Properties

Label 637.2.bz.a.4.10
Level 637637
Weight 22
Character 637.4
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 756756
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [637,2,Mod(4,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([10, 7])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.4"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.bz (of order 4242, degree 1212, 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: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 756756
Relative dimension: 6363 over Q(ζ42)\Q(\zeta_{42})
Twist minimal: yes
Sato-Tate group: SU(2)[C42]\mathrm{SU}(2)[C_{42}]

Embedding invariants

Embedding label 4.10
Character χ\chi == 637.4
Dual form 637.2.bz.a.478.10

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+(0.9382751.94835i)q2+(1.735220.535243i)q3+(1.66872+2.09251i)q4+(0.6946112.25187i)q5+(2.670952.87860i)q6+(0.169018+2.64035i)q7+(1.42609+0.325495i)q8+(0.2457740.167566i)q9+(3.73570+3.46622i)q10+(3.121544.57845i)q11+(1.77559+4.52413i)q12+(3.604680.0792810i)q13+(5.302902.14807i)q14+(2.410603.53570i)q15+(0.487235+2.13472i)q16+(4.045585.07300i)q17+(0.5570800.321630i)q18+(5.119272.95561i)q19+(5.87118+2.30427i)q20+(1.11995+4.67204i)q21+(11.84931.78599i)q22+(2.23094+2.79752i)q23+(2.648790.198499i)q24+(0.457252+0.311749i)q25+(3.22771+7.09756i)q26+(3.05979+3.83685i)q27+(5.242914.75967i)q28+(3.726870.561736i)q29+(4.62697+8.01415i)q30+(2.687471.55161i)q31+(5.989284.77629i)q32+(2.965959.61539i)q33+(6.08810+12.6421i)q34+(6.063131.45341i)q35+(0.0594949+0.793905i)q36+(6.104244.86797i)q37+(0.955279+12.7473i)q38+(6.29733+1.79181i)q39+(0.2576023.43746i)q40+(4.27454+4.60686i)q41+(8.051946.56570i)q42+(1.76691+1.63945i)q43+(4.37148+14.1720i)q44+(0.5480540.437059i)q45+(7.54377+1.72182i)q46+(4.565336.69610i)q47+(1.98805+3.44340i)q48+(6.942870.892530i)q49+(1.03643+0.598380i)q50+(9.735246.63738i)q51+(6.181107.41053i)q52+(1.330333.38963i)q53+(10.3464+2.36151i)q54+(12.47833.84906i)q55+(1.10045+3.71035i)q56+(10.46502.38857i)q57+(4.591296.73418i)q58+(0.684133+0.156149i)q59+(11.4211+0.855894i)q60+(13.60122.05004i)q61+(0.501493+6.69196i)q62+(0.400892+0.677250i)q63+(10.97995.28765i)q64+(2.32532+8.17235i)q65+(21.5170+3.24317i)q66+(12.51237.22396i)q67+17.3662q68+(2.37382+6.04839i)q69+(8.5206210.4494i)q70+(0.03631390.240927i)q71+(0.4050370.158965i)q72+(4.54953+6.67294i)q73+(15.21207.32570i)q74+(0.626570+0.785694i)q75+(14.72735.78004i)q76+(11.5611+9.01578i)q77+(9.39970+10.5882i)q78+(5.41989+9.38753i)q79+(4.468672.57999i)q80+(3.58177+9.12619i)q81+(12.9865+4.00580i)q82+(2.65968+5.52288i)q83+(11.64525.45283i)q84+(8.61364+12.6339i)q85+(4.85207+1.90430i)q86+(6.166262.96952i)q87+(5.941855.51323i)q88+(2.282864.74041i)q89+(0.337317+1.47788i)q90+(0.8185849.50421i)q91+(2.131019.33655i)q92+(5.493821.25393i)q93+(17.32992.61206i)q94+(3.09976+13.5810i)q95+(7.8362111.4936i)q96+(8.895965.13608i)q97+(4.77536+14.3646i)q981.64833iq99+O(q100)q+(-0.938275 - 1.94835i) q^{2} +(1.73522 - 0.535243i) q^{3} +(-1.66872 + 2.09251i) q^{4} +(-0.694611 - 2.25187i) q^{5} +(-2.67095 - 2.87860i) q^{6} +(-0.169018 + 2.64035i) q^{7} +(1.42609 + 0.325495i) q^{8} +(0.245774 - 0.167566i) q^{9} +(-3.73570 + 3.46622i) q^{10} +(3.12154 - 4.57845i) q^{11} +(-1.77559 + 4.52413i) q^{12} +(-3.60468 - 0.0792810i) q^{13} +(5.30290 - 2.14807i) q^{14} +(-2.41060 - 3.53570i) q^{15} +(0.487235 + 2.13472i) q^{16} +(-4.04558 - 5.07300i) q^{17} +(-0.557080 - 0.321630i) q^{18} +(-5.11927 - 2.95561i) q^{19} +(5.87118 + 2.30427i) q^{20} +(1.11995 + 4.67204i) q^{21} +(-11.8493 - 1.78599i) q^{22} +(-2.23094 + 2.79752i) q^{23} +(2.64879 - 0.198499i) q^{24} +(-0.457252 + 0.311749i) q^{25} +(3.22771 + 7.09756i) q^{26} +(-3.05979 + 3.83685i) q^{27} +(-5.24291 - 4.75967i) q^{28} +(3.72687 - 0.561736i) q^{29} +(-4.62697 + 8.01415i) q^{30} +(-2.68747 - 1.55161i) q^{31} +(5.98928 - 4.77629i) q^{32} +(2.96595 - 9.61539i) q^{33} +(-6.08810 + 12.6421i) q^{34} +(6.06313 - 1.45341i) q^{35} +(-0.0594949 + 0.793905i) q^{36} +(6.10424 - 4.86797i) q^{37} +(-0.955279 + 12.7473i) q^{38} +(-6.29733 + 1.79181i) q^{39} +(-0.257602 - 3.43746i) q^{40} +(-4.27454 + 4.60686i) q^{41} +(8.05194 - 6.56570i) q^{42} +(-1.76691 + 1.63945i) q^{43} +(4.37148 + 14.1720i) q^{44} +(-0.548054 - 0.437059i) q^{45} +(7.54377 + 1.72182i) q^{46} +(4.56533 - 6.69610i) q^{47} +(1.98805 + 3.44340i) q^{48} +(-6.94287 - 0.892530i) q^{49} +(1.03643 + 0.598380i) q^{50} +(-9.73524 - 6.63738i) q^{51} +(6.18110 - 7.41053i) q^{52} +(-1.33033 - 3.38963i) q^{53} +(10.3464 + 2.36151i) q^{54} +(-12.4783 - 3.84906i) q^{55} +(-1.10045 + 3.71035i) q^{56} +(-10.4650 - 2.38857i) q^{57} +(-4.59129 - 6.73418i) q^{58} +(-0.684133 + 0.156149i) q^{59} +(11.4211 + 0.855894i) q^{60} +(13.6012 - 2.05004i) q^{61} +(-0.501493 + 6.69196i) q^{62} +(0.400892 + 0.677250i) q^{63} +(-10.9799 - 5.28765i) q^{64} +(2.32532 + 8.17235i) q^{65} +(-21.5170 + 3.24317i) q^{66} +(12.5123 - 7.22396i) q^{67} +17.3662 q^{68} +(-2.37382 + 6.04839i) q^{69} +(-8.52062 - 10.4494i) q^{70} +(0.0363139 - 0.240927i) q^{71} +(0.405037 - 0.158965i) q^{72} +(4.54953 + 6.67294i) q^{73} +(-15.2120 - 7.32570i) q^{74} +(-0.626570 + 0.785694i) q^{75} +(14.7273 - 5.78004i) q^{76} +(11.5611 + 9.01578i) q^{77} +(9.39970 + 10.5882i) q^{78} +(5.41989 + 9.38753i) q^{79} +(4.46867 - 2.57999i) q^{80} +(-3.58177 + 9.12619i) q^{81} +(12.9865 + 4.00580i) q^{82} +(-2.65968 + 5.52288i) q^{83} +(-11.6452 - 5.45283i) q^{84} +(-8.61364 + 12.6339i) q^{85} +(4.85207 + 1.90430i) q^{86} +(6.16626 - 2.96952i) q^{87} +(5.94185 - 5.51323i) q^{88} +(2.28286 - 4.74041i) q^{89} +(-0.337317 + 1.47788i) q^{90} +(0.818584 - 9.50421i) q^{91} +(-2.13101 - 9.33655i) q^{92} +(-5.49382 - 1.25393i) q^{93} +(-17.3299 - 2.61206i) q^{94} +(-3.09976 + 13.5810i) q^{95} +(7.83621 - 11.4936i) q^{96} +(8.89596 - 5.13608i) q^{97} +(4.77536 + 14.3646i) q^{98} -1.64833i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 756q21q25q3+115q415q614q7+50q916q1024q1126q1210q1338q146q15125q16+15q179q1827q1915q20++105q98+O(q100) 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(521)e\left(\frac{5}{21}\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 −0.938275 1.94835i −0.663461 1.37769i −0.912452 0.409184i 0.865813π-0.865813\pi
0.248991 0.968506i 0.419901π-0.419901\pi
33 1.73522 0.535243i 1.00183 0.309023i 0.249902 0.968271i 0.419602π-0.419602\pi
0.751925 + 0.659248i 0.229125π0.229125\pi
44 −1.66872 + 2.09251i −0.834360 + 1.04625i
55 −0.694611 2.25187i −0.310639 1.00707i −0.967461 0.253022i 0.918576π-0.918576\pi
0.656821 0.754046i 0.271901π-0.271901\pi
66 −2.67095 2.87860i −1.09041 1.17518i
77 −0.169018 + 2.64035i −0.0638827 + 0.997957i
88 1.42609 + 0.325495i 0.504198 + 0.115080i
99 0.245774 0.167566i 0.0819246 0.0558553i
1010 −3.73570 + 3.46622i −1.18133 + 1.09611i
1111 3.12154 4.57845i 0.941178 1.38046i 0.0164347 0.999865i 0.494768π-0.494768\pi
0.924744 0.380590i 0.124279π-0.124279\pi
1212 −1.77559 + 4.52413i −0.512569 + 1.30600i
1313 −3.60468 0.0792810i −0.999758 0.0219886i
1414 5.30290 2.14807i 1.41726 0.574095i
1515 −2.41060 3.53570i −0.622414 0.912914i
1616 0.487235 + 2.13472i 0.121809 + 0.533679i
1717 −4.04558 5.07300i −0.981197 1.23038i −0.973092 0.230415i 0.925992π-0.925992\pi
−0.00810449 0.999967i 0.502580π-0.502580\pi
1818 −0.557080 0.321630i −0.131305 0.0758090i
1919 −5.11927 2.95561i −1.17444 0.678064i −0.219720 0.975563i 0.570514π-0.570514\pi
−0.954722 + 0.297499i 0.903848π0.903848\pi
2020 5.87118 + 2.30427i 1.31284 + 0.515250i
2121 1.11995 + 4.67204i 0.244392 + 1.01952i
2222 −11.8493 1.78599i −2.52627 0.380775i
2323 −2.23094 + 2.79752i −0.465184 + 0.583322i −0.957984 0.286820i 0.907402π-0.907402\pi
0.492800 + 0.870142i 0.335973π0.335973\pi
2424 2.64879 0.198499i 0.540682 0.0405185i
2525 −0.457252 + 0.311749i −0.0914505 + 0.0623499i
2626 3.22771 + 7.09756i 0.633007 + 1.39195i
2727 −3.05979 + 3.83685i −0.588856 + 0.738402i
2828 −5.24291 4.75967i −0.990817 0.899494i
2929 3.72687 0.561736i 0.692063 0.104312i 0.206413 0.978465i 0.433821π-0.433821\pi
0.485650 + 0.874153i 0.338583π0.338583\pi
3030 −4.62697 + 8.01415i −0.844765 + 1.46318i
3131 −2.68747 1.55161i −0.482683 0.278677i 0.238851 0.971056i 0.423229π-0.423229\pi
−0.721534 + 0.692379i 0.756563π0.756563\pi
3232 5.98928 4.77629i 1.05876 0.844336i
3333 2.96595 9.61539i 0.516306 1.67382i
3434 −6.08810 + 12.6421i −1.04410 + 2.16810i
3535 6.06313 1.45341i 1.02486 0.245671i
3636 −0.0594949 + 0.793905i −0.00991582 + 0.132317i
3737 6.10424 4.86797i 1.00353 0.800290i 0.0236198 0.999721i 0.492481π-0.492481\pi
0.979912 + 0.199431i 0.0639095π0.0639095\pi
3838 −0.955279 + 12.7473i −0.154967 + 2.06789i
3939 −6.29733 + 1.79181i −1.00838 + 0.286919i
4040 −0.257602 3.43746i −0.0407304 0.543510i
4141 −4.27454 + 4.60686i −0.667572 + 0.719471i −0.972500 0.232904i 0.925177π-0.925177\pi
0.304928 + 0.952375i 0.401368π0.401368\pi
4242 8.05194 6.56570i 1.24244 1.01311i
4343 −1.76691 + 1.63945i −0.269451 + 0.250014i −0.803312 0.595558i 0.796931π-0.796931\pi
0.533861 + 0.845572i 0.320740π0.320740\pi
4444 4.37148 + 14.1720i 0.659026 + 2.13651i
4545 −0.548054 0.437059i −0.0816991 0.0651528i
4646 7.54377 + 1.72182i 1.11227 + 0.253868i
4747 4.56533 6.69610i 0.665921 0.976727i −0.333501 0.942750i 0.608230π-0.608230\pi
0.999423 0.0339774i 0.0108174π-0.0108174\pi
4848 1.98805 + 3.44340i 0.286950 + 0.497013i
4949 −6.94287 0.892530i −0.991838 0.127504i
5050 1.03643 + 0.598380i 0.146573 + 0.0846238i
5151 −9.73524 6.63738i −1.36321 0.929418i
5252 6.18110 7.41053i 0.857164 1.02766i
5353 −1.33033 3.38963i −0.182735 0.465602i 0.809926 0.586532i 0.199507π-0.199507\pi
−0.992661 + 0.120931i 0.961412π0.961412\pi
5454 10.3464 + 2.36151i 1.40797 + 0.321361i
5555 −12.4783 3.84906i −1.68258 0.519007i
5656 −1.10045 + 3.71035i −0.147054 + 0.495816i
5757 −10.4650 2.38857i −1.38613 0.316374i
5858 −4.59129 6.73418i −0.602866 0.884241i
5959 −0.684133 + 0.156149i −0.0890666 + 0.0203289i −0.266822 0.963746i 0.585974π-0.585974\pi
0.177755 + 0.984075i 0.443116π0.443116\pi
6060 11.4211 + 0.855894i 1.47446 + 0.110495i
6161 13.6012 2.05004i 1.74145 0.262481i 0.800089 0.599882i 0.204786π-0.204786\pi
0.941361 + 0.337400i 0.109548π0.109548\pi
6262 −0.501493 + 6.69196i −0.0636896 + 0.849879i
6363 0.400892 + 0.677250i 0.0505076 + 0.0853255i
6464 −10.9799 5.28765i −1.37249 0.660956i
6565 2.32532 + 8.17235i 0.288420 + 1.01366i
6666 −21.5170 + 3.24317i −2.64856 + 0.399206i
6767 12.5123 7.22396i 1.52862 0.882547i 0.529196 0.848500i 0.322494π-0.322494\pi
0.999420 0.0340468i 0.0108395π-0.0108395\pi
6868 17.3662 2.10597
6969 −2.37382 + 6.04839i −0.285774 + 0.728141i
7070 −8.52062 10.4494i −1.01841 1.24894i
7171 0.0363139 0.240927i 0.00430967 0.0285928i −0.986573 0.163323i 0.947779π-0.947779\pi
0.990882 + 0.134730i 0.0430168π0.0430168\pi
7272 0.405037 0.158965i 0.0477341 0.0187342i
7373 4.54953 + 6.67294i 0.532482 + 0.781008i 0.994374 0.105928i 0.0337814π-0.0337814\pi
−0.461891 + 0.886937i 0.652829π0.652829\pi
7474 −15.2120 7.32570i −1.76836 0.851595i
7575 −0.626570 + 0.785694i −0.0723501 + 0.0907241i
7676 14.7273 5.78004i 1.68934 0.663016i
7777 11.5611 + 9.01578i 1.31751 + 1.02744i
7878 9.39970 + 10.5882i 1.06431 + 1.19888i
7979 5.41989 + 9.38753i 0.609786 + 1.05618i 0.991275 + 0.131807i 0.0420778π0.0420778\pi
−0.381490 + 0.924373i 0.624589π0.624589\pi
8080 4.46867 2.57999i 0.499612 0.288451i
8181 −3.58177 + 9.12619i −0.397974 + 1.01402i
8282 12.9865 + 4.00580i 1.43412 + 0.442366i
8383 −2.65968 + 5.52288i −0.291938 + 0.606215i −0.994421 0.105485i 0.966360π-0.966360\pi
0.702483 + 0.711700i 0.252075π0.252075\pi
8484 −11.6452 5.45283i −1.27059 0.594953i
8585 −8.61364 + 12.6339i −0.934280 + 1.37034i
8686 4.85207 + 1.90430i 0.523212 + 0.205346i
8787 6.16626 2.96952i 0.661093 0.318366i
8888 5.94185 5.51323i 0.633403 0.587712i
8989 2.28286 4.74041i 0.241983 0.502482i −0.744239 0.667914i 0.767187π-0.767187\pi
0.986221 + 0.165432i 0.0529017π0.0529017\pi
9090 −0.337317 + 1.47788i −0.0355563 + 0.155782i
9191 0.818584 9.50421i 0.0858109 0.996311i
9292 −2.13101 9.33655i −0.222173 0.973402i
9393 −5.49382 1.25393i −0.569683 0.130026i
9494 −17.3299 2.61206i −1.78744 0.269413i
9595 −3.09976 + 13.5810i −0.318029 + 1.39338i
9696 7.83621 11.4936i 0.799780 1.17306i
9797 8.89596 5.13608i 0.903248 0.521490i 0.0249952 0.999688i 0.492043π-0.492043\pi
0.878252 + 0.478197i 0.158710π0.158710\pi
9898 4.77536 + 14.3646i 0.482384 + 1.45104i
9999 1.64833i 0.165663i
100100 0.110688 1.47703i 0.0110688 0.147703i
101101 13.6048 4.19652i 1.35373 0.417570i 0.468803 0.883303i 0.344686π-0.344686\pi
0.884925 + 0.465733i 0.154209π0.154209\pi
102102 −3.79758 + 25.1953i −0.376017 + 2.49471i
103103 −11.4647 + 3.53638i −1.12965 + 0.348450i −0.802576 0.596550i 0.796538π-0.796538\pi
−0.327071 + 0.945000i 0.606062π0.606062\pi
104104 −5.11478 1.28637i −0.501546 0.126139i
105105 9.74291 5.76722i 0.950811 0.562823i
106106 −5.35596 + 5.77236i −0.520217 + 0.560661i
107107 −11.5716 5.57260i −1.11867 0.538724i −0.219190 0.975682i 0.570341π-0.570341\pi
−0.899482 + 0.436959i 0.856056π0.856056\pi
108108 −2.92272 12.8053i −0.281239 1.23219i
109109 4.77461 + 0.357807i 0.457324 + 0.0342717i 0.301401 0.953497i 0.402546π-0.402546\pi
0.155923 + 0.987769i 0.450165π0.450165\pi
110110 4.20881 + 27.9236i 0.401294 + 2.66241i
111111 7.98663 11.7142i 0.758058 1.11187i
112112 −5.71874 + 0.925665i −0.540370 + 0.0874671i
113113 −0.634449 8.46613i −0.0596839 0.796427i −0.944086 0.329700i 0.893052π-0.893052\pi
0.884402 0.466727i 0.154567π-0.154567\pi
114114 5.16530 + 22.6306i 0.483774 + 2.11955i
115115 7.84929 + 3.08062i 0.731950 + 0.287269i
116116 −5.04367 + 8.73590i −0.468293 + 0.811108i
117117 −0.899221 + 0.584536i −0.0831330 + 0.0540404i
118118 0.946138 + 1.18642i 0.0870991 + 0.109219i
119119 14.0782 9.82431i 1.29055 0.900593i
120120 −2.28687 5.82686i −0.208762 0.531917i
121121 −7.19949 18.3440i −0.654499 1.66764i
122122 −16.7558 24.5763i −1.51700 2.22503i
123123 −4.95147 + 10.2818i −0.446459 + 0.927081i
124124 7.73139 3.03435i 0.694299 0.272492i
125125 −8.19256 6.53335i −0.732765 0.584361i
126126 0.943372 1.41652i 0.0840423 0.126194i
127127 −4.40766 + 0.664348i −0.391116 + 0.0589513i −0.341657 0.939825i 0.610988π-0.610988\pi
−0.0494597 + 0.998776i 0.515750π0.515750\pi
128128 11.0328i 0.975172i
129129 −2.18846 + 3.79053i −0.192683 + 0.333737i
130130 13.7408 12.1984i 1.20515 1.06987i
131131 −4.99675 + 4.63631i −0.436568 + 0.405076i −0.867602 0.497260i 0.834340π-0.834340\pi
0.431033 + 0.902336i 0.358149π0.358149\pi
132132 15.1709 + 22.2517i 1.32046 + 1.93676i
133133 8.66910 13.0171i 0.751706 1.12873i
134134 −25.8147 17.6002i −2.23005 1.52042i
135135 10.7655 + 4.22513i 0.926543 + 0.363641i
136136 −4.11811 8.55135i −0.353125 0.733272i
137137 −4.54740 + 1.03791i −0.388511 + 0.0886750i −0.412314 0.911042i 0.635279π-0.635279\pi
0.0238038 + 0.999717i 0.492422π0.492422\pi
138138 14.0117 1.05003i 1.19275 0.0893844i
139139 −9.25457 + 2.85466i −0.784962 + 0.242129i −0.661226 0.750186i 0.729964π-0.729964\pi
−0.123736 + 0.992315i 0.539488π0.539488\pi
140140 −7.07640 + 15.1125i −0.598065 + 1.27724i
141141 4.33778 14.0627i 0.365307 1.18430i
142142 −0.503483 + 0.155304i −0.0422513 + 0.0130328i
143143 −11.6151 + 16.2564i −0.971305 + 1.35943i
144144 0.477455 + 0.443014i 0.0397879 + 0.0369178i
145145 −3.85368 8.00225i −0.320031 0.664551i
146146 8.73249 15.1251i 0.722706 1.25176i
147147 −12.5251 + 2.16739i −1.03305 + 0.178763i
148148 20.8965i 1.71768i
149149 4.11313 + 0.308237i 0.336961 + 0.0252517i 0.242136 0.970242i 0.422152π-0.422152\pi
0.0948246 + 0.995494i 0.469771π0.469771\pi
150150 2.11870 + 0.483580i 0.172991 + 0.0394841i
151151 2.33616 0.916874i 0.190114 0.0746141i −0.268374 0.963315i 0.586486π-0.586486\pi
0.458488 + 0.888701i 0.348391π0.348391\pi
152152 −6.33849 5.88126i −0.514120 0.477033i
153153 −1.84436 0.568909i −0.149108 0.0459936i
154154 6.71837 30.9843i 0.541382 2.49679i
155155 −1.62728 + 7.12960i −0.130707 + 0.572663i
156156 6.75911 16.1673i 0.541162 1.29442i
157157 −1.38809 0.428169i −0.110782 0.0341716i 0.238869 0.971052i 0.423223π-0.423223\pi
−0.349650 + 0.936880i 0.613700π0.613700\pi
158158 13.2048 19.3679i 1.05052 1.54083i
159159 −4.12269 5.16969i −0.326951 0.409983i
160160 −14.9158 10.1694i −1.17920 0.803964i
161161 −7.00934 6.36330i −0.552414 0.501498i
162162 21.1417 1.58435i 1.66105 0.124478i
163163 1.79228 5.81044i 0.140382 0.455109i −0.857892 0.513830i 0.828226π-0.828226\pi
0.998274 + 0.0587213i 0.0187023π0.0187023\pi
164164 −2.50688 16.6321i −0.195755 1.29875i
165165 −23.7128 −1.84604
166166 13.2560 1.02887
167167 −2.55599 16.9579i −0.197788 1.31224i −0.838686 0.544615i 0.816676π-0.816676\pi
0.640898 0.767626i 0.278562π-0.278562\pi
168168 0.0764150 + 7.02727i 0.00589555 + 0.542166i
169169 12.9874 + 0.571565i 0.999033 + 0.0439665i
170170 32.6972 + 4.92830i 2.50776 + 0.377984i
171171 −1.75344 + 0.131402i −0.134089 + 0.0100486i
172172 −0.482091 6.43306i −0.0367591 0.490516i
173173 −0.703258 1.79187i −0.0534677 0.136233i 0.901644 0.432478i 0.142361π-0.142361\pi
−0.955112 + 0.296245i 0.904266π0.904266\pi
174174 −11.5713 9.22781i −0.877218 0.699558i
175175 −0.745843 1.26000i −0.0563804 0.0952468i
176176 11.2946 + 4.43281i 0.851364 + 0.334136i
177177 −1.10354 + 0.637130i −0.0829473 + 0.0478896i
178178 −11.3779 −0.852811
179179 7.92768 20.1994i 0.592542 1.50977i −0.248405 0.968656i 0.579906π-0.579906\pi
0.840947 0.541117i 0.181998π-0.181998\pi
180180 1.82910 0.417480i 0.136333 0.0311171i
181181 3.86077 + 1.85925i 0.286969 + 0.138197i 0.571831 0.820372i 0.306233π-0.306233\pi
−0.284862 + 0.958569i 0.591948π0.591948\pi
182182 −19.2856 + 7.32267i −1.42954 + 0.542793i
183183 22.5037 10.8372i 1.66352 0.801109i
184184 −4.09210 + 3.26334i −0.301673 + 0.240577i
185185 −15.2021 10.3646i −1.11768 0.762023i
186186 2.71163 + 11.8804i 0.198826 + 0.871114i
187187 −35.8549 + 2.68695i −2.62197 + 0.196489i
188188 6.39341 + 20.7269i 0.466287 + 1.51167i
189189 −9.61346 8.72739i −0.699276 0.634825i
190190 29.3689 6.70325i 2.13064 0.486305i
191191 15.9506 + 14.8000i 1.15415 + 1.07089i 0.996517 + 0.0833934i 0.0265758π0.0265758\pi
0.157630 + 0.987498i 0.449615π0.449615\pi
192192 −21.8827 3.29829i −1.57925 0.238033i
193193 −3.84263 12.4575i −0.276598 0.896710i −0.982158 0.188059i 0.939780π-0.939780\pi
0.705559 0.708651i 0.250696π-0.250696\pi
194194 −18.3537 12.5134i −1.31772 0.898407i
195195 8.40913 + 12.9362i 0.602190 + 0.926379i
196196 13.4533 13.0386i 0.960952 0.931331i
197197 −9.99328 5.76962i −0.711992 0.411069i 0.0998065 0.995007i 0.468178π-0.468178\pi
−0.811798 + 0.583938i 0.801511π0.801511\pi
198198 −3.21151 + 1.54658i −0.228232 + 0.109911i
199199 3.11599 13.6520i 0.220886 0.967767i −0.735926 0.677062i 0.763253π-0.763253\pi
0.956813 0.290705i 0.0938898π-0.0938898\pi
200200 −0.753555 + 0.295748i −0.0532844 + 0.0209126i
201201 17.8449 19.2322i 1.25868 1.35654i
202202 −20.9413 22.5694i −1.47343 1.58798i
203203 0.853270 + 9.93518i 0.0598878 + 0.697313i
204204 30.1342 9.29516i 2.10981 0.650791i
205205 13.3432 + 6.42575i 0.931930 + 0.448794i
206206 17.6471 + 19.0191i 1.22953 + 1.32512i
207207 −0.0795399 + 1.06139i −0.00552841 + 0.0737714i
208208 −1.58708 7.73360i −0.110044 0.536228i
209209 −29.5121 + 14.2123i −2.04140 + 0.983085i
210210 −20.3781 13.5713i −1.40622 0.936511i
211211 5.43894 3.70821i 0.374432 0.255283i −0.361452 0.932391i 0.617719π-0.617719\pi
0.735884 + 0.677107i 0.236767π0.236767\pi
212212 9.31279 + 2.87262i 0.639605 + 0.197292i
213213 −0.0659422 0.437498i −0.00451828 0.0299769i
214214 27.7742i 1.89860i
215215 4.91915 + 2.84007i 0.335483 + 0.193691i
216216 −5.61240 + 4.47574i −0.381875 + 0.304535i
217217 4.55102 6.83359i 0.308943 0.463895i
218218 −3.78276 9.63832i −0.256201 0.652789i
219219 11.4661 + 9.14388i 0.774805 + 0.617886i
220220 28.8771 19.6881i 1.94689 1.32737i
221221 14.1808 + 18.6073i 0.953905 + 1.25166i
222222 −30.3171 4.56956i −2.03475 0.306689i
223223 −17.4707 + 6.85673i −1.16992 + 0.459161i −0.869156 0.494537i 0.835338π-0.835338\pi
−0.300766 + 0.953698i 0.597242π0.597242\pi
224224 11.5988 + 16.6210i 0.774975 + 1.11054i
225225 −0.0601422 + 0.153240i −0.00400948 + 0.0102160i
226226 −15.8997 + 9.17969i −1.05763 + 0.610624i
227227 22.0053i 1.46054i 0.683158 + 0.730270i 0.260606π0.260606\pi
−0.683158 + 0.730270i 0.739394π0.739394\pi
228228 22.4613 17.9123i 1.48754 1.18627i
229229 11.5458 + 12.4434i 0.762966 + 0.822282i 0.988383 0.151980i 0.0485651π-0.0485651\pi
−0.225417 + 0.974262i 0.572375π0.572375\pi
230230 −1.36267 18.1836i −0.0898520 1.19899i
231231 24.8867 + 9.45632i 1.63742 + 0.622180i
232232 5.49769 + 0.411995i 0.360941 + 0.0270488i
233233 −3.91084 + 9.96465i −0.256207 + 0.652806i −0.999876 0.0157425i 0.994989π-0.994989\pi
0.743669 + 0.668548i 0.233084π0.233084\pi
234234 1.98260 + 1.20354i 0.129606 + 0.0786779i
235235 −18.2499 5.62935i −1.19049 0.367218i
236236 0.814884 1.69212i 0.0530445 0.110148i
237237 14.4293 + 13.3884i 0.937284 + 0.869672i
238238 −32.3504 18.2114i −2.09697 1.18047i
239239 25.8101 5.89099i 1.66952 0.381056i 0.719803 0.694178i 0.244232π-0.244232\pi
0.949713 + 0.313122i 0.101375π0.101375\pi
240240 6.37319 6.86866i 0.411388 0.443370i
241241 −14.9183 11.8970i −0.960973 0.766350i 0.0113638 0.999935i 0.496383π-0.496383\pi
−0.972336 + 0.233585i 0.924954π0.924954\pi
242242 −28.9854 + 31.2388i −1.86325 + 2.00811i
243243 −0.230189 + 3.07165i −0.0147666 + 0.197047i
244244 −18.4068 + 31.8815i −1.17837 + 2.04100i
245245 2.81272 + 16.2544i 0.179698 + 1.03846i
246246 24.6784 1.57344
247247 18.2190 + 11.0599i 1.15925 + 0.703725i
248248 −3.32752 3.08749i −0.211298 0.196056i
249249 −1.65903 + 11.0070i −0.105137 + 0.697539i
250250 −5.04237 + 22.0920i −0.318907 + 1.39722i
251251 10.0910 9.36311i 0.636940 0.590994i −0.294161 0.955756i 0.595040π-0.595040\pi
0.931101 + 0.364762i 0.118850π0.118850\pi
252252 −2.08613 0.291271i −0.131414 0.0183484i
253253 5.84432 + 18.9468i 0.367429 + 1.19118i
254254 5.42998 + 7.96431i 0.340707 + 0.499725i
255255 −8.18432 + 26.5329i −0.512522 + 1.66156i
256256 −0.464060 + 0.223479i −0.0290037 + 0.0139675i
257257 4.51139 + 5.65710i 0.281413 + 0.352880i 0.902369 0.430965i 0.141827π-0.141827\pi
−0.620956 + 0.783845i 0.713255π0.713255\pi
258258 9.43865 + 0.707329i 0.587625 + 0.0440364i
259259 11.8214 + 16.9401i 0.734547 + 1.05261i
260260 −20.9810 8.77162i −1.30119 0.543993i
261261 0.821840 0.762556i 0.0508706 0.0472011i
262262 13.7215 + 5.38528i 0.847715 + 0.332704i
263263 9.92917 + 17.1978i 0.612259 + 1.06046i 0.990859 + 0.134903i 0.0430722π0.0430722\pi
−0.378600 + 0.925560i 0.623594π0.623594\pi
264264 7.35947 12.7470i 0.452944 0.784522i
265265 −6.70895 + 5.35021i −0.412128 + 0.328661i
266266 −33.4959 4.67679i −2.05376 0.286752i
267267 1.42398 9.44752i 0.0871464 0.578179i
268268 −5.76327 + 38.2368i −0.352048 + 2.33568i
269269 11.1108 + 5.35066i 0.677434 + 0.326235i 0.740772 0.671757i 0.234460π-0.234460\pi
−0.0633372 + 0.997992i 0.520174π0.520174\pi
270270 −1.86893 24.9392i −0.113740 1.51775i
271271 −21.5371 17.1753i −1.30829 1.04333i −0.995623 0.0934617i 0.970207π-0.970207\pi
−0.312665 0.949863i 0.601222π-0.601222\pi
272272 8.85826 11.1079i 0.537111 0.673516i
273273 −3.66664 16.9300i −0.221915 1.02465i
274274 6.28893 + 7.88607i 0.379928 + 0.476415i
275275 3.06665i 0.184926i
276276 −8.69508 15.0603i −0.523382 0.906525i
277277 −11.9794 15.0217i −0.719772 0.902565i 0.278553 0.960421i 0.410145π-0.410145\pi
−0.998325 + 0.0578557i 0.981574π0.981574\pi
278278 14.2452 + 15.3527i 0.854370 + 0.920792i
279279 −0.920506 + 0.0689824i −0.0551092 + 0.00412987i
280280 9.11962 0.0991674i 0.545002 0.00592639i
281281 −6.73269 13.9806i −0.401639 0.834012i −0.999475 0.0323935i 0.989687π-0.989687\pi
0.597836 0.801618i 0.296027π-0.296027\pi
282282 −31.4692 + 4.74321i −1.87396 + 0.282454i
283283 2.65450 + 1.80981i 0.157794 + 0.107582i 0.639643 0.768672i 0.279082π-0.279082\pi
−0.481849 + 0.876254i 0.660035π0.660035\pi
284284 0.443545 + 0.478028i 0.0263195 + 0.0283657i
285285 1.89035 + 25.2250i 0.111975 + 1.49420i
286286 42.5713 + 7.37735i 2.51729 + 0.436232i
287287 −11.4412 12.0649i −0.675355 0.712170i
288288 0.671665 2.17748i 0.0395782 0.128310i
289289 −5.58572 + 24.4726i −0.328572 + 1.43957i
290290 −11.9754 + 15.0166i −0.703218 + 0.881807i
291291 12.6874 13.6737i 0.743746 0.801568i
292292 −21.5551 1.61533i −1.26142 0.0945301i
293293 −3.31647 + 1.91476i −0.193750 + 0.111862i −0.593737 0.804659i 0.702348π-0.702348\pi
0.399987 + 0.916521i 0.369015π0.369015\pi
294294 15.9748 + 22.3696i 0.931670 + 1.30462i
295295 0.826834 + 1.43212i 0.0481401 + 0.0833812i
296296 10.2897 4.95525i 0.598076 0.288018i
297297 8.01561 + 25.9860i 0.465113 + 1.50786i
298298 −3.25870 8.30302i −0.188771 0.480981i
299299 8.26363 9.90728i 0.477898 0.572953i
300300 −0.598502 2.62221i −0.0345545 0.151393i
301301 −4.03008 4.94235i −0.232290 0.284872i
302302 −3.97835 3.69137i −0.228928 0.212414i
303303 21.3611 14.5638i 1.22716 0.836666i
304304 3.81511 12.3683i 0.218811 0.709369i
305305 −14.0640 29.2041i −0.805299 1.67222i
306306 0.622082 + 4.12725i 0.0355621 + 0.235939i
307307 9.42018 + 19.5612i 0.537638 + 1.11642i 0.976031 + 0.217633i 0.0698336π0.0698336\pi
−0.438393 + 0.898783i 0.644452π0.644452\pi
308308 −38.1579 + 9.14692i −2.17425 + 0.521194i
309309 −18.0009 + 12.2728i −1.02403 + 0.698174i
310310 15.4178 3.51901i 0.875671 0.199866i
311311 14.6312 2.20530i 0.829659 0.125051i 0.279537 0.960135i 0.409819π-0.409819\pi
0.550122 + 0.835084i 0.314581π0.314581\pi
312312 −9.56377 + 0.505528i −0.541442 + 0.0286199i
313313 −1.51784 2.62898i −0.0857934 0.148599i 0.819936 0.572456i 0.194009π-0.194009\pi
−0.905729 + 0.423857i 0.860676π0.860676\pi
314314 0.468188 + 3.10623i 0.0264214 + 0.175294i
315315 1.24662 1.37318i 0.0702389 0.0773701i
316316 −28.6878 4.32399i −1.61381 0.243243i
317317 0.689517 4.57465i 0.0387271 0.256938i −0.961086 0.276248i 0.910909π-0.910909\pi
0.999814 + 0.0193101i 0.00614699π0.00614699\pi
318318 −6.20414 + 12.8830i −0.347911 + 0.722444i
319319 9.06169 18.8168i 0.507357 1.05354i
320320 −4.28034 + 28.3982i −0.239278 + 1.58751i
321321 −23.0620 3.47603i −1.28719 0.194013i
322322 −5.82123 + 19.6272i −0.324404 + 1.09378i
323323 5.71661 + 37.9272i 0.318081 + 2.11033i
324324 −13.1197 22.7240i −0.728871 1.26244i
325325 1.67296 1.08751i 0.0927994 0.0603240i
326326 −13.0024 + 1.95980i −0.720137 + 0.108543i
327327 8.47649 1.93470i 0.468751 0.106989i
328328 −7.59538 + 5.17844i −0.419385 + 0.285932i
329329 16.9084 + 13.1858i 0.932191 + 0.726957i
330330 22.2491 + 46.2008i 1.22477 + 2.54327i
331331 1.99971 + 13.2672i 0.109914 + 0.729233i 0.974109 + 0.226077i 0.0725900π0.0725900\pi
−0.864195 + 0.503157i 0.832172π0.832172\pi
332332 −7.11842 14.7816i −0.390674 0.811243i
333333 0.684558 2.21928i 0.0375136 0.121616i
334334 −30.6416 + 20.8911i −1.67664 + 1.14311i
335335 −24.9586 23.1582i −1.36363 1.26527i
336336 −9.42780 + 4.66715i −0.514329 + 0.254614i
337337 3.82698 + 16.7671i 0.208469 + 0.913362i 0.965586 + 0.260083i 0.0837499π0.0837499\pi
−0.757117 + 0.653279i 0.773393π0.773393\pi
338338 −11.0722 25.8403i −0.602247 1.40553i
339339 −5.63235 14.3510i −0.305907 0.779439i
340340 −12.0628 39.1065i −0.654196 2.12085i
341341 −15.4930 + 7.46103i −0.838992 + 0.404037i
342342 1.90123 + 3.29303i 0.102807 + 0.178067i
343343 3.53006 18.1807i 0.190605 0.981667i
344344 −3.05340 + 1.76288i −0.164628 + 0.0950482i
345345 15.2691 + 1.14426i 0.822060 + 0.0616049i
346346 −2.83134 + 3.05146i −0.152214 + 0.164047i
347347 −21.5031 + 26.9640i −1.15434 + 1.44750i −0.281462 + 0.959572i 0.590819π0.590819\pi
−0.872883 + 0.487930i 0.837752π0.837752\pi
348348 −4.07603 + 17.8583i −0.218498 + 0.957303i
349349 −4.40441 + 14.2788i −0.235763 + 0.764324i 0.757945 + 0.652319i 0.226204π0.226204\pi
−0.993708 + 0.112006i 0.964273π0.964273\pi
350350 −1.75511 + 2.63539i −0.0938144 + 0.140867i
351351 11.3337 13.5880i 0.604950 0.725276i
352352 −3.17227 42.3310i −0.169082 2.25625i
353353 −13.9287 15.0116i −0.741351 0.798987i 0.243954 0.969787i 0.421555π-0.421555\pi
−0.985306 + 0.170800i 0.945365π0.945365\pi
354354 2.27678 + 1.55228i 0.121009 + 0.0825028i
355355 −0.567762 + 0.0855763i −0.0301337 + 0.00454192i
356356 6.10989 + 12.6873i 0.323824 + 0.672427i
357357 19.1704 24.5826i 1.01461 1.30105i
358358 −46.7938 + 3.50671i −2.47313 + 0.185335i
359359 2.59999 + 2.80212i 0.137222 + 0.147890i 0.797924 0.602758i 0.205932π-0.205932\pi
−0.660702 + 0.750649i 0.729741π0.729741\pi
360360 −0.639312 0.801672i −0.0336947 0.0422518i
361361 7.97131 + 13.8067i 0.419543 + 0.726670i
362362 9.26662i 0.487043i
363363 −22.3112 27.9773i −1.17103 1.46843i
364364 18.5217 + 17.5728i 0.970799 + 0.921063i
365365 11.8665 14.8801i 0.621119 0.778858i
366366 −42.2293 33.6767i −2.20736 1.76031i
367367 0.549649 + 7.33456i 0.0286915 + 0.382861i 0.993003 + 0.118090i 0.0376772π0.0376772\pi
−0.964311 + 0.264771i 0.914704π0.914704\pi
368368 −7.05890 3.39938i −0.367970 0.177205i
369369 −0.278619 + 1.84851i −0.0145043 + 0.0962298i
370370 −5.93014 + 39.3439i −0.308293 + 2.04539i
371371 9.17465 2.93963i 0.476324 0.152618i
372372 11.7915 9.40342i 0.611362 0.487545i
373373 1.87971 3.25575i 0.0973276 0.168576i −0.813250 0.581914i 0.802304π-0.802304\pi
0.910578 + 0.413338i 0.135637π0.135637\pi
374374 38.8769 + 67.3367i 2.01027 + 3.48190i
375375 −17.7128 6.95176i −0.914685 0.358988i
376376 8.69010 8.06323i 0.448158 0.415830i
377377 −13.4787 + 1.72941i −0.694189 + 0.0890690i
378378 −7.98393 + 26.9191i −0.410649 + 1.38457i
379379 18.9410 + 1.41943i 0.972936 + 0.0729115i 0.551703 0.834041i 0.313978π-0.313978\pi
0.421233 + 0.906952i 0.361597π0.361597\pi
380380 −23.2456 29.1491i −1.19248 1.49532i
381381 −7.29265 + 3.51196i −0.373614 + 0.179923i
382382 13.8695 44.9639i 0.709626 2.30055i
383383 2.81075 + 4.12261i 0.143622 + 0.210655i 0.891309 0.453396i 0.149788π-0.149788\pi
−0.747687 + 0.664052i 0.768835π0.768835\pi
384384 5.90524 + 19.1443i 0.301351 + 0.976954i
385385 12.2719 32.2966i 0.625435 1.64599i
386386 −20.6661 + 19.1753i −1.05188 + 0.975999i
387387 −0.159544 + 0.699008i −0.00811008 + 0.0355326i
388388 −4.09757 + 27.1856i −0.208022 + 1.38014i
389389 19.2655 + 17.8757i 0.976797 + 0.906335i 0.995620 0.0934875i 0.0298015π-0.0298015\pi
−0.0188233 + 0.999823i 0.505992π0.505992\pi
390390 17.3141 28.5216i 0.876734 1.44425i
391391 23.2172 1.17415
392392 −9.61062 3.53269i −0.485409 0.178428i
393393 −6.18889 + 10.7195i −0.312188 + 0.540726i
394394 −1.86479 + 24.8839i −0.0939467 + 1.25363i
395395 17.3748 18.7256i 0.874222 0.942187i
396396 3.44914 + 2.75060i 0.173326 + 0.138223i
397397 21.1642 22.8096i 1.06220 1.14478i 0.0731326 0.997322i 0.476700π-0.476700\pi
0.989068 0.147458i 0.0471091π-0.0471091\pi
398398 −29.5226 + 6.73833i −1.47983 + 0.337762i
399399 8.07543 27.2276i 0.404277 1.36308i
400400 −0.888286 0.824209i −0.0444143 0.0412104i
401401 −4.72855 + 9.81895i −0.236133 + 0.490335i −0.985037 0.172344i 0.944866π-0.944866\pi
0.748904 + 0.662678i 0.230580π0.230580\pi
402402 −54.2145 16.7230i −2.70397 0.834065i
403403 9.56444 + 5.80612i 0.476439 + 0.289223i
404404 −13.9213 + 35.4710i −0.692613 + 1.76475i
405405 23.0390 + 1.72653i 1.14482 + 0.0857920i
406406 18.5566 10.9844i 0.920948 0.545146i
407407 −3.23316 43.1435i −0.160262 2.13855i
408408 −11.7229 12.6342i −0.580369 0.625488i
409409 −6.57767 + 5.24551i −0.325245 + 0.259374i −0.772475 0.635045i 0.780982π-0.780982\pi
0.447231 + 0.894419i 0.352410π0.352410\pi
410410 32.0263i 1.58167i
411411 −7.33519 + 4.23497i −0.361818 + 0.208896i
412412 11.7314 29.8912i 0.577966 1.47263i
413413 −0.296657 1.83274i −0.0145975 0.0901833i
414414 2.14258 0.840901i 0.105302 0.0413280i
415415 14.2843 + 2.15301i 0.701187 + 0.105687i
416416 −21.9681 + 16.7422i −1.07707 + 0.820852i
417417 −14.5307 + 9.90690i −0.711574 + 0.485143i
418418 55.3810 + 44.1649i 2.70877 + 2.16017i
419419 12.7008 + 32.3612i 0.620476 + 1.58095i 0.801845 + 0.597533i 0.203852π0.203852\pi
−0.181368 + 0.983415i 0.558053π0.558053\pi
420420 −4.19022 + 30.0110i −0.204462 + 1.46439i
421421 −6.39115 + 5.09677i −0.311485 + 0.248401i −0.766737 0.641962i 0.778121π-0.778121\pi
0.455251 + 0.890363i 0.349549π0.349549\pi
422422 −12.3281 7.11763i −0.600122 0.346481i
423423 2.41072i 0.117213i
424424 −0.793861 5.26693i −0.0385533 0.255785i
425425 3.43135 + 1.05843i 0.166445 + 0.0513415i
426426 −0.790526 + 0.538972i −0.0383011 + 0.0261133i
427427 3.11399 + 36.2583i 0.150697 + 1.75466i
428428 30.9705 14.9146i 1.49702 0.720926i
429429 −11.4536 + 34.4252i −0.552986 + 1.66207i
430430 0.917935 12.2490i 0.0442667 0.590698i
431431 −19.6258 21.1516i −0.945344 1.01884i −0.999793 0.0203218i 0.993531π-0.993531\pi
0.0544497 0.998517i 0.482660π-0.482660\pi
432432 −9.68142 4.66233i −0.465798 0.224316i
433433 4.44389 1.37076i 0.213560 0.0658745i −0.186129 0.982525i 0.559594π-0.559594\pi
0.399689 + 0.916651i 0.369118π0.369118\pi
434434 −17.5843 2.45517i −0.844075 0.117852i
435435 −10.9701 11.8230i −0.525977 0.566869i
436436 −8.71620 + 9.39383i −0.417430 + 0.449883i
437437 19.6892 7.72744i 0.941862 0.369654i
438438 7.05715 30.9194i 0.337203 1.47738i
439439 −18.4626 + 8.89112i −0.881172 + 0.424350i −0.819052 0.573719i 0.805500π-0.805500\pi
−0.0621193 + 0.998069i 0.519786π0.519786\pi
440440 −16.5424 9.55073i −0.788626 0.455313i
441441 −1.85593 + 0.944026i −0.0883778 + 0.0449536i
442442 22.9479 45.0879i 1.09152 2.14461i
443443 −13.6621 9.31465i −0.649105 0.442553i 0.193488 0.981103i 0.438020π-0.438020\pi
−0.842594 + 0.538550i 0.818972π0.818972\pi
444444 11.1847 + 36.2599i 0.530802 + 1.72082i
445445 −12.2605 1.84797i −0.581203 0.0876023i
446446 29.7516 + 27.6054i 1.40878 + 1.30716i
447447 7.30215 1.66667i 0.345380 0.0788307i
448448 15.8170 28.0971i 0.747284 1.32746i
449449 2.33096 + 7.55679i 0.110005 + 0.356627i 0.993791 0.111264i 0.0354900π-0.0354900\pi
−0.883786 + 0.467891i 0.845014π0.845014\pi
450450 0.354994 0.0266031i 0.0167346 0.00125408i
451451 7.74916 + 33.9513i 0.364894 + 1.59870i
452452 18.7742 + 12.8000i 0.883063 + 0.602062i
453453 3.56299 2.84139i 0.167404 0.133500i
454454 42.8739 20.6470i 2.01217 0.969011i
455455 −21.9709 + 4.75838i −1.03001 + 0.223076i
456456 −14.1466 6.81263i −0.662474 0.319030i
457457 −32.9500 + 7.52061i −1.54133 + 0.351800i −0.906957 0.421224i 0.861601π-0.861601\pi
−0.634378 + 0.773023i 0.718744π0.718744\pi
458458 13.4109 34.1705i 0.626652 1.59668i
459459 31.8429 1.48630
460460 −19.5445 + 11.2840i −0.911267 + 0.526120i
461461 −21.6829 8.50992i −1.00987 0.396347i −0.198015 0.980199i 0.563449π-0.563449\pi
−0.811860 + 0.583852i 0.801545π0.801545\pi
462462 −4.92633 57.3605i −0.229194 2.66865i
463463 2.28915 + 1.82553i 0.106386 + 0.0848397i 0.675238 0.737600i 0.264041π-0.264041\pi
−0.568852 + 0.822440i 0.692612π0.692612\pi
464464 3.01501 + 7.68212i 0.139968 + 0.356633i
465465 0.992379 + 13.2424i 0.0460205 + 0.614101i
466466 23.0840 1.72991i 1.06935 0.0801365i
467467 11.2055 + 1.68896i 0.518531 + 0.0781560i 0.403094 0.915159i 0.367935π-0.367935\pi
0.115437 + 0.993315i 0.463173π0.463173\pi
468468 0.277402 2.85706i 0.0128229 0.132067i
469469 16.9590 + 34.2577i 0.783092 + 1.58187i
470470 6.15549 + 40.8390i 0.283932 + 1.88376i
471471 −2.63781 −0.121544
472472 −1.02646 −0.0472466
473473 1.99068 + 13.2073i 0.0915317 + 0.607273i
474474 12.5467 40.6753i 0.576288 1.86828i
475475 3.26221 0.244469i 0.149681 0.0112170i
476476 −2.93520 + 45.8529i −0.134535 + 2.10166i
477477 −0.894947 0.610165i −0.0409768 0.0279375i
478478 −35.6947 44.7597i −1.63264 2.04726i
479479 1.01107 1.48296i 0.0461969 0.0677584i −0.802445 0.596725i 0.796468π-0.796468\pi
0.848642 + 0.528967i 0.177421π0.177421\pi
480480 −31.3253 9.66257i −1.42980 0.441034i
481481 −22.3898 + 17.0635i −1.02089 + 0.778030i
482482 −9.18193 + 40.2287i −0.418225 + 1.83237i
483483 −15.5686 7.28999i −0.708398 0.331706i
484484 50.3989 + 15.5460i 2.29086 + 0.706637i
485485 −17.7450 16.4650i −0.805760 0.747636i
486486 6.20063 2.43357i 0.281266 0.110389i
487487 36.2067 + 8.26395i 1.64068 + 0.374475i 0.940581 0.339568i 0.110281π-0.110281\pi
0.700101 + 0.714043i 0.253138π0.253138\pi
488488 20.0637 + 1.50357i 0.908242 + 0.0680633i
489489 11.0417i 0.499322i
490490 29.0301 20.7313i 1.31145 0.936544i
491491 13.5386 23.4495i 0.610989 1.05826i −0.380086 0.924951i 0.624105π-0.624105\pi
0.991074 0.133312i 0.0425612π-0.0425612\pi
492492 −13.2522 27.5185i −0.597456 1.24063i
493493 −17.9270 16.6339i −0.807393 0.749151i
494494 4.45409 45.8742i 0.200399 2.06398i
495495 −3.71182 + 1.14495i −0.166834 + 0.0514615i
496496 2.00282 6.49298i 0.0899292 0.291543i
497497 0.629994 + 0.136602i 0.0282591 + 0.00612745i
498498 23.0020 7.09519i 1.03075 0.317943i
499499 7.01335 0.525578i 0.313961 0.0235281i 0.0831821 0.996534i 0.473492π-0.473492\pi
0.230779 + 0.973006i 0.425873π0.425873\pi
500500 27.3422 6.24068i 1.22278 0.279092i
501501 −13.5118 28.0575i −0.603662 1.25352i
502502 −27.7108 10.8757i −1.23679 0.485405i
503503 17.2209 + 11.7410i 0.767842 + 0.523506i 0.882735 0.469872i 0.155700π-0.155700\pi
−0.114892 + 0.993378i 0.536652π0.536652\pi
504504 0.351265 + 1.09631i 0.0156466 + 0.0488333i
505505 −18.9001 27.7213i −0.841042 1.23358i
506506 31.4314 29.1641i 1.39730 1.29650i
507507 22.8419 5.95965i 1.01445 0.264677i
508508 5.96500 10.3317i 0.264654 0.458394i
509509 10.1530i 0.450024i 0.974356 + 0.225012i 0.0722421π0.0722421\pi
−0.974356 + 0.225012i 0.927758π0.927758\pi
510510 59.3745 8.94927i 2.62915 0.396280i
511511 −18.3878 + 10.8845i −0.813430 + 0.481502i
512512 18.1224 + 14.4522i 0.800906 + 0.638701i
513513 27.0041 10.5983i 1.19226 0.467928i
514514 6.78908 14.0977i 0.299453 0.621822i
515515 15.9270 + 23.3606i 0.701826 + 1.02939i
516516 −4.27979 10.9047i −0.188407 0.480053i
517517 −16.4070 41.8042i −0.721577 1.83855i
518518 21.9135 38.9267i 0.962823 1.71034i
519519 −2.17939 2.73287i −0.0956647 0.119960i
520520 0.656047 + 12.4114i 0.0287696 + 0.544274i
521521 21.3850 37.0398i 0.936892 1.62274i 0.165667 0.986182i 0.447022π-0.447022\pi
0.771225 0.636562i 0.219644π-0.219644\pi
522522 −2.25684 0.885743i −0.0987791 0.0387679i
523523 3.29514 + 14.4370i 0.144087 + 0.631285i 0.994461 + 0.105106i 0.0335183π0.0335183\pi
−0.850374 + 0.526178i 0.823625π0.823625\pi
524524 −1.36334 18.1925i −0.0595576 0.794741i
525525 −1.96860 1.78716i −0.0859169 0.0779980i
526526 24.1911 35.4818i 1.05478 1.54708i
527527 3.00105 + 19.9107i 0.130728 + 0.867322i
528528 21.9712 + 1.64652i 0.956175 + 0.0716554i
529529 2.26900 + 9.94114i 0.0986522 + 0.432223i
530530 16.7189 + 8.05141i 0.726224 + 0.349731i
531531 −0.141977 + 0.153015i −0.00616127 + 0.00664027i
532532 12.7721 + 39.8621i 0.553742 + 1.72824i
533533 15.7736 16.2674i 0.683230 0.704618i
534534 −19.7431 + 6.08995i −0.854369 + 0.263538i
535535 −4.51101 + 29.9286i −0.195028 + 1.29393i
536536 20.1949 6.22931i 0.872288 0.269065i
537537 2.94464 39.2936i 0.127071 1.69564i
538538 26.6680i 1.14974i
539539 −25.7588 + 29.0015i −1.10951 + 1.24918i
540540 −26.8057 + 15.4763i −1.15353 + 0.665992i
541541 6.18826 9.07651i 0.266054 0.390230i −0.669843 0.742502i 0.733639π-0.733639\pi
0.935897 + 0.352273i 0.114591π0.114591\pi
542542 −13.2557 + 58.0770i −0.569381 + 2.49462i
543543 7.69443 + 1.15975i 0.330199 + 0.0497696i
544544 −48.4602 11.0607i −2.07771 0.474224i
545545 −2.51076 11.0003i −0.107549 0.471203i
546546 −29.5452 + 23.0289i −1.26442 + 0.985545i
547547 −2.63688 + 11.5529i −0.112745 + 0.493968i 0.886752 + 0.462246i 0.152956π0.152956\pi
−0.999497 + 0.0317219i 0.989901π0.989901\pi
548548 5.41650 11.2475i 0.231381 0.480468i
549549 2.99929 2.78294i 0.128007 0.118773i
550550 5.97489 2.87736i 0.254770 0.122691i
551551 −20.7392 8.13952i −0.883518 0.346755i
552552 −5.35399 + 7.85287i −0.227881 + 0.334240i
553553 −25.7024 + 12.7237i −1.09298 + 0.541069i
554554 −18.0275 + 37.4345i −0.765915 + 1.59044i
555555 −31.9266 9.84805i −1.35521 0.418026i
556556 9.46990 24.1289i 0.401613 1.02329i
557557 −27.2522 + 15.7340i −1.15471 + 0.666673i −0.950031 0.312156i 0.898949π-0.898949\pi
−0.204680 + 0.978829i 0.565615π0.565615\pi
558558 0.998089 + 1.72874i 0.0422525 + 0.0731835i
559559 6.49912 5.76961i 0.274883 0.244029i
560560 6.05678 + 12.2349i 0.255946 + 0.517019i
561561 −60.7778 + 23.8535i −2.56604 + 1.00710i
562562 −20.9219 + 26.2353i −0.882538 + 1.10667i
563563 4.02820 + 1.93988i 0.169769 + 0.0817562i 0.516838 0.856083i 0.327109π-0.327109\pi
−0.347070 + 0.937839i 0.612823π0.612823\pi
564564 22.1879 + 32.5437i 0.934279 + 1.37033i
565565 −18.6240 + 7.30937i −0.783516 + 0.307507i
566566 1.03548 6.86998i 0.0435246 0.288767i
567567 −23.4909 10.9996i −0.986527 0.461940i
568568 0.130207 0.331763i 0.00546339 0.0139205i
569569 24.2453 1.01642 0.508209 0.861234i 0.330308π-0.330308\pi
0.508209 + 0.861234i 0.330308π0.330308\pi
570570 47.3735 27.3511i 1.98426 1.14561i
571571 22.4274 3.38039i 0.938559 0.141465i 0.338091 0.941114i 0.390219π-0.390219\pi
0.600468 + 0.799649i 0.294981π0.294981\pi
572572 −14.6342 51.4321i −0.611888 2.15048i
573573 35.5994 + 17.1438i 1.48719 + 0.716191i
574574 −12.7716 + 33.6117i −0.533078 + 1.40293i
575575 0.147981 1.97467i 0.00617123 0.0823493i
576576 −3.58460 + 0.540292i −0.149359 + 0.0225122i
577577 −19.1836 1.43762i −0.798625 0.0598487i −0.330836 0.943688i 0.607331π-0.607331\pi
−0.467790 + 0.883840i 0.654950π0.654950\pi
578578 52.9221 12.0791i 2.20127 0.502426i
579579 −13.3356 19.5597i −0.554208 0.812874i
580580 23.1755 + 5.28966i 0.962311 + 0.219641i
581581 −14.1328 7.95594i −0.586327 0.330068i
582582 −38.5454 11.8897i −1.59776 0.492843i
583583 −19.6719 4.48999i −0.814729 0.185956i
584584 4.31602 + 10.9970i 0.178598 + 0.455061i
585585 1.94091 + 1.61891i 0.0802467 + 0.0669335i
586586 6.84238 + 4.66506i 0.282656 + 0.192712i
587587 −13.8706 8.00822i −0.572503 0.330534i 0.185646 0.982617i 0.440562π-0.440562\pi
−0.758148 + 0.652082i 0.773896π0.773896\pi
588588 16.3656 29.8257i 0.674906 1.22999i
589589 9.17192 + 15.8862i 0.377922 + 0.654581i
590590 2.01447 2.95468i 0.0829343 0.121642i
591591 −20.4286 4.66271i −0.840322 0.191798i
592592 13.3659 + 10.6590i 0.549337 + 0.438081i
593593 5.20235 + 16.8656i 0.213635 + 0.692587i 0.997435 + 0.0715742i 0.0228023π0.0228023\pi
−0.783801 + 0.621013i 0.786722π0.786722\pi
594594 43.1088 39.9992i 1.76878 1.64119i
595595 −31.9020 24.8783i −1.30785 1.01991i
596596 −7.50865 + 8.09241i −0.307566 + 0.331478i
597597 −1.90025 25.3570i −0.0777719 1.03779i
598598 −27.0564 6.80468i −1.10642 0.278264i
599599 0.298732 3.98630i 0.0122058 0.162876i −0.987770 0.155918i 0.950166π-0.950166\pi
0.999976 0.00695733i 0.00221461π-0.00221461\pi
600600 −1.14928 + 0.916523i −0.0469193 + 0.0374169i
601601 −0.199824 + 2.66647i −0.00815101 + 0.108768i −0.999795 0.0202351i 0.993559π-0.993559\pi
0.991644 + 0.129003i 0.0411776π0.0411776\pi
602602 −5.84809 + 12.4893i −0.238350 + 0.509025i
603603 1.86470 3.87209i 0.0759364 0.157684i
604604 −1.97983 + 6.41844i −0.0805580 + 0.261163i
605605 −36.3075 + 28.9543i −1.47611 + 1.17716i
606606 −48.4179 27.9541i −1.96684 1.13556i
607607 15.8271 27.4134i 0.642403 1.11268i −0.342491 0.939521i 0.611271π-0.611271\pi
0.984895 0.173154i 0.0553960π-0.0553960\pi
608608 −44.7776 + 6.74914i −1.81597 + 0.273714i
609609 6.79835 + 16.7830i 0.275483 + 0.680081i
610610 −43.7039 + 54.8029i −1.76952 + 2.21891i
611611 −16.9874 + 23.7754i −0.687237 + 0.961848i
612612 4.26817 2.90999i 0.172530 0.117629i
613613 −16.7386 + 1.25438i −0.676066 + 0.0506641i −0.408338 0.912831i 0.633892π-0.633892\pi
−0.267727 + 0.963495i 0.586273π0.586273\pi
614614 29.2733 36.7076i 1.18137 1.48140i
615615 26.5927 + 4.00820i 1.07232 + 0.161626i
616616 13.5526 + 16.6204i 0.546048 + 0.669654i
617617 −25.2596 9.91366i −1.01691 0.399109i −0.202430 0.979297i 0.564884π-0.564884\pi
−0.814483 + 0.580188i 0.802979π0.802979\pi
618618 40.8014 + 23.5567i 1.64127 + 0.947589i
619619 −29.9607 17.2978i −1.20422 0.695258i −0.242731 0.970094i 0.578043π-0.578043\pi
−0.961491 + 0.274836i 0.911377π0.911377\pi
620620 −12.2033 15.3024i −0.490095 0.614560i
621621 −3.90744 17.1196i −0.156800 0.686986i
622622 −18.0248 26.4375i −0.722727 1.06005i
623623 12.1305 + 6.82875i 0.485997 + 0.273588i
624624 −6.89329 12.5700i −0.275952 0.503202i
625625 −10.0326 + 25.5625i −0.401302 + 1.02250i
626626 −3.69801 + 5.42398i −0.147802 + 0.216786i
627627 −43.6029 + 40.4576i −1.74133 + 1.61572i
628628 3.21229 2.19010i 0.128184 0.0873945i
629629 −49.3904 11.2730i −1.96932 0.449485i
630630 −3.84511 1.14042i −0.153193 0.0454355i
631631 18.4491 + 19.8834i 0.734447 + 0.791546i 0.984256 0.176749i 0.0565582π-0.0565582\pi
−0.249809 + 0.968295i 0.580368π0.580368\pi
632632 4.67365 + 15.1516i 0.185908 + 0.602698i
633633 7.45294 9.34570i 0.296228 0.371458i
634634 −9.55996 + 2.94886i −0.379675 + 0.117114i
635635 4.55763 + 9.46402i 0.180864 + 0.375568i
636636 17.6973 0.701742
637637 24.9560 + 3.76772i 0.988795 + 0.149283i
638638 −45.1640 −1.78806
639639 −0.0314462 0.0652986i −0.00124399 0.00258317i
640640 24.8445 7.66351i 0.982065 0.302927i
641641 −1.01414 + 1.27169i −0.0400560 + 0.0502286i −0.801456 0.598054i 0.795941π-0.795941\pi
0.761400 + 0.648282i 0.224512π0.224512\pi
642642 14.8659 + 48.1942i 0.586712 + 1.90207i
643643 −0.0168931 0.0182065i −0.000666200 0.000717993i 0.732719 0.680532i 0.238251π-0.238251\pi
−0.733385 + 0.679814i 0.762061π0.762061\pi
644644 25.0119 4.04855i 0.985607 0.159535i
645645 10.0559 + 2.29520i 0.395951 + 0.0903733i
646646 68.5317 46.7241i 2.69634 1.83834i
647647 4.11797 3.82092i 0.161894 0.150216i −0.595066 0.803677i 0.702874π-0.702874\pi
0.756960 + 0.653461i 0.226684π0.226684\pi
648648 −8.07844 + 11.8489i −0.317351 + 0.465469i
649649 −1.42063 + 3.61970i −0.0557645 + 0.142086i
650650 −3.68854 2.23914i −0.144676 0.0878262i
651651 4.23936 14.2937i 0.166154 0.560213i
652652 9.16758 + 13.4464i 0.359030 + 0.526601i
653653 −6.15421 26.9634i −0.240833 1.05516i −0.940261 0.340455i 0.889419π-0.889419\pi
0.699428 0.714703i 0.253438π-0.253438\pi
654654 −11.7228 14.6999i −0.458396 0.574810i
655655 13.9112 + 8.03162i 0.543555 + 0.313821i
656656 −11.9171 6.88031i −0.465283 0.268631i
657657 2.23631 + 0.877688i 0.0872469 + 0.0342419i
658658 9.82579 45.3154i 0.383049 1.76658i
659659 7.47439 + 1.12658i 0.291161 + 0.0438854i 0.292999 0.956113i 0.405347π-0.405347\pi
−0.00183771 + 0.999998i 0.500585π0.500585\pi
660660 39.5701 49.6193i 1.54026 1.93143i
661661 −4.97270 + 0.372652i −0.193416 + 0.0144945i −0.171086 0.985256i 0.554727π-0.554727\pi
−0.0223299 + 0.999751i 0.507108π0.507108\pi
662662 23.9729 16.3445i 0.931734 0.635245i
663663 34.5662 + 24.6974i 1.34244 + 0.959169i
664664 −5.59061 + 7.01040i −0.216958 + 0.272056i
665665 −35.3345 10.4799i −1.37021 0.406392i
666666 −4.96624 + 0.748540i −0.192438 + 0.0290053i
667667 −6.74298 + 11.6792i −0.261089 + 0.452220i
668668 39.7498 + 22.9495i 1.53797 + 0.887945i
669669 −26.6454 + 21.2490i −1.03017 + 0.821533i
670670 −21.7022 + 70.3567i −0.838428 + 2.71812i
671671 33.0705 68.6715i 1.27667 2.65104i
672672 29.0227 + 22.6329i 1.11957 + 0.873085i
673673 −1.44110 + 19.2302i −0.0555504 + 0.741268i 0.897993 + 0.440011i 0.145025π0.145025\pi
−0.953543 + 0.301257i 0.902594π0.902594\pi
674674 29.0774 23.1884i 1.12002 0.893185i
675675 0.202959 2.70830i 0.00781189 0.104242i
676676 −22.8684 + 26.2225i −0.879554 + 1.00856i
677677 0.701787 + 9.36470i 0.0269719 + 0.359915i 0.994318 + 0.106454i 0.0339498π0.0339498\pi
−0.967346 + 0.253461i 0.918431π0.918431\pi
678678 −22.6760 + 24.4390i −0.870868 + 0.938572i
679679 12.0575 + 24.3565i 0.462723 + 0.934717i
680680 −16.3961 + 15.2133i −0.628760 + 0.583404i
681681 11.7782 + 38.1839i 0.451340 + 1.46321i
682682 29.0734 + 23.1852i 1.11328 + 0.887809i
683683 −22.0605 5.03515i −0.844120 0.192665i −0.221472 0.975167i 0.571086π-0.571086\pi
−0.622648 + 0.782502i 0.713943π0.713943\pi
684684 2.65105 3.88837i 0.101365 0.148676i
685685 5.49592 + 9.51922i 0.209988 + 0.363711i
686686 −38.7345 + 10.1807i −1.47889 + 0.388702i
687687 26.6946 + 15.4122i 1.01846 + 0.588011i
688688 −4.36066 2.97305i −0.166249 0.113346i
689689 4.52669 + 12.3240i 0.172453 + 0.469507i
690690 −12.0972 30.8231i −0.460532 1.17342i
691691 26.6405 + 6.08052i 1.01345 + 0.231314i 0.696829 0.717237i 0.254594π-0.254594\pi
0.316624 + 0.948551i 0.397451π0.397451\pi
692692 4.92305 + 1.51856i 0.187146 + 0.0577270i
693693 4.35215 + 0.278596i 0.165325 + 0.0105830i
694694 72.7110 + 16.5958i 2.76007 + 0.629969i
695695 12.8566 + 18.8572i 0.487680 + 0.715296i
696696 9.76019 2.22770i 0.369959 0.0844408i
697697 40.6636 + 3.04732i 1.54024 + 0.115425i
698698 31.9525 4.81607i 1.20942 0.182291i
699699 −1.45264 + 19.3841i −0.0549437 + 0.733173i
700700 3.88116 + 0.541898i 0.146694 + 0.0204818i
701701 6.66388 + 3.20916i 0.251691 + 0.121208i 0.555476 0.831533i 0.312536π-0.312536\pi
−0.303785 + 0.952741i 0.598250π0.598250\pi
702702 −37.1084 9.33276i −1.40057 0.352242i
703703 −45.6372 + 6.87869i −1.72124 + 0.259435i
704704 −58.4834 + 33.7654i −2.20418 + 1.27258i
705705 −34.6806 −1.30615
706706 −16.1788 + 41.2230i −0.608899 + 1.55145i
707707 8.78083 + 36.6307i 0.330237 + 1.37764i
708708 0.508302 3.37236i 0.0191032 0.126741i
709709 36.4665 14.3120i 1.36953 0.537500i 0.437281 0.899325i 0.355942π-0.355942\pi
0.932246 + 0.361826i 0.117846π0.117846\pi
710710 0.699449 + 1.02590i 0.0262499 + 0.0385015i
711711 2.90510 + 1.39902i 0.108950 + 0.0524674i
712712 4.79854 6.01717i 0.179833 0.225503i
713713 10.3362 4.05667i 0.387095 0.151924i
714714 −65.8825 14.2854i −2.46559 0.534617i
715715 44.6753 + 14.8639i 1.67076 + 0.555879i
716716 29.0383 + 50.2959i 1.08521 + 1.87965i
717717 41.6330 24.0368i 1.55481 0.897671i
718718 3.02000 7.69484i 0.112705 0.287169i
719719 14.3052 + 4.41258i 0.533495 + 0.164561i 0.549786 0.835306i 0.314709π-0.314709\pi
−0.0162903 + 0.999867i 0.505186π0.505186\pi
720720 0.665965 1.38289i 0.0248190 0.0515373i
721721 −7.39955 30.8684i −0.275573 1.14960i
722722 19.4210 28.4854i 0.722775 1.06012i
723723 −32.2543 12.6589i −1.19955 0.470788i
724724 −10.3331 + 4.97613i −0.384025 + 0.184937i
725725 −1.52900 + 1.41871i −0.0567857 + 0.0526894i
726726 −33.5755 + 69.7203i −1.24611 + 2.58756i
727727 4.02987 17.6560i 0.149460 0.654825i −0.843576 0.537010i 0.819554π-0.819554\pi
0.993036 0.117815i 0.0375891π-0.0375891\pi
728728 4.26094 13.2874i 0.157921 0.492463i
729729 −5.30006 23.2211i −0.196299 0.860041i
730730 −40.1255 9.15839i −1.48511 0.338967i
731731 15.4651 + 2.33099i 0.571997 + 0.0862147i
732732 −14.8754 + 65.1734i −0.549811 + 2.40888i
733733 −10.8773 + 15.9540i −0.401761 + 0.589275i −0.972800 0.231648i 0.925588π-0.925588\pi
0.571039 + 0.820923i 0.306541π0.306541\pi
734734 13.7746 7.95275i 0.508428 0.293541i
735735 13.5808 + 26.6994i 0.500934 + 0.984823i
736736 27.4107i 1.01037i
737737 5.98293 79.8366i 0.220384 2.94082i
738738 3.86297 1.19157i 0.142198 0.0438622i
739739 2.24051 14.8648i 0.0824186 0.546812i −0.909073 0.416638i 0.863208π-0.863208\pi
0.991491 0.130174i 0.0415536π-0.0415536\pi
740740 47.0562 14.5149i 1.72982 0.533579i
741741 37.5337 + 9.43972i 1.37883 + 0.346777i
742742 −14.3358 15.1172i −0.526283 0.554971i
743743 20.4899 22.0829i 0.751703 0.810143i −0.235117 0.971967i 0.575547π-0.575547\pi
0.986820 + 0.161824i 0.0517377π0.0517377\pi
744744 −7.42652 3.57643i −0.272270 0.131118i
745745 −2.16292 9.47635i −0.0792431 0.347187i
746746 −8.10702 0.607537i −0.296819 0.0222435i
747747 0.271766 + 1.80305i 0.00994341 + 0.0659702i
748748 54.2093 79.5105i 1.98209 2.90719i
749749 16.6694 29.6112i 0.609087 1.08197i
750750 3.07503 + 41.0334i 0.112284 + 1.49833i
751751 5.80089 + 25.4154i 0.211677 + 0.927420i 0.963427 + 0.267971i 0.0863531π0.0863531\pi
−0.751750 + 0.659449i 0.770790π0.770790\pi
752752 16.5187 + 6.48310i 0.602374 + 0.236414i
753753 12.4986 21.6482i 0.455474 0.788903i
754754 16.0162 + 24.6386i 0.583277 + 0.897284i
755755 −3.68740 4.62386i −0.134198 0.168279i
756756 34.3043 5.55268i 1.24764 0.201949i
757757 −18.0523 45.9966i −0.656123 1.67177i −0.737719 0.675108i 0.764097π-0.764097\pi
0.0815960 0.996665i 0.473998π-0.473998\pi
758758 −15.0064 38.2356i −0.545055 1.38878i
759759 20.2823 + 29.7487i 0.736201 + 1.07981i
760760 −8.84107 + 18.3587i −0.320699 + 0.665939i
761761 −25.0610 + 9.83573i −0.908462 + 0.356545i −0.773124 0.634254i 0.781307π-0.781307\pi
−0.135338 + 0.990800i 0.543212π0.543212\pi
762762 13.6850 + 10.9134i 0.495756 + 0.395352i
763763 −1.75173 + 12.5461i −0.0634168 + 0.454201i
764764 −57.5863 + 8.67974i −2.08340 + 0.314022i
765765 4.54843i 0.164449i
766766 5.39502 9.34445i 0.194930 0.337629i
767767 2.47846 0.508628i 0.0894921 0.0183655i
768768 −0.685628 + 0.636170i −0.0247405 + 0.0229558i
769769 −11.6942 17.1522i −0.421702 0.618523i 0.555326 0.831633i 0.312593π-0.312593\pi
−0.977028 + 0.213109i 0.931641π0.931641\pi
770770 −74.4394 + 6.39313i −2.68261 + 0.230393i
771771 10.8562 + 7.40160i 0.390975 + 0.266562i
772772 32.4797 + 12.7473i 1.16897 + 0.458787i
773773 −7.40248 15.3714i −0.266249 0.552871i 0.724389 0.689392i 0.242122π-0.242122\pi
−0.990637 + 0.136521i 0.956408π0.956408\pi
774774 1.51161 0.345014i 0.0543336 0.0124013i
775775 1.71256 0.128339i 0.0615171 0.00461007i
776776 14.3582 4.42891i 0.515429 0.158989i
777777 29.5798 + 23.0674i 1.06117 + 0.827538i
778778 16.7518 54.3082i 0.600583 1.94704i
779779 35.4987 10.9499i 1.27187 0.392321i
780780 −41.1016 3.99070i −1.47167 0.142890i
781781 −0.989719 0.918325i −0.0354149 0.0328602i
782782 −21.7842 45.2353i −0.779000 1.61761i
783783 −9.24814 + 16.0182i −0.330501 + 0.572445i
784784 −1.47751 15.2559i −0.0527682 0.544854i
785785 3.42322i 0.122180i
786786 26.6922 + 2.00030i 0.952078 + 0.0713484i
787787 0.508023 + 0.115953i 0.0181091 + 0.00413328i 0.231566 0.972819i 0.425615π-0.425615\pi
−0.213457 + 0.976953i 0.568472π0.568472\pi
788788 28.7490 11.2831i 1.02414 0.401945i
789789 26.4343 + 24.5274i 0.941085 + 0.873199i
790790 −52.7863 16.2824i −1.87805 0.579303i
791791 22.4608 0.244240i 0.798613 0.00868417i
792792 0.536522 2.35066i 0.0190645 0.0835270i
793793 −49.1903 + 6.31144i −1.74680 + 0.224126i
794794 −64.2989 19.8336i −2.28188 0.703867i
795795 −8.77782 + 12.8747i −0.311317 + 0.456619i
796796 23.3673 + 29.3017i 0.828232 + 1.03857i
797797 21.0288 + 14.3372i 0.744880 + 0.507850i 0.875283 0.483611i 0.160675π-0.160675\pi
−0.130403 + 0.991461i 0.541627π0.541627\pi
798798 −60.6258 + 9.81320i −2.14613 + 0.347383i
799799 −52.4387 + 3.92974i −1.85515 + 0.139024i
800800 −1.24961 + 4.05112i −0.0441802 + 0.143229i
801801 −0.233263 1.54760i −0.00824194 0.0546817i
802802 23.5674 0.832194
803803 44.7533 1.57931
804804 10.4655 + 69.4339i 0.369089 + 2.44874i
805805 −9.46057 + 20.2042i −0.333441 + 0.712103i
806806 2.33827 24.0826i 0.0823619 0.848273i
807807 22.1435 + 3.33759i 0.779487 + 0.117489i
808808 20.7676 1.55631i 0.730601 0.0547510i
809809 −3.46684 46.2618i −0.121888 1.62648i −0.638055 0.769991i 0.720261π-0.720261\pi
0.516167 0.856488i 0.327358π-0.327358\pi
810810 −18.2530 46.5079i −0.641345 1.63412i
811811 −10.7052 8.53715i −0.375912 0.299780i 0.417249 0.908792i 0.362994π-0.362994\pi
−0.793161 + 0.609013i 0.791566π0.791566\pi
812812 −22.2133 14.7936i −0.779535 0.519152i
813813 −46.5646 18.2752i −1.63309 0.640941i
814814 −81.0250 + 46.7798i −2.83993 + 1.63963i
815815 −14.3293 −0.501934
816816 9.42556 24.0159i 0.329961 0.840726i
817817 13.8909 3.17050i 0.485980 0.110922i
818818 16.3917 + 7.89385i 0.573124 + 0.276002i
819819 −1.39139 2.47305i −0.0486192 0.0864154i
820820 −35.7120 + 17.1980i −1.24712 + 0.600581i
821821 −18.5470 + 14.7908i −0.647296 + 0.516201i −0.891207 0.453596i 0.850141π-0.850141\pi
0.243912 + 0.969797i 0.421569π0.421569\pi
822822 15.1336 + 10.3179i 0.527846 + 0.359879i
823823 8.76241 + 38.3906i 0.305438 + 1.33821i 0.861790 + 0.507265i 0.169344π0.169344\pi
−0.556352 + 0.830947i 0.687799π0.687799\pi
824824 −17.5007 + 1.31150i −0.609666 + 0.0456881i
825825 1.64140 + 5.32129i 0.0571463 + 0.185264i
826826 −3.29247 + 2.29761i −0.114560 + 0.0799440i
827827 −4.15413 + 0.948153i −0.144453 + 0.0329705i −0.294136 0.955764i 0.595032π-0.595032\pi
0.149683 + 0.988734i 0.452175π0.452175\pi
828828 −2.08823 1.93760i −0.0725711 0.0673361i
829829 −11.6167 1.75094i −0.403465 0.0608125i −0.0558247 0.998441i 0.517779π-0.517779\pi
−0.347640 + 0.937628i 0.613017π0.613017\pi
830830 −9.20777 29.8508i −0.319606 1.03614i
831831 −28.8271 19.6540i −1.00000 0.681789i
832832 39.1599 + 19.9308i 1.35762 + 0.690975i
833833 23.5601 + 38.8319i 0.816309 + 1.34545i
834834 32.9359 + 19.0156i 1.14048 + 0.658455i
835835 −36.4116 + 17.5349i −1.26007 + 0.606820i
836836 19.5082 85.4708i 0.674704 2.95607i
837837 14.1764 5.56381i 0.490007 0.192314i
838838 51.1340 55.1093i 1.76639 1.90372i
839839 24.0886 + 25.9613i 0.831629 + 0.896283i 0.995930 0.0901271i 0.0287273π-0.0287273\pi
−0.164301 + 0.986410i 0.552537π0.552537\pi
840840 15.7714 5.05330i 0.544166 0.174355i
841841 −14.1376 + 4.36087i −0.487503 + 0.150375i
842842 15.9269 + 7.67001i 0.548878 + 0.264326i
843843 −19.1657 20.6557i −0.660102 0.711420i
844844 −1.31661 + 17.5690i −0.0453197 + 0.604750i
845845 −7.73412 29.6431i −0.266062 1.01975i
846846 −4.69692 + 2.26192i −0.161483 + 0.0777663i
847847 49.6513 15.9087i 1.70604 0.546629i
848848 6.58772 4.49143i 0.226223 0.154236i
849849 5.57482 + 1.71960i 0.191327 + 0.0590166i
850850 −1.15736 7.67857i −0.0396971 0.263373i
851851 27.9369i 0.957664i
852852 1.02551 + 0.592077i 0.0351333 + 0.0202842i
853853 10.4393 8.32510i 0.357436 0.285046i −0.428264 0.903654i 0.640874π-0.640874\pi
0.785700 + 0.618608i 0.212303π0.212303\pi
854854 67.7220 40.0874i 2.31740 1.37176i
855855 1.51386 + 3.85726i 0.0517730 + 0.131915i
856856 −14.6883 11.7135i −0.502036 0.400360i
857857 16.7173 11.3977i 0.571053 0.389337i −0.243088 0.970004i 0.578160π-0.578160\pi
0.814141 + 0.580667i 0.197208π0.197208\pi
858858 77.8190 9.98468i 2.65670 0.340872i
859859 −37.3341 5.62721i −1.27382 0.191998i −0.522903 0.852392i 0.675151π-0.675151\pi
−0.750919 + 0.660394i 0.770389π0.770389\pi
860860 −14.1516 + 5.55408i −0.482564 + 0.189393i
861861 −26.3107 14.8114i −0.896666 0.504771i
862862 −22.7963 + 58.0840i −0.776445 + 1.97835i
863863 −40.6775 + 23.4852i −1.38468 + 0.799444i −0.992709 0.120535i 0.961539π-0.961539\pi
−0.391968 + 0.919979i 0.628206π0.628206\pi
864864 37.5944i 1.27899i
865865 −3.54658 + 2.82830i −0.120587 + 0.0961651i
866866 −6.84031 7.37210i −0.232443 0.250514i
867867 3.40638 + 45.4550i 0.115687 + 1.54373i
868868 6.70499 + 20.9264i 0.227582 + 0.710289i
869869 59.8988 + 4.48879i 2.03193 + 0.152272i
870870 −12.7423 + 32.4668i −0.432004 + 1.10073i
871871 −45.6754 + 25.0481i −1.54765 + 0.848721i
872872 6.69254 + 2.06437i 0.226638 + 0.0699086i
873873 1.32576 2.75297i 0.0448703 0.0931740i
874874 −33.5296 31.1109i −1.13416 1.05234i
875875 18.6350 20.5270i 0.629978 0.693938i
876876 −38.2673 + 8.73427i −1.29293 + 0.295104i
877877 −1.99463 + 2.14970i −0.0673540 + 0.0725904i −0.765830 0.643043i 0.777672π-0.777672\pi
0.698476 + 0.715634i 0.253862π0.253862\pi
878878 34.6460 + 27.6292i 1.16925 + 0.932442i
879879 −4.72992 + 5.09765i −0.159536 + 0.171939i
880880 2.13676 28.5131i 0.0720303 0.961177i
881881 19.6612 34.0542i 0.662402 1.14731i −0.317581 0.948231i 0.602871π-0.602871\pi
0.979983 0.199082i 0.0637962π-0.0637962\pi
882882 3.58067 + 2.73025i 0.120567 + 0.0919322i
883883 −18.7527 −0.631079 −0.315539 0.948912i 0.602185π-0.602185\pi
−0.315539 + 0.948912i 0.602185π0.602185\pi
884884 −62.5997 1.37681i −2.10546 0.0463072i
885885 2.20127 + 2.04248i 0.0739948 + 0.0686571i
886886 −5.32939 + 35.3582i −0.179044 + 1.18788i
887887 10.7845 47.2498i 0.362107 1.58649i −0.385731 0.922611i 0.626051π-0.626051\pi
0.747837 0.663882i 0.231092π-0.231092\pi
888888 15.2026 14.1059i 0.510165 0.473364i
889889 −1.00914 11.7500i −0.0338453 0.394083i
890890 7.90322 + 25.6216i 0.264917 + 0.858838i
891891 30.6032 + 44.8867i 1.02525 + 1.50376i
892892 14.8059 47.9995i 0.495738 1.60714i
893893 −43.1623 + 20.7858i −1.44437 + 0.695572i
894894 −10.0987 12.6633i −0.337750 0.423526i
895895 −50.9931 3.82141i −1.70451 0.127735i
896896 −29.1305 1.86474i −0.973180 0.0622966i
897897 9.03638 21.6143i 0.301716 0.721681i
898898 12.5362 11.6319i 0.418338 0.388161i
899899 −10.8874 4.27300i −0.363116 0.142513i
900900 −0.220295 0.381563i −0.00734317 0.0127188i
901901 −11.8136 + 20.4618i −0.393569 + 0.681681i
902902 58.8781 46.9537i 1.96043 1.56339i
903903 −9.63842 6.41897i −0.320747 0.213610i
904904 1.85091 12.2800i 0.0615602 0.408425i
905905 1.50506 9.98542i 0.0500299 0.331927i
906906 −8.87907 4.27594i −0.294987 0.142058i
907907 3.26508 + 43.5694i 0.108415 + 1.44670i 0.740634 + 0.671909i 0.234525π0.234525\pi
−0.632219 + 0.774790i 0.717856π0.717856\pi
908908 −46.0462 36.7206i −1.52810 1.21862i
909909 2.64051 3.31110i 0.0875802 0.109822i
910910 29.8857 + 38.3422i 0.990701 + 1.27103i
911911 −12.8158 16.0706i −0.424608 0.532441i 0.522806 0.852452i 0.324885π-0.324885\pi
−0.947414 + 0.320010i 0.896314π0.896314\pi
912912 23.5036i 0.778284i
913913 16.9840 + 29.4171i 0.562087 + 0.973564i
914914 45.5689 + 57.1416i 1.50729 + 1.89008i
915915 −40.0353 43.1478i −1.32353 1.42642i
916916 −45.3046 + 3.39511i −1.49691 + 0.112178i
917917 −11.3969 13.9768i −0.376360 0.461554i
918918 −29.8774 62.0411i −0.986102 2.04766i
919919 6.04187 0.910665i 0.199303 0.0300401i −0.0486321 0.998817i 0.515486π-0.515486\pi
0.247935 + 0.968777i 0.420248π0.420248\pi
920920 10.1910 + 6.94813i 0.335989 + 0.229073i
921921 26.8160 + 28.9008i 0.883619 + 0.952314i
922922 3.76426 + 50.2305i 0.123969 + 1.65425i
923923 −0.150001 + 0.865587i −0.00493735 + 0.0284911i
924924 −61.3163 + 36.2956i −2.01716 + 1.19404i
925925 −1.27359 + 4.12889i −0.0418755 + 0.135757i
926926 1.40893 6.17291i 0.0463002 0.202854i
927927 −2.22514 + 2.79024i −0.0730832 + 0.0916434i
928928 19.6383 21.1650i 0.644657 0.694775i
929929 15.7988 + 1.18396i 0.518342 + 0.0388443i 0.331333 0.943514i 0.392502π-0.392502\pi
0.187009 + 0.982358i 0.440121π0.440121\pi
930930 24.8696 14.3585i 0.815508 0.470834i
931931 32.9045 + 25.0895i 1.07840 + 0.822277i
932932 −14.3250 24.8117i −0.469232 0.812734i
933933 24.2079 11.6579i 0.792532 0.381663i
934934 −7.22319 23.4170i −0.236350 0.766228i
935935 30.9559 + 78.8742i 1.01236 + 2.57946i
936936 −1.47263 + 0.540907i −0.0481345 + 0.0176801i
937937 −2.33868 10.2464i −0.0764012 0.334736i 0.922254 0.386585i 0.126345π-0.126345\pi
−0.998655 + 0.0518496i 0.983488π0.983488\pi
938938 50.8337 65.1851i 1.65978 2.12837i
939939 −4.04092 3.74943i −0.131871 0.122358i
940940 42.2334 28.7943i 1.37750 0.939166i
941941 12.1568 39.4113i 0.396300 1.28477i −0.509282 0.860600i 0.670089π-0.670089\pi
0.905582 0.424172i 0.139435π-0.139435\pi
942942 2.47499 + 5.13938i 0.0806397 + 0.167450i
943943 −3.35150 22.2358i −0.109140 0.724096i
944944 −0.666667 1.38435i −0.0216982 0.0450567i
945945 −12.9754 + 27.7104i −0.422089 + 0.901420i
946946 23.8646 16.2706i 0.775906 0.529004i
947947 −1.22555 + 0.279725i −0.0398251 + 0.00908983i −0.242387 0.970180i 0.577930π-0.577930\pi
0.202562 + 0.979269i 0.435073π0.435073\pi
948948 −52.0939 + 7.85189i −1.69193 + 0.255018i
949949 −15.8706 24.4145i −0.515180 0.792528i
950950 −3.53716 6.12655i −0.114761 0.198771i
951951 −1.25209 8.30706i −0.0406017 0.269375i
952952 23.2746 9.42792i 0.754333 0.305561i
953953 −7.38664 1.11336i −0.239277 0.0360652i 0.0283090 0.999599i 0.490988π-0.490988\pi
−0.267586 + 0.963534i 0.586226π0.586226\pi
954954 −0.349107 + 2.31617i −0.0113027 + 0.0749888i
955955 22.2483 46.1990i 0.719937 1.49497i
956956 −30.7429 + 63.8383i −0.994296 + 2.06468i
957957 5.65243 37.5014i 0.182717 1.21225i
958958 −3.83799 0.578484i −0.124000 0.0186900i
959959 −1.97186 12.1821i −0.0636748 0.393382i
960960 7.77264 + 51.5681i 0.250861 + 1.66435i
961961 −10.6850 18.5070i −0.344678 0.597000i
962962 54.2535 + 27.6128i 1.74920 + 0.890273i
963963 −3.77778 + 0.569409i −0.121737 + 0.0183489i
964964 49.7890 11.3640i 1.60359 0.366010i
965965 −25.3836 + 17.3062i −0.817126 + 0.557107i
966966 0.404223 + 37.1731i 0.0130057 + 1.19603i
967967 −4.03968 8.38848i −0.129907 0.269755i 0.825862 0.563872i 0.190689π-0.190689\pi
−0.955770 + 0.294117i 0.904975π0.904975\pi
968968 −4.29622 28.5035i −0.138086 0.916138i
969969 30.2199 + 62.7522i 0.970801 + 2.01589i
970970 −15.4298 + 50.0222i −0.495421 + 1.60612i
971971 7.34801 5.00979i 0.235809 0.160772i −0.439651 0.898169i 0.644898π-0.644898\pi
0.675460 + 0.737397i 0.263945π0.263945\pi
972972 −6.04334 5.60740i −0.193840 0.179858i
973973 −5.97310 24.9178i −0.191489 0.798827i
974974 −17.8708 78.2971i −0.572618 2.50880i
975975 2.32088 2.78250i 0.0743275 0.0891113i
976976 11.0032 + 28.0358i 0.352205 + 0.897403i
977977 −3.39198 10.9965i −0.108519 0.351810i 0.884983 0.465623i 0.154170π-0.154170\pi
−0.993502 + 0.113813i 0.963693π0.963693\pi
978978 −21.5130 + 10.3601i −0.687911 + 0.331280i
979979 −14.5777 25.2493i −0.465905 0.806972i
980980 −38.7062 21.2384i −1.23642 0.678437i
981981 1.23343 0.712121i 0.0393804 0.0227363i
982982 −58.3908 4.37579i −1.86333 0.139637i
983983 −36.8126 + 39.6745i −1.17414 + 1.26542i −0.216877 + 0.976199i 0.569587π0.569587\pi
−0.957262 + 0.289222i 0.906603π0.906603\pi
984984 −10.4079 + 13.0511i −0.331792 + 0.416054i
985985 −6.05102 + 26.5112i −0.192801 + 0.844718i
986986 −15.5881 + 50.5352i −0.496425 + 1.60937i
987987 36.3974 + 13.8301i 1.15854 + 0.440217i
988988 −53.5454 + 19.6676i −1.70351 + 0.625709i
989989 −0.644517 8.60048i −0.0204944 0.273479i
990990 5.71346 + 6.15765i 0.181586 + 0.195703i
991991 31.0226 + 21.1508i 0.985465 + 0.671879i 0.944921 0.327299i 0.106138π-0.106138\pi
0.0405442 + 0.999178i 0.487091π0.487091\pi
992992 −23.5069 + 3.54310i −0.746345 + 0.112493i
993993 10.5711 + 21.9512i 0.335465 + 0.696600i
994994 −0.324959 1.35562i −0.0103071 0.0429976i
995995 −32.9070 + 2.46604i −1.04322 + 0.0781788i
996996 −20.2637 21.8391i −0.642081 0.691999i
997997 −8.96865 11.2463i −0.284040 0.356175i 0.619259 0.785187i 0.287433π-0.287433\pi
−0.903299 + 0.429012i 0.858862π0.858862\pi
998998 −7.60446 13.1713i −0.240715 0.416931i
999999 38.3160i 1.21227i
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 637.2.bz.a.4.10 yes 756
13.10 even 6 637.2.bp.a.543.10 756
49.37 even 21 637.2.bp.a.576.10 yes 756
637.478 even 42 inner 637.2.bz.a.478.10 yes 756
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.bp.a.543.10 756 13.10 even 6
637.2.bp.a.576.10 yes 756 49.37 even 21
637.2.bz.a.4.10 yes 756 1.1 even 1 trivial
637.2.bz.a.478.10 yes 756 637.478 even 42 inner