Properties

Label 161.2.g.a.68.4
Level 161161
Weight 22
Character 161.68
Analytic conductor 1.2861.286
Analytic rank 00
Dimension 2828
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [161,2,Mod(45,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) 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("161.45"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 161=723 161 = 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 161.g (of order 66, degree 22, 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: 1.285591472541.28559147254
Analytic rank: 00
Dimension: 2828
Relative dimension: 1414 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 68.4
Character χ\chi == 161.68
Dual form 161.2.g.a.45.4

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+(1.06863+1.85092i)q2+(2.39984+1.38555i)q3+(1.283942.22386i)q4+(1.927423.33839i)q55.92256iq6+(2.368351.17938i)q7+1.21373q8+(2.339494.05212i)q9+(4.11940+7.13501i)q10+(1.51548+0.874964i)q11+(6.16253+3.55794i)q120.204932iq13+(4.713833.12331i)q14+10.6821iq15+(1.270862.20120i)q16+(0.8299971.43760i)q17+(5.00011+8.66045i)q18+(2.012673.48605i)q199.89880q20+(7.317750.451142i)q213.74005iq22+(4.79290+0.167754i)q23+(2.91275+1.68168i)q24+(4.929898.53883i)q25+(0.379314+0.218997i)q26+4.65264iq27+(0.418059+6.78112i)q288.95599q29+(19.771811.4153i)q30+(3.785152.18536i)q31+(3.92989+6.80678i)q32+(2.424614.19955i)q33+3.54784q34+(8.50202+5.63331i)q3512.0151q36+(5.48330+3.16579i)q37+(4.30161+7.45060i)q38+(0.283944+0.491805i)q39+(2.339364.05189i)q405.27084iq41+(6.98494+14.0267i)q4210.2031iq43+(3.89159+2.24681i)q44+(9.0183815.6203i)q45+(4.811349.05055i)q46+(0.4166580.240557i)q47+7.04338iq48+(4.21814+5.58635i)q49+21.0729q50+(3.98373+2.30000i)q51+(0.455740+0.263122i)q52+(6.22805+3.59576i)q53+(8.611694.97196i)q54+6.74569iq55+(2.874521.43144i)q56+11.1546iq57+(9.5706516.5769i)q58+(2.96207+1.71015i)q59+(23.755513.7153i)q60+(1.45607+2.52199i)q61+9.34135iq62+(10.3197+6.83769i)q6311.7150q64+(0.6841440.394991i)q65+(5.18203+8.97554i)q66+(7.10467+4.10188i)q67+(2.13134+3.69159i)q68+(11.26987.04338i)q69+(1.3413021.7565i)q70+2.87254q71+(2.839504.91816i)q72+(8.52674+4.92292i)q73+(11.7192+6.76611i)q74+(23.6619+13.6612i)q7510.3366q76+(4.621100.284893i)q771.21373q78+(6.642883.83527i)q79+(4.898988.48527i)q80+(0.572014+0.990758i)q81+(9.75591+5.63258i)q820.832284q83+(10.398915.6944i)q846.39901q85+(18.8852+10.9034i)q86+(21.493012.4090i)q87+(1.83938+1.06197i)q88+(1.276732.21136i)q89+38.5493q90+(0.241693+0.485351i)q91+(6.52687+10.4433i)q92+(6.05584+10.4890i)q93+(0.8905070.514134i)q94+(7.7585313.4382i)q95+(18.862210.8901i)q96+16.3072q97+(14.8475+1.83770i)q98+8.18789iq99+O(q100)q+(-1.06863 + 1.85092i) q^{2} +(-2.39984 + 1.38555i) q^{3} +(-1.28394 - 2.22386i) q^{4} +(1.92742 - 3.33839i) q^{5} -5.92256i q^{6} +(-2.36835 - 1.17938i) q^{7} +1.21373 q^{8} +(2.33949 - 4.05212i) q^{9} +(4.11940 + 7.13501i) q^{10} +(-1.51548 + 0.874964i) q^{11} +(6.16253 + 3.55794i) q^{12} -0.204932i q^{13} +(4.71383 - 3.12331i) q^{14} +10.6821i q^{15} +(1.27086 - 2.20120i) q^{16} +(-0.829997 - 1.43760i) q^{17} +(5.00011 + 8.66045i) q^{18} +(2.01267 - 3.48605i) q^{19} -9.89880 q^{20} +(7.31775 - 0.451142i) q^{21} -3.74005i q^{22} +(-4.79290 + 0.167754i) q^{23} +(-2.91275 + 1.68168i) q^{24} +(-4.92989 - 8.53883i) q^{25} +(0.379314 + 0.218997i) q^{26} +4.65264i q^{27} +(0.418059 + 6.78112i) q^{28} -8.95599 q^{29} +(-19.7718 - 11.4153i) q^{30} +(3.78515 - 2.18536i) q^{31} +(3.92989 + 6.80678i) q^{32} +(2.42461 - 4.19955i) q^{33} +3.54784 q^{34} +(-8.50202 + 5.63331i) q^{35} -12.0151 q^{36} +(5.48330 + 3.16579i) q^{37} +(4.30161 + 7.45060i) q^{38} +(0.283944 + 0.491805i) q^{39} +(2.33936 - 4.05189i) q^{40} -5.27084i q^{41} +(-6.98494 + 14.0267i) q^{42} -10.2031i q^{43} +(3.89159 + 2.24681i) q^{44} +(-9.01838 - 15.6203i) q^{45} +(4.81134 - 9.05055i) q^{46} +(-0.416658 - 0.240557i) q^{47} +7.04338i q^{48} +(4.21814 + 5.58635i) q^{49} +21.0729 q^{50} +(3.98373 + 2.30000i) q^{51} +(-0.455740 + 0.263122i) q^{52} +(-6.22805 + 3.59576i) q^{53} +(-8.61169 - 4.97196i) q^{54} +6.74569i q^{55} +(-2.87452 - 1.43144i) q^{56} +11.1546i q^{57} +(9.57065 - 16.5769i) q^{58} +(-2.96207 + 1.71015i) q^{59} +(23.7555 - 13.7153i) q^{60} +(-1.45607 + 2.52199i) q^{61} +9.34135i q^{62} +(-10.3197 + 6.83769i) q^{63} -11.7150 q^{64} +(-0.684144 - 0.394991i) q^{65} +(5.18203 + 8.97554i) q^{66} +(-7.10467 + 4.10188i) q^{67} +(-2.13134 + 3.69159i) q^{68} +(11.2698 - 7.04338i) q^{69} +(-1.34130 - 21.7565i) q^{70} +2.87254 q^{71} +(2.83950 - 4.91816i) q^{72} +(-8.52674 + 4.92292i) q^{73} +(-11.7192 + 6.76611i) q^{74} +(23.6619 + 13.6612i) q^{75} -10.3366 q^{76} +(4.62110 - 0.284893i) q^{77} -1.21373 q^{78} +(-6.64288 - 3.83527i) q^{79} +(-4.89898 - 8.48527i) q^{80} +(0.572014 + 0.990758i) q^{81} +(9.75591 + 5.63258i) q^{82} -0.832284 q^{83} +(-10.3989 - 15.6944i) q^{84} -6.39901 q^{85} +(18.8852 + 10.9034i) q^{86} +(21.4930 - 12.4090i) q^{87} +(-1.83938 + 1.06197i) q^{88} +(1.27673 - 2.21136i) q^{89} +38.5493 q^{90} +(-0.241693 + 0.485351i) q^{91} +(6.52687 + 10.4433i) q^{92} +(-6.05584 + 10.4890i) q^{93} +(0.890507 - 0.514134i) q^{94} +(-7.75853 - 13.4382i) q^{95} +(-18.8622 - 10.8901i) q^{96} +16.3072 q^{97} +(-14.8475 + 1.83770i) q^{98} +8.18789i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q4q26q312q4+12q8+4q9+6q12+22q1836q2422q2512q2644q296q3210q3516q39+18q4636q47+28q49+84q50+146q98+O(q100) 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/161Z)×\left(\mathbb{Z}/161\mathbb{Z}\right)^\times.

nn 2424 120120
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 1-1

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 −1.06863 + 1.85092i −0.755636 + 1.30880i 0.189421 + 0.981896i 0.439339π0.439339\pi
−0.945057 + 0.326904i 0.893995π0.893995\pi
33 −2.39984 + 1.38555i −1.38555 + 0.799947i −0.992810 0.119702i 0.961806π-0.961806\pi
−0.392740 + 0.919650i 0.628473π0.628473\pi
44 −1.28394 2.22386i −0.641972 1.11193i
55 1.92742 3.33839i 0.861968 1.49297i −0.00805796 0.999968i 0.502565π-0.502565\pi
0.870026 0.493005i 0.164102π-0.164102\pi
66 5.92256i 2.41788i
77 −2.36835 1.17938i −0.895151 0.445763i
88 1.21373 0.429117
99 2.33949 4.05212i 0.779832 1.35071i
1010 4.11940 + 7.13501i 1.30267 + 2.25629i
1111 −1.51548 + 0.874964i −0.456935 + 0.263811i −0.710755 0.703440i 0.751646π-0.751646\pi
0.253820 + 0.967252i 0.418313π0.418313\pi
1212 6.16253 + 3.55794i 1.77897 + 1.02709i
1313 0.204932i 0.0568380i −0.999596 0.0284190i 0.990953π-0.990953\pi
0.999596 0.0284190i 0.00904727π-0.00904727\pi
1414 4.71383 3.12331i 1.25982 0.834739i
1515 10.6821i 2.75812i
1616 1.27086 2.20120i 0.317716 0.550300i
1717 −0.829997 1.43760i −0.201304 0.348669i 0.747645 0.664099i 0.231185π-0.231185\pi
−0.948949 + 0.315430i 0.897851π0.897851\pi
1818 5.00011 + 8.66045i 1.17854 + 2.04129i
1919 2.01267 3.48605i 0.461739 0.799755i −0.537309 0.843385i 0.680559π-0.680559\pi
0.999048 + 0.0436305i 0.0138924π0.0138924\pi
2020 −9.89880 −2.21344
2121 7.31775 0.451142i 1.59686 0.0984473i
2222 3.74005i 0.797382i
2323 −4.79290 + 0.167754i −0.999388 + 0.0349791i
2424 −2.91275 + 1.68168i −0.594562 + 0.343271i
2525 −4.92989 8.53883i −0.985979 1.70777i
2626 0.379314 + 0.218997i 0.0743896 + 0.0429489i
2727 4.65264i 0.895402i
2828 0.418059 + 6.78112i 0.0790057 + 1.28151i
2929 −8.95599 −1.66309 −0.831543 0.555460i 0.812542π-0.812542\pi
−0.831543 + 0.555460i 0.812542π0.812542\pi
3030 −19.7718 11.4153i −3.60982 2.08413i
3131 3.78515 2.18536i 0.679832 0.392501i −0.119959 0.992779i 0.538276π-0.538276\pi
0.799792 + 0.600277i 0.204943π0.204943\pi
3232 3.92989 + 6.80678i 0.694714 + 1.20328i
3333 2.42461 4.19955i 0.422071 0.731048i
3434 3.54784 0.608450
3535 −8.50202 + 5.63331i −1.43710 + 0.952203i
3636 −12.0151 −2.00252
3737 5.48330 + 3.16579i 0.901449 + 0.520452i 0.877670 0.479265i 0.159097π-0.159097\pi
0.0237791 + 0.999717i 0.492430π0.492430\pi
3838 4.30161 + 7.45060i 0.697813 + 1.20865i
3939 0.283944 + 0.491805i 0.0454674 + 0.0787519i
4040 2.33936 4.05189i 0.369885 0.640660i
4141 5.27084i 0.823166i −0.911372 0.411583i 0.864976π-0.864976\pi
0.911372 0.411583i 0.135024π-0.135024\pi
4242 −6.98494 + 14.0267i −1.07780 + 2.16436i
4343 10.2031i 1.55596i −0.628287 0.777981i 0.716244π-0.716244\pi
0.628287 0.777981i 0.283756π-0.283756\pi
4444 3.89159 + 2.24681i 0.586679 + 0.338719i
4545 −9.01838 15.6203i −1.34438 2.32853i
4646 4.81134 9.05055i 0.709393 1.33443i
4747 −0.416658 0.240557i −0.0607758 0.0350889i 0.469304 0.883037i 0.344505π-0.344505\pi
−0.530080 + 0.847948i 0.677838π0.677838\pi
4848 7.04338i 1.01662i
4949 4.21814 + 5.58635i 0.602591 + 0.798050i
5050 21.0729 2.98016
5151 3.98373 + 2.30000i 0.557833 + 0.322065i
5252 −0.455740 + 0.263122i −0.0631998 + 0.0364884i
5353 −6.22805 + 3.59576i −0.855488 + 0.493916i −0.862499 0.506059i 0.831102π-0.831102\pi
0.00701084 + 0.999975i 0.497768π0.497768\pi
5454 −8.61169 4.97196i −1.17190 0.676598i
5555 6.74569i 0.909588i
5656 −2.87452 1.43144i −0.384124 0.191284i
5757 11.1546i 1.47747i
5858 9.57065 16.5769i 1.25669 2.17665i
5959 −2.96207 + 1.71015i −0.385629 + 0.222643i −0.680264 0.732967i 0.738135π-0.738135\pi
0.294636 + 0.955610i 0.404802π0.404802\pi
6060 23.7555 13.7153i 3.06683 1.77063i
6161 −1.45607 + 2.52199i −0.186431 + 0.322908i −0.944058 0.329780i 0.893025π-0.893025\pi
0.757627 + 0.652688i 0.226359π0.226359\pi
6262 9.34135i 1.18635i
6363 −10.3197 + 6.83769i −1.30016 + 0.861468i
6464 −11.7150 −1.46437
6565 −0.684144 0.394991i −0.0848576 0.0489926i
6666 5.18203 + 8.97554i 0.637864 + 1.10481i
6767 −7.10467 + 4.10188i −0.867973 + 0.501125i −0.866674 0.498875i 0.833747π-0.833747\pi
−0.00129901 + 0.999999i 0.500413π0.500413\pi
6868 −2.13134 + 3.69159i −0.258463 + 0.447671i
6969 11.2698 7.04338i 1.35672 0.847923i
7070 −1.34130 21.7565i −0.160316 2.60040i
7171 2.87254 0.340908 0.170454 0.985366i 0.445477π-0.445477\pi
0.170454 + 0.985366i 0.445477π0.445477\pi
7272 2.83950 4.91816i 0.334639 0.579611i
7373 −8.52674 + 4.92292i −0.997980 + 0.576184i −0.907650 0.419728i 0.862125π-0.862125\pi
−0.0903298 + 0.995912i 0.528792π0.528792\pi
7474 −11.7192 + 6.76611i −1.36234 + 0.786545i
7575 23.6619 + 13.6612i 2.73224 + 1.57746i
7676 −10.3366 −1.18569
7777 4.62110 0.284893i 0.526623 0.0324666i
7878 −1.21373 −0.137427
7979 −6.64288 3.83527i −0.747383 0.431502i 0.0773647 0.997003i 0.475349π-0.475349\pi
−0.824747 + 0.565501i 0.808683π0.808683\pi
8080 −4.89898 8.48527i −0.547722 0.948682i
8181 0.572014 + 0.990758i 0.0635571 + 0.110084i
8282 9.75591 + 5.63258i 1.07736 + 0.622014i
8383 −0.832284 −0.0913551 −0.0456775 0.998956i 0.514545π-0.514545\pi
−0.0456775 + 0.998956i 0.514545π0.514545\pi
8484 −10.3989 15.6944i −1.13461 1.71240i
8585 −6.39901 −0.694070
8686 18.8852 + 10.9034i 2.03644 + 1.17574i
8787 21.4930 12.4090i 2.30429 1.33038i
8888 −1.83938 + 1.06197i −0.196078 + 0.113206i
8989 1.27673 2.21136i 0.135333 0.234404i −0.790392 0.612602i 0.790123π-0.790123\pi
0.925725 + 0.378198i 0.123456π0.123456\pi
9090 38.5493 4.06345
9191 −0.241693 + 0.485351i −0.0253363 + 0.0508786i
9292 6.52687 + 10.4433i 0.680473 + 1.08879i
9393 −6.05584 + 10.4890i −0.627961 + 1.08766i
9494 0.890507 0.514134i 0.0918487 0.0530289i
9595 −7.75853 13.4382i −0.796008 1.37873i
9696 −18.8622 10.8901i −1.92512 1.11147i
9797 16.3072 1.65574 0.827871 0.560919i 0.189552π-0.189552\pi
0.827871 + 0.560919i 0.189552π0.189552\pi
9898 −14.8475 + 1.83770i −1.49983 + 0.185636i
9999 8.18789i 0.822914i
100100 −12.6594 + 21.9267i −1.26594 + 2.19267i
101101 3.28009 1.89376i 0.326381 0.188436i −0.327852 0.944729i 0.606325π-0.606325\pi
0.654233 + 0.756293i 0.272992π0.272992\pi
102102 −8.51426 + 4.91571i −0.843038 + 0.486728i
103103 8.15645 14.1274i 0.803679 1.39201i −0.113501 0.993538i 0.536206π-0.536206\pi
0.917179 0.398474i 0.130460π-0.130460\pi
104104 0.248732i 0.0243901i
105105 12.5983 25.2990i 1.22947 2.46893i
106106 15.3702i 1.49288i
107107 5.70603 + 3.29438i 0.551622 + 0.318479i 0.749776 0.661692i 0.230161π-0.230161\pi
−0.198154 + 0.980171i 0.563495π0.563495\pi
108108 10.3468 5.97374i 0.995623 0.574823i
109109 −0.721798 + 0.416730i −0.0691357 + 0.0399155i −0.534169 0.845377i 0.679376π-0.679376\pi
0.465034 + 0.885293i 0.346042π0.346042\pi
110110 −12.4858 7.20865i −1.19047 0.687318i
111111 −17.5454 −1.66534
112112 −5.60589 + 3.71438i −0.529707 + 0.350976i
113113 0.292918i 0.0275554i −0.999905 0.0137777i 0.995614π-0.995614\pi
0.999905 0.0137777i 0.00438572π-0.00438572\pi
114114 −20.6464 11.9202i −1.93371 1.11643i
115115 −8.67790 + 16.3239i −0.809218 + 1.52221i
116116 11.4990 + 19.9168i 1.06765 + 1.84923i
117117 −0.830411 0.479438i −0.0767716 0.0443241i
118118 7.31008i 0.672948i
119119 0.270252 + 4.38361i 0.0247739 + 0.401845i
120120 12.9652i 1.18355i
121121 −3.96888 + 6.87430i −0.360807 + 0.624936i
122122 −3.11201 5.39016i −0.281748 0.488002i
123123 7.30301 + 12.6492i 0.658490 + 1.14054i
124124 −9.71983 5.61175i −0.872867 0.503950i
125125 −18.7337 −1.67559
126126 −1.62806 26.4080i −0.145039 2.35261i
127127 14.3002 1.26894 0.634470 0.772947i 0.281218π-0.281218\pi
0.634470 + 0.772947i 0.281218π0.281218\pi
128128 4.65919 8.06995i 0.411818 0.713290i
129129 14.1369 + 24.4859i 1.24469 + 2.15586i
130130 1.46219 0.844199i 0.128243 0.0740411i
131131 −1.48125 0.855202i −0.129418 0.0747194i 0.433893 0.900964i 0.357139π-0.357139\pi
−0.563311 + 0.826245i 0.690473π0.690473\pi
132132 −12.4523 −1.08383
133133 −8.87808 + 5.88248i −0.769827 + 0.510076i
134134 17.5336i 1.51467i
135135 15.5323 + 8.96760i 1.33681 + 0.771808i
136136 −1.00739 1.74485i −0.0863829 0.149620i
137137 13.9951 8.08008i 1.19568 0.690328i 0.236093 0.971730i 0.424133π-0.424133\pi
0.959590 + 0.281403i 0.0907997π0.0907997\pi
138138 0.993532 + 28.3862i 0.0845751 + 2.41640i
139139 3.58058i 0.303701i 0.988404 + 0.151850i 0.0485232π0.0485232\pi
−0.988404 + 0.151850i 0.951477π0.951477\pi
140140 23.4438 + 11.6744i 1.98136 + 0.986668i
141141 1.33322 0.112277
142142 −3.06968 + 5.31685i −0.257602 + 0.446180i
143143 0.179308 + 0.310571i 0.0149945 + 0.0259713i
144144 −5.94636 10.2994i −0.495530 0.858283i
145145 −17.2620 + 29.8986i −1.43353 + 2.48294i
146146 21.0431i 1.74154i
147147 −17.8630 7.56192i −1.47332 0.623697i
148148 16.2588i 1.33646i
149149 −11.2771 6.51085i −0.923858 0.533389i −0.0389938 0.999239i 0.512415π-0.512415\pi
−0.884864 + 0.465850i 0.845749π0.845749\pi
150150 −50.5717 + 29.1976i −4.12917 + 2.38397i
151151 3.83347 + 6.63977i 0.311963 + 0.540337i 0.978787 0.204879i 0.0656800π-0.0656800\pi
−0.666824 + 0.745215i 0.732347π0.732347\pi
152152 2.44283 4.23111i 0.198140 0.343188i
153153 −7.76710 −0.627933
154154 −4.41093 + 8.85774i −0.355443 + 0.713777i
155155 16.8484i 1.35330i
156156 0.729136 1.26290i 0.0583776 0.101113i
157157 −7.19948 12.4699i −0.574581 0.995204i −0.996087 0.0883781i 0.971832π-0.971832\pi
0.421506 0.906826i 0.361502π-0.361502\pi
158158 14.1976 8.19698i 1.12950 0.652116i
159159 9.96422 17.2585i 0.790214 1.36869i
160160 30.2982 2.39528
161161 11.5491 + 5.25534i 0.910196 + 0.414178i
162162 −2.44509 −0.192104
163163 0.164926 0.285661i 0.0129180 0.0223747i −0.859494 0.511146i 0.829221π-0.829221\pi
0.872412 + 0.488771i 0.162555π0.162555\pi
164164 −11.7216 + 6.76746i −0.915302 + 0.528450i
165165 −9.34648 16.1886i −0.727623 1.26028i
166166 0.889405 1.54049i 0.0690312 0.119566i
167167 10.3335i 0.799627i −0.916596 0.399814i 0.869075π-0.869075\pi
0.916596 0.399814i 0.130925π-0.130925\pi
168168 8.88173 0.547563i 0.685241 0.0422454i
169169 12.9580 0.996769
170170 6.83818 11.8441i 0.524465 0.908400i
171171 −9.41727 16.3112i −0.720157 1.24735i
172172 −22.6903 + 13.1002i −1.73012 + 0.998884i
173173 −6.14735 3.54917i −0.467374 0.269839i 0.247766 0.968820i 0.420304π-0.420304\pi
−0.715140 + 0.698981i 0.753637π0.753637\pi
174174 53.0424i 4.02114i
175175 1.60520 + 26.0371i 0.121342 + 1.96822i
176176 4.44784i 0.335268i
177177 4.73900 8.20819i 0.356205 0.616965i
178178 2.72871 + 4.72626i 0.204525 + 0.354248i
179179 9.81217 + 16.9952i 0.733396 + 1.27028i 0.955423 + 0.295239i 0.0953993π0.0953993\pi
−0.222027 + 0.975040i 0.571267π0.571267\pi
180180 −23.1582 + 40.1111i −1.72611 + 2.98971i
181181 −5.51100 −0.409629 −0.204815 0.978801i 0.565659π-0.565659\pi
−0.204815 + 0.978801i 0.565659π0.565659\pi
182182 −0.640067 0.966016i −0.0474449 0.0716058i
183183 8.06985i 0.596541i
184184 −5.81726 + 0.203607i −0.428854 + 0.0150101i
185185 21.1372 12.2036i 1.55404 0.897226i
186186 −12.9429 22.4178i −0.949020 1.64375i
187187 2.51569 + 1.45244i 0.183966 + 0.106213i
188188 1.23545i 0.0901044i
189189 5.48722 11.0191i 0.399137 0.801520i
190190 33.1640 2.40597
191191 18.5510 + 10.7104i 1.34230 + 0.774977i 0.987145 0.159830i 0.0510947π-0.0510947\pi
0.355155 + 0.934807i 0.384428π0.384428\pi
192192 28.1141 16.2317i 2.02896 1.17142i
193193 −2.72633 4.72214i −0.196246 0.339907i 0.751063 0.660231i 0.229542π-0.229542\pi
−0.947308 + 0.320324i 0.896208π0.896208\pi
194194 −17.4263 + 30.1833i −1.25114 + 2.16704i
195195 2.18912 0.156766
196196 7.00739 16.5531i 0.500528 1.18236i
197197 −6.78385 −0.483329 −0.241665 0.970360i 0.577693π-0.577693\pi
−0.241665 + 0.970360i 0.577693π0.577693\pi
198198 −15.1552 8.74983i −1.07703 0.621824i
199199 −0.946823 1.63995i −0.0671185 0.116253i 0.830513 0.556999i 0.188047π-0.188047\pi
−0.897632 + 0.440746i 0.854714π0.854714\pi
200200 −5.98354 10.3638i −0.423100 0.732831i
201201 11.3667 19.6877i 0.801747 1.38867i
202202 8.09492i 0.569556i
203203 21.2109 + 10.5625i 1.48871 + 0.741342i
204204 11.8123i 0.827027i
205205 −17.5961 10.1591i −1.22897 0.709543i
206206 17.4325 + 30.1939i 1.21458 + 2.10371i
207207 −10.5332 + 19.8139i −0.732108 + 1.37716i
208208 −0.451097 0.260441i −0.0312780 0.0180583i
209209 7.04406i 0.487248i
210210 33.3636 + 50.3538i 2.30231 + 3.47474i
211211 14.1714 0.975599 0.487800 0.872956i 0.337800π-0.337800\pi
0.487800 + 0.872956i 0.337800π0.337800\pi
212212 15.9929 + 9.23352i 1.09840 + 0.634161i
213213 −6.89364 + 3.98004i −0.472344 + 0.272708i
214214 −12.1953 + 7.04094i −0.833652 + 0.481309i
215215 −34.0620 19.6657i −2.32301 1.34119i
216216 5.64703i 0.384232i
217217 −11.5419 + 0.711564i −0.783515 + 0.0483041i
218218 1.78132i 0.120646i
219219 13.6419 23.6284i 0.921833 1.59666i
220220 15.0014 8.66109i 1.01140 0.583930i
221221 −0.294610 + 0.170093i −0.0198176 + 0.0114417i
222222 18.7496 32.4752i 1.25839 2.17959i
223223 25.9587i 1.73832i −0.494528 0.869162i 0.664659π-0.664659\pi
0.494528 0.869162i 0.335341π-0.335341\pi
224224 −1.27959 20.7556i −0.0854965 1.38679i
225225 −46.1338 −3.07559
226226 0.542169 + 0.313021i 0.0360645 + 0.0208219i
227227 −0.107801 0.186717i −0.00715502 0.0123929i 0.862426 0.506184i 0.168944π-0.168944\pi
−0.869581 + 0.493791i 0.835611π0.835611\pi
228228 24.8063 14.3219i 1.64284 0.948492i
229229 −0.651636 + 1.12867i −0.0430613 + 0.0745844i −0.886753 0.462244i 0.847044π-0.847044\pi
0.843691 + 0.536828i 0.180378π0.180378\pi
230230 −20.9408 33.5063i −1.38079 2.20934i
231231 −10.6952 + 7.08646i −0.703691 + 0.466255i
232232 −10.8701 −0.713658
233233 1.93886 3.35821i 0.127019 0.220004i −0.795501 0.605952i 0.792792π-0.792792\pi
0.922520 + 0.385948i 0.126126π0.126126\pi
234234 1.77481 1.02469i 0.116023 0.0669858i
235235 −1.60615 + 0.927310i −0.104774 + 0.0604911i
236236 7.60626 + 4.39148i 0.495125 + 0.285861i
237237 21.2558 1.38071
238238 −8.40253 4.18425i −0.544655 0.271224i
239239 −11.5086 −0.744427 −0.372214 0.928147i 0.621401π-0.621401\pi
−0.372214 + 0.928147i 0.621401π0.621401\pi
240240 23.5135 + 13.5755i 1.51779 + 0.876298i
241241 −0.170470 0.295263i −0.0109810 0.0190196i 0.860483 0.509480i 0.170162π-0.170162\pi
−0.871464 + 0.490460i 0.836829π0.836829\pi
242242 −8.48253 14.6922i −0.545278 0.944449i
243243 −14.8334 8.56408i −0.951564 0.549386i
244244 7.47807 0.478734
245245 26.7795 3.31454i 1.71088 0.211758i
246246 −31.2169 −1.99031
247247 −0.714405 0.412462i −0.0454565 0.0262443i
248248 4.59413 2.65242i 0.291727 0.168429i
249249 1.99735 1.15317i 0.126577 0.0730792i
250250 20.0194 34.6746i 1.26614 2.19302i
251251 −20.2808 −1.28011 −0.640057 0.768327i 0.721089π-0.721089\pi
−0.640057 + 0.768327i 0.721089π0.721089\pi
252252 28.4560 + 14.1704i 1.79256 + 0.892649i
253253 7.11677 4.44784i 0.447427 0.279633i
254254 −15.2817 + 26.4686i −0.958857 + 1.66079i
255255 15.3566 8.86615i 0.961669 0.555220i
256256 −1.75706 3.04332i −0.109816 0.190207i
257257 17.7715 + 10.2604i 1.10856 + 0.640026i 0.938455 0.345401i 0.112257π-0.112257\pi
0.170102 + 0.985426i 0.445590π0.445590\pi
258258 −60.4287 −3.76213
259259 −9.25270 13.9646i −0.574935 0.867716i
260260 2.02858i 0.125807i
261261 −20.9525 + 36.2908i −1.29693 + 2.24634i
262262 3.16583 1.82779i 0.195585 0.112921i
263263 6.29979 3.63718i 0.388461 0.224278i −0.293032 0.956103i 0.594664π-0.594664\pi
0.681493 + 0.731824i 0.261331π0.261331\pi
264264 2.94281 5.09710i 0.181118 0.313705i
265265 27.7222i 1.70296i
266266 −1.40063 22.7188i −0.0858779 1.39298i
267267 7.07589i 0.433038i
268268 18.2440 + 10.5332i 1.11443 + 0.643416i
269269 13.9099 8.03088i 0.848101 0.489651i −0.0119088 0.999929i 0.503791π-0.503791\pi
0.860010 + 0.510278i 0.170457π0.170457\pi
270270 −33.1967 + 19.1661i −2.02029 + 1.16641i
271271 8.48238 + 4.89730i 0.515268 + 0.297490i 0.734996 0.678071i 0.237184π-0.237184\pi
−0.219729 + 0.975561i 0.570517π0.570517\pi
272272 −4.21925 −0.255830
273273 −0.0924537 1.49964i −0.00559555 0.0907625i
274274 34.5385i 2.08655i
275275 14.9423 + 8.62696i 0.901056 + 0.520225i
276276 −30.1332 16.0190i −1.81381 0.964232i
277277 5.37245 + 9.30536i 0.322800 + 0.559105i 0.981065 0.193681i 0.0620427π-0.0620427\pi
−0.658265 + 0.752786i 0.728709π0.728709\pi
278278 −6.62737 3.82632i −0.397483 0.229487i
279279 20.4505i 1.22434i
280280 −10.3191 + 6.83729i −0.616685 + 0.408606i
281281 11.1537i 0.665376i −0.943037 0.332688i 0.892044π-0.892044\pi
0.943037 0.332688i 0.107956π-0.107956\pi
282282 −1.42472 + 2.46768i −0.0848406 + 0.146948i
283283 −8.61689 14.9249i −0.512221 0.887193i −0.999900 0.0141696i 0.995490π-0.995490\pi
0.487679 0.873023i 0.337844π-0.337844\pi
284284 −3.68818 6.38811i −0.218853 0.379065i
285285 37.2385 + 21.4997i 2.20582 + 1.27353i
286286 −0.766458 −0.0453216
287287 −6.21631 + 12.4832i −0.366937 + 0.736858i
288288 36.7759 2.16704
289289 7.12221 12.3360i 0.418953 0.725649i
290290 −36.8933 63.9011i −2.16645 3.75240i
291291 −39.1346 + 22.5944i −2.29411 + 1.32451i
292292 21.8957 + 12.6415i 1.28135 + 0.739788i
293293 −8.91155 −0.520618 −0.260309 0.965525i 0.583824π-0.583824\pi
−0.260309 + 0.965525i 0.583824π0.583824\pi
294294 33.0855 24.9822i 1.92959 1.45699i
295295 13.1847i 0.767644i
296296 6.65522 + 3.84239i 0.386827 + 0.223335i
297297 −4.07089 7.05100i −0.236217 0.409140i
298298 24.1022 13.9154i 1.39620 0.806097i
299299 0.0343782 + 0.982220i 0.00198814 + 0.0568032i
300300 70.1610i 4.05075i
301301 −12.0333 + 24.1646i −0.693590 + 1.39282i
302302 −16.3863 −0.942923
303303 −5.24779 + 9.08944i −0.301478 + 0.522175i
304304 −5.11566 8.86059i −0.293403 0.508190i
305305 5.61293 + 9.72188i 0.321396 + 0.556673i
306306 8.30016 14.3763i 0.474489 0.821838i
307307 17.5645i 1.00246i 0.865314 + 0.501230i 0.167119π0.167119\pi
−0.865314 + 0.501230i 0.832881π0.832881\pi
308308 −6.56679 9.91087i −0.374178 0.564724i
309309 45.2046i 2.57160i
310310 31.1851 + 18.0047i 1.77119 + 1.02260i
311311 2.32221 1.34073i 0.131681 0.0760259i −0.432713 0.901532i 0.642443π-0.642443\pi
0.564393 + 0.825506i 0.309110π0.309110\pi
312312 0.344630 + 0.596917i 0.0195108 + 0.0337938i
313313 −3.71224 + 6.42979i −0.209828 + 0.363433i −0.951660 0.307152i 0.900624π-0.900624\pi
0.741832 + 0.670586i 0.233957π0.233957\pi
314314 30.7744 1.73670
315315 2.93643 + 47.6303i 0.165449 + 2.68367i
316316 19.6971i 1.10805i
317317 −0.398442 + 0.690122i −0.0223787 + 0.0387611i −0.876998 0.480494i 0.840457π-0.840457\pi
0.854619 + 0.519255i 0.173791π0.173791\pi
318318 21.2961 + 36.8860i 1.19423 + 2.06846i
319319 13.5726 7.83617i 0.759922 0.438741i
320320 −22.5797 + 39.1091i −1.26224 + 2.18627i
321321 −18.2581 −1.01907
322322 −22.0689 + 15.7605i −1.22985 + 0.878296i
323323 −6.68205 −0.371799
324324 1.46887 2.54415i 0.0816038 0.141342i
325325 −1.74988 + 1.01029i −0.0970660 + 0.0560411i
326326 0.352491 + 0.610532i 0.0195227 + 0.0338143i
327327 1.15480 2.00017i 0.0638606 0.110610i
328328 6.39735i 0.353234i
329329 0.703082 + 1.06112i 0.0387622 + 0.0585015i
330330 39.9518 2.19927
331331 −5.96961 + 10.3397i −0.328119 + 0.568319i −0.982139 0.188159i 0.939748π-0.939748\pi
0.654019 + 0.756478i 0.273081π0.273081\pi
332332 1.06861 + 1.85088i 0.0586474 + 0.101580i
333333 25.6563 14.8127i 1.40596 0.811730i
334334 19.1264 + 11.0427i 1.04655 + 0.604227i
335335 31.6242i 1.72781i
336336 8.30680 16.6812i 0.453173 0.910032i
337337 17.0561i 0.929104i −0.885546 0.464552i 0.846215π-0.846215\pi
0.885546 0.464552i 0.153785π-0.153785\pi
338338 −13.8473 + 23.9843i −0.753195 + 1.30457i
339339 0.405853 + 0.702957i 0.0220429 + 0.0381794i
340340 8.21597 + 14.2305i 0.445574 + 0.771756i
341341 −3.82421 + 6.62373i −0.207093 + 0.358695i
342342 40.2544 2.17671
343343 −3.40160 18.2052i −0.183669 0.982988i
344344 12.3838i 0.667689i
345345 −1.79197 51.1984i −0.0964764 2.75643i
346346 13.1385 7.58551i 0.706330 0.407800i
347347 −3.29852 5.71320i −0.177074 0.306701i 0.763803 0.645449i 0.223330π-0.223330\pi
−0.940877 + 0.338748i 0.889996π0.889996\pi
348348 −55.1915 31.8648i −2.95858 1.70814i
349349 36.4610i 1.95171i −0.218417 0.975855i 0.570089π-0.570089\pi
0.218417 0.975855i 0.429911π-0.429911\pi
350350 −49.9081 24.8530i −2.66770 1.32845i
351351 0.953478 0.0508929
352352 −11.9114 6.87703i −0.634878 0.366547i
353353 8.67372 5.00778i 0.461656 0.266537i −0.251084 0.967965i 0.580787π-0.580787\pi
0.712740 + 0.701428i 0.247454π0.247454\pi
354354 10.1285 + 17.5430i 0.538323 + 0.932402i
355355 5.53659 9.58965i 0.293852 0.508966i
356356 −6.55700 −0.347520
357357 −6.72227 10.1455i −0.355780 0.536958i
358358 −41.9424 −2.21672
359359 −3.27783 1.89246i −0.172997 0.0998801i 0.411001 0.911635i 0.365179π-0.365179\pi
−0.583998 + 0.811755i 0.698513π0.698513\pi
360360 −10.9458 18.9587i −0.576896 0.999213i
361361 1.39830 + 2.42193i 0.0735947 + 0.127470i
362362 5.88923 10.2004i 0.309531 0.536123i
363363 21.9963i 1.15451i
364364 1.38967 0.0856739i 0.0728385 0.00449053i
365365 37.9541i 1.98661i
366366 14.9367 + 8.62369i 0.780752 + 0.450768i
367367 −4.53149 7.84876i −0.236542 0.409702i 0.723178 0.690662i 0.242681π-0.242681\pi
−0.959720 + 0.280960i 0.909347π0.909347\pi
368368 −5.72186 + 10.7633i −0.298273 + 0.561077i
369369 −21.3581 12.3311i −1.11186 0.641931i
370370 52.1646i 2.71191i
371371 18.9909 1.17080i 0.985960 0.0607849i
372372 31.1014 1.61253
373373 −19.1866 11.0774i −0.993446 0.573566i −0.0871431 0.996196i 0.527774π-0.527774\pi
−0.906302 + 0.422630i 0.861107π0.861107\pi
374374 −5.37669 + 3.10423i −0.278022 + 0.160516i
375375 44.9579 25.9565i 2.32162 1.34039i
376376 −0.505708 0.291971i −0.0260799 0.0150572i
377377 1.83537i 0.0945265i
378378 14.5316 + 21.9318i 0.747427 + 1.12805i
379379 20.0332i 1.02904i 0.857479 + 0.514519i 0.172029π0.172029\pi
−0.857479 + 0.514519i 0.827971π0.827971\pi
380380 −19.9230 + 34.5077i −1.02203 + 1.77021i
381381 −34.3183 + 19.8137i −1.75818 + 1.01509i
382382 −39.6482 + 22.8909i −2.02858 + 1.17120i
383383 −8.45906 + 14.6515i −0.432238 + 0.748658i −0.997066 0.0765509i 0.975609π-0.975609\pi
0.564828 + 0.825209i 0.308943π0.308943\pi
384384 25.8222i 1.31773i
385385 7.95571 15.9761i 0.405461 0.814219i
386386 11.6538 0.593161
387387 −41.3443 23.8702i −2.10165 1.21339i
388388 −20.9375 36.2648i −1.06294 1.84107i
389389 22.8244 13.1777i 1.15724 0.668136i 0.206603 0.978425i 0.433759π-0.433759\pi
0.950642 + 0.310289i 0.100426π0.100426\pi
390390 −2.33936 + 4.05189i −0.118458 + 0.205175i
391391 4.21925 + 6.75102i 0.213377 + 0.341414i
392392 5.11966 + 6.78030i 0.258582 + 0.342457i
393393 4.73970 0.239086
394394 7.24943 12.5564i 0.365221 0.632582i
395395 −25.6072 + 14.7844i −1.28844 + 0.743881i
396396 18.2087 10.5128i 0.915021 0.528288i
397397 −13.6338 7.87148i −0.684261 0.395058i 0.117197 0.993109i 0.462609π-0.462609\pi
−0.801459 + 0.598050i 0.795942π0.795942\pi
398398 4.04722 0.202869
399399 13.1555 26.4180i 0.658600 1.32256i
400400 −25.0609 −1.25304
401401 −33.1621 19.1461i −1.65603 0.956112i −0.974518 0.224309i 0.927987π-0.927987\pi
−0.681516 0.731803i 0.738679π-0.738679\pi
402402 24.2937 + 42.0778i 1.21166 + 2.09865i
403403 −0.447850 0.775699i −0.0223090 0.0386403i
404404 −8.42290 4.86296i −0.419055 0.241941i
405405 4.41005 0.219137
406406 −42.2170 + 27.9723i −2.09519 + 1.38824i
407407 −11.0798 −0.549205
408408 4.83515 + 2.79157i 0.239375 + 0.138204i
409409 −7.35607 + 4.24703i −0.363734 + 0.210002i −0.670718 0.741713i 0.734014π-0.734014\pi
0.306983 + 0.951715i 0.400680π0.400680\pi
410410 37.6075 21.7127i 1.85730 1.07231i
411411 −22.3907 + 38.7818i −1.10445 + 1.91297i
412412 −41.8897 −2.06376
413413 9.03212 0.556834i 0.444442 0.0274000i
414414 −25.4178 40.6698i −1.24922 1.99881i
415415 −1.60416 + 2.77849i −0.0787452 + 0.136391i
416416 1.39493 0.805363i 0.0683920 0.0394861i
417417 −4.96107 8.59282i −0.242944 0.420792i
418418 −13.0380 7.52750i −0.637710 0.368182i
419419 −9.67094 −0.472456 −0.236228 0.971698i 0.575911π-0.575911\pi
−0.236228 + 0.971698i 0.575911π0.575911\pi
420420 −72.4369 + 4.46577i −3.53456 + 0.217907i
421421 19.7189i 0.961042i 0.876983 + 0.480521i 0.159553π0.159553\pi
−0.876983 + 0.480521i 0.840447π0.840447\pi
422422 −15.1440 + 26.2302i −0.737198 + 1.27686i
423423 −1.94954 + 1.12557i −0.0947897 + 0.0547269i
424424 −7.55914 + 4.36427i −0.367104 + 0.211948i
425425 −8.18360 + 14.1744i −0.396963 + 0.687560i
426426 17.0128i 0.824272i
427427 6.42287 4.25570i 0.310825 0.205948i
428428 16.9192i 0.817819i
429429 −0.860624 0.496881i −0.0415513 0.0239897i
430430 72.7994 42.0308i 3.51070 2.02690i
431431 14.6709 8.47027i 0.706674 0.407998i −0.103154 0.994665i 0.532894π-0.532894\pi
0.809828 + 0.586667i 0.199560π0.199560\pi
432432 10.2414 + 5.91288i 0.492740 + 0.284483i
433433 32.0100 1.53830 0.769152 0.639065i 0.220679π-0.220679\pi
0.769152 + 0.639065i 0.220679π0.220679\pi
434434 11.0170 22.1236i 0.528832 1.06197i
435435 95.6692i 4.58699i
436436 1.85350 + 1.07012i 0.0887664 + 0.0512493i
437437 −9.06173 + 17.0459i −0.433481 + 0.815417i
438438 29.1563 + 50.5002i 1.39314 + 2.41299i
439439 −22.8492 13.1920i −1.09053 0.629620i −0.156815 0.987628i 0.550123π-0.550123\pi
−0.933719 + 0.358008i 0.883456π0.883456\pi
440440 8.18741i 0.390320i
441441 32.5049 4.02317i 1.54785 0.191580i
442442 0.727068i 0.0345831i
443443 0.574139 0.994438i 0.0272782 0.0472472i −0.852064 0.523438i 0.824649π-0.824649\pi
0.879342 + 0.476190i 0.157983π0.157983\pi
444444 22.5273 + 39.0185i 1.06910 + 1.85173i
445445 −4.92159 8.52445i −0.233306 0.404098i
446446 48.0476 + 27.7403i 2.27512 + 1.31354i
447447 36.0844 1.70673
448448 27.7451 + 13.8164i 1.31083 + 0.652762i
449449 −20.0207 −0.944838 −0.472419 0.881374i 0.656619π-0.656619\pi
−0.472419 + 0.881374i 0.656619π0.656619\pi
450450 49.3000 85.3902i 2.32403 4.02533i
451451 4.61179 + 7.98786i 0.217161 + 0.376133i
452452 −0.651408 + 0.376090i −0.0306396 + 0.0176898i
453453 −18.3994 10.6229i −0.864482 0.499109i
454454 0.460799 0.0216264
455455 1.15445 + 1.74234i 0.0541213 + 0.0816821i
456456 13.5387i 0.634006i
457457 15.0469 + 8.68734i 0.703865 + 0.406377i 0.808785 0.588104i 0.200125π-0.200125\pi
−0.104920 + 0.994481i 0.533459π0.533459\pi
458458 −1.39272 2.41226i −0.0650774 0.112717i
459459 6.68863 3.86168i 0.312199 0.180248i
460460 47.4439 1.66056i 2.21208 0.0774240i
461461 15.2031i 0.708081i −0.935230 0.354040i 0.884807π-0.884807\pi
0.935230 0.354040i 0.115193π-0.115193\pi
462462 −1.68730 27.3688i −0.0785001 1.27331i
463463 0.731023 0.0339735 0.0169868 0.999856i 0.494593π-0.494593\pi
0.0169868 + 0.999856i 0.494593π0.494593\pi
464464 −11.3818 + 19.7139i −0.528389 + 0.915196i
465465 23.3443 + 40.4335i 1.08256 + 1.87506i
466466 4.14386 + 7.17737i 0.191961 + 0.332485i
467467 20.5833 35.6513i 0.952481 1.64975i 0.212451 0.977172i 0.431855π-0.431855\pi
0.740030 0.672574i 0.234811π-0.234811\pi
468468 2.46229i 0.113819i
469469 21.6640 1.33559i 1.00035 0.0616720i
470470 3.96381i 0.182837i
471471 34.5552 + 19.9505i 1.59222 + 0.919269i
472472 −3.59514 + 2.07565i −0.165480 + 0.0955397i
473473 8.92737 + 15.4627i 0.410481 + 0.710973i
474474 −22.7146 + 39.3429i −1.04332 + 1.80708i
475475 −39.6890 −1.82106
476476 9.40153 6.22931i 0.430919 0.285520i
477477 33.6491i 1.54069i
478478 12.2984 21.3015i 0.562516 0.974306i
479479 −9.59591 16.6206i −0.438448 0.759415i 0.559122 0.829086i 0.311138π-0.311138\pi
−0.997570 + 0.0696707i 0.977805π0.977805\pi
480480 −72.7109 + 41.9797i −3.31879 + 1.91610i
481481 0.648772 1.12371i 0.0295815 0.0512366i
482482 0.728679 0.0331904
483483 −34.9975 + 3.38986i −1.59244 + 0.154244i
484484 20.3833 0.926512
485485 31.4308 54.4397i 1.42720 2.47198i
486486 31.7029 18.3037i 1.43807 0.830271i
487487 −1.56672 2.71364i −0.0709948 0.122967i 0.828343 0.560222i 0.189284π-0.189284\pi
−0.899338 + 0.437255i 0.855951π0.855951\pi
488488 −1.76727 + 3.06101i −0.0800007 + 0.138565i
489489 0.914055i 0.0413350i
490490 −22.4825 + 53.1089i −1.01565 + 2.39921i
491491 35.3438 1.59504 0.797522 0.603290i 0.206144π-0.206144\pi
0.797522 + 0.603290i 0.206144π0.206144\pi
492492 18.7533 32.4817i 0.845464 1.46439i
493493 7.43345 + 12.8751i 0.334786 + 0.579866i
494494 1.52687 0.881539i 0.0686971 0.0396623i
495495 27.3344 + 15.7815i 1.22859 + 0.709326i
496496 11.1092i 0.498816i
497497 −6.80317 3.38781i −0.305164 0.151964i
498498 4.92926i 0.220885i
499499 −8.70475 + 15.0771i −0.389678 + 0.674942i −0.992406 0.123005i 0.960747π-0.960747\pi
0.602728 + 0.797947i 0.294080π0.294080\pi
500500 24.0530 + 41.6611i 1.07568 + 1.86314i
501501 14.3175 + 24.7987i 0.639660 + 1.10792i
502502 21.6727 37.5382i 0.967300 1.67541i
503503 8.82795 0.393619 0.196809 0.980442i 0.436942π-0.436942\pi
0.196809 + 0.980442i 0.436942π0.436942\pi
504504 −12.5253 + 8.29907i −0.557921 + 0.369670i
505505 14.6003i 0.649704i
506506 0.627408 + 17.9257i 0.0278917 + 0.796894i
507507 −31.0972 + 17.9540i −1.38107 + 0.797363i
508508 −18.3607 31.8017i −0.814624 1.41097i
509509 15.3321 + 8.85200i 0.679584 + 0.392358i 0.799698 0.600402i 0.204993π-0.204993\pi
−0.120114 + 0.992760i 0.538326π0.538326\pi
510510 37.8986i 1.67818i
511511 26.0003 1.60293i 1.15018 0.0709094i
512512 26.1474 1.15556
513513 16.2194 + 9.36425i 0.716102 + 0.413442i
514514 −37.9824 + 21.9291i −1.67533 + 0.967253i
515515 −31.4418 54.4588i −1.38549 2.39974i
516516 36.3021 62.8770i 1.59811 2.76801i
517517 0.841916 0.0370274
518518 35.7351 2.20308i 1.57011 0.0967979i
519519 19.6702 0.863427
520520 −0.830363 0.479410i −0.0364138 0.0210235i
521521 3.42606 + 5.93411i 0.150098 + 0.259978i 0.931263 0.364346i 0.118708π-0.118708\pi
−0.781165 + 0.624325i 0.785374π0.785374\pi
522522 −44.7810 77.5629i −1.96001 3.39484i
523523 −9.90492 + 17.1558i −0.433112 + 0.750172i −0.997139 0.0755843i 0.975918π-0.975918\pi
0.564028 + 0.825756i 0.309251π0.309251\pi
524524 4.39213i 0.191871i
525525 −39.9279 60.2609i −1.74260 2.63000i
526526 15.5472i 0.677891i
527527 −6.28332 3.62768i −0.273706 0.158024i
528528 −6.16270 10.6741i −0.268197 0.464531i
529529 22.9437 1.60805i 0.997553 0.0699153i
530530 −51.3116 29.6248i −2.22883 1.28682i
531531 16.0036i 0.694495i
532532 24.4807 + 12.1908i 1.06137 + 0.528538i
533533 −1.08017 −0.0467872
534534 −13.0969 7.56152i −0.566760 0.327219i
535535 21.9958 12.6993i 0.950962 0.549038i
536536 −8.62311 + 4.97856i −0.372462 + 0.215041i
537537 −47.0953 27.1905i −2.03231 1.17336i
538538 34.3282i 1.47999i
539539 −11.2804 4.77529i −0.485880 0.205687i
540540 46.0556i 1.98192i
541541 5.21528 9.03313i 0.224222 0.388365i −0.731863 0.681451i 0.761349π-0.761349\pi
0.956086 + 0.293087i 0.0946825π0.0946825\pi
542542 −18.1291 + 10.4668i −0.778710 + 0.449588i
543543 13.2255 7.63576i 0.567562 0.327682i
544544 6.52360 11.2992i 0.279697 0.484450i
545545 3.21286i 0.137624i
546546 2.87452 + 1.43144i 0.123018 + 0.0612600i
547547 −28.3266 −1.21116 −0.605580 0.795785i 0.707059π-0.707059\pi
−0.605580 + 0.795785i 0.707059π0.707059\pi
548548 −35.9379 20.7487i −1.53519 0.886342i
549549 6.81296 + 11.8004i 0.290770 + 0.503628i
550550 −31.9357 + 18.4381i −1.36174 + 0.786202i
551551 −18.0255 + 31.2210i −0.767911 + 1.33006i
552552 13.6784 8.54873i 0.582191 0.363858i
553553 11.2094 + 16.9177i 0.476673 + 0.719415i
554554 −22.9647 −0.975676
555555 −33.8174 + 58.5734i −1.43547 + 2.48630i
556556 7.96269 4.59726i 0.337693 0.194967i
557557 −21.6038 + 12.4730i −0.915384 + 0.528497i −0.882159 0.470951i 0.843911π-0.843911\pi
−0.0332242 + 0.999448i 0.510578π0.510578\pi
558558 37.8523 + 21.8540i 1.60242 + 0.925156i
559559 −2.09095 −0.0884378
560560 1.59513 + 25.8738i 0.0674067 + 1.09337i
561561 −8.04968 −0.339858
562562 20.6447 + 11.9192i 0.870844 + 0.502782i
563563 −9.04897 15.6733i −0.381368 0.660550i 0.609890 0.792486i 0.291214π-0.291214\pi
−0.991258 + 0.131937i 0.957880π0.957880\pi
564564 −1.71178 2.96488i −0.0720788 0.124844i
565565 −0.977875 0.564576i −0.0411395 0.0237519i
566566 36.8331 1.54821
567567 −0.186251 3.02108i −0.00782180 0.126873i
568568 3.48647 0.146289
569569 12.2131 + 7.05123i 0.511999 + 0.295603i 0.733655 0.679522i 0.237813π-0.237813\pi
−0.221656 + 0.975125i 0.571146π0.571146\pi
570570 −79.5884 + 45.9504i −3.33359 + 1.92465i
571571 −28.6167 + 16.5218i −1.19757 + 0.691418i −0.960013 0.279956i 0.909680π-0.909680\pi
−0.237558 + 0.971373i 0.576347π0.576347\pi
572572 0.460444 0.797512i 0.0192521 0.0333457i
573573 −59.3591 −2.47976
574574 −16.4625 24.8458i −0.687130 1.03704i
575575 25.0609 + 40.0987i 1.04511 + 1.67223i
576576 −27.4071 + 47.4705i −1.14196 + 1.97794i
577577 −8.24985 + 4.76305i −0.343446 + 0.198288i −0.661795 0.749685i 0.730205π-0.730205\pi
0.318349 + 0.947974i 0.396872π0.396872\pi
578578 15.2220 + 26.3653i 0.633153 + 1.09665i
579579 13.0855 + 7.55493i 0.543816 + 0.313972i
580580 88.6535 3.68114
581581 1.97114 + 0.981577i 0.0817766 + 0.0407227i
582582 96.5802i 4.00338i
583583 6.29233 10.8986i 0.260601 0.451375i
584584 −10.3491 + 5.97507i −0.428250 + 0.247250i
585585 −3.20110 + 1.84816i −0.132349 + 0.0764119i
586586 9.52316 16.4946i 0.393398 0.681385i
587587 32.6248i 1.34657i −0.739383 0.673285i 0.764883π-0.764883\pi
0.739383 0.673285i 0.235117π-0.235117\pi
588588 6.11850 + 49.4339i 0.252323 + 2.03862i
589589 17.5936i 0.724932i
590590 −24.4039 14.0896i −1.00469 0.580059i
591591 16.2802 9.39936i 0.669677 0.386638i
592592 13.9371 8.04656i 0.572809 0.330712i
593593 38.1901 + 22.0491i 1.56828 + 0.905447i 0.996370 + 0.0851318i 0.0271311π0.0271311\pi
0.571911 + 0.820316i 0.306202π0.306202\pi
594594 17.4011 0.713977
595595 15.1551 + 7.54685i 0.621298 + 0.309391i
596596 33.4383i 1.36968i
597597 4.54445 + 2.62374i 0.185992 + 0.107383i
598598 −1.85475 0.985999i −0.0758464 0.0403205i
599599 −16.9745 29.4008i −0.693561 1.20128i −0.970663 0.240443i 0.922707π-0.922707\pi
0.277102 0.960841i 0.410626π-0.410626\pi
600600 28.7191 + 16.5810i 1.17245 + 0.676915i
601601 36.3934i 1.48452i 0.670112 + 0.742260i 0.266246π0.266246\pi
−0.670112 + 0.742260i 0.733754π0.733754\pi
602602 −31.8675 48.0958i −1.29882 1.96024i
603603 38.3853i 1.56317i
604604 9.84392 17.0502i 0.400544 0.693762i
605605 15.2994 + 26.4993i 0.622008 + 1.07735i
606606 −11.2159 19.4265i −0.455615 0.789149i
607607 38.8257 + 22.4160i 1.57589 + 0.909839i 0.995424 + 0.0955520i 0.0304616π0.0304616\pi
0.580463 + 0.814287i 0.302872π0.302872\pi
608608 31.6384 1.28310
609609 −65.5377 + 4.04043i −2.65572 + 0.163726i
610610 −23.9926 −0.971432
611611 −0.0492980 + 0.0853867i −0.00199438 + 0.00345437i
612612 9.97252 + 17.2729i 0.403115 + 0.698216i
613613 −6.87254 + 3.96787i −0.277579 + 0.160261i −0.632327 0.774702i 0.717900π-0.717900\pi
0.354748 + 0.934962i 0.384567π0.384567\pi
614614 −32.5106 18.7700i −1.31202 0.757496i
615615 56.3038 2.27039
616616 5.60874 0.345782i 0.225983 0.0139319i
617617 17.5849i 0.707940i −0.935257 0.353970i 0.884831π-0.884831\pi
0.935257 0.353970i 0.115169π-0.115169\pi
618618 −83.6703 48.3071i −3.36571 1.94320i
619619 17.9338 + 31.0622i 0.720820 + 1.24850i 0.960672 + 0.277687i 0.0895677π0.0895677\pi
−0.239852 + 0.970809i 0.577099π0.577099\pi
620620 −37.4684 + 21.6324i −1.50477 + 0.868778i
621621 −0.780498 22.2996i −0.0313203 0.894854i
622622 5.73099i 0.229792i
623623 −5.63177 + 3.73153i −0.225632 + 0.149500i
624624 1.44342 0.0577829
625625 −11.4582 + 19.8462i −0.458329 + 0.793850i
626626 −7.93404 13.7422i −0.317108 0.549247i
627627 −9.75989 16.9046i −0.389773 0.675106i
628628 −18.4875 + 32.0212i −0.737730 + 1.27779i
629629 10.5104i 0.419076i
630630 −91.2980 45.4641i −3.63740 1.81133i
631631 44.9970i 1.79130i −0.444755 0.895652i 0.646709π-0.646709\pi
0.444755 0.895652i 0.353291π-0.353291\pi
632632 −8.06263 4.65496i −0.320714 0.185165i
633633 −34.0091 + 19.6352i −1.35174 + 0.780428i
634634 −0.851575 1.47497i −0.0338204 0.0585786i
635635 27.5625 47.7397i 1.09379 1.89449i
636636 −51.1740 −2.02918
637637 1.14482 0.864433i 0.0453596 0.0342501i
638638 33.4959i 1.32611i
639639 6.72029 11.6399i 0.265850 0.460467i
640640 −17.9604 31.1084i −0.709948 1.22967i
641641 −30.2125 + 17.4432i −1.19332 + 0.688964i −0.959058 0.283209i 0.908601π-0.908601\pi
−0.234263 + 0.972173i 0.575268π0.575268\pi
642642 19.5112 33.7943i 0.770044 1.33375i
643643 −1.84376 −0.0727106 −0.0363553 0.999339i 0.511575π-0.511575\pi
−0.0363553 + 0.999339i 0.511575π0.511575\pi
644644 −3.14127 32.4311i −0.123783 1.27796i
645645 108.991 4.29153
646646 7.14065 12.3680i 0.280945 0.486611i
647647 19.2967 11.1410i 0.758632 0.437997i −0.0701722 0.997535i 0.522355π-0.522355\pi
0.828804 + 0.559538i 0.189022π0.189022\pi
648648 0.694268 + 1.20251i 0.0272734 + 0.0472390i
649649 2.99264 5.18340i 0.117471 0.203466i
650650 4.31853i 0.169387i
651651 26.7128 17.6995i 1.04696 0.693699i
652652 −0.847026 −0.0331721
653653 9.39204 16.2675i 0.367539 0.636596i −0.621641 0.783302i 0.713534π-0.713534\pi
0.989180 + 0.146706i 0.0468672π0.0468672\pi
654654 2.46811 + 4.27490i 0.0965108 + 0.167162i
655655 −5.71000 + 3.29667i −0.223108 + 0.128811i
656656 −11.6022 6.69852i −0.452989 0.261533i
657657 46.0685i 1.79731i
658658 −2.71539 + 0.167405i −0.105857 + 0.00652612i
659659 37.4963i 1.46065i −0.683100 0.730325i 0.739369π-0.739369\pi
0.683100 0.730325i 0.260631π-0.260631\pi
660660 −24.0007 + 41.5705i −0.934227 + 1.61813i
661661 −16.1735 28.0133i −0.629076 1.08959i −0.987737 0.156124i 0.950100π-0.950100\pi
0.358661 0.933468i 0.383233π-0.383233\pi
662662 −12.7586 22.0986i −0.495877 0.858885i
663663 0.471346 0.816394i 0.0183055 0.0317061i
664664 −1.01016 −0.0392020
665665 2.52622 + 40.9765i 0.0979626 + 1.58900i
666666 63.3171i 2.45349i
667667 42.9251 1.50240i 1.66207 0.0581732i
668668 −22.9801 + 13.2676i −0.889128 + 0.513338i
669669 35.9671 + 62.2968i 1.39057 + 2.40853i
670670 −58.5339 33.7946i −2.26136 1.30560i
671671 5.09605i 0.196731i
672672 31.8288 + 48.0373i 1.22782 + 1.85308i
673673 −35.4082 −1.36489 −0.682443 0.730939i 0.739082π-0.739082\pi
−0.682443 + 0.730939i 0.739082π0.739082\pi
674674 31.5695 + 18.2267i 1.21601 + 0.702064i
675675 39.7281 22.9370i 1.52914 0.882847i
676676 −16.6373 28.8167i −0.639898 1.10834i
677677 −21.7250 + 37.6288i −0.834960 + 1.44619i 0.0591026 + 0.998252i 0.481176π0.481176\pi
−0.894063 + 0.447942i 0.852157π0.852157\pi
678678 −1.73483 −0.0666256
679679 −38.6210 19.2323i −1.48214 0.738068i
680680 −7.76664 −0.297837
681681 0.517412 + 0.298728i 0.0198273 + 0.0114473i
682682 −8.17334 14.1566i −0.312974 0.542086i
683683 16.4252 + 28.4493i 0.628494 + 1.08858i 0.987854 + 0.155384i 0.0496616π0.0496616\pi
−0.359360 + 0.933199i 0.617005π0.617005\pi
684684 −24.1825 + 41.8853i −0.924641 + 1.60153i
685685 62.2948i 2.38016i
686686 37.3315 + 13.1585i 1.42532 + 0.502395i
687687 3.61149i 0.137787i
688688 −22.4591 12.9668i −0.856246 0.494354i
689689 0.736889 + 1.27633i 0.0280732 + 0.0486242i
690690 96.6792 + 51.3954i 3.68052 + 1.95659i
691691 −3.00191 1.73316i −0.114198 0.0659323i 0.441813 0.897107i 0.354335π-0.354335\pi
−0.556011 + 0.831175i 0.687669π0.687669\pi
692692 18.2278i 0.692915i
693693 9.65661 19.3918i 0.366824 0.736632i
694694 14.0996 0.535213
695695 11.9534 + 6.90128i 0.453417 + 0.261780i
696696 26.0866 15.0611i 0.988808 0.570889i
697697 −7.57734 + 4.37478i −0.287012 + 0.165707i
698698 67.4864 + 38.9633i 2.55440 + 1.47478i
699699 10.7456i 0.406435i
700700 55.8418 36.9999i 2.11062 1.39847i
701701 36.7209i 1.38693i −0.720491 0.693464i 0.756083π-0.756083\pi
0.720491 0.693464i 0.243917π-0.243917\pi
702702 −1.01892 + 1.76481i −0.0384565 + 0.0666086i
703703 22.0722 12.7434i 0.832468 0.480626i
704704 17.7538 10.2502i 0.669122 0.386318i
705705 2.56967 4.45080i 0.0967793 0.167627i
706706 21.4059i 0.805620i
707707 −10.0018 + 0.616618i −0.376158 + 0.0231903i
708708 −24.3384 −0.914694
709709 12.5304 + 7.23444i 0.470590 + 0.271695i 0.716486 0.697601i 0.245749π-0.245749\pi
−0.245897 + 0.969296i 0.579082π0.579082\pi
710710 11.8331 + 20.4956i 0.444090 + 0.769186i
711711 −31.0820 + 17.9452i −1.16567 + 0.672997i
712712 1.54960 2.68399i 0.0580737 0.100587i
713713 −17.7752 + 11.1092i −0.665687 + 0.416041i
714714 25.9622 1.60058i 0.971611 0.0599003i
715715 1.38241 0.0516992
716716 25.1966 43.6417i 0.941640 1.63097i
717717 27.6187 15.9457i 1.03144 0.595502i
718718 7.00559 4.04468i 0.261446 0.150946i
719719 21.2999 + 12.2975i 0.794354 + 0.458620i 0.841493 0.540268i 0.181677π-0.181677\pi
−0.0471393 + 0.998888i 0.515010π0.515010\pi
720720 −45.8445 −1.70852
721721 −35.9788 + 23.8390i −1.33992 + 0.887811i
722722 −5.97706 −0.222443
723723 0.818204 + 0.472390i 0.0304293 + 0.0175684i
724724 7.07582 + 12.2557i 0.262971 + 0.455478i
725725 44.1521 + 76.4737i 1.63977 + 2.84016i
726726 40.7135 + 23.5059i 1.51102 + 0.872387i
727727 −25.3332 −0.939557 −0.469779 0.882784i 0.655666π-0.655666\pi
−0.469779 + 0.882784i 0.655666π0.655666\pi
728728 −0.293349 + 0.589083i −0.0108722 + 0.0218329i
729729 44.0317 1.63080
730730 −70.2501 40.5589i −2.60007 1.50115i
731731 −14.6680 + 8.46857i −0.542515 + 0.313221i
732732 −17.9462 + 10.3612i −0.663310 + 0.382962i
733733 6.83443 11.8376i 0.252436 0.437231i −0.711760 0.702422i 0.752102π-0.752102\pi
0.964196 + 0.265191i 0.0854351π0.0854351\pi
734734 19.3699 0.714958
735735 −59.6742 + 45.0587i −2.20112 + 1.66202i
736736 −19.9774 31.9649i −0.736378 1.17824i
737737 7.17799 12.4326i 0.264405 0.457963i
738738 45.6478 26.3548i 1.68032 0.970133i
739739 7.37651 + 12.7765i 0.271349 + 0.469990i 0.969208 0.246245i 0.0791969π-0.0791969\pi
−0.697858 + 0.716236i 0.745864π0.745864\pi
740740 −54.2781 31.3375i −1.99530 1.15199i
741741 2.28594 0.0839763
742742 −18.1272 + 36.4019i −0.665472 + 1.33636i
743743 28.7849i 1.05602i 0.849240 + 0.528008i 0.177061π0.177061\pi
−0.849240 + 0.528008i 0.822939π0.822939\pi
744744 −7.35012 + 12.7308i −0.269469 + 0.466733i
745745 −43.4715 + 25.0983i −1.59267 + 0.919529i
746746 41.0068 23.6753i 1.50137 0.866814i
747747 −1.94712 + 3.37252i −0.0712416 + 0.123394i
748748 7.45938i 0.272742i
749749 −9.62854 14.5318i −0.351819 0.530980i
750750 110.952i 4.05138i
751751 4.42625 + 2.55549i 0.161516 + 0.0932513i 0.578579 0.815626i 0.303607π-0.303607\pi
−0.417063 + 0.908877i 0.636941π0.636941\pi
752752 −1.05903 + 0.611431i −0.0386189 + 0.0222966i
753753 48.6708 28.1001i 1.77366 1.02402i
754754 −3.39713 1.96134i −0.123716 0.0714277i
755755 29.5548 1.07561
756756 −31.5501 + 1.94508i −1.14747 + 0.0707419i
757757 23.5243i 0.855004i 0.904014 + 0.427502i 0.140606π0.140606\pi
−0.904014 + 0.427502i 0.859394π0.859394\pi
758758 −37.0800 21.4081i −1.34680 0.777578i
759759 −10.9164 + 20.5347i −0.396241 + 0.745364i
760760 −9.41672 16.3102i −0.341580 0.591635i
761761 7.69396 + 4.44211i 0.278906 + 0.161026i 0.632928 0.774211i 0.281853π-0.281853\pi
−0.354022 + 0.935237i 0.615186π0.615186\pi
762762 84.6940i 3.06814i
763763 2.20095 0.135690i 0.0796798 0.00491230i
764764 55.0062i 1.99005i
765765 −14.9705 + 25.9296i −0.541258 + 0.937486i
766766 −18.0792 31.3141i −0.653229 1.13143i
767767 0.350465 + 0.607024i 0.0126546 + 0.0219184i
768768 8.43333 + 4.86899i 0.304312 + 0.175694i
769769 −5.85712 −0.211213 −0.105607 0.994408i 0.533678π-0.533678\pi
−0.105607 + 0.994408i 0.533678π0.533678\pi
770770 21.0689 + 31.7980i 0.759269 + 1.14592i
771771 −56.8651 −2.04795
772772 −7.00091 + 12.1259i −0.251968 + 0.436422i
773773 20.5386 + 35.5739i 0.738721 + 1.27950i 0.953071 + 0.302746i 0.0979033π0.0979033\pi
−0.214350 + 0.976757i 0.568763π0.568763\pi
774774 88.3637 51.0168i 3.17617 1.83376i
775775 −37.3207 21.5471i −1.34060 0.773996i
776776 19.7924 0.710506
777777 41.5536 + 20.6927i 1.49073 + 0.742345i
778778 56.3284i 2.01947i
779779 −18.3744 10.6085i −0.658331 0.380088i
780780 −2.81070 4.86828i −0.100639 0.174312i
781781 −4.35328 + 2.51337i −0.155773 + 0.0899353i
782782 −17.0044 + 0.595164i −0.608078 + 0.0212830i
783783 41.6691i 1.48913i
784784 17.6574 2.18547i 0.630620 0.0780527i
785785 −55.5057 −1.98108
786786 −5.06499 + 8.77282i −0.180662 + 0.312916i
787787 −14.2477 24.6778i −0.507876 0.879667i −0.999958 0.00911848i 0.997097π-0.997097\pi
0.492082 0.870549i 0.336236π-0.336236\pi
788788 8.71009 + 15.0863i 0.310284 + 0.537428i
789789 −10.0790 + 17.4573i −0.358822 + 0.621497i
790790 63.1961i 2.24841i
791791 −0.345461 + 0.693732i −0.0122832 + 0.0246663i
792792 9.93785i 0.353126i
793793 0.516838 + 0.298397i 0.0183535 + 0.0105964i
794794 29.1390 16.8234i 1.03411 0.597041i
795795 −38.4105 66.5289i −1.36228 2.35954i
796796 −2.43134 + 4.21120i −0.0861764 + 0.149262i
797797 35.2018 1.24691 0.623455 0.781859i 0.285728π-0.285728\pi
0.623455 + 0.781859i 0.285728π0.285728\pi
798798 34.8394 + 52.5810i 1.23330 + 1.86135i
799799 0.798648i 0.0282541i
800800 38.7479 67.1134i 1.36995 2.37282i
801801 −5.97381 10.3469i −0.211074 0.365591i
802802 70.8760 40.9203i 2.50272 1.44495i
803803 8.61475 14.9212i 0.304008 0.526557i
804804 −58.3769 −2.05880
805805 39.8043 28.4261i 1.40292 1.00189i
806806 1.91435 0.0674300
807807 −22.2544 + 38.5457i −0.783390 + 1.35687i
808808 3.98112 2.29850i 0.140055 0.0808611i
809809 −8.24264 14.2767i −0.289796 0.501941i 0.683965 0.729515i 0.260254π-0.260254\pi
−0.973761 + 0.227574i 0.926921π0.926921\pi
810810 −4.71271 + 8.16265i −0.165588 + 0.286806i
811811 3.18946i 0.111997i 0.998431 + 0.0559985i 0.0178342π0.0178342\pi
−0.998431 + 0.0559985i 0.982166π0.982166\pi
812812 −3.74413 60.7316i −0.131393 2.13126i
813813 −27.1418 −0.951905
814814 11.8402 20.5078i 0.414999 0.718799i
815815 −0.635765 1.10118i −0.0222699 0.0385726i
816816 10.1255 5.84599i 0.354465 0.204650i
817817 −35.5686 20.5356i −1.24439 0.718448i
818818 18.1540i 0.634740i
819819 1.40126 + 2.11484i 0.0489641 + 0.0738987i
820820 52.1749i 1.82203i
821821 −0.356735 + 0.617882i −0.0124501 + 0.0215642i −0.872183 0.489179i 0.837296π-0.837296\pi
0.859733 + 0.510743i 0.170630π0.170630\pi
822822 −47.8548 82.8869i −1.66913 2.89101i
823823 −8.49394 14.7119i −0.296080 0.512826i 0.679155 0.733994i 0.262346π-0.262346\pi
−0.975236 + 0.221169i 0.929013π0.929013\pi
824824 9.89969 17.1468i 0.344872 0.597336i
825825 −47.8123 −1.66461
826826 −8.62135 + 17.3128i −0.299975 + 0.602390i
827827 24.4522i 0.850285i 0.905127 + 0.425142i 0.139776π0.139776\pi
−0.905127 + 0.425142i 0.860224π0.860224\pi
828828 57.5872 2.01558i 2.00129 0.0700463i
829829 −3.16909 + 1.82968i −0.110067 + 0.0635473i −0.554023 0.832501i 0.686908π-0.686908\pi
0.443956 + 0.896049i 0.353575π0.353575\pi
830830 −3.42851 5.93836i −0.119005 0.206123i
831831 −25.7861 14.8876i −0.894509 0.516445i
832832 2.40078i 0.0832320i
833833 4.52988 10.7006i 0.156951 0.370755i
834834 21.2062 0.734311
835835 −34.4971 19.9169i −1.19382 0.689254i
836836 15.6650 9.04418i 0.541785 0.312799i
837837 10.1677 + 17.6109i 0.351447 + 0.608723i
838838 10.3347 17.9002i 0.357005 0.618351i
839839 −51.2893 −1.77070 −0.885351 0.464923i 0.846082π-0.846082\pi
−0.885351 + 0.464923i 0.846082π0.846082\pi
840840 15.2908 30.7061i 0.527584 1.05946i
841841 51.2098 1.76586
842842 −36.4982 21.0723i −1.25781 0.726198i
843843 15.4540 + 26.7672i 0.532265 + 0.921911i
844844 −18.1953 31.5152i −0.626307 1.08480i
845845 24.9755 43.2589i 0.859184 1.48815i
846846 4.81126i 0.165414i
847847 17.5071 11.5999i 0.601550 0.398578i
848848 18.2789i 0.627700i
849849 41.3584 + 23.8783i 1.41942 + 0.819500i
850850 −17.4905 30.2944i −0.599919 1.03909i
851851 −26.8120 14.2534i −0.919102 0.488602i
852852 17.7021 + 10.2203i 0.606464 + 0.350142i
853853 37.4884i 1.28358i 0.766881 + 0.641790i 0.221808π0.221808\pi
−0.766881 + 0.641790i 0.778192π0.778192\pi
854854 1.01329 + 16.4360i 0.0346740 + 0.562429i
855855 −72.6041 −2.48301
856856 6.92555 + 3.99847i 0.236710 + 0.136665i
857857 24.2615 14.0074i 0.828756 0.478483i −0.0246704 0.999696i 0.507854π-0.507854\pi
0.853427 + 0.521213i 0.174520π0.174520\pi
858858 1.83938 1.06197i 0.0627953 0.0362549i
859859 27.1045 + 15.6488i 0.924793 + 0.533929i 0.885161 0.465285i 0.154048π-0.154048\pi
0.0396317 + 0.999214i 0.487382π0.487382\pi
860860 100.999i 3.44403i
861861 −2.37790 38.5706i −0.0810385 1.31448i
862862 36.2064i 1.23319i
863863 18.7314 32.4438i 0.637625 1.10440i −0.348328 0.937373i 0.613250π-0.613250\pi
0.985953 0.167025i 0.0534162π-0.0534162\pi
864864 −31.6695 + 18.2844i −1.07742 + 0.622048i
865865 −23.6970 + 13.6815i −0.805724 + 0.465185i
866866 −34.2069 + 59.2481i −1.16240 + 2.01333i
867867 39.4727i 1.34056i
868868 16.4016 + 24.7539i 0.556706 + 0.840203i
869869 13.4229 0.455340
870870 177.076 + 102.235i 6.00345 + 3.46609i
871871 0.840608 + 1.45598i 0.0284829 + 0.0493339i
872872 −0.876065 + 0.505796i −0.0296673 + 0.0171284i
873873 38.1505 66.0787i 1.29120 2.23642i
874874 −21.8670 34.9884i −0.739663 1.18350i
875875 44.3679 + 22.0941i 1.49991 + 0.746917i
876876 −70.0617 −2.36717
877877 −26.9369 + 46.6560i −0.909593 + 1.57546i −0.0949631 + 0.995481i 0.530273π0.530273\pi
−0.814630 + 0.579981i 0.803060π0.803060\pi
878878 48.8348 28.1948i 1.64809 0.951527i
879879 21.3863 12.3474i 0.721342 0.416467i
880880 14.8486 + 8.57285i 0.500547 + 0.288991i
881881 −4.08101 −0.137493 −0.0687464 0.997634i 0.521900π-0.521900\pi
−0.0687464 + 0.997634i 0.521900π0.521900\pi
882882 −27.2891 + 64.4633i −0.918873 + 2.17059i
883883 30.2362 1.01753 0.508764 0.860906i 0.330103π-0.330103\pi
0.508764 + 0.860906i 0.330103π0.330103\pi
884884 0.756526 + 0.436781i 0.0254447 + 0.0146905i
885885 −18.2681 31.6412i −0.614075 1.06361i
886886 1.22709 + 2.12537i 0.0412247 + 0.0714034i
887887 34.5006 + 19.9189i 1.15842 + 0.668812i 0.950924 0.309425i 0.100137π-0.100137\pi
0.207492 + 0.978237i 0.433470π0.433470\pi
888888 −21.2953 −0.714624
889889 −33.8679 16.8654i −1.13589 0.565646i
890890 21.0375 0.705177
891891 −1.73375 1.00098i −0.0580829 0.0335342i
892892 −57.7284 + 33.3295i −1.93289 + 1.11596i
893893 −1.67719 + 0.968327i −0.0561251 + 0.0324038i
894894 −38.5609 + 66.7895i −1.28967 + 2.23377i
895895 75.6487 2.52866
896896 −20.5521 + 13.6175i −0.686598 + 0.454929i
897897 −1.44342 2.30954i −0.0481943 0.0771133i
898898 21.3948 37.0569i 0.713953 1.23660i
899899 −33.8997 + 19.5720i −1.13062 + 0.652764i
900900 59.2333 + 102.595i 1.97444 + 3.41983i
901901 10.3385 + 5.96895i 0.344426 + 0.198855i
902902 −19.7132 −0.656378
903903 −4.60306 74.6639i −0.153180 2.48466i
904904 0.355522i 0.0118245i
905905 −10.6220 + 18.3979i −0.353088 + 0.611566i
906906 39.3244 22.7040i 1.30647 0.754289i
907907 −26.4224 + 15.2550i −0.877340 + 0.506532i −0.869780 0.493439i 0.835740π-0.835740\pi
−0.00755954 + 0.999971i 0.502406π0.502406\pi
908908 −0.276822 + 0.479469i −0.00918665 + 0.0159117i
909909 17.7218i 0.587794i
910910 −4.45861 + 0.274876i −0.147802 + 0.00911204i
911911 6.86165i 0.227337i −0.993519 0.113668i 0.963740π-0.963740\pi
0.993519 0.113668i 0.0362601π-0.0362601\pi
912912 24.5536 + 14.1760i 0.813050 + 0.469415i
913913 1.26131 0.728218i 0.0417433 0.0241005i
914914 −32.1592 + 18.5671i −1.06373 + 0.614146i
915915 −26.9403 15.5540i −0.890619 0.514199i
916916 3.34666 0.110577
917917 2.49952 + 3.77237i 0.0825413 + 0.124575i
918918 16.5069i 0.544807i
919919 22.6047 + 13.0508i 0.745659 + 0.430506i 0.824123 0.566411i 0.191668π-0.191668\pi
−0.0784645 + 0.996917i 0.525002π0.525002\pi
920920 −10.5326 + 19.8127i −0.347249 + 0.653206i
921921 −24.3365 42.1521i −0.801916 1.38896i
922922 28.1398 + 16.2465i 0.926737 + 0.535052i
923923 0.588676i 0.0193765i
924924 29.4913 + 14.6859i 0.970192 + 0.483131i
925925 62.4279i 2.05262i
926926 −0.781193 + 1.35307i −0.0256716 + 0.0444645i
927927 −38.1639 66.1019i −1.25347 2.17107i
928928 −35.1961 60.9614i −1.15537 2.00116i
929929 −19.4884 11.2516i −0.639394 0.369155i 0.144987 0.989434i 0.453686π-0.453686\pi
−0.784381 + 0.620279i 0.787019π0.787019\pi
930930 −99.7857 −3.27210
931931 27.9640 3.46115i 0.916484 0.113434i
932932 −9.95757 −0.326171
933933 −3.71530 + 6.43509i −0.121633 + 0.210675i
934934 43.9919 + 76.1962i 1.43946 + 2.49322i
935935 9.69759 5.59890i 0.317145 0.183104i
936936 −1.00789 0.581906i −0.0329440 0.0190202i
937937 −25.6250 −0.837132 −0.418566 0.908186i 0.637467π-0.637467\pi
−0.418566 + 0.908186i 0.637467π0.637467\pi
938938 −20.6787 + 41.5256i −0.675184 + 1.35586i
939939 20.5740i 0.671407i
940940 4.12441 + 2.38123i 0.134523 + 0.0776671i
941941 22.5938 + 39.1336i 0.736537 + 1.27572i 0.954046 + 0.299661i 0.0968737π0.0968737\pi
−0.217509 + 0.976058i 0.569793π0.569793\pi
942942 −73.8536 + 42.6394i −2.40628 + 1.38927i
943943 0.884202 + 25.2626i 0.0287936 + 0.822663i
944944 8.69348i 0.282949i
945945 −26.2098 39.5569i −0.852604 1.28679i
946946 −38.1602 −1.24070
947947 −1.93187 + 3.34609i −0.0627772 + 0.108733i −0.895706 0.444647i 0.853329π-0.853329\pi
0.832929 + 0.553380i 0.186662π0.186662\pi
948948 −27.2913 47.2699i −0.886380 1.53526i
949949 1.00887 + 1.74741i 0.0327492 + 0.0567232i
950950 42.4129 73.4614i 1.37606 2.38340i
951951 2.20824i 0.0716072i
952952 0.328011 + 5.32050i 0.0106309 + 0.172438i
953953 46.4045i 1.50319i 0.659626 + 0.751594i 0.270715π0.270715\pi
−0.659626 + 0.751594i 0.729285π0.729285\pi
954954 −62.2819 35.9584i −2.01645 1.16420i
955955 71.5109 41.2869i 2.31404 1.33601i
956956 14.7764 + 25.5934i 0.477901 + 0.827749i
957957 −21.7148 + 37.6111i −0.701940 + 1.21580i
958958 41.0180 1.32523
959959 −42.6747 + 2.63092i −1.37804 + 0.0849568i
960960 125.141i 4.03891i
961961 −5.94844 + 10.3030i −0.191885 + 0.332355i
962962 1.38660 + 2.40165i 0.0447056 + 0.0774324i
963963 26.6984 15.4143i 0.860345 0.496720i
964964 −0.437749 + 0.758203i −0.0140989 + 0.0244201i
965965 −21.0191 −0.676630
966966 31.1251 68.4002i 1.00143 2.20074i
967967 −48.6298 −1.56383 −0.781914 0.623386i 0.785757π-0.785757\pi
−0.781914 + 0.623386i 0.785757π0.785757\pi
968968 −4.81713 + 8.34351i −0.154828 + 0.268171i
969969 16.0359 9.25831i 0.515146 0.297420i
970970 67.1758 + 116.352i 2.15688 + 3.73583i
971971 17.8488 30.9150i 0.572795 0.992109i −0.423483 0.905904i 0.639193π-0.639193\pi
0.996277 0.0862053i 0.0274741π-0.0274741\pi
972972 43.9832i 1.41076i
973973 4.22285 8.48005i 0.135378 0.271858i
974974 6.69698 0.214585
975975 2.79963 4.84910i 0.0896598 0.155295i
976976 3.70094 + 6.41022i 0.118464 + 0.205186i
977977 20.4258 11.7928i 0.653479 0.377286i −0.136309 0.990666i 0.543524π-0.543524\pi
0.789788 + 0.613380i 0.210191π0.210191\pi
978978 −1.69185 0.976788i −0.0540993 0.0312342i
979979 4.46837i 0.142810i
980980 −41.7545 55.2981i −1.33380 1.76643i
981981 3.89975i 0.124510i
982982 −37.7695 + 65.4187i −1.20527 + 2.08759i
983983 −5.05628 8.75774i −0.161270 0.279329i 0.774054 0.633119i 0.218226π-0.218226\pi
−0.935325 + 0.353791i 0.884892π0.884892\pi
984984 8.86384 + 15.3526i 0.282569 + 0.489424i
985985 −13.0753 + 22.6471i −0.416615 + 0.721598i
986986 −31.7745 −1.01190
987987 −3.15752 1.57237i −0.100505 0.0500490i
988988 2.11831i 0.0673925i
989989 1.71161 + 48.9025i 0.0544261 + 1.55501i
990990 −58.4207 + 33.7292i −1.85673 + 1.07198i
991991 −17.7089 30.6727i −0.562541 0.974350i −0.997274 0.0737905i 0.976490π-0.976490\pi
0.434732 0.900560i 0.356843π-0.356843\pi
992992 29.7504 + 17.1764i 0.944578 + 0.545352i
993993 33.0847i 1.04991i
994994 13.5406 8.97183i 0.429483 0.284569i
995995 −7.29970 −0.231416
996996 −5.12897 2.96121i −0.162518 0.0938296i
997997 46.7706 27.0030i 1.48124 0.855195i 0.481467 0.876464i 0.340104π-0.340104\pi
0.999774 + 0.0212694i 0.00677078π0.00677078\pi
998998 −18.6043 32.2236i −0.588910 1.02002i
999999 −14.7293 + 25.5119i −0.466014 + 0.807159i
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 161.2.g.a.68.4 yes 28
7.2 even 3 1127.2.c.c.1126.23 28
7.3 odd 6 inner 161.2.g.a.45.3 28
7.5 odd 6 1127.2.c.c.1126.21 28
23.22 odd 2 inner 161.2.g.a.68.3 yes 28
161.45 even 6 inner 161.2.g.a.45.4 yes 28
161.68 even 6 1127.2.c.c.1126.22 28
161.114 odd 6 1127.2.c.c.1126.24 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.2.g.a.45.3 28 7.3 odd 6 inner
161.2.g.a.45.4 yes 28 161.45 even 6 inner
161.2.g.a.68.3 yes 28 23.22 odd 2 inner
161.2.g.a.68.4 yes 28 1.1 even 1 trivial
1127.2.c.c.1126.21 28 7.5 odd 6
1127.2.c.c.1126.22 28 161.68 even 6
1127.2.c.c.1126.23 28 7.2 even 3
1127.2.c.c.1126.24 28 161.114 odd 6