Properties

Label 507.2.k.k.188.7
Level 507507
Weight 22
Character 507.188
Analytic conductor 4.0484.048
Analytic rank 00
Dimension 9696
Inner twists 1616

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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] = [507,2,Mod(80,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 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("507.80"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 507=3132 507 = 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 507.k (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [96,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.048415382484.04841538248
Analytic rank: 00
Dimension: 9696
Relative dimension: 2424 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 188.7
Character χ\chi == 507.188
Dual form 507.2.k.k.89.7

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.26815+0.339800i)q2+(0.2288001.71687i)q3+(0.239309+0.138165i)q4+(2.12536+2.12536i)q5+(0.873546+2.09951i)q6+(0.7559452.82123i)q7+(2.113232.11323i)q8+(2.89530+0.785641i)q9+(3.417471.97308i)q10+(0.689573+2.57352i)q11+(0.291966+0.379251i)q12+3.83461iq14+(3.162694.13525i)q15+(1.68549+2.91935i)q16+(0.09941620.172194i)q17+(3.404721.98013i)q18+(5.12548+1.37337i)q19+(0.8022690.214967i)q20+(5.016650.652364i)q21+(1.748973.02930i)q22+(1.650382.85855i)q23+(4.111663.14464i)q24+4.03430iq25+(2.01129+4.79111i)q27+(0.208891+0.779591i)q28+(3.232581.86633i)q29+(2.60561+6.31880i)q30+(0.5505500.550550i)q31+(0.401535+1.49855i)q32+(4.260631.77273i)q33+(0.184586+0.184586i)q34+(7.602774.38946i)q35+(0.5843240.588041i)q36+(4.928781.32066i)q376.96655q38+8.98276q40+(3.680050.986066i)q41+(6.583530.877359i)q42+(10.09425.82790i)q43+(0.5205920.520592i)q44+(7.823324.48378i)q45+(1.12160+4.18587i)q46+(4.295864.29586i)q47+(5.39780+2.22582i)q48+(1.325680.765385i)q49+(1.370865.11610i)q50+(0.272889+0.210083i)q5113.6276iq53+(4.178645.39241i)q54+(4.00407+6.93525i)q55+(4.364427.55939i)q56+(1.185199.11402i)q57+(4.73357+1.26836i)q58+(3.22482+0.864088i)q59+(0.185512+1.42658i)q60+(1.35047+2.33909i)q61+(0.511103+0.885257i)q62+(0.0277830+8.76220i)q638.77879iq64+(4.80075+3.69585i)q66+(1.95320+7.28944i)q67+(0.0475824+0.0274717i)q68+(5.285372.17946i)q69+(8.14992+8.14992i)q70+(1.38405+5.16536i)q71+(4.45820+7.77869i)q72+(3.46215+3.46215i)q73+(5.80168+3.34960i)q74+(6.926380.923049i)q75+(1.41633+0.379503i)q76+7.78177q7711.1376q79+(9.78695+2.62241i)q80+(7.765544.54934i)q81+(4.33179+2.50096i)q82+(1.840141.84014i)q83+(1.290660.537009i)q84+(0.1546790.577269i)q85+(10.8207+10.8207i)q86+(2.46463+5.97694i)q87+(6.89568+3.98122i)q88+(0.2843491.06120i)q89+(11.4447+3.02775i)q90+0.912102iq92+(1.071190.819258i)q93+(3.98807+6.90753i)q94+(7.97458+13.8124i)q95+(2.66469+0.346516i)q96+(11.74963.14829i)q97+(1.94125+0.520155i)q98+(4.018396.90936i)q99+O(q100)q+(-1.26815 + 0.339800i) q^{2} +(-0.228800 - 1.71687i) q^{3} +(-0.239309 + 0.138165i) q^{4} +(2.12536 + 2.12536i) q^{5} +(0.873546 + 2.09951i) q^{6} +(0.755945 - 2.82123i) q^{7} +(2.11323 - 2.11323i) q^{8} +(-2.89530 + 0.785641i) q^{9} +(-3.41747 - 1.97308i) q^{10} +(0.689573 + 2.57352i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(3.16269 - 4.13525i) q^{15} +(-1.68549 + 2.91935i) q^{16} +(-0.0994162 - 0.172194i) q^{17} +(3.40472 - 1.98013i) q^{18} +(5.12548 + 1.37337i) q^{19} +(-0.802269 - 0.214967i) q^{20} +(-5.01665 - 0.652364i) q^{21} +(-1.74897 - 3.02930i) q^{22} +(1.65038 - 2.85855i) q^{23} +(-4.11166 - 3.14464i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(0.208891 + 0.779591i) q^{28} +(-3.23258 - 1.86633i) q^{29} +(-2.60561 + 6.31880i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-0.401535 + 1.49855i) q^{32} +(4.26063 - 1.77273i) q^{33} +(0.184586 + 0.184586i) q^{34} +(7.60277 - 4.38946i) q^{35} +(0.584324 - 0.588041i) q^{36} +(4.92878 - 1.32066i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(3.68005 - 0.986066i) q^{41} +(6.58353 - 0.877359i) q^{42} +(10.0942 - 5.82790i) q^{43} +(-0.520592 - 0.520592i) q^{44} +(-7.82332 - 4.48378i) q^{45} +(-1.12160 + 4.18587i) q^{46} +(4.29586 - 4.29586i) q^{47} +(5.39780 + 2.22582i) q^{48} +(-1.32568 - 0.765385i) q^{49} +(-1.37086 - 5.11610i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(-4.17864 - 5.39241i) q^{54} +(-4.00407 + 6.93525i) q^{55} +(-4.36442 - 7.55939i) q^{56} +(1.18519 - 9.11402i) q^{57} +(4.73357 + 1.26836i) q^{58} +(3.22482 + 0.864088i) q^{59} +(-0.185512 + 1.42658i) q^{60} +(1.35047 + 2.33909i) q^{61} +(-0.511103 + 0.885257i) q^{62} +(0.0277830 + 8.76220i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(1.95320 + 7.28944i) q^{67} +(0.0475824 + 0.0274717i) q^{68} +(-5.28537 - 2.17946i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-1.38405 + 5.16536i) q^{71} +(-4.45820 + 7.77869i) q^{72} +(3.46215 + 3.46215i) q^{73} +(-5.80168 + 3.34960i) q^{74} +(6.92638 - 0.923049i) q^{75} +(-1.41633 + 0.379503i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(-9.78695 + 2.62241i) q^{80} +(7.76554 - 4.54934i) q^{81} +(-4.33179 + 2.50096i) q^{82} +(-1.84014 - 1.84014i) q^{83} +(1.29066 - 0.537009i) q^{84} +(0.154679 - 0.577269i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(-2.46463 + 5.97694i) q^{87} +(6.89568 + 3.98122i) q^{88} +(-0.284349 - 1.06120i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(-1.07119 - 0.819258i) q^{93} +(-3.98807 + 6.90753i) q^{94} +(7.97458 + 13.8124i) q^{95} +(2.66469 + 0.346516i) q^{96} +(-11.7496 - 3.14829i) q^{97} +(1.94125 + 0.520155i) q^{98} +(-4.01839 - 6.90936i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 96q+24q9+8q16112q22168q27+256q40+56q42+188q488q5556q61184q66+72q81+112q87296q94+O(q100) 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/507Z)×\left(\mathbb{Z}/507\mathbb{Z}\right)^\times.

nn 170170 340340
χ(n)\chi(n) 1-1 e(512)e\left(\frac{5}{12}\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 −1.26815 + 0.339800i −0.896718 + 0.240275i −0.677606 0.735425i 0.736983π-0.736983\pi
−0.219112 + 0.975700i 0.570316π0.570316\pi
33 −0.228800 1.71687i −0.132098 0.991237i
44 −0.239309 + 0.138165i −0.119655 + 0.0690826i
55 2.12536 + 2.12536i 0.950489 + 0.950489i 0.998831 0.0483414i 0.0153935π-0.0153935\pi
−0.0483414 + 0.998831i 0.515394π0.515394\pi
66 0.873546 + 2.09951i 0.356624 + 0.857120i
77 0.755945 2.82123i 0.285720 1.06632i −0.662591 0.748982i 0.730543π-0.730543\pi
0.948311 0.317342i 0.102790π-0.102790\pi
88 2.11323 2.11323i 0.747141 0.747141i
99 −2.89530 + 0.785641i −0.965100 + 0.261880i
1010 −3.41747 1.97308i −1.08070 0.623942i
1111 0.689573 + 2.57352i 0.207914 + 0.775946i 0.988541 + 0.150949i 0.0482331π0.0482331\pi
−0.780627 + 0.624997i 0.785100π0.785100\pi
1212 0.291966 + 0.379251i 0.0842833 + 0.109480i
1313 0 0
1414 3.83461i 1.02484i
1515 3.16269 4.13525i 0.816602 1.06772i
1616 −1.68549 + 2.91935i −0.421373 + 0.729839i
1717 −0.0994162 0.172194i −0.0241120 0.0417632i 0.853718 0.520736i 0.174342π-0.174342\pi
−0.877830 + 0.478973i 0.841009π0.841009\pi
1818 3.40472 1.98013i 0.802499 0.466722i
1919 5.12548 + 1.37337i 1.17586 + 0.315072i 0.793285 0.608850i 0.208369π-0.208369\pi
0.382580 + 0.923922i 0.375036π0.375036\pi
2020 −0.802269 0.214967i −0.179393 0.0480681i
2121 −5.01665 0.652364i −1.09472 0.142358i
2222 −1.74897 3.02930i −0.372881 0.645848i
2323 1.65038 2.85855i 0.344129 0.596048i −0.641066 0.767485i 0.721508π-0.721508\pi
0.985195 + 0.171437i 0.0548410π0.0548410\pi
2424 −4.11166 3.14464i −0.839289 0.641897i
2525 4.03430i 0.806861i
2626 0 0
2727 2.01129 + 4.79111i 0.387073 + 0.922049i
2828 0.208891 + 0.779591i 0.0394766 + 0.147329i
2929 −3.23258 1.86633i −0.600274 0.346568i 0.168875 0.985637i 0.445987π-0.445987\pi
−0.769149 + 0.639069i 0.779320π0.779320\pi
3030 −2.60561 + 6.31880i −0.475716 + 1.15365i
3131 0.550550 0.550550i 0.0988817 0.0988817i −0.655935 0.754817i 0.727726π-0.727726\pi
0.754817 + 0.655935i 0.227726π0.227726\pi
3232 −0.401535 + 1.49855i −0.0709820 + 0.264908i
3333 4.26063 1.77273i 0.741681 0.308593i
3434 0.184586 + 0.184586i 0.0316563 + 0.0316563i
3535 7.60277 4.38946i 1.28510 0.741955i
3636 0.584324 0.588041i 0.0973873 0.0980069i
3737 4.92878 1.32066i 0.810287 0.217116i 0.170191 0.985411i 0.445561π-0.445561\pi
0.640096 + 0.768295i 0.278895π0.278895\pi
3838 −6.96655 −1.13012
3939 0 0
4040 8.98276 1.42030
4141 3.68005 0.986066i 0.574727 0.153998i 0.0402633 0.999189i 0.487180π-0.487180\pi
0.534464 + 0.845192i 0.320514π0.320514\pi
4242 6.58353 0.877359i 1.01586 0.135379i
4343 10.0942 5.82790i 1.53936 0.888747i 0.540479 0.841358i 0.318243π-0.318243\pi
0.998876 0.0473894i 0.0150902π-0.0150902\pi
4444 −0.520592 0.520592i −0.0784823 0.0784823i
4545 −7.82332 4.48378i −1.16623 0.668403i
4646 −1.12160 + 4.18587i −0.165371 + 0.617173i
4747 4.29586 4.29586i 0.626616 0.626616i −0.320599 0.947215i 0.603884π-0.603884\pi
0.947215 + 0.320599i 0.103884π0.103884\pi
4848 5.39780 + 2.22582i 0.779105 + 0.321270i
4949 −1.32568 0.765385i −0.189384 0.109341i
5050 −1.37086 5.11610i −0.193868 0.723526i
5151 −0.272889 + 0.210083i −0.0382120 + 0.0294175i
5252 0 0
5353 13.6276i 1.87189i −0.352142 0.935947i 0.614546π-0.614546\pi
0.352142 0.935947i 0.385454π-0.385454\pi
5454 −4.17864 5.39241i −0.568641 0.733814i
5555 −4.00407 + 6.93525i −0.539908 + 0.935149i
5656 −4.36442 7.55939i −0.583220 1.01017i
5757 1.18519 9.11402i 0.156982 1.20718i
5858 4.73357 + 1.26836i 0.621548 + 0.166543i
5959 3.22482 + 0.864088i 0.419836 + 0.112495i 0.462551 0.886593i 0.346934π-0.346934\pi
−0.0427154 + 0.999087i 0.513601π0.513601\pi
6060 −0.185512 + 1.42658i −0.0239495 + 0.184170i
6161 1.35047 + 2.33909i 0.172910 + 0.299489i 0.939436 0.342724i 0.111350π-0.111350\pi
−0.766526 + 0.642213i 0.778016π0.778016\pi
6262 −0.511103 + 0.885257i −0.0649102 + 0.112428i
6363 0.0277830 + 8.76220i 0.00350032 + 1.10393i
6464 8.77879i 1.09735i
6565 0 0
6666 −4.80075 + 3.69585i −0.590932 + 0.454928i
6767 1.95320 + 7.28944i 0.238621 + 0.890547i 0.976483 + 0.215595i 0.0691690π0.0691690\pi
−0.737862 + 0.674952i 0.764164π0.764164\pi
6868 0.0475824 + 0.0274717i 0.00577022 + 0.00333144i
6969 −5.28537 2.17946i −0.636284 0.262376i
7070 −8.14992 + 8.14992i −0.974102 + 0.974102i
7171 −1.38405 + 5.16536i −0.164257 + 0.613016i 0.833877 + 0.551951i 0.186116π0.186116\pi
−0.998134 + 0.0610649i 0.980550π0.980550\pi
7272 −4.45820 + 7.77869i −0.525404 + 0.916727i
7373 3.46215 + 3.46215i 0.405214 + 0.405214i 0.880066 0.474852i 0.157498π-0.157498\pi
−0.474852 + 0.880066i 0.657498π0.657498\pi
7474 −5.80168 + 3.34960i −0.674431 + 0.389383i
7575 6.92638 0.923049i 0.799790 0.106585i
7676 −1.41633 + 0.379503i −0.162464 + 0.0435320i
7777 7.78177 0.886815
7878 0 0
7979 −11.1376 −1.25308 −0.626540 0.779389i 0.715530π-0.715530\pi
−0.626540 + 0.779389i 0.715530π0.715530\pi
8080 −9.78695 + 2.62241i −1.09421 + 0.293194i
8181 7.76554 4.54934i 0.862837 0.505482i
8282 −4.33179 + 2.50096i −0.478366 + 0.276185i
8383 −1.84014 1.84014i −0.201981 0.201981i 0.598867 0.800848i 0.295618π-0.295618\pi
−0.800848 + 0.598867i 0.795618π0.795618\pi
8484 1.29066 0.537009i 0.140823 0.0585925i
8585 0.154679 0.577269i 0.0167773 0.0626136i
8686 −10.8207 + 10.8207i −1.16682 + 1.16682i
8787 −2.46463 + 5.97694i −0.264236 + 0.640795i
8888 6.89568 + 3.98122i 0.735082 + 0.424400i
8989 −0.284349 1.06120i −0.0301409 0.112487i 0.949217 0.314624i 0.101878π-0.101878\pi
−0.979357 + 0.202136i 0.935212π0.935212\pi
9090 11.4447 + 3.02775i 1.20638 + 0.319153i
9191 0 0
9292 0.912102i 0.0950932i
9393 −1.07119 0.819258i −0.111077 0.0849531i
9494 −3.98807 + 6.90753i −0.411338 + 0.712458i
9595 7.97458 + 13.8124i 0.818175 + 1.41712i
9696 2.66469 + 0.346516i 0.271964 + 0.0353661i
9797 −11.7496 3.14829i −1.19299 0.319661i −0.392923 0.919571i 0.628536π-0.628536\pi
−0.800067 + 0.599911i 0.795203π0.795203\pi
9898 1.94125 + 0.520155i 0.196095 + 0.0525436i
9999 −4.01839 6.90936i −0.403863 0.694417i
100100 −0.557400 0.965446i −0.0557400 0.0965446i
101101 −6.19691 + 10.7334i −0.616616 + 1.06801i 0.373483 + 0.927637i 0.378164π0.378164\pi
−0.990099 + 0.140373i 0.955170π0.955170\pi
102102 0.274678 0.359144i 0.0271971 0.0355606i
103103 5.68798i 0.560453i 0.959934 + 0.280226i 0.0904096π0.0904096\pi
−0.959934 + 0.280226i 0.909590π0.909590\pi
104104 0 0
105105 −9.27566 12.0487i −0.905212 1.17583i
106106 4.63065 + 17.2818i 0.449769 + 1.67856i
107107 6.72785 + 3.88433i 0.650406 + 0.375512i 0.788612 0.614891i 0.210800π-0.210800\pi
−0.138206 + 0.990404i 0.544134π0.544134\pi
108108 −1.14328 0.868665i −0.110013 0.0835874i
109109 −7.18355 + 7.18355i −0.688060 + 0.688060i −0.961803 0.273743i 0.911738π-0.911738\pi
0.273743 + 0.961803i 0.411738π0.411738\pi
110110 2.72116 10.1555i 0.259453 0.968291i
111111 −3.39512 8.15992i −0.322250 0.774506i
112112 6.96202 + 6.96202i 0.657849 + 0.657849i
113113 −14.7985 + 8.54390i −1.39212 + 0.803743i −0.993550 0.113394i 0.963828π-0.963828\pi
−0.398573 + 0.917136i 0.630495π0.630495\pi
114114 1.59395 + 11.9607i 0.149287 + 1.12022i
115115 9.58310 2.56778i 0.893628 0.239447i
116116 1.03145 0.0957674
117117 0 0
118118 −4.38317 −0.403504
119119 −0.560951 + 0.150306i −0.0514223 + 0.0137786i
120120 −2.05526 15.4222i −0.187618 1.40785i
121121 3.37877 1.95074i 0.307161 0.177340i
122122 −2.50742 2.50742i −0.227011 0.227011i
123123 −2.53494 6.09256i −0.228568 0.549348i
124124 −0.0556848 + 0.207818i −0.00500064 + 0.0186627i
125125 2.05245 2.05245i 0.183577 0.183577i
126126 −3.01263 11.1023i −0.268386 0.989076i
127127 −8.33573 4.81263i −0.739676 0.427052i 0.0822755 0.996610i 0.473781π-0.473781\pi
−0.821952 + 0.569557i 0.807115π0.807115\pi
128128 2.17996 + 8.13573i 0.192683 + 0.719103i
129129 −12.3153 15.9971i −1.08430 1.40846i
130130 0 0
131131 11.9013i 1.03982i 0.854221 + 0.519910i 0.174035π0.174035\pi
−0.854221 + 0.519910i 0.825965π0.825965\pi
132132 −0.774679 + 1.01290i −0.0674272 + 0.0881618i
133133 7.74916 13.4219i 0.671937 1.16383i
134134 −4.95390 8.58041i −0.427952 0.741234i
135135 −5.90811 + 14.4575i −0.508489 + 1.24431i
136136 −0.573976 0.153796i −0.0492180 0.0131879i
137137 −16.8029 4.50231i −1.43557 0.384659i −0.544587 0.838704i 0.683314π-0.683314\pi
−0.890979 + 0.454045i 0.849980π0.849980\pi
138138 7.44322 + 0.967917i 0.633609 + 0.0823945i
139139 −1.16453 2.01702i −0.0987737 0.171081i 0.812404 0.583096i 0.198159π-0.198159\pi
−0.911177 + 0.412014i 0.864825π0.864825\pi
140140 −1.21294 + 2.10088i −0.102512 + 0.177557i
141141 −8.35834 6.39255i −0.703899 0.538350i
142142 7.02076i 0.589169i
143143 0 0
144144 2.58644 9.77660i 0.215536 0.814717i
145145 −2.90377 10.8370i −0.241145 0.899964i
146146 −5.56697 3.21409i −0.460725 0.266000i
147147 −1.01075 + 2.45115i −0.0833653 + 0.202168i
148148 −0.997033 + 0.997033i −0.0819556 + 0.0819556i
149149 4.08308 15.2383i 0.334499 1.24837i −0.569913 0.821705i 0.693023π-0.693023\pi
0.904412 0.426661i 0.140310π-0.140310\pi
150150 −8.47004 + 3.52415i −0.691576 + 0.287746i
151151 8.56897 + 8.56897i 0.697333 + 0.697333i 0.963834 0.266502i 0.0858678π-0.0858678\pi
−0.266502 + 0.963834i 0.585868π0.585868\pi
152152 13.7336 7.92908i 1.11394 0.643133i
153153 0.423123 + 0.420448i 0.0342074 + 0.0339912i
154154 −9.86845 + 2.64424i −0.795222 + 0.213079i
155155 2.34023 0.187972
156156 0 0
157157 −3.26731 −0.260759 −0.130380 0.991464i 0.541620π-0.541620\pi
−0.130380 + 0.991464i 0.541620π0.541620\pi
158158 14.1242 3.78456i 1.12366 0.301084i
159159 −23.3968 + 3.11800i −1.85549 + 0.247273i
160160 −4.03836 + 2.33155i −0.319260 + 0.184325i
161161 −6.81701 6.81701i −0.537256 0.537256i
162162 −8.30200 + 8.40797i −0.652267 + 0.660593i
163163 −1.50848 + 5.62972i −0.118153 + 0.440954i −0.999503 0.0315098i 0.989968π-0.989968\pi
0.881350 + 0.472463i 0.156635π0.156635\pi
164164 −0.744429 + 0.744429i −0.0581302 + 0.0581302i
165165 12.8231 + 5.28769i 0.998275 + 0.411646i
166166 2.95885 + 1.70829i 0.229651 + 0.132589i
167167 0.409254 + 1.52736i 0.0316690 + 0.118190i 0.979951 0.199239i 0.0638470π-0.0638470\pi
−0.948282 + 0.317429i 0.897180π0.897180\pi
168168 −11.9799 + 9.22274i −0.924272 + 0.711550i
169169 0 0
170170 0.784624i 0.0601779i
171171 −15.9188 + 0.0504748i −1.21734 + 0.00385991i
172172 −1.61043 + 2.78934i −0.122794 + 0.212685i
173173 6.21160 + 10.7588i 0.472259 + 0.817977i 0.999496 0.0317413i 0.0101053π-0.0101053\pi
−0.527237 + 0.849718i 0.676772π0.676772\pi
174174 1.09456 8.41714i 0.0829787 0.638101i
175175 11.3817 + 3.04971i 0.860374 + 0.230537i
176176 −8.67529 2.32454i −0.653925 0.175219i
177177 0.745689 5.73431i 0.0560494 0.431017i
178178 0.721194 + 1.24914i 0.0540557 + 0.0936273i
179179 8.15142 14.1187i 0.609265 1.05528i −0.382096 0.924123i 0.624798π-0.624798\pi
0.991362 0.131156i 0.0418689π-0.0418689\pi
180180 2.49170 0.00790061i 0.185720 0.000588876i
181181 9.29621i 0.690982i 0.938422 + 0.345491i 0.112288π0.112288\pi
−0.938422 + 0.345491i 0.887712π0.887712\pi
182182 0 0
183183 3.70692 2.85377i 0.274024 0.210957i
184184 −2.55313 9.52842i −0.188219 0.702444i
185185 13.2823 + 7.66855i 0.976535 + 0.563803i
186186 1.63681 + 0.674952i 0.120017 + 0.0494899i
187187 0.374590 0.374590i 0.0273928 0.0273928i
188188 −0.434500 + 1.62158i −0.0316892 + 0.118266i
189189 15.0372 2.05249i 1.09380 0.149297i
190190 −14.8064 14.8064i −1.07417 1.07417i
191191 −1.75656 + 1.01415i −0.127100 + 0.0733813i −0.562202 0.827000i 0.690046π-0.690046\pi
0.435102 + 0.900381i 0.356712π0.356712\pi
192192 −15.0721 + 2.00859i −1.08773 + 0.144957i
193193 3.83737 1.02822i 0.276220 0.0740130i −0.118050 0.993008i 0.537664π-0.537664\pi
0.394270 + 0.918995i 0.370998π0.370998\pi
194194 15.9700 1.14658
195195 0 0
196196 0.422998 0.0302142
197197 6.65511 1.78323i 0.474157 0.127050i −0.0138237 0.999904i 0.504400π-0.504400\pi
0.487981 + 0.872855i 0.337734π0.337734\pi
198198 7.44372 + 7.39667i 0.529002 + 0.525658i
199199 5.49109 3.17028i 0.389253 0.224735i −0.292584 0.956240i 0.594515π-0.594515\pi
0.681836 + 0.731505i 0.261182π0.261182\pi
200200 8.52542 + 8.52542i 0.602838 + 0.602838i
201201 12.0681 5.02122i 0.851221 0.354169i
202202 4.21142 15.7172i 0.296315 1.10586i
203203 −7.70898 + 7.70898i −0.541065 + 0.541065i
204204 0.0362786 0.0879785i 0.00254001 0.00615973i
205205 9.91717 + 5.72568i 0.692645 + 0.399899i
206206 −1.93277 7.21321i −0.134663 0.502568i
207207 −2.53256 + 9.57296i −0.176025 + 0.665367i
208208 0 0
209209 14.1376i 0.977916i
210210 15.8571 + 12.1277i 1.09424 + 0.836889i
211211 0.401137 0.694790i 0.0276154 0.0478313i −0.851887 0.523725i 0.824542π-0.824542\pi
0.879503 + 0.475894i 0.157875π0.157875\pi
212212 1.88286 + 3.26121i 0.129315 + 0.223981i
213213 9.18494 + 1.19441i 0.629342 + 0.0818396i
214214 −9.85182 2.63979i −0.673457 0.180452i
215215 33.8402 + 9.06747i 2.30789 + 0.618396i
216216 14.3751 + 5.87440i 0.978098 + 0.399702i
217217 −1.13704 1.96941i −0.0771873 0.133692i
218218 6.66886 11.5508i 0.451672 0.782319i
219219 5.15193 6.73621i 0.348135 0.455191i
220220 2.21289i 0.149193i
221221 0 0
222222 7.07826 + 9.19435i 0.475062 + 0.617084i
223223 0.799768 + 2.98478i 0.0535565 + 0.199875i 0.987520 0.157492i 0.0503410π-0.0503410\pi
−0.933964 + 0.357368i 0.883674π0.883674\pi
224224 3.92421 + 2.26564i 0.262197 + 0.151380i
225225 −3.16952 11.6805i −0.211301 0.778701i
226226 15.8635 15.8635i 1.05522 1.05522i
227227 −6.70715 + 25.0314i −0.445169 + 1.66139i 0.270320 + 0.962770i 0.412870π0.412870\pi
−0.715489 + 0.698624i 0.753796π0.753796\pi
228228 0.975614 + 2.34482i 0.0646116 + 0.155289i
229229 −19.6410 19.6410i −1.29791 1.29791i −0.929768 0.368147i 0.879992π-0.879992\pi
−0.368147 0.929768i 0.620008π-0.620008\pi
230230 −11.2803 + 6.51267i −0.743799 + 0.429433i
231231 −1.78047 13.3603i −0.117146 0.879043i
232232 −10.7752 + 2.88720i −0.707425 + 0.189554i
233233 −14.4551 −0.946988 −0.473494 0.880797i 0.657007π-0.657007\pi
−0.473494 + 0.880797i 0.657007π0.657007\pi
234234 0 0
235235 18.2605 1.19118
236236 −0.891116 + 0.238774i −0.0580067 + 0.0155428i
237237 2.54829 + 19.1219i 0.165529 + 1.24210i
238238 0.660297 0.381222i 0.0428007 0.0247110i
239239 −4.24248 4.24248i −0.274423 0.274423i 0.556455 0.830878i 0.312161π-0.312161\pi
−0.830878 + 0.556455i 0.812161π0.812161\pi
240240 6.74159 + 16.2029i 0.435168 + 1.04590i
241241 −6.38724 + 23.8375i −0.411438 + 1.53551i 0.380426 + 0.924811i 0.375777π0.375777\pi
−0.791864 + 0.610697i 0.790889π0.790889\pi
242242 −3.62193 + 3.62193i −0.232827 + 0.232827i
243243 −9.58739 12.2915i −0.615031 0.788503i
244244 −0.646361 0.373177i −0.0413790 0.0238902i
245245 −1.19084 4.44427i −0.0760799 0.283934i
246246 5.28494 + 6.86491i 0.336956 + 0.437691i
247247 0 0
248248 2.32688i 0.147757i
249249 −2.73826 + 3.58031i −0.173530 + 0.226893i
250250 −1.90540 + 3.30024i −0.120508 + 0.208726i
251251 −10.8649 18.8186i −0.685789 1.18782i −0.973188 0.230010i 0.926124π-0.926124\pi
0.287400 0.957811i 0.407209π-0.407209\pi
252252 −1.21728 2.09304i −0.0766814 0.131849i
253253 8.49459 + 2.27612i 0.534051 + 0.143098i
254254 12.2063 + 3.27066i 0.765891 + 0.205220i
255255 −1.02649 0.133484i −0.0642812 0.00835912i
256256 3.24975 + 5.62873i 0.203109 + 0.351796i
257257 −8.15559 + 14.1259i −0.508732 + 0.881149i 0.491217 + 0.871037i 0.336552π0.336552\pi
−0.999949 + 0.0101119i 0.996781π0.996781\pi
258258 21.0535 + 16.1019i 1.31073 + 1.00246i
259259 14.9036i 0.926062i
260260 0 0
261261 10.8255 + 2.86394i 0.670084 + 0.177273i
262262 −4.04406 15.0926i −0.249843 0.932426i
263263 −9.95602 5.74811i −0.613914 0.354444i 0.160582 0.987023i 0.448663π-0.448663\pi
−0.774496 + 0.632579i 0.781996π0.781996\pi
264264 5.25752 12.7499i 0.323578 0.784702i
265265 28.9635 28.9635i 1.77922 1.77922i
266266 −5.26633 + 19.6542i −0.322899 + 1.20508i
267267 −1.75689 + 0.730994i −0.107520 + 0.0447361i
268268 −1.47457 1.47457i −0.0900734 0.0900734i
269269 9.64658 5.56946i 0.588162 0.339576i −0.176208 0.984353i 0.556383π-0.556383\pi
0.764371 + 0.644777i 0.223050π0.223050\pi
270270 2.57970 20.3419i 0.156995 1.23797i
271271 5.86962 1.57276i 0.356554 0.0955383i −0.0760956 0.997101i 0.524245π-0.524245\pi
0.432650 + 0.901562i 0.357579π0.357579\pi
272272 0.670260 0.0406405
273273 0 0
274274 22.8384 1.37972
275275 −10.3824 + 2.78195i −0.626080 + 0.167758i
276276 1.56596 0.208689i 0.0942599 0.0125616i
277277 −24.0591 + 13.8905i −1.44557 + 0.834600i −0.998213 0.0597558i 0.980968π-0.980968\pi
−0.447356 + 0.894356i 0.647634π0.647634\pi
278278 2.16218 + 2.16218i 0.129679 + 0.129679i
279279 −1.16147 + 2.02654i −0.0695356 + 0.121326i
280280 6.79047 25.3424i 0.405808 1.51450i
281281 11.6187 11.6187i 0.693113 0.693113i −0.269803 0.962916i 0.586958π-0.586958\pi
0.962916 + 0.269803i 0.0869585π0.0869585\pi
282282 12.7718 + 5.26655i 0.760551 + 0.313619i
283283 −23.0251 13.2935i −1.36870 0.790219i −0.377938 0.925831i 0.623367π-0.623367\pi
−0.990762 + 0.135612i 0.956700π0.956700\pi
284284 −0.382456 1.42735i −0.0226946 0.0846974i
285285 21.8895 16.8516i 1.29662 0.998203i
286286 0 0
287287 11.1277i 0.656845i
288288 −0.0147574 4.65421i −0.000869591 0.274252i
289289 8.48023 14.6882i 0.498837 0.864011i
290290 7.36482 + 12.7563i 0.432477 + 0.749073i
291291 −2.71691 + 20.8929i −0.159268 + 1.22476i
292292 −1.30687 0.350176i −0.0764790 0.0204925i
293293 −2.79628 0.749260i −0.163360 0.0437722i 0.176212 0.984352i 0.443616π-0.443616\pi
−0.339572 + 0.940580i 0.610282π0.610282\pi
294294 0.448883 3.45188i 0.0261794 0.201318i
295295 5.01740 + 8.69039i 0.292124 + 0.505974i
296296 7.62480 13.2065i 0.443182 0.767614i
297297 −10.9431 + 8.47992i −0.634982 + 0.492055i
298298 20.7118i 1.19980i
299299 0 0
300300 −1.53001 + 1.17788i −0.0883354 + 0.0680049i
301301 −8.81115 32.8837i −0.507866 1.89538i
302302 −13.7785 7.95501i −0.792862 0.457759i
303303 19.8457 + 8.18351i 1.14010 + 0.470131i
304304 −12.6483 + 12.6483i −0.725429 + 0.725429i
305305 −2.10116 + 7.84164i −0.120312 + 0.449011i
306306 −0.679451 0.389414i −0.0388416 0.0222613i
307307 13.9565 + 13.9565i 0.796541 + 0.796541i 0.982548 0.186007i 0.0595549π-0.0595549\pi
−0.186007 + 0.982548i 0.559555π0.559555\pi
308308 −1.86225 + 1.07517i −0.106111 + 0.0612635i
309309 9.76553 1.30141i 0.555541 0.0740346i
310310 −2.96777 + 0.795211i −0.168558 + 0.0451649i
311311 −26.9755 −1.52964 −0.764821 0.644243i 0.777172π-0.777172\pi
−0.764821 + 0.644243i 0.777172π0.777172\pi
312312 0 0
313313 −23.9660 −1.35464 −0.677320 0.735689i 0.736859π-0.736859\pi
−0.677320 + 0.735689i 0.736859π0.736859\pi
314314 4.14344 1.11023i 0.233828 0.0626539i
315315 −18.5638 + 18.6819i −1.04595 + 1.05260i
316316 2.66533 1.53883i 0.149937 0.0865660i
317317 21.6899 + 21.6899i 1.21823 + 1.21823i 0.968253 + 0.249973i 0.0804218π0.0804218\pi
0.249973 + 0.968253i 0.419578π0.419578\pi
318318 28.6112 11.9043i 1.60444 0.667562i
319319 2.57394 9.60608i 0.144113 0.537837i
320320 18.6581 18.6581i 1.04302 1.04302i
321321 5.12956 12.4396i 0.286304 0.694311i
322322 10.9614 + 6.32857i 0.610856 + 0.352678i
323323 −0.273070 1.01911i −0.0151940 0.0567049i
324324 −1.22980 + 2.16162i −0.0683224 + 0.120090i
325325 0 0
326326 7.65191i 0.423800i
327327 13.9768 + 10.6896i 0.772921 + 0.591139i
328328 5.69301 9.86058i 0.314344 0.544460i
329329 −8.87216 15.3670i −0.489138 0.847212i
330330 −18.0583 2.34831i −0.994079 0.129270i
331331 −0.640966 0.171746i −0.0352307 0.00944003i 0.241161 0.970485i 0.422472π-0.422472\pi
−0.276391 + 0.961045i 0.589139π0.589139\pi
332332 0.694605 + 0.186119i 0.0381214 + 0.0102146i
333333 −13.2327 + 7.69597i −0.725150 + 0.421737i
334334 −1.03799 1.79785i −0.0567964 0.0983742i
335335 −11.3414 + 19.6439i −0.619648 + 1.07326i
336336 10.3600 13.5458i 0.565184 0.738985i
337337 25.0872i 1.36659i 0.730143 + 0.683294i 0.239453π0.239453\pi
−0.730143 + 0.683294i 0.760547π0.760547\pi
338338 0 0
339339 18.0547 + 23.4522i 0.980596 + 1.27375i
340340 0.0427425 + 0.159517i 0.00231804 + 0.00865103i
341341 1.79650 + 1.03721i 0.0972858 + 0.0561680i
342342 20.1702 5.47321i 1.09068 0.295957i
343343 11.2955 11.2955i 0.609900 0.609900i
344344 9.01573 33.6472i 0.486096 1.81413i
345345 −6.60117 15.8654i −0.355395 0.854167i
346346 −11.5331 11.5331i −0.620023 0.620023i
347347 14.2117 8.20511i 0.762923 0.440474i −0.0674214 0.997725i 0.521477π-0.521477\pi
0.830344 + 0.557251i 0.188144π0.188144\pi
348348 −0.235995 1.77086i −0.0126507 0.0949282i
349349 −28.9532 + 7.75800i −1.54983 + 0.415276i −0.929427 0.369006i 0.879698π-0.879698\pi
−0.620405 + 0.784282i 0.713032π0.713032\pi
350350 −15.4700 −0.826905
351351 0 0
352352 −4.13344 −0.220313
353353 6.50846 1.74394i 0.346410 0.0928203i −0.0814189 0.996680i 0.525945π-0.525945\pi
0.427829 + 0.903860i 0.359279π0.359279\pi
354354 1.00287 + 7.52535i 0.0533020 + 0.399968i
355355 −13.9199 + 8.03664i −0.738790 + 0.426540i
356356 0.214669 + 0.214669i 0.0113774 + 0.0113774i
357357 0.386403 + 0.928692i 0.0204506 + 0.0491516i
358358 −5.53970 + 20.6744i −0.292782 + 1.09268i
359359 −6.76884 + 6.76884i −0.357246 + 0.357246i −0.862797 0.505551i 0.831289π-0.831289\pi
0.505551 + 0.862797i 0.331289π0.331289\pi
360360 −26.0078 + 7.05723i −1.37073 + 0.371948i
361361 7.92989 + 4.57832i 0.417363 + 0.240964i
362362 −3.15885 11.7890i −0.166025 0.619616i
363363 −4.12223 5.35459i −0.216361 0.281043i
364364 0 0
365365 14.7166i 0.770303i
366366 −3.73123 + 4.87862i −0.195034 + 0.255010i
367367 6.01337 10.4155i 0.313895 0.543682i −0.665307 0.746570i 0.731699π-0.731699\pi
0.979202 + 0.202888i 0.0650326π0.0650326\pi
368368 5.56341 + 9.63611i 0.290013 + 0.502317i
369369 −9.88015 + 5.74615i −0.514340 + 0.299133i
370370 −19.4497 5.21154i −1.01114 0.270935i
371371 −38.4465 10.3017i −1.99604 0.534838i
372372 0.369539 + 0.0480548i 0.0191597 + 0.00249152i
373373 −6.67932 11.5689i −0.345842 0.599016i 0.639664 0.768654i 0.279073π-0.279073\pi
−0.985506 + 0.169638i 0.945740π0.945740\pi
374374 −0.347751 + 0.602323i −0.0179818 + 0.0311454i
375375 −3.99340 3.05420i −0.206218 0.157718i
376376 18.1563i 0.936340i
377377 0 0
378378 −18.3720 + 7.71252i −0.944955 + 0.396689i
379379 8.01497 + 29.9123i 0.411701 + 1.53649i 0.791352 + 0.611360i 0.209377π0.209377\pi
−0.379651 + 0.925130i 0.623956π0.623956\pi
380380 −3.81678 2.20362i −0.195797 0.113043i
381381 −6.35546 + 15.4125i −0.325600 + 0.789607i
382382 1.88297 1.88297i 0.0963413 0.0963413i
383383 2.65388 9.90441i 0.135607 0.506092i −0.864388 0.502826i 0.832294π-0.832294\pi
0.999995 0.00326604i 0.00103961π-0.00103961\pi
384384 13.4692 5.60417i 0.687349 0.285987i
385385 16.5390 + 16.5390i 0.842908 + 0.842908i
386386 −4.51698 + 2.60788i −0.229908 + 0.132738i
387387 −24.6472 + 24.8040i −1.25289 + 1.26086i
388388 3.24677 0.869969i 0.164830 0.0441660i
389389 30.1074 1.52650 0.763252 0.646101i 0.223602π-0.223602\pi
0.763252 + 0.646101i 0.223602π0.223602\pi
390390 0 0
391391 −0.656299 −0.0331905
392392 −4.41892 + 1.18405i −0.223189 + 0.0598033i
393393 20.4330 2.72302i 1.03071 0.137358i
394394 −7.83374 + 4.52281i −0.394658 + 0.227856i
395395 −23.6714 23.6714i −1.19104 1.19104i
396396 1.91627 + 1.09827i 0.0962962 + 0.0551903i
397397 0.888280 3.31510i 0.0445815 0.166380i −0.940046 0.341048i 0.889218π-0.889218\pi
0.984628 + 0.174667i 0.0558850π0.0558850\pi
398398 −5.88626 + 5.88626i −0.295052 + 0.295052i
399399 −24.8168 10.2334i −1.24239 0.512310i
400400 −11.7776 6.79978i −0.588878 0.339989i
401401 5.16404 + 19.2725i 0.257880 + 0.962421i 0.966466 + 0.256796i 0.0826668π0.0826668\pi
−0.708586 + 0.705625i 0.750666π0.750666\pi
402402 −13.5980 + 10.4684i −0.678207 + 0.522117i
403403 0 0
404404 3.42479i 0.170390i
405405 26.1735 + 6.83558i 1.30057 + 0.339663i
406406 7.15664 12.3957i 0.355178 0.615186i
407407 6.79751 + 11.7736i 0.336940 + 0.583598i
408408 −0.132723 + 1.02063i −0.00657076 + 0.0505288i
409409 −5.35240 1.43417i −0.264659 0.0709152i 0.124049 0.992276i 0.460412π-0.460412\pi
−0.388708 + 0.921361i 0.627079π0.627079\pi
410410 −14.5220 3.89117i −0.717193 0.192171i
411411 −3.88540 + 29.8785i −0.191653 + 1.47380i
412412 −0.785880 1.36118i −0.0387175 0.0670608i
413413 4.87557 8.44474i 0.239911 0.415538i
414414 −0.0412217 13.0005i −0.00202594 0.638941i
415415 7.82191i 0.383962i
416416 0 0
417417 −3.19652 + 2.46083i −0.156534 + 0.120508i
418418 −4.80394 17.9286i −0.234969 0.876914i
419419 −29.8207 17.2170i −1.45684 0.841106i −0.457983 0.888961i 0.651428π-0.651428\pi
−0.998854 + 0.0478553i 0.984761π0.984761\pi
420420 3.88446 + 1.60179i 0.189542 + 0.0781591i
421421 −18.6143 + 18.6143i −0.907208 + 0.907208i −0.996046 0.0888383i 0.971685π-0.971685\pi
0.0888383 + 0.996046i 0.471685π0.471685\pi
422422 −0.272613 + 1.01740i −0.0132706 + 0.0495265i
423423 −9.06281 + 15.8128i −0.440649 + 0.768846i
424424 −28.7983 28.7983i −1.39857 1.39857i
425425 0.694683 0.401075i 0.0336971 0.0194550i
426426 −12.0537 + 1.60635i −0.584006 + 0.0778279i
427427 7.61997 2.04177i 0.368756 0.0988080i
428428 −2.14672 −0.103765
429429 0 0
430430 −45.9956 −2.21811
431431 −10.9232 + 2.92686i −0.526152 + 0.140982i −0.512111 0.858919i 0.671136π-0.671136\pi
−0.0140414 + 0.999901i 0.504470π0.504470\pi
432432 −17.3770 2.20369i −0.836049 0.106025i
433433 −5.37469 + 3.10308i −0.258291 + 0.149124i −0.623555 0.781780i 0.714312π-0.714312\pi
0.365264 + 0.930904i 0.380979π0.380979\pi
434434 2.11114 + 2.11114i 0.101338 + 0.101338i
435435 −17.9414 + 7.46490i −0.860223 + 0.357915i
436436 0.726573 2.71161i 0.0347965 0.129862i
437437 12.3848 12.3848i 0.592447 0.592447i
438438 −4.24446 + 10.2932i −0.202808 + 0.491826i
439439 33.5869 + 19.3914i 1.60301 + 0.925501i 0.990880 + 0.134748i 0.0430224π0.0430224\pi
0.612135 + 0.790753i 0.290311π0.290311\pi
440440 6.19427 + 23.1173i 0.295300 + 1.10208i
441441 4.43957 + 1.17451i 0.211408 + 0.0559288i
442442 0 0
443443 18.3132i 0.870087i −0.900409 0.435043i 0.856733π-0.856733\pi
0.900409 0.435043i 0.143267π-0.143267\pi
444444 1.93990 + 1.48366i 0.0920636 + 0.0704113i
445445 1.65110 2.85978i 0.0782694 0.135567i
446446 −2.02845 3.51338i −0.0960500 0.166364i
447447 −27.0963 3.52361i −1.28161 0.166661i
448448 −24.7669 6.63628i −1.17013 0.313535i
449449 1.87306 + 0.501884i 0.0883950 + 0.0236854i 0.302745 0.953071i 0.402097π-0.402097\pi
−0.214350 + 0.976757i 0.568763π0.568763\pi
450450 7.98846 + 13.7357i 0.376580 + 0.647505i
451451 5.07532 + 8.79072i 0.238988 + 0.413939i
452452 2.36094 4.08927i 0.111049 0.192343i
453453 12.7512 16.6724i 0.599106 0.783338i
454454 34.0227i 1.59676i
455455 0 0
456456 −16.7555 21.7646i −0.784646 1.01922i
457457 −1.50820 5.62868i −0.0705507 0.263299i 0.921637 0.388053i 0.126852π-0.126852\pi
−0.992188 + 0.124755i 0.960186π0.960186\pi
458458 31.5818 + 18.2337i 1.47572 + 0.852007i
459459 0.625045 0.822646i 0.0291746 0.0383978i
460460 −1.93854 + 1.93854i −0.0903851 + 0.0903851i
461461 3.70361 13.8221i 0.172494 0.643758i −0.824470 0.565905i 0.808527π-0.808527\pi
0.996965 0.0778529i 0.0248064π-0.0248064\pi
462462 6.79773 + 16.3379i 0.316259 + 0.760106i
463463 2.99038 + 2.99038i 0.138975 + 0.138975i 0.773172 0.634197i 0.218669π-0.218669\pi
−0.634197 + 0.773172i 0.718669π0.718669\pi
464464 10.8969 6.29136i 0.505878 0.292069i
465465 −0.535446 4.01788i −0.0248307 0.186325i
466466 18.3313 4.91185i 0.849181 0.227537i
467467 37.5105 1.73578 0.867888 0.496759i 0.165477π-0.165477\pi
0.867888 + 0.496759i 0.165477π0.165477\pi
468468 0 0
469469 22.0417 1.01779
470470 −23.1571 + 6.20491i −1.06816 + 0.286211i
471471 0.747560 + 5.60955i 0.0344458 + 0.258474i
472472 8.64081 4.98877i 0.397726 0.229627i
473473 21.9589 + 21.9589i 1.00967 + 1.00967i
474474 −9.72922 23.3835i −0.446878 1.07404i
475475 −5.54058 + 20.6777i −0.254219 + 0.948759i
476476 0.113474 0.113474i 0.00520106 0.00520106i
477477 10.7064 + 39.4560i 0.490212 + 1.80656i
478478 6.82169 + 3.93851i 0.312017 + 0.180143i
479479 0.528588 + 1.97272i 0.0241518 + 0.0901358i 0.976950 0.213469i 0.0684763π-0.0684763\pi
−0.952798 + 0.303605i 0.901810π0.901810\pi
480480 4.92695 + 6.39989i 0.224883 + 0.292114i
481481 0 0
482482 32.3999i 1.47578i
483483 −10.1442 + 13.2637i −0.461577 + 0.603518i
484484 −0.539048 + 0.933658i −0.0245022 + 0.0424390i
485485 −18.2808 31.6633i −0.830090 1.43776i
486486 16.3349 + 12.3297i 0.740967 + 0.559288i
487487 24.2264 + 6.49144i 1.09780 + 0.294155i 0.761869 0.647731i 0.224282π-0.224282\pi
0.335933 + 0.941886i 0.390948π0.390948\pi
488488 7.79690 + 2.08917i 0.352949 + 0.0945724i
489489 10.0106 + 1.30178i 0.452697 + 0.0588687i
490490 3.02033 + 5.23136i 0.136444 + 0.236329i
491491 3.76608 6.52305i 0.169961 0.294381i −0.768445 0.639916i 0.778969π-0.778969\pi
0.938406 + 0.345535i 0.112302π0.112302\pi
492492 1.44842 + 1.10776i 0.0652996 + 0.0499419i
493493 0.742173i 0.0334258i
494494 0 0
495495 6.14436 23.2254i 0.276169 1.04390i
496496 0.679304 + 2.53520i 0.0305016 + 0.113834i
497497 13.5264 + 7.80946i 0.606741 + 0.350302i
498498 2.25594 5.47083i 0.101091 0.245154i
499499 −8.71539 + 8.71539i −0.390154 + 0.390154i −0.874742 0.484588i 0.838970π-0.838970\pi
0.484588 + 0.874742i 0.338970π0.338970\pi
500500 −0.207593 + 0.774749i −0.00928385 + 0.0346478i
501501 2.52864 1.05210i 0.112971 0.0470042i
502502 20.1729 + 20.1729i 0.900362 + 0.900362i
503503 2.03490 1.17485i 0.0907316 0.0523839i −0.453948 0.891028i 0.649985π-0.649985\pi
0.544679 + 0.838644i 0.316651π0.316651\pi
504504 18.5753 + 18.4579i 0.827409 + 0.822178i
505505 −35.9829 + 9.64160i −1.60122 + 0.429046i
506506 −11.5458 −0.513276
507507 0 0
508508 2.65975 0.118008
509509 −28.9544 + 7.75830i −1.28338 + 0.343881i −0.835142 0.550034i 0.814615π-0.814615\pi
−0.448238 + 0.893914i 0.647948π0.647948\pi
510510 1.34710 0.179522i 0.0596506 0.00794937i
511511 12.3847 7.15031i 0.547867 0.316311i
512512 −17.9453 17.9453i −0.793080 0.793080i
513513 3.72888 + 27.3189i 0.164634 + 1.20616i
514514 5.54254 20.6850i 0.244471 0.912377i
515515 −12.0890 + 12.0890i −0.532705 + 0.532705i
516516 5.15741 + 2.12670i 0.227042 + 0.0936226i
517517 14.0178 + 8.09318i 0.616502 + 0.355938i
518518 5.06423 + 18.9000i 0.222509 + 0.830416i
519519 17.0503 13.1261i 0.748424 0.576174i
520520 0 0
521521 5.94611i 0.260504i −0.991481 0.130252i 0.958421π-0.958421\pi
0.991481 0.130252i 0.0415786π-0.0415786\pi
522522 −14.7016 + 0.0466154i −0.643471 + 0.00204030i
523523 0.429973 0.744735i 0.0188014 0.0325650i −0.856472 0.516194i 0.827348π-0.827348\pi
0.875273 + 0.483629i 0.160682π0.160682\pi
524524 −1.64434 2.84809i −0.0718335 0.124419i
525525 2.63184 20.2387i 0.114863 0.883288i
526526 14.5789 + 3.90641i 0.635672 + 0.170328i
527527 −0.149535 0.0400678i −0.00651385 0.00174538i
528528 −2.00603 + 15.4262i −0.0873011 + 0.671340i
529529 6.05247 + 10.4832i 0.263151 + 0.455791i
530530 −26.8883 + 46.5719i −1.16795 + 2.02295i
531531 −10.0157 + 0.0317575i −0.434644 + 0.00137816i
532532 4.28266i 0.185677i
533533 0 0
534534 1.97961 1.52400i 0.0856662 0.0659500i
535535 6.04351 + 22.5547i 0.261284 + 0.975124i
536536 19.5318 + 11.2767i 0.843647 + 0.487080i
537537 −26.1050 10.7646i −1.12651 0.464526i
538538 −10.3408 + 10.3408i −0.445824 + 0.445824i
539539 1.05558 3.93947i 0.0454669 0.169685i
540540 −0.583665 4.27612i −0.0251169 0.184015i
541541 5.67009 + 5.67009i 0.243776 + 0.243776i 0.818410 0.574634i 0.194856π-0.194856\pi
−0.574634 + 0.818410i 0.694856π0.694856\pi
542542 −6.90914 + 3.98899i −0.296773 + 0.171342i
543543 15.9604 2.12697i 0.684926 0.0912772i
544544 0.297960 0.0798382i 0.0127749 0.00342303i
545545 −30.5353 −1.30799
546546 0 0
547547 −29.3587 −1.25529 −0.627643 0.778501i 0.715980π-0.715980\pi
−0.627643 + 0.778501i 0.715980π0.715980\pi
548548 4.64314 1.24413i 0.198345 0.0531465i
549549 −5.74771 5.71137i −0.245306 0.243755i
550550 12.2211 7.05585i 0.521109 0.300863i
551551 −14.0053 14.0053i −0.596647 0.596647i
552552 −15.7749 + 6.56351i −0.671425 + 0.279361i
553553 −8.41943 + 31.4217i −0.358031 + 1.33619i
554554 25.7905 25.7905i 1.09573 1.09573i
555555 10.1269 24.5586i 0.429864 1.04245i
556556 0.557363 + 0.321794i 0.0236375 + 0.0136471i
557557 −9.67941 36.1240i −0.410130 1.53062i −0.794395 0.607402i 0.792212π-0.792212\pi
0.384265 0.923223i 0.374455π-0.374455\pi
558558 0.784303 2.96463i 0.0332022 0.125503i
559559 0 0
560560 29.5936i 1.25056i
561561 −0.728830 0.557417i −0.0307712 0.0235342i
562562 −10.7862 + 18.6823i −0.454989 + 0.788064i
563563 −6.70261 11.6093i −0.282481 0.489272i 0.689514 0.724272i 0.257824π-0.257824\pi
−0.971995 + 0.235000i 0.924491π0.924491\pi
564564 2.88346 + 0.374965i 0.121415 + 0.0157889i
565565 −49.6109 13.2932i −2.08715 0.559250i
566566 33.7164 + 9.03429i 1.41721 + 0.379740i
567567 −6.96439 25.3474i −0.292477 1.06449i
568568 7.99078 + 13.8404i 0.335286 + 0.580732i
569569 11.3396 19.6407i 0.475380 0.823382i −0.524223 0.851581i 0.675644π-0.675644\pi
0.999602 + 0.0281995i 0.00897737π0.00897737\pi
570570 −22.0330 + 28.8084i −0.922861 + 1.20665i
571571 21.9369i 0.918032i 0.888428 + 0.459016i 0.151798π0.151798\pi
−0.888428 + 0.459016i 0.848202π0.848202\pi
572572 0 0
573573 2.14307 + 2.78375i 0.0895279 + 0.116293i
574574 3.78118 + 14.1115i 0.157823 + 0.589004i
575575 11.5322 + 6.65814i 0.480928 + 0.277664i
576576 6.89698 + 25.4172i 0.287374 + 1.05905i
577577 18.7633 18.7633i 0.781126 0.781126i −0.198895 0.980021i 0.563735π-0.563735\pi
0.980021 + 0.198895i 0.0637354π0.0637354\pi
578578 −5.76316 + 21.5084i −0.239716 + 0.894632i
579579 −2.64332 6.35302i −0.109852 0.264023i
580580 2.19219 + 2.19219i 0.0910259 + 0.0910259i
581581 −6.58249 + 3.80040i −0.273088 + 0.157667i
582582 −3.65395 27.4185i −0.151461 1.13653i
583583 35.0709 9.39722i 1.45249 0.389193i
584584 14.6327 0.605504
585585 0 0
586586 3.80070 0.157005
587587 11.8276 3.16920i 0.488178 0.130807i −0.00632980 0.999980i 0.502015π-0.502015\pi
0.494508 + 0.869173i 0.335348π0.335348\pi
588588 −0.0967820 0.726234i −0.00399122 0.0299494i
589589 3.57794 2.06572i 0.147426 0.0851166i
590590 −9.31581 9.31581i −0.383526 0.383526i
591591 −4.58427 11.0180i −0.188572 0.453219i
592592 −4.45193 + 16.6148i −0.182973 + 0.682865i
593593 −32.4467 + 32.4467i −1.33243 + 1.33243i −0.429232 + 0.903194i 0.641216π0.641216\pi
−0.903194 + 0.429232i 0.858784π0.858784\pi
594594 10.9960 14.4723i 0.451172 0.593805i
595595 −1.51168 0.872768i −0.0619728 0.0357800i
596596 1.12828 + 4.21079i 0.0462161 + 0.172481i
597597 −6.69933 8.70213i −0.274185 0.356155i
598598 0 0
599599 11.5870i 0.473430i −0.971579 0.236715i 0.923929π-0.923929\pi
0.971579 0.236715i 0.0760708π-0.0760708\pi
600600 12.6864 16.5877i 0.517922 0.677189i
601601 2.26709 3.92671i 0.0924764 0.160174i −0.816076 0.577944i 0.803855π-0.803855\pi
0.908553 + 0.417771i 0.137188π0.137188\pi
602602 22.3477 + 38.7074i 0.910826 + 1.57760i
603603 −11.3820 19.5706i −0.463510 0.796977i
604604 −3.23457 0.866700i −0.131613 0.0352655i
605605 11.3271 + 3.03509i 0.460513 + 0.123394i
606606 −27.9481 3.63437i −1.13531 0.147636i
607607 −6.51641 11.2868i −0.264493 0.458115i 0.702938 0.711251i 0.251871π-0.251871\pi
−0.967431 + 0.253136i 0.918538π0.918538\pi
608608 −4.11611 + 7.12932i −0.166930 + 0.289132i
609609 14.9992 + 11.4715i 0.607797 + 0.464850i
610610 10.6583i 0.431544i
611611 0 0
612612 −0.159348 0.0421562i −0.00644128 0.00170406i
613613 −0.930978 3.47446i −0.0376019 0.140332i 0.944573 0.328301i 0.106476π-0.106476\pi
−0.982175 + 0.187969i 0.939809π0.939809\pi
614614 −22.4414 12.9565i −0.905661 0.522884i
615615 7.56121 18.3365i 0.304897 0.739401i
616616 16.4447 16.4447i 0.662575 0.662575i
617617 1.71888 6.41496i 0.0691997 0.258257i −0.922656 0.385624i 0.873986π-0.873986\pi
0.991856 + 0.127368i 0.0406528π0.0406528\pi
618618 −11.9419 + 4.96871i −0.480375 + 0.199871i
619619 −13.3334 13.3334i −0.535916 0.535916i 0.386411 0.922327i 0.373715π-0.373715\pi
−0.922327 + 0.386411i 0.873715π0.873715\pi
620620 −0.560039 + 0.323339i −0.0224917 + 0.0129856i
621621 17.0150 + 2.15779i 0.682789 + 0.0865892i
622622 34.2090 9.16628i 1.37166 0.367534i
623623 −3.20885 −0.128560
624624 0 0
625625 28.8959 1.15584
626626 30.3925 8.14365i 1.21473 0.325486i
627627 24.2724 3.23468i 0.969346 0.129181i
628628 0.781896 0.451428i 0.0312011 0.0180139i
629629 −0.717411 0.717411i −0.0286051 0.0286051i
630630 17.1936 29.9994i 0.685008 1.19520i
631631 −0.381334 + 1.42316i −0.0151807 + 0.0566550i −0.973101 0.230380i 0.926003π-0.926003\pi
0.957920 + 0.287035i 0.0926697π0.0926697\pi
632632 −23.5364 + 23.5364i −0.936227 + 0.936227i
633633 −1.28465 0.529733i −0.0510601 0.0210550i
634634 −34.8763 20.1358i −1.38511 0.799696i
635635 −7.48784 27.9450i −0.297146 1.10896i
636636 5.16828 3.97879i 0.204936 0.157769i
637637 0 0
638638 13.0566i 0.516915i
639639 −0.0508676 16.0426i −0.00201229 0.634637i
640640 −12.6581 + 21.9245i −0.500357 + 0.866644i
641641 7.43034 + 12.8697i 0.293481 + 0.508323i 0.974630 0.223821i 0.0718530π-0.0718530\pi
−0.681150 + 0.732144i 0.738520π0.738520\pi
642642 −2.27808 + 17.5183i −0.0899086 + 0.691392i
643643 46.9319 + 12.5754i 1.85081 + 0.495924i 0.999583 0.0288681i 0.00919027π-0.00919027\pi
0.851230 + 0.524792i 0.175857π0.175857\pi
644644 2.57325 + 0.689499i 0.101400 + 0.0271701i
645645 7.82503 60.1740i 0.308110 2.36935i
646646 0.692588 + 1.19960i 0.0272495 + 0.0471975i
647647 18.8371 32.6268i 0.740562 1.28269i −0.211678 0.977340i 0.567893π-0.567893\pi
0.952240 0.305351i 0.0987739π-0.0987739\pi
648648 6.79658 26.0242i 0.266995 1.02233i
649649 8.89499i 0.349159i
650650 0 0
651651 −3.12107 + 2.40275i −0.122324 + 0.0941714i
652652 −0.416839 1.55566i −0.0163247 0.0609245i
653653 −19.2876 11.1357i −0.754782 0.435774i 0.0726369 0.997358i 0.476859π-0.476859\pi
−0.827419 + 0.561585i 0.810192π0.810192\pi
654654 −21.3571 8.80675i −0.835128 0.344371i
655655 −25.2945 + 25.2945i −0.988339 + 0.988339i
656656 −3.32401 + 12.4054i −0.129781 + 0.484348i
657657 −12.7440 7.30396i −0.497190 0.284955i
658658 16.4729 + 16.4729i 0.642182 + 0.642182i
659659 −23.2104 + 13.4005i −0.904148 + 0.522010i −0.878544 0.477662i 0.841484π-0.841484\pi
−0.0256043 + 0.999672i 0.508151π0.508151\pi
660660 −3.79925 + 0.506310i −0.147886 + 0.0197081i
661661 −16.8775 + 4.52232i −0.656459 + 0.175898i −0.571647 0.820499i 0.693696π-0.693696\pi
−0.0848116 + 0.996397i 0.527029π0.527029\pi
662662 0.871200 0.0338602
663663 0 0
664664 −7.77728 −0.301817
665665 44.9962 12.0567i 1.74488 0.467538i
666666 14.1660 14.2561i 0.548922 0.552414i
667667 −10.6700 + 6.16031i −0.413143 + 0.238528i
668668 −0.308966 0.308966i −0.0119543 0.0119543i
669669 4.94149 2.05602i 0.191049 0.0794902i
670670 7.70763 28.7653i 0.297772 1.11130i
671671 −5.08844 + 5.08844i −0.196437 + 0.196437i
672672 2.99196 7.25574i 0.115417 0.279896i
673673 −30.8369 17.8037i −1.18867 0.686281i −0.230669 0.973032i 0.574091π-0.574091\pi
−0.958005 + 0.286751i 0.907425π0.907425\pi
674674 −8.52464 31.8144i −0.328357 1.22544i
675675 −19.3288 + 8.11416i −0.743965 + 0.312314i
676676 0 0
677677 16.3795i 0.629517i 0.949172 + 0.314758i 0.101924π0.101924\pi
−0.949172 + 0.314758i 0.898076π0.898076\pi
678678 −30.8651 23.6060i −1.18537 0.906583i
679679 −17.7641 + 30.7683i −0.681723 + 1.18078i
680680 −0.893032 1.54678i −0.0342462 0.0593162i
681681 44.5104 + 5.78813i 1.70564 + 0.221801i
682682 −2.63067 0.704886i −0.100734 0.0269915i
683683 −37.1052 9.94232i −1.41979 0.380432i −0.534382 0.845243i 0.679456π-0.679456\pi
−0.885410 + 0.464811i 0.846122π0.846122\pi
684684 3.80253 2.21150i 0.145394 0.0845588i
685685 −26.1431 45.2812i −0.998876 1.73010i
686686 −10.4862 + 18.1626i −0.400364 + 0.693451i
687687 −29.2272 + 38.2150i −1.11509 + 1.45799i
688688 39.2915i 1.49797i
689689 0 0
690690 13.7624 + 17.8767i 0.523924 + 0.680554i
691691 4.99988 + 18.6598i 0.190204 + 0.709853i 0.993456 + 0.114213i 0.0364347π0.0364347\pi
−0.803252 + 0.595640i 0.796899π0.796899\pi
692692 −2.97299 1.71645i −0.113016 0.0652498i
693693 −22.5306 + 6.11368i −0.855865 + 0.232239i
694694 −15.2344 + 15.2344i −0.578292 + 0.578292i
695695 1.81185 6.76192i 0.0687274 0.256494i
696696 7.42231 + 17.8390i 0.281342 + 0.676186i
697697 −0.535651 0.535651i −0.0202892 0.0202892i
698698 34.0809 19.6766i 1.28998 0.744771i
699699 3.30734 + 24.8176i 0.125095 + 0.938689i
700700 −3.14510 + 0.842728i −0.118874 + 0.0318521i
701701 −12.7471 −0.481453 −0.240726 0.970593i 0.577386π-0.577386\pi
−0.240726 + 0.970593i 0.577386π0.577386\pi
702702 0 0
703703 27.0761 1.02120
704704 22.5924 6.05362i 0.851483 0.228154i
705705 −4.17800 31.3509i −0.157353 1.18074i
706706 −7.66111 + 4.42315i −0.288330 + 0.166467i
707707 25.5967 + 25.5967i 0.962664 + 0.962664i
708708 0.613831 + 1.47530i 0.0230692 + 0.0554452i
709709 11.2814 42.1029i 0.423683 1.58121i −0.343099 0.939299i 0.611477π-0.611477\pi
0.766782 0.641907i 0.221857π-0.221857\pi
710710 14.9216 14.9216i 0.559999 0.559999i
711711 32.2468 8.75017i 1.20935 0.328157i
712712 −2.84346 1.64168i −0.106563 0.0615244i
713713 −0.665155 2.48239i −0.0249102 0.0929663i
714714 −0.805586 1.04642i −0.0301483 0.0391613i
715715 0 0
716716 4.50497i 0.168359i
717717 −6.31311 + 8.25447i −0.235767 + 0.308269i
718718 6.28386 10.8840i 0.234512 0.406186i
719719 17.7809 + 30.7974i 0.663116 + 1.14855i 0.979793 + 0.200017i 0.0640996π0.0640996\pi
−0.316677 + 0.948534i 0.602567π0.602567\pi
720720 26.2759 15.2817i 0.979245 0.569515i
721721 16.0471 + 4.29980i 0.597624 + 0.160133i
722722 −11.6120 3.11143i −0.432154 0.115795i
723723 42.3873 + 5.51205i 1.57640 + 0.204995i
724724 −1.28441 2.22467i −0.0477348 0.0826791i
725725 7.52933 13.0412i 0.279632 0.484338i
726726 7.04710 + 5.38970i 0.261542 + 0.200030i
727727 26.2936i 0.975176i −0.873074 0.487588i 0.837877π-0.837877\pi
0.873074 0.487588i 0.162123π-0.162123\pi
728728 0 0
729729 −18.9094 + 19.2726i −0.700349 + 0.713801i
730730 −5.00071 18.6629i −0.185084 0.690745i
731731 −2.00706 1.15878i −0.0742338 0.0428589i
732732 −0.492809 + 1.19510i −0.0182147 + 0.0441722i
733733 5.72217 5.72217i 0.211353 0.211353i −0.593489 0.804842i 0.702250π-0.702250\pi
0.804842 + 0.593489i 0.202250π0.202250\pi
734734 −4.08668 + 15.2517i −0.150842 + 0.562951i
735735 −7.35779 + 3.06137i −0.271396 + 0.112920i
736736 3.62099 + 3.62099i 0.133471 + 0.133471i
737737 −17.4127 + 10.0532i −0.641403 + 0.370314i
738738 10.5770 10.6443i 0.389344 0.391821i
739739 −19.8431 + 5.31693i −0.729939 + 0.195587i −0.604602 0.796528i 0.706668π-0.706668\pi
−0.125337 + 0.992114i 0.540001π0.540001\pi
740740 −4.23811 −0.155796
741741 0 0
742742 52.2565 1.91840
743743 −33.2196 + 8.90116i −1.21871 + 0.326552i −0.810173 0.586191i 0.800627π-0.800627\pi
−0.408535 + 0.912743i 0.633960π0.633960\pi
744744 −3.99496 + 0.532391i −0.146462 + 0.0195184i
745745 41.0648 23.7087i 1.50450 0.868621i
746746 12.4015 + 12.4015i 0.454051 + 0.454051i
747747 6.77344 + 3.88207i 0.247827 + 0.142037i
748748 −0.0378875 + 0.141398i −0.00138531 + 0.00517003i
749749 16.0445 16.0445i 0.586252 0.586252i
750750 6.10205 + 2.51623i 0.222815 + 0.0918796i
751751 −25.8847 14.9445i −0.944546 0.545334i −0.0531635 0.998586i 0.516930π-0.516930\pi
−0.891382 + 0.453252i 0.850264π0.850264\pi
752752 5.30051 + 19.7818i 0.193290 + 0.721367i
753753 −29.8233 + 22.9594i −1.08682 + 0.836687i
754754 0 0
755755 36.4243i 1.32562i
756756 −3.31496 + 2.56880i −0.120564 + 0.0934264i
757757 −11.1534 + 19.3182i −0.405376 + 0.702132i −0.994365 0.106009i 0.966193π-0.966193\pi
0.588989 + 0.808141i 0.299526π0.299526\pi
758758 −20.3284 35.2098i −0.738360 1.27888i
759759 1.96424 15.1049i 0.0712975 0.548274i
760760 46.0409 + 12.3366i 1.67008 + 0.447496i
761761 25.5783 + 6.85369i 0.927214 + 0.248446i 0.690666 0.723174i 0.257317π-0.257317\pi
0.236547 + 0.971620i 0.423984π0.423984\pi
762762 2.82251 21.7050i 0.102249 0.786288i
763763 14.8361 + 25.6968i 0.537101 + 0.930287i
764764 0.280241 0.485391i 0.0101387 0.0175608i
765765 0.00568485 + 1.79289i 0.000205536 + 0.0648221i
766766 13.4621i 0.486404i
767767 0 0
768768 8.92027 6.86726i 0.321882 0.247801i
769769 −3.17804 11.8606i −0.114603 0.427704i 0.884654 0.466248i 0.154395π-0.154395\pi
−0.999257 + 0.0385441i 0.987728π0.987728\pi
770770 −26.5940 15.3540i −0.958380 0.553321i
771771 26.1184 + 10.7701i 0.940630 + 0.387876i
772772 −0.776254 + 0.776254i −0.0279380 + 0.0279380i
773773 −5.96678 + 22.2683i −0.214610 + 0.800937i 0.771693 + 0.635995i 0.219410π0.219410\pi
−0.986303 + 0.164941i 0.947256π0.947256\pi
774774 22.8279 39.8303i 0.820534 1.43167i
775775 2.22108 + 2.22108i 0.0797837 + 0.0797837i
776776 −31.4827 + 18.1765i −1.13016 + 0.652500i
777777 −25.5875 + 3.40994i −0.917947 + 0.122331i
778778 −38.1807 + 10.2305i −1.36884 + 0.366780i
779779 20.2162 0.724321
780780 0 0
781781 −14.2476 −0.509818
782782 0.832286 0.223010i 0.0297625 0.00797484i
783783 2.44013 19.2413i 0.0872031 0.687630i
784784 4.46886 2.58010i 0.159602 0.0921463i
785785 −6.94420 6.94420i −0.247849 0.247849i
786786 −24.9868 + 10.3963i −0.891251 + 0.370825i
787787 12.8168 47.8331i 0.456871 1.70507i −0.225657 0.974207i 0.572453π-0.572453\pi
0.682528 0.730859i 0.260880π-0.260880\pi
788788 −1.34625 + 1.34625i −0.0479581 + 0.0479581i
789789 −7.59083 + 18.4084i −0.270241 + 0.655356i
790790 38.0625 + 21.9754i 1.35420 + 0.781849i
791791 12.9174 + 48.2086i 0.459292 + 1.71410i
792792 −23.0929 6.10931i −0.820570 0.217085i
793793 0 0
794794 4.50589i 0.159908i
795795 −56.3535 43.0998i −1.99865 1.52859i
796796 −0.876045 + 1.51735i −0.0310506 + 0.0537812i
797797 2.55365 + 4.42306i 0.0904550 + 0.156673i 0.907703 0.419614i 0.137835π-0.137835\pi
−0.817248 + 0.576287i 0.804501π0.804501\pi
798798 34.9487 + 4.54473i 1.23717 + 0.160882i
799799 −1.16680 0.312643i −0.0412784 0.0110605i
800800 −6.04560 1.61991i −0.213744 0.0572726i
801801 1.65700 + 2.84911i 0.0585472 + 0.100668i
802802 −13.0976 22.6856i −0.462491 0.801058i
803803 −6.52251 + 11.2973i −0.230175 + 0.398674i
804804 −2.19426 + 2.86902i −0.0773856 + 0.101183i
805805 28.9772i 1.02131i
806806 0 0
807807 −11.7692 15.2877i −0.414295 0.538151i
808808 9.58659 + 35.7776i 0.337255 + 1.25865i
809809 0.216848 + 0.125197i 0.00762398 + 0.00440171i 0.503807 0.863816i 0.331932π-0.331932\pi
−0.496183 + 0.868218i 0.665266π0.665266\pi
810810 −35.5147 + 0.225220i −1.24786 + 0.00791344i
811811 0.345058 0.345058i 0.0121166 0.0121166i −0.701023 0.713139i 0.747273π-0.747273\pi
0.713139 + 0.701023i 0.247273π0.247273\pi
812812 0.779717 2.90994i 0.0273627 0.102119i
813813 −4.04320 9.71754i −0.141801 0.340809i
814814 −12.6210 12.6210i −0.442364 0.442364i
815815 −15.1712 + 8.75912i −0.531425 + 0.306818i
816816 −0.153356 1.15075i −0.00536852 0.0402844i
817817 59.7416 16.0077i 2.09009 0.560039i
818818 7.27498 0.254364
819819 0 0
820820 −3.16436 −0.110504
821821 27.7769 7.44280i 0.969421 0.259756i 0.260838 0.965383i 0.416001π-0.416001\pi
0.708583 + 0.705627i 0.249335π0.249335\pi
822822 −5.22544 39.2107i −0.182258 1.36763i
823823 1.74844 1.00946i 0.0609468 0.0351877i −0.469217 0.883083i 0.655464π-0.655464\pi
0.530164 + 0.847895i 0.322130π0.322130\pi
824824 12.0200 + 12.0200i 0.418737 + 0.418737i
825825 7.15174 + 17.1887i 0.248991 + 0.598433i
826826 −3.31344 + 12.3659i −0.115289 + 0.430265i
827827 0.657151 0.657151i 0.0228514 0.0228514i −0.695589 0.718440i 0.744856π-0.744856\pi
0.718440 + 0.695589i 0.244856π0.244856\pi
828828 −0.716585 2.64081i −0.0249031 0.0917745i
829829 −40.2809 23.2562i −1.39902 0.807722i −0.404726 0.914438i 0.632633π-0.632633\pi
−0.994289 + 0.106716i 0.965966π0.965966\pi
830830 2.65788 + 9.91936i 0.0922565 + 0.344306i
831831 29.3530 + 38.1282i 1.01824 + 1.32265i
832832 0 0
833833 0.304367i 0.0105457i
834834 3.21747 4.20688i 0.111412 0.145673i
835835 −2.37637 + 4.11600i −0.0822377 + 0.142440i
836836 −1.95332 3.38325i −0.0675570 0.117012i
837837 3.74506 + 1.53043i 0.129448 + 0.0528993i
838838 43.6675 + 11.7007i 1.50847 + 0.404193i
839839 41.9982 + 11.2534i 1.44994 + 0.388510i 0.896003 0.444048i 0.146458π-0.146458\pi
0.553937 + 0.832558i 0.313125π0.313125\pi
840840 −45.0633 5.86003i −1.55483 0.202190i
841841 −7.53364 13.0486i −0.259781 0.449953i
842842 17.2806 29.9309i 0.595530 1.03149i
843843 −22.6062 17.2895i −0.778598 0.595480i
844844 0.221693i 0.00763098i
845845 0 0
846846 6.11981 23.1326i 0.210403 0.795314i
847847 −2.94930 11.0069i −0.101339 0.378203i
848848 39.7838 + 22.9692i 1.36618 + 0.788765i
849849 −17.5552 + 42.5727i −0.602492 + 1.46109i
850850 −0.744677 + 0.744677i −0.0255422 + 0.0255422i
851851 4.35920 16.2688i 0.149431 0.557686i
852852 −2.36307 + 0.983206i −0.0809573 + 0.0336841i
853853 0.0191114 + 0.0191114i 0.000654362 + 0.000654362i 0.707434 0.706780i 0.249853π-0.249853\pi
−0.706780 + 0.707434i 0.749853π0.749853\pi
854854 −8.96948 + 5.17853i −0.306929 + 0.177206i
855855 −33.9404 33.7258i −1.16074 1.15340i
856856 22.4260 6.00903i 0.766505 0.205384i
857857 5.89068 0.201222 0.100611 0.994926i 0.467920π-0.467920\pi
0.100611 + 0.994926i 0.467920π0.467920\pi
858858 0 0
859859 11.6341 0.396949 0.198475 0.980106i 0.436401π-0.436401\pi
0.198475 + 0.980106i 0.436401π0.436401\pi
860860 −9.35109 + 2.50562i −0.318870 + 0.0854408i
861861 −19.1048 + 2.54601i −0.651089 + 0.0867678i
862862 12.8577 7.42341i 0.437936 0.252842i
863863 19.9075 + 19.9075i 0.677660 + 0.677660i 0.959470 0.281811i 0.0909350π-0.0909350\pi
−0.281811 + 0.959470i 0.590935π0.590935\pi
864864 −7.98731 + 1.09022i −0.271734 + 0.0370901i
865865 −9.66445 + 36.0682i −0.328601 + 1.22636i
866866 5.76148 5.76148i 0.195783 0.195783i
867867 −27.1580 11.1988i −0.922335 0.380332i
868868 0.544208 + 0.314199i 0.0184716 + 0.0106646i
869869 −7.68020 28.6629i −0.260533 0.972323i
870870 20.2158 15.5631i 0.685379 0.527638i
871871 0 0
872872 30.3610i 1.02815i
873873 36.4920 0.115708i 1.23507 0.00391612i
874874 −11.4975 + 19.9142i −0.388908 + 0.673608i
875875 −4.23889 7.34198i −0.143301 0.248204i
876876 −0.302194 + 2.32385i −0.0102102 + 0.0785158i
877877 −13.4570 3.60580i −0.454412 0.121759i 0.0243510 0.999703i 0.492248π-0.492248\pi
−0.478763 + 0.877944i 0.658915π0.658915\pi
878878 −49.1824 13.1784i −1.65983 0.444749i
879879 −0.646595 + 4.97228i −0.0218091 + 0.167711i
880880 −13.4976 23.3786i −0.455005 0.788092i
881881 −3.83326 + 6.63940i −0.129146 + 0.223687i −0.923346 0.383969i 0.874557π-0.874557\pi
0.794200 + 0.607656i 0.207890π0.207890\pi
882882 −6.02915 + 0.0191171i −0.203012 + 0.000643705i
883883 7.52156i 0.253121i −0.991959 0.126560i 0.959606π-0.959606\pi
0.991959 0.126560i 0.0403937π-0.0403937\pi
884884 0 0
885885 13.7723 10.6026i 0.462951 0.356403i
886886 6.22283 + 23.2239i 0.209060 + 0.780222i
887887 36.5051 + 21.0762i 1.22572 + 0.707670i 0.966132 0.258049i 0.0830797π-0.0830797\pi
0.259589 + 0.965719i 0.416413π0.416413\pi
888888 −24.4185 10.0691i −0.819431 0.337898i
889889 −19.8789 + 19.8789i −0.666716 + 0.666716i
890890 −1.12208 + 4.18768i −0.0376123 + 0.140371i
891891 17.0627 + 16.8477i 0.571623 + 0.564418i
892892 −0.603784 0.603784i −0.0202162 0.0202162i
893893 27.9181 16.1185i 0.934245 0.539386i
894894 35.5596 4.73887i 1.18929 0.158491i
895895 47.3319 12.6826i 1.58213 0.423931i
896896 24.6007 0.821850
897897 0 0
898898 −2.54586 −0.0849564
899899 −2.80720 + 0.752187i −0.0936254 + 0.0250868i
900900 2.37234 + 2.35734i 0.0790779 + 0.0785780i
901901 −2.34659 + 1.35480i −0.0781762 + 0.0451351i
902902 −9.42336 9.42336i −0.313764 0.313764i
903903 −54.4411 + 22.6514i −1.81169 + 0.753792i
904904 −13.2174 + 49.3279i −0.439603 + 1.64062i
905905 −19.7578 + 19.7578i −0.656771 + 0.656771i
906906 −10.5052 + 25.4760i −0.349012 + 0.846383i
907907 32.3487 + 18.6765i 1.07412 + 0.620143i 0.929304 0.369316i 0.120408π-0.120408\pi
0.144815 + 0.989459i 0.453741π0.453741\pi
908908 −1.85339 6.91694i −0.0615069 0.229547i
909909 9.50935 35.9449i 0.315405 1.19222i
910910 0 0
911911 20.5977i 0.682434i 0.939985 + 0.341217i 0.110839π0.110839\pi
−0.939985 + 0.341217i 0.889161π0.889161\pi
912912 24.6094 + 18.8216i 0.814899 + 0.623244i
913913 3.46673 6.00455i 0.114732 0.198722i
914914 3.82525 + 6.62553i 0.126528 + 0.219153i
915915 13.9438 + 1.81326i 0.460969 + 0.0599444i
916916 7.41398 + 1.98657i 0.244965 + 0.0656381i
917917 33.5762 + 8.99672i 1.10878 + 0.297098i
918918 −0.513116 + 1.25563i −0.0169353 + 0.0414419i
919919 19.6678 + 34.0657i 0.648782 + 1.12372i 0.983414 + 0.181375i 0.0580546π0.0580546\pi
−0.334632 + 0.942349i 0.608612π0.608612\pi
920920 14.8250 25.6776i 0.488765 0.846567i
921921 20.7683 27.1548i 0.684339 0.894782i
922922 18.7869i 0.618715i
923923 0 0
924924 2.27201 + 2.95124i 0.0747437 + 0.0970888i
925925 5.32796 + 19.8842i 0.175182 + 0.653789i
926926 −4.80838 2.77612i −0.158013 0.0912289i
927927 −4.46871 16.4684i −0.146772 0.540893i
928928 4.09478 4.09478i 0.134418 0.134418i
929929 −5.44472 + 20.3200i −0.178635 + 0.666676i 0.817268 + 0.576257i 0.195487π0.195487\pi
−0.995904 + 0.0904192i 0.971179π0.971179\pi
930930 2.04430 + 4.91333i 0.0670353 + 0.161115i
931931 −5.74361 5.74361i −0.188239 0.188239i
932932 3.45925 1.99720i 0.113311 0.0654204i
933933 6.17200 + 46.3135i 0.202062 + 1.51624i
934934 −47.5689 + 12.7460i −1.55650 + 0.417063i
935935 1.59228 0.0520730
936936 0 0
937937 2.05438 0.0671138 0.0335569 0.999437i 0.489317π-0.489317\pi
0.0335569 + 0.999437i 0.489317π0.489317\pi
938938 −27.9521 + 7.48976i −0.912670 + 0.244549i
939939 5.48343 + 41.1466i 0.178945 + 1.34277i
940940 −4.36990 + 2.52297i −0.142531 + 0.0822901i
941941 −41.3493 41.3493i −1.34795 1.34795i −0.887888 0.460059i 0.847828π-0.847828\pi
−0.460059 0.887888i 0.652172π-0.652172\pi
942942 −2.85414 6.85973i −0.0929930 0.223502i
943943 3.25477 12.1470i 0.105990 0.395560i
944944 −7.95798 + 7.95798i −0.259010 + 0.259010i
945945 36.3218 + 27.5972i 1.18155 + 0.897737i
946946 −35.3089 20.3856i −1.14799 0.662793i
947947 7.83402 + 29.2370i 0.254571 + 0.950074i 0.968328 + 0.249680i 0.0803255π0.0803255\pi
−0.713757 + 0.700393i 0.753008π0.753008\pi
948948 −3.25181 4.22395i −0.105614 0.137188i
949949 0 0
950950 28.1052i 0.911852i
951951 32.2761 42.2014i 1.04663 1.36848i
952952 −0.867788 + 1.50305i −0.0281252 + 0.0487142i
953953 4.74184 + 8.21310i 0.153603 + 0.266048i 0.932550 0.361042i 0.117579π-0.117579\pi
−0.778946 + 0.627091i 0.784246π0.784246\pi
954954 −26.9845 46.3981i −0.873654 1.50219i
955955 −5.88875 1.57789i −0.190556 0.0510592i
956956 1.60143 + 0.429101i 0.0517938 + 0.0138781i
957957 −17.0813 2.22125i −0.552161 0.0718030i
958958 −1.34066 2.32209i −0.0433147 0.0750233i
959959 −25.4041 + 44.0012i −0.820341 + 1.42087i
960960 −36.3025 27.7646i −1.17166 0.896097i
961961 30.3938i 0.980445i
962962 0 0
963963 −22.5308 5.96062i −0.726046 0.192078i
964964 −1.76499 6.58703i −0.0568465 0.212154i
965965 10.3411 + 5.97046i 0.332893 + 0.192196i
966966 8.35738 20.2673i 0.268894 0.652090i
967967 17.7922 17.7922i 0.572158 0.572158i −0.360573 0.932731i 0.617419π-0.617419\pi
0.932731 + 0.360573i 0.117419π0.117419\pi
968968 3.01778 11.2625i 0.0969950 0.361990i
969969 −1.68721 + 0.701999i −0.0542008 + 0.0225515i
970970 33.9421 + 33.9421i 1.08981 + 1.08981i
971971 16.0499 9.26639i 0.515065 0.297373i −0.219848 0.975534i 0.570556π-0.570556\pi
0.734913 + 0.678161i 0.237223π0.237223\pi
972972 3.99261 + 1.61684i 0.128063 + 0.0518600i
973973 −6.57078 + 1.76063i −0.210649 + 0.0564434i
974974 −32.9285 −1.05510
975975 0 0
976976 −9.10483 −0.291439
977977 −29.7416 + 7.96925i −0.951519 + 0.254959i −0.701007 0.713155i 0.747266π-0.747266\pi
−0.250512 + 0.968113i 0.580599π0.580599\pi
978978 −13.1374 + 1.75076i −0.420086 + 0.0559831i
979979 2.53495 1.46355i 0.0810174 0.0467754i
980980 0.899023 + 0.899023i 0.0287182 + 0.0287182i
981981 15.1549 26.4422i 0.483857 0.844236i
982982 −2.55943 + 9.55192i −0.0816747 + 0.304814i
983983 19.1428 19.1428i 0.610561 0.610561i −0.332531 0.943092i 0.607903π-0.607903\pi
0.943092 + 0.332531i 0.107903π0.107903\pi
984984 −18.2319 7.51807i −0.581212 0.239667i
985985 17.9345 + 10.3545i 0.571441 + 0.329921i
986986 −0.252190 0.941188i −0.00803138 0.0299735i
987987 −24.3533 + 18.7483i −0.775173 + 0.596766i
988988 0 0
989989 38.4731i 1.22337i
990990 0.100010 + 31.5412i 0.00317852 + 1.00244i
991991 −3.12167 + 5.40689i −0.0991631 + 0.171755i −0.911338 0.411658i 0.864950π-0.864950\pi
0.812175 + 0.583413i 0.198283π0.198283\pi
992992 0.603961 + 1.04609i 0.0191758 + 0.0332134i
993993 −0.148213 + 1.13975i −0.00470341 + 0.0361689i
994994 −19.8071 5.30731i −0.628244 0.168338i
995995 18.4085 + 4.93255i 0.583589 + 0.156372i
996996 0.160617 1.23513i 0.00508933 0.0391367i
997997 0.917609 + 1.58935i 0.0290610 + 0.0503351i 0.880190 0.474621i 0.157415π-0.157415\pi
−0.851129 + 0.524956i 0.824082π0.824082\pi
998998 8.09094 14.0139i 0.256114 0.443603i
999999 16.2407 + 20.9581i 0.513832 + 0.663085i
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 507.2.k.k.188.7 96
3.2 odd 2 inner 507.2.k.k.188.18 96
13.2 odd 12 inner 507.2.k.k.89.8 96
13.3 even 3 inner 507.2.k.k.80.18 96
13.4 even 6 507.2.f.g.239.8 yes 48
13.5 odd 4 inner 507.2.k.k.488.17 96
13.6 odd 12 507.2.f.g.437.18 yes 48
13.7 odd 12 507.2.f.g.437.8 yes 48
13.8 odd 4 inner 507.2.k.k.488.7 96
13.9 even 3 507.2.f.g.239.18 yes 48
13.10 even 6 inner 507.2.k.k.80.8 96
13.11 odd 12 inner 507.2.k.k.89.18 96
13.12 even 2 inner 507.2.k.k.188.17 96
39.2 even 12 inner 507.2.k.k.89.17 96
39.5 even 4 inner 507.2.k.k.488.8 96
39.8 even 4 inner 507.2.k.k.488.18 96
39.11 even 12 inner 507.2.k.k.89.7 96
39.17 odd 6 507.2.f.g.239.17 yes 48
39.20 even 12 507.2.f.g.437.17 yes 48
39.23 odd 6 inner 507.2.k.k.80.17 96
39.29 odd 6 inner 507.2.k.k.80.7 96
39.32 even 12 507.2.f.g.437.7 yes 48
39.35 odd 6 507.2.f.g.239.7 48
39.38 odd 2 inner 507.2.k.k.188.8 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.f.g.239.7 48 39.35 odd 6
507.2.f.g.239.8 yes 48 13.4 even 6
507.2.f.g.239.17 yes 48 39.17 odd 6
507.2.f.g.239.18 yes 48 13.9 even 3
507.2.f.g.437.7 yes 48 39.32 even 12
507.2.f.g.437.8 yes 48 13.7 odd 12
507.2.f.g.437.17 yes 48 39.20 even 12
507.2.f.g.437.18 yes 48 13.6 odd 12
507.2.k.k.80.7 96 39.29 odd 6 inner
507.2.k.k.80.8 96 13.10 even 6 inner
507.2.k.k.80.17 96 39.23 odd 6 inner
507.2.k.k.80.18 96 13.3 even 3 inner
507.2.k.k.89.7 96 39.11 even 12 inner
507.2.k.k.89.8 96 13.2 odd 12 inner
507.2.k.k.89.17 96 39.2 even 12 inner
507.2.k.k.89.18 96 13.11 odd 12 inner
507.2.k.k.188.7 96 1.1 even 1 trivial
507.2.k.k.188.8 96 39.38 odd 2 inner
507.2.k.k.188.17 96 13.12 even 2 inner
507.2.k.k.188.18 96 3.2 odd 2 inner
507.2.k.k.488.7 96 13.8 odd 4 inner
507.2.k.k.488.8 96 39.5 even 4 inner
507.2.k.k.488.17 96 13.5 odd 4 inner
507.2.k.k.488.18 96 39.8 even 4 inner