0.548067i
683683 2.34480 5.66085i 0.0897213 0.216606i −0.872649 0.488348i 0.837600π-0.837600\pi
0.962370 + 0.271742i 0.0875996π0.0875996\pi
684684 0.427415i 0.0163426i
685685 6.79610 8.02596i 0.259666 0.306656i
686686 35.4825 14.6973i 1.35473 0.561146i
687687 −31.4163 + 13.0130i −1.19861 + 0.496479i
688688 18.5914 18.5914i 0.708790 0.708790i
689689 5.32713 + 5.32713i 0.202948 + 0.202948i
690690 −2.83529 34.1705i −0.107938 1.30085i
691691 −6.87633 + 2.84827i −0.261588 + 0.108353i −0.509623 0.860398i 0.670215π-0.670215\pi
0.248035 + 0.968751i 0.420215π0.420215\pi
692692 −23.3039 9.65279i −0.885881 0.366944i
693693 0.680955 0.0258674
694694 −15.3626 6.36339i −0.583156 0.241551i
695695 0.843229 + 1.63770i 0.0319855 + 0.0621217i
696696 16.4284 0.622715
697697 −26.2372 14.9311i −0.993806 0.565555i
698698 40.3115i 1.52581i
699699 −2.86741 + 2.86741i −0.108455 + 0.108455i
700700 −27.6624 + 17.2763i −1.04554 + 0.652984i
701701 25.3350i 0.956891i −0.878117 0.478445i 0.841200π-0.841200\pi
0.878117 0.478445i 0.158800π-0.158800\pi
702702 25.5181 + 10.5699i 0.963119 + 0.398937i
703703 1.76893 + 4.27058i 0.0667165 + 0.161068i
704704 −4.10568 9.91200i −0.154739 0.373573i
705705 3.13902 1.61623i 0.118222 0.0608708i
706706 −20.4160 20.4160i −0.768365 0.768365i
707707 36.2552 15.0174i 1.36352 0.564788i
708708 18.0287 + 43.5252i 0.677562 + 1.63578i
709709 6.10174 14.7309i 0.229156 0.553231i −0.766919 0.641744i 0.778211π-0.778211\pi
0.996075 + 0.0885126i 0.0282113π0.0282113\pi
710710 1.61519 5.04379i 0.0606168 0.189290i
711711 0.0982755 + 0.0407070i 0.00368562 + 0.00152663i
712712 −3.60794 3.60794i −0.135213 0.135213i
713713 39.7615i 1.48908i
714714 −5.22897 + 41.7233i −0.195689 + 1.56146i
715715 −5.51138 1.76492i −0.206114 0.0660044i
716716 −32.1908 + 32.1908i −1.20303 + 1.20303i
717717 −11.5593 + 27.9066i −0.431689 + 1.04219i
718718 −52.5296 −1.96039
719719 7.42813 17.9331i 0.277022 0.668791i −0.722728 0.691132i 0.757112π-0.757112\pi
0.999750 + 0.0223415i 0.00711210π0.00711210\pi
720720 −0.141994 1.71129i −0.00529181 0.0637759i
721721 1.67670 + 4.04790i 0.0624434 + 0.150752i
722722 27.5997 27.5997i 1.02716 1.02716i
723723 −15.0307 + 15.0307i −0.558997 + 0.558997i
724724 −2.28369 5.51330i −0.0848725 0.204900i
725725 48.8781 + 11.2965i 1.81529 + 0.419543i
726726 −14.6141 + 35.2815i −0.542380 + 1.30942i
727727 −26.1442 −0.969633 −0.484817 0.874616i 0.661114π-0.661114\pi
−0.484817 + 0.874616i 0.661114π0.661114\pi
728728 2.47000 5.96311i 0.0915444 0.221008i
729729 17.1622 17.1622i 0.635639 0.635639i
730730 −4.30428 + 13.4411i −0.159308 + 0.497478i
731731 −4.56537 + 36.4283i −0.168856 + 1.34735i
732732 9.09503i 0.336162i
733733 −3.23474 3.23474i −0.119478 0.119478i 0.644840 0.764318i 0.276924π-0.276924\pi
−0.764318 + 0.644840i 0.776924π0.776924\pi
734734 −16.5851 6.86978i −0.612168 0.253568i
735735 −0.246936 + 0.771115i −0.00910837 + 0.0284430i
736736 −12.3967 + 29.9284i −0.456950 + 1.10317i
737737 −2.14328 5.17435i −0.0789489 0.190599i
738738 −3.70314 + 1.53389i −0.136315 + 0.0564633i
739739 28.5736 + 28.5736i 1.05110 + 1.05110i 0.998622 + 0.0524727i 0.0167103π0.0167103\pi
0.0524727 + 0.998622i 0.483290π0.483290\pi
740740 17.0121 + 33.0406i 0.625378 + 1.21460i
741741 −1.23905 2.99133i −0.0455177 0.109889i
742742 −6.13952 14.8221i −0.225389 0.544137i
743743 −21.6747 8.97795i −0.795168 0.329369i −0.0521484 0.998639i 0.516607π-0.516607\pi
−0.743019 + 0.669270i 0.766607π0.766607\pi
744744 16.1366i 0.591598i
745745 13.8764 16.3876i 0.508393 0.600394i
746746 17.2052 17.2052i 0.629927 0.629927i
747747 1.70972i 0.0625553i
748748 8.49949 + 4.83689i 0.310772 + 0.176854i
749749 14.9462 0.546121
750750 −6.11220 + 42.0505i −0.223186 + 1.53547i
751751 −29.7279 12.3137i −1.08479 0.449333i −0.232600 0.972572i 0.574723π-0.574723\pi
−0.852186 + 0.523239i 0.824723π0.824723\pi
752752 −2.58218 −0.0941624
753753 −29.5290 12.2313i −1.07610 0.445734i
754754 −51.7536 + 21.4370i −1.88475 + 0.780690i
755755 −3.15708 + 0.261959i −0.114898 + 0.00953367i
756756 −22.8177 22.8177i −0.829873 0.829873i
757757 25.3721 25.3721i 0.922165 0.922165i −0.0750172 0.997182i 0.523901π-0.523901\pi
0.997182 + 0.0750172i 0.0239012π0.0239012\pi
758758 −23.9255 + 9.91025i −0.869012 + 0.359957i
759759 −6.56697 + 2.72013i −0.238366 + 0.0987343i
760760 −0.885920 + 1.04624i −0.0321357 + 0.0379511i
761761 26.9643i 0.977453i −0.872437 0.488727i 0.837462π-0.837462\pi
0.872437 0.488727i 0.162538π-0.162538\pi
762762 −15.4887 + 37.3931i −0.561098 + 1.35461i
763763 −5.00607 5.00607i −0.181232 0.181232i
764764 −26.5265 −0.959695
765765 1.62300 + 1.76500i 0.0586796 + 0.0638138i
766766 11.9162 0.430549
767767 −20.1318 20.1318i −0.726918 0.726918i
768768 −4.88788 + 11.8004i −0.176376 + 0.425809i
769769 13.1666i 0.474800i 0.971412 + 0.237400i 0.0762952π0.0762952\pi
−0.971412 + 0.237400i 0.923705π0.923705\pi
770770 9.40501 + 7.96383i 0.338933 + 0.286996i
771771 −12.8514 + 5.32324i −0.462834 + 0.191712i
772772 −41.2675 + 17.0936i −1.48525 + 0.615210i
773773 22.4347 22.4347i 0.806920 0.806920i −0.177247 0.984166i 0.556719π-0.556719\pi
0.984166 + 0.177247i 0.0567191π0.0567191\pi
774774 3.44688 + 3.44688i 0.123895 + 0.123895i
775775 11.0959 48.0102i 0.398578 1.72458i
776776 −12.9141 + 5.34918i −0.463587 + 0.192024i
777777 30.6046 + 12.6768i 1.09793 + 0.454779i
778778 −3.42839 −0.122914
779779 −4.57325 1.89430i −0.163854 0.0678705i
780780 −11.9162 23.1434i −0.426667 0.828665i
781781 −1.09791 −0.0392861
782782 −9.27317 33.7658i −0.331608 1.20746i
783783 49.6360i 1.77385i
784784 0.418728 0.418728i 0.0149546 0.0149546i
785785 8.22317 + 6.96309i 0.293497 + 0.248523i
786786 6.15119i 0.219406i
787787 −10.3704 4.29554i −0.369663 0.153120i 0.190115 0.981762i 0.439114π-0.439114\pi
−0.559779 + 0.828642i 0.689114π0.689114\pi
788788 −18.1310 43.7720i −0.645889 1.55931i
789789 4.35092 + 10.5041i 0.154897 + 0.373954i
790790 0.881258 + 1.71156i 0.0313538 + 0.0608947i
791791 −11.0218 11.0218i −0.391891 0.391891i
792792 0.212612 0.0880667i 0.00755483 0.00312931i
793793 2.10337 + 5.07799i 0.0746930 + 0.180325i
794794 10.3525 24.9932i 0.367398 0.886977i
795795 −10.9212 3.49732i −0.387335 0.124037i
796796 −52.3668 21.6911i −1.85609 0.768819i
797797 23.8591 + 23.8591i 0.845134 + 0.845134i 0.989521 0.144388i 0.0461212π-0.0461212\pi
−0.144388 + 0.989521i 0.546121π0.546121\pi
798798 6.89502i 0.244081i
799799 2.84683 2.21274i 0.100714 0.0782811i
800800 23.3204 32.6776i 0.824499 1.15533i
801801 −1.03472 + 1.03472i −0.0365600 + 0.0365600i
802802 −23.2012 + 56.0125i −0.819261 + 1.97787i
803803 2.92579 0.103249
804804 9.64074 23.2748i 0.340003 0.820839i
805805 −2.00182 24.1256i −0.0705549 0.850315i
806806 21.0564 + 50.8346i 0.741679 + 1.79057i
807807 11.8213 11.8213i 0.416131 0.416131i
808808 9.37764 9.37764i 0.329904 0.329904i
809809 −5.44317 13.1410i −0.191372 0.462012i 0.798847 0.601534i 0.205443π-0.205443\pi
−0.990219 + 0.139522i 0.955443π0.955443\pi
810810 −45.5588 + 3.78024i −1.60077 + 0.132824i
811811 −9.42238 + 22.7476i −0.330865 + 0.798778i 0.667659 + 0.744467i 0.267296π0.267296\pi
−0.998524 + 0.0543111i 0.982704π0.982704\pi
812812 65.4455 2.29669
813813 −11.5937 + 27.9896i −0.406608 + 0.981639i
814814 9.92972 9.92972i 0.348037 0.348037i
815815 3.44777 + 1.10409i 0.120770 + 0.0386745i
816816 −5.82141 21.1971i −0.203790 0.742047i
817817 6.01999i 0.210613i
818818 20.2719 + 20.2719i 0.708790 + 0.708790i
819819 −1.71016 0.708372i −0.0597578 0.0247525i
820820 −37.9011 12.1372i −1.32356 0.423848i
821821 9.55514 23.0681i 0.333477 0.805084i −0.664835 0.746991i 0.731498π-0.731498\pi
0.998311 0.0580931i 0.0185020π-0.0185020\pi
822822 −6.84060 16.5147i −0.238593 0.576015i
823823 −26.6778 + 11.0503i −0.929931 + 0.385190i −0.795652 0.605753i 0.792872π-0.792872\pi
−0.134279 + 0.990944i 0.542872π0.542872\pi
824824 1.04702 + 1.04702i 0.0364745 + 0.0364745i
825825 8.68839 1.45183i 0.302491 0.0505464i
826826 23.2019 + 56.0144i 0.807298 + 1.94899i
827827 6.20037 + 14.9690i 0.215608 + 0.520524i 0.994267 0.106923i 0.0340999π-0.0340999\pi
−0.778659 + 0.627447i 0.784100π0.784100\pi
828828 −2.35650 0.976095i −0.0818941 0.0339216i
829829 22.2311i 0.772117i 0.922474 + 0.386058i 0.126164π0.126164\pi
−0.922474 + 0.386058i 0.873836π0.873836\pi
830830 19.9953 23.6137i 0.694046 0.819645i
831831 15.3286 15.3286i 0.531744 0.531744i
832832 29.1641i 1.01108i
833833 −0.102824 + 0.820464i −0.00356266 + 0.0284274i
834834 3.13090 0.108414
835835 44.0026 22.6562i 1.52277 0.784052i
836836 1.48150 + 0.613656i 0.0512386 + 0.0212237i
837837 48.7546 1.68521
838838 −27.7436 11.4918i −0.958386 0.396977i
839839 43.2196 17.9021i 1.49211 0.618051i 0.520332 0.853964i 0.325808π-0.325808\pi
0.971774 + 0.235914i 0.0758082π0.0758082\pi
840840 0.812410 + 9.79102i 0.0280308 + 0.337822i
841841 −50.6764 50.6764i −1.74746 1.74746i
842842 43.0675 43.0675i 1.48420 1.48420i
843843 47.0428 19.4858i 1.62024 0.671125i
844844 51.4751 21.3217i 1.77185 0.733923i
845845 −10.1787 8.61899i −0.350159 0.296502i
846846 0.478741i 0.0164594i
847847 −10.3181 + 24.9100i −0.354533 + 0.855919i
848848 5.93039 + 5.93039i 0.203650 + 0.203650i
849849 30.8359 1.05829
850850 1.77417 + 43.3584i 0.0608536 + 1.48718i
851851 −27.5851 −0.945604
852852 −3.49205 3.49205i −0.119636 0.119636i
853853 14.6828 35.4475i 0.502731 1.21370i −0.445259 0.895402i 0.646889π-0.646889\pi
0.947990 0.318299i 0.103111π-0.103111\pi
854854 11.7048i 0.400529i
855855 0.300051 + 0.254073i 0.0102615 + 0.00868911i
856856 4.66658 1.93296i 0.159500 0.0660672i
857857 −5.10428 + 2.11426i −0.174359 + 0.0722218i −0.468155 0.883646i 0.655081π-0.655081\pi
0.293796 + 0.955868i 0.405081π0.405081\pi
858858 −6.95529 + 6.95529i −0.237450 + 0.237450i
859859 10.1314 + 10.1314i 0.345680 + 0.345680i 0.858498 0.512817i 0.171398π-0.171398\pi
−0.512817 + 0.858498i 0.671398π0.671398\pi
860860 4.00215 + 48.2332i 0.136472 + 1.64474i
861861 −32.7737 + 13.5753i −1.11692 + 0.462645i
862862 39.9746 + 16.5580i 1.36154 + 0.563969i
863863 −9.68459 −0.329667 −0.164834 0.986321i 0.552709π-0.552709\pi
−0.164834 + 0.986321i 0.552709π0.552709\pi
864864 36.6974 + 15.2006i 1.24847 + 0.517134i
865865 −20.6292 + 10.6217i −0.701413 + 0.361147i
866866 −50.9025 −1.72974
867867 24.5825 + 18.3811i 0.834864 + 0.624255i
868868 64.2833i 2.18192i
869869 0.282196 0.282196i 0.00957284 0.00957284i
870870 55.1012 65.0727i 1.86811 2.20617i
871871 15.2245i 0.515862i
872872 −2.21045 0.915599i −0.0748553 0.0310061i
873873 1.53409 + 3.70362i 0.0519211 + 0.125349i
874874 −2.19724 5.30462i −0.0743229 0.179431i
875875 −4.31543 + 29.6891i −0.145888 + 1.00368i
876876 9.30590 + 9.30590i 0.314417 + 0.314417i
877877 −13.8214 + 5.72500i −0.466714 + 0.193319i −0.603632 0.797263i 0.706280π-0.706280\pi
0.136918 + 0.990582i 0.456280π0.456280\pi
878878 17.7578 + 42.8711i 0.599297 + 1.44683i
879879 4.71625 11.3860i 0.159075 0.384041i
880880 −6.13550 1.96479i −0.206828 0.0662329i
881881 9.80896 + 4.06301i 0.330472 + 0.136886i 0.541749 0.840540i 0.317762π-0.317762\pi
−0.211277 + 0.977426i 0.567762π0.567762\pi
882882 0.0776330 + 0.0776330i 0.00261404 + 0.00261404i
883883 52.5251i 1.76761i −0.467855 0.883805i 0.654973π-0.654973\pi
0.467855 0.883805i 0.345027π-0.345027\pi
884884 −16.3141 20.9891i −0.548703 0.705941i
885885 41.2724 + 13.2167i 1.38736 + 0.444276i
886886 48.1243 48.1243i 1.61677 1.61677i
887887 −6.57850 + 15.8819i −0.220884 + 0.533262i −0.995011 0.0997691i 0.968190π-0.968190\pi
0.774126 + 0.633031i 0.218190π0.218190\pi
888888 11.1950 0.375680
889889 −10.9356 + 26.4009i −0.366768 + 0.885457i
890890 −26.3922 + 2.18989i −0.884667 + 0.0734052i
891891 3.62669 + 8.75561i 0.121499 + 0.293324i
892892 −22.4412 + 22.4412i −0.751386 + 0.751386i
893893 0.418062 0.418062i 0.0139899 0.0139899i
894894 −13.9673 33.7200i −0.467135 1.12776i
895895 3.46287 + 41.7340i 0.115751 + 1.39501i
896896 7.27703 17.5683i 0.243108 0.586916i
897897 19.3220 0.645143
898898 25.2701 61.0075i 0.843276 2.03585i
899899 −69.9185 + 69.9185i −2.33191 + 2.33191i
900900 2.57298 + 1.83620i 0.0857658 + 0.0612067i
901901 −11.6201 1.45629i −0.387122 0.0485160i
902902 15.0380i 0.500712i
903903 30.5057 + 30.5057i 1.01517 + 1.01517i
904904 −4.86673 2.01586i −0.161865 0.0670467i
905905 −5.22794 1.67415i −0.173782 0.0556508i
906906 −2.06057 + 4.97465i −0.0684577 + 0.165272i
907907 4.28190 + 10.3374i 0.142178 + 0.343248i 0.978888 0.204398i 0.0655238π-0.0655238\pi
−0.836710 + 0.547647i 0.815524π0.815524\pi
908908 −24.0288 + 9.95305i −0.797423 + 0.330304i
909909 −2.68941 2.68941i −0.0892022 0.0892022i
910910 −15.3354 29.7841i −0.508363 0.987334i
911911 1.24981 + 3.01730i 0.0414080 + 0.0999677i 0.943230 0.332139i 0.107770π-0.107770\pi
−0.901822 + 0.432107i 0.857770π0.857770\pi
912912 −1.37936 3.33008i −0.0456753 0.110270i
913913 −5.92619 2.45471i −0.196128 0.0812390i
914914 26.8343i 0.887599i
915915 −6.38484 5.40646i −0.211076 0.178732i
916916 −32.3715 + 32.3715i −1.06958 + 1.06958i
917917 4.34296i 0.143417i
918918 −41.4027 + 11.3705i −1.36649 + 0.375284i
919919 32.6905 1.07836 0.539179 0.842191i 0.318735π-0.318735\pi
0.539179 + 0.842191i 0.318735π0.318735\pi
920920 −3.74514 7.27373i −0.123473 0.239808i
921921 1.24490 + 0.515655i 0.0410209 + 0.0169914i
922922 36.6220 1.20608
923923 2.75729 + 1.14211i 0.0907574 + 0.0375930i
924924 10.6170 4.39769i 0.349272 0.144673i
925925 33.3077 + 7.69795i 1.09515 + 0.253107i
926926 44.0198 + 44.0198i 1.44658 + 1.44658i
927927 0.300273 0.300273i 0.00986227 0.00986227i
928928 −74.4264 + 30.8284i −2.44317 + 1.01199i
929929 −7.83598 + 3.24577i −0.257090 + 0.106490i −0.507506 0.861648i 0.669433π-0.669433\pi
0.250416 + 0.968138i 0.419433π0.419433\pi
930930 −63.9172 54.1228i −2.09593 1.77476i
931931 0.135586i 0.00444367i
932932 −2.08921 + 5.04381i −0.0684344 + 0.165215i
933933 −23.2368 23.2368i −0.760739 0.760739i
934934 69.2208 2.26497
935935 8.44802 3.09152i 0.276280 0.101104i
936936 −0.625569 −0.0204473
937937 −22.0610 22.0610i −0.720703 0.720703i 0.248045 0.968748i 0.420212π-0.420212\pi
−0.968748 + 0.248045i 0.920212π0.920212\pi
938938 12.4071 29.9533i 0.405105 0.978009i
939939 17.9184i 0.584744i
940940 3.07165 3.62752i 0.100186 0.118317i
941941 19.9946 8.28202i 0.651804 0.269986i −0.0321810 0.999482i 0.510245π-0.510245\pi
0.683985 + 0.729496i 0.260245π0.260245\pi
942942 16.9204 7.00868i 0.551298 0.228355i
943943 20.8880 20.8880i 0.680208 0.680208i
944944 −22.4116 22.4116i −0.729435 0.729435i
945945 −29.5822 + 2.45458i −0.962309 + 0.0798475i
946946 16.8963 6.99868i 0.549347 0.227547i
947947 −3.63370 1.50513i −0.118079 0.0489101i 0.322862 0.946446i 0.395355π-0.395355\pi
−0.440941 + 0.897536i 0.645355π0.645355\pi
948948 1.79513 0.0583031
949949 −7.34786 3.04358i −0.238522 0.0987989i
950950 1.17275 + 7.01825i 0.0380491 + 0.227702i
951951 43.8964 1.42344
952952 2.65708 + 9.67506i 0.0861166 + 0.313571i
953953 4.24356i 0.137462i −0.997635 0.0687312i 0.978105π-0.978105\pi
0.997635 0.0687312i 0.0218951π-0.0218951\pi
954954 −1.09950 + 1.09950i −0.0355978 + 0.0355978i
955955 −15.7684 + 18.6220i −0.510255 + 0.602593i
956956 40.6658i 1.31523i
957957 −16.3309 6.76447i −0.527902 0.218664i
958958 −0.478328 1.15479i −0.0154541 0.0373095i
959959 −4.82971 11.6600i −0.155959 0.376519i
960960 −20.3215 39.4680i −0.655873 1.27383i
961961 46.7567 + 46.7567i 1.50828 + 1.50828i
962962 −35.2671 + 14.6081i −1.13706 + 0.470985i
963963 −0.554353 1.33833i −0.0178638 0.0431270i
964964 −10.9515 + 26.4392i −0.352723 + 0.851549i
965965 −12.5312 + 39.1315i −0.403393 + 1.25969i
966966 −38.0149 15.7463i −1.22311 0.506628i
967967 −25.3036 25.3036i −0.813708 0.813708i 0.171480 0.985188i 0.445145π-0.445145\pi
−0.985188 + 0.171480i 0.945145π0.945145\pi
968968 9.11197i 0.292870i
969969 4.37437 + 2.48937i 0.140525 + 0.0799700i
970970 −22.1261 + 69.0938i −0.710425 + 2.21847i
971971 −26.0013 + 26.0013i −0.834423 + 0.834423i −0.988118 0.153695i 0.950883π-0.950883\pi
0.153695 + 0.988118i 0.450883π0.450883\pi
972972 −2.50733 + 6.05324i −0.0804228 + 0.194158i
973973 2.21053 0.0708664
974974 −1.81468 + 4.38103i −0.0581462 + 0.140377i
975975 −23.3304 5.39204i −0.747172 0.172684i
976976 2.34156 + 5.65303i 0.0749516 + 0.180949i
977977 −18.3472 + 18.3472i −0.586977 + 0.586977i −0.936812 0.349834i 0.886238π-0.886238\pi
0.349834 + 0.936812i 0.386238π0.386238\pi
978978 4.35104 4.35104i 0.139131 0.139131i
979979 2.10094 + 5.07211i 0.0671463 + 0.162105i
980980 0.0901393 + 1.08634i 0.00287939 + 0.0347019i
981981 −0.262585 + 0.633935i −0.00838368 + 0.0202400i
982982 15.3652 0.490322
983983 −12.6630 + 30.5712i −0.403888 + 0.975071i 0.582825 + 0.812598i 0.301947π0.301947\pi
−0.986713 + 0.162474i 0.948053π0.948053\pi
984984 −8.47711 + 8.47711i −0.270241 + 0.270241i
985985 −41.5064 13.2917i −1.32250 0.423509i
986986 43.0689 75.6817i 1.37159 2.41020i
987987 4.23697i 0.134864i
988988 −3.08229 3.08229i −0.0980606 0.0980606i
989989 −33.1905 13.7480i −1.05540 0.437160i
990990 0.364275 1.13753i 0.0115774 0.0361532i
991991 13.3710 32.2804i 0.424744 1.02542i −0.556186 0.831058i 0.687736π-0.687736\pi
0.980930 0.194364i 0.0622643π-0.0622643\pi
992992 30.2810 + 73.1049i 0.961423 + 2.32108i
993993 0.816987 0.338407i 0.0259263 0.0107390i
994994 −4.49406 4.49406i −0.142543 0.142543i
995995 −46.3564 + 23.8682i −1.46960 + 0.756674i
996996 −11.0416 26.6567i −0.349865 0.844649i
997997 −6.29396 15.1950i −0.199332 0.481229i 0.792331 0.610092i 0.208867π-0.208867\pi
−0.991662 + 0.128862i 0.958867π0.958867\pi
998998 14.7809 + 6.12244i 0.467881 + 0.193802i
999999 33.8241i 1.07015i
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 85.2.m.a.9.1 24
3.2 odd 2 765.2.bh.b.604.6 24
5.2 odd 4 425.2.m.e.26.6 24
5.3 odd 4 425.2.m.e.26.1 24
5.4 even 2 inner 85.2.m.a.9.6 yes 24
15.14 odd 2 765.2.bh.b.604.1 24
17.2 even 8 inner 85.2.m.a.19.6 yes 24
17.6 odd 16 1445.2.b.i.579.4 24
17.11 odd 16 1445.2.b.i.579.3 24
51.2 odd 8 765.2.bh.b.19.1 24
85.2 odd 8 425.2.m.e.376.6 24
85.19 even 8 inner 85.2.m.a.19.1 yes 24
85.23 even 16 7225.2.a.by.1.3 24
85.28 even 16 7225.2.a.by.1.4 24
85.53 odd 8 425.2.m.e.376.1 24
85.57 even 16 7225.2.a.by.1.22 24
85.62 even 16 7225.2.a.by.1.21 24
85.74 odd 16 1445.2.b.i.579.21 24
85.79 odd 16 1445.2.b.i.579.22 24
255.104 odd 8 765.2.bh.b.19.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.m.a.9.1 24 1.1 even 1 trivial
85.2.m.a.9.6 yes 24 5.4 even 2 inner
85.2.m.a.19.1 yes 24 85.19 even 8 inner
85.2.m.a.19.6 yes 24 17.2 even 8 inner
425.2.m.e.26.1 24 5.3 odd 4
425.2.m.e.26.6 24 5.2 odd 4
425.2.m.e.376.1 24 85.53 odd 8
425.2.m.e.376.6 24 85.2 odd 8
765.2.bh.b.19.1 24 51.2 odd 8
765.2.bh.b.19.6 24 255.104 odd 8
765.2.bh.b.604.1 24 15.14 odd 2
765.2.bh.b.604.6 24 3.2 odd 2
1445.2.b.i.579.3 24 17.11 odd 16
1445.2.b.i.579.4 24 17.6 odd 16
1445.2.b.i.579.21 24 85.74 odd 16
1445.2.b.i.579.22 24 85.79 odd 16
7225.2.a.by.1.3 24 85.23 even 16
7225.2.a.by.1.4 24 85.28 even 16
7225.2.a.by.1.21 24 85.62 even 16
7225.2.a.by.1.22 24 85.57 even 16