Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(137,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.q (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 873.34 | ||
Character | \(\chi\) | \(=\) | 920.873 |
Dual form | 920.2.q.a.137.34 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.79740 | + | 1.79740i | 1.03773 | + | 1.03773i | 0.999260 | + | 0.0384679i | \(0.0122477\pi\) |
0.0384679 | + | 0.999260i | \(0.487752\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.878232 | + | 2.05638i | 0.392758 | + | 0.919642i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78887 | − | 1.78887i | −0.676128 | − | 0.676128i | 0.282994 | − | 0.959122i | \(-0.408672\pi\) |
−0.959122 | + | 0.282994i | \(0.908672\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.46127i | 1.15376i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.939750i | 0.283345i | 0.989914 | + | 0.141673i | \(0.0452480\pi\) | ||||
−0.989914 | + | 0.141673i | \(0.954752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.75254 | + | 2.75254i | 0.763418 | + | 0.763418i | 0.976939 | − | 0.213520i | \(-0.0684929\pi\) |
−0.213520 | + | 0.976939i | \(0.568493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.11760 | + | 5.27467i | −0.546763 | + | 1.36191i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.360642 | − | 0.360642i | −0.0874686 | − | 0.0874686i | 0.662019 | − | 0.749487i | \(-0.269700\pi\) |
−0.749487 | + | 0.662019i | \(0.769700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0967405 | 0.0221938 | 0.0110969 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110969 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 6.43060i | − | 1.40327i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.60123 | + | 4.52063i | −0.333879 | + | 0.942616i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.45742 | + | 3.61196i | −0.691483 | + | 0.722393i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.829091 | + | 0.829091i | −0.159559 | + | 0.159559i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.97211i | 1.48038i | 0.672396 | + | 0.740191i | \(0.265265\pi\) | ||||
−0.672396 | + | 0.740191i | \(0.734735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56913 | 0.281823 | 0.140912 | − | 0.990022i | \(-0.454997\pi\) | ||||
0.140912 | + | 0.990022i | \(0.454997\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.68910 | + | 1.68910i | −0.294035 | + | 0.294035i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.10755 | − | 5.24963i | 0.356241 | − | 0.887350i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.364907 | − | 0.364907i | −0.0599903 | − | 0.0599903i | 0.676475 | − | 0.736465i | \(-0.263507\pi\) |
−0.736465 | + | 0.676475i | \(0.763507\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.89483i | 1.58444i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.742731 | −0.115995 | −0.0579975 | − | 0.998317i | \(-0.518472\pi\) | ||||
−0.0579975 | + | 0.998317i | \(0.518472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.73328 | − | 4.73328i | 0.721818 | − | 0.721818i | −0.247157 | − | 0.968975i | \(-0.579496\pi\) |
0.968975 | + | 0.247157i | \(0.0794964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.11770 | + | 3.03980i | −1.06104 | + | 0.453147i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.67229 | − | 2.67229i | 0.389793 | − | 0.389793i | −0.484821 | − | 0.874614i | \(-0.661115\pi\) |
0.874614 | + | 0.484821i | \(0.161115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 0.599920i | − | 0.0857029i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.29644i | − | 0.181537i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.26494 | + | 6.26494i | −0.860556 | + | 0.860556i | −0.991403 | − | 0.130846i | \(-0.958231\pi\) |
0.130846 | + | 0.991403i | \(0.458231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.93248 | + | 0.825319i | −0.260576 | + | 0.111286i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.173881 | + | 0.173881i | 0.0230311 | + | 0.0230311i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 14.3575i | − | 1.86919i | −0.355712 | − | 0.934596i | \(-0.615762\pi\) | ||
0.355712 | − | 0.934596i | \(-0.384238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.0607i | − | 1.41618i | −0.706124 | − | 0.708089i | \(-0.749558\pi\) | ||
0.706124 | − | 0.708089i | \(-0.250442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.19175 | − | 6.19175i | 0.780087 | − | 0.780087i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.24291 | + | 8.07766i | −0.402233 | + | 1.00191i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.54924 | − | 2.54924i | −0.311439 | − | 0.311439i | 0.534028 | − | 0.845467i | \(-0.320678\pi\) |
−0.845467 | + | 0.534028i | \(0.820678\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.0034 | + | 5.24732i | −1.32465 | + | 0.631703i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.30693 | −0.985851 | −0.492926 | − | 0.870071i | \(-0.664073\pi\) | ||||
−0.492926 | + | 0.870071i | \(0.664073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.23791 | − | 4.23791i | −0.496010 | − | 0.496010i | 0.414183 | − | 0.910193i | \(-0.364067\pi\) |
−0.910193 | + | 0.414183i | \(0.864067\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.7065 | + | 0.277784i | −1.46722 | + | 0.0320757i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.68109 | − | 1.68109i | 0.191577 | − | 0.191577i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.19554 | 0.359526 | 0.179763 | − | 0.983710i | \(-0.442467\pi\) | ||||
0.179763 | + | 0.983710i | \(0.442467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.40341 | 0.822601 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.25214 | − | 6.25214i | 0.686262 | − | 0.686262i | −0.275142 | − | 0.961404i | \(-0.588725\pi\) |
0.961404 | + | 0.275142i | \(0.0887248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.424891 | − | 1.05835i | 0.0460859 | − | 0.114794i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.3290 | + | 14.3290i | −1.53623 | + | 1.53623i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.8361 | 1.78462 | 0.892309 | − | 0.451425i | \(-0.149084\pi\) | ||||
0.892309 | + | 0.451425i | \(0.149084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.84786i | − | 1.03234i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.82034 | + | 2.82034i | 0.292456 | + | 0.292456i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0849607 | + | 0.198935i | 0.00871678 | + | 0.0204103i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.66643 | + | 6.66643i | 0.676873 | + | 0.676873i | 0.959291 | − | 0.282418i | \(-0.0911366\pi\) |
−0.282418 | + | 0.959291i | \(0.591137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.25273 | −0.326912 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.37689 | 0.634524 | 0.317262 | − | 0.948338i | \(-0.397237\pi\) | ||||
0.317262 | + | 0.948338i | \(0.397237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.118775 | − | 0.118775i | 0.0117032 | − | 0.0117032i | −0.701231 | − | 0.712934i | \(-0.747366\pi\) |
0.712934 | + | 0.701231i | \(0.247366\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.2238 | − | 5.64757i | 1.29051 | − | 0.551146i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.23266 | + | 7.23266i | 0.699208 | + | 0.699208i | 0.964240 | − | 0.265032i | \(-0.0853825\pi\) |
−0.265032 | + | 0.964240i | \(0.585382\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9817 | 1.05185 | 0.525927 | − | 0.850529i | \(-0.323718\pi\) | ||||
0.525927 | + | 0.850529i | \(0.323718\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.31176i | − | 0.124507i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3798 | + | 11.3798i | −1.07052 | + | 1.07052i | −0.0732051 | + | 0.997317i | \(0.523323\pi\) |
−0.997317 | + | 0.0732051i | \(0.976677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7024 | + | 0.677422i | −0.998003 | + | 0.0631700i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.52731 | + | 9.52731i | −0.880800 | + | 0.880800i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.29028i | 0.118280i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1169 | 0.919716 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.33498 | − | 1.33498i | −0.120371 | − | 0.120371i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4640 | − | 3.93762i | −0.935928 | − | 0.352192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0958360 | + | 0.0958360i | −0.00850407 | + | 0.00850407i | −0.711346 | − | 0.702842i | \(-0.751914\pi\) |
0.702842 | + | 0.711346i | \(0.251914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.0152 | 1.49810 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.25882 | 0.372094 | 0.186047 | − | 0.982541i | \(-0.440432\pi\) | ||||
0.186047 | + | 0.982541i | \(0.440432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.173056 | − | 0.173056i | −0.0150058 | − | 0.0150058i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.43306 | − | 0.976793i | −0.209405 | − | 0.0840690i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.57409 | − | 1.57409i | −0.134483 | − | 0.134483i | 0.636661 | − | 0.771144i | \(-0.280315\pi\) |
−0.771144 | + | 0.636661i | \(0.780315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.6617i | − | 1.15877i | −0.815053 | − | 0.579387i | \(-0.803292\pi\) | ||
0.815053 | − | 0.579387i | \(-0.196708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.60632 | 0.808998 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.58670 | + | 2.58670i | −0.216311 | + | 0.216311i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.3937 | + | 7.00136i | −1.36142 | + | 0.581431i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.07829 | − | 1.07829i | 0.0889363 | − | 0.0889363i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.460684 | 0.0377407 | 0.0188704 | − | 0.999822i | \(-0.493993\pi\) | ||||
0.0188704 | + | 0.999822i | \(0.493993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.79803 | 0.227700 | 0.113850 | − | 0.993498i | \(-0.463682\pi\) | ||||
0.113850 | + | 0.993498i | \(0.463682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.24828 | − | 1.24828i | 0.100918 | − | 0.100918i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.37806 | + | 3.22672i | 0.110688 | + | 0.259177i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4704 | + | 16.4704i | 1.31448 | + | 1.31448i | 0.918075 | + | 0.396406i | \(0.129743\pi\) |
0.396406 | + | 0.918075i | \(0.370257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.5212 | −1.78605 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.9512 | − | 5.22241i | 0.863074 | − | 0.411584i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.58729 | − | 7.58729i | −0.594282 | − | 0.594282i | 0.344503 | − | 0.938785i | \(-0.388047\pi\) |
−0.938785 | + | 0.344503i | \(0.888047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.95687 | − | 1.99002i | −0.385892 | − | 0.154923i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4325 | − | 10.4325i | 0.807290 | − | 0.807290i | −0.176933 | − | 0.984223i | \(-0.556618\pi\) |
0.984223 | + | 0.176933i | \(0.0566176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.15300i | 0.165615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.334845i | 0.0256063i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.02168 | + | 7.02168i | 0.533849 | + | 0.533849i | 0.921715 | − | 0.387867i | \(-0.126788\pi\) |
−0.387867 | + | 0.921715i | \(0.626788\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.6462 | − | 0.276465i | 0.955960 | − | 0.0208988i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.8062 | − | 25.8062i | 1.93971 | − | 1.93971i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.58904i | − | 0.343001i | −0.985184 | − | 0.171500i | \(-0.945139\pi\) | ||
0.985184 | − | 0.171500i | \(-0.0548615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.4761i | − | 1.07600i | −0.842944 | − | 0.538001i | \(-0.819180\pi\) | ||
0.842944 | − | 0.538001i | \(-0.180820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.8805 | − | 19.8805i | 1.46961 | − | 1.46961i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.429915 | − | 1.07086i | 0.0316079 | − | 0.0787312i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.338914 | − | 0.338914i | 0.0247838 | − | 0.0247838i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.96626 | 0.215764 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.2791i | 1.25027i | 0.780516 | + | 0.625136i | \(0.214956\pi\) | ||||
−0.780516 | + | 0.625136i | \(0.785044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.77664 | + | 2.77664i | 0.199867 | + | 0.199867i | 0.799943 | − | 0.600076i | \(-0.204863\pi\) |
−0.600076 | + | 0.799943i | \(0.704863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.3476 | + | 8.68996i | −1.45712 | + | 0.622301i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.8758 | + | 13.8758i | −0.988612 | + | 0.988612i | −0.999936 | − | 0.0113241i | \(-0.996395\pi\) |
0.0113241 | + | 0.999936i | \(0.496395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.4300 | −1.80269 | −0.901344 | − | 0.433104i | \(-0.857418\pi\) | ||||
−0.901344 | + | 0.433104i | \(0.857418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.16399i | − | 0.646378i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.2610 | − | 14.2610i | 1.00093 | − | 1.00093i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.652290 | − | 1.52734i | −0.0455579 | − | 0.106674i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.6471 | − | 5.54229i | −1.08755 | − | 0.385216i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0909119i | 0.00628850i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8824 | −1.02455 | −0.512273 | − | 0.858822i | \(-0.671197\pi\) | ||||
−0.512273 | + | 0.858822i | \(0.671197\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.9309 | − | 14.9309i | −1.02305 | − | 1.02305i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.8903 | + | 5.57651i | 0.947314 | + | 0.380315i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.80696 | − | 2.80696i | −0.190549 | − | 0.190549i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 15.2344i | − | 1.02945i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.98537i | − | 0.133550i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.07979 | − | 6.07979i | −0.407133 | − | 0.407133i | 0.473604 | − | 0.880738i | \(-0.342953\pi\) |
−0.880738 | + | 0.473604i | \(0.842953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.5020 | − | 11.9671i | −0.833466 | − | 0.797804i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.0463 | + | 21.0463i | 1.39689 | + | 1.39689i | 0.808783 | + | 0.588107i | \(0.200127\pi\) |
0.588107 | + | 0.808783i | \(0.299873\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.7303 | −1.30382 | −0.651908 | − | 0.758298i | \(-0.726031\pi\) | ||||
−0.651908 | + | 0.758298i | \(0.726031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.04316 | 0.397611 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.55466 | − | 4.55466i | −0.298386 | − | 0.298386i | 0.541995 | − | 0.840381i | \(-0.317669\pi\) |
−0.840381 | + | 0.541995i | \(0.817669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.84213 | + | 3.14835i | 0.511564 | + | 0.205376i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.74365 | + | 5.74365i | 0.373090 | + | 0.373090i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.7095i | − | 1.59832i | −0.601117 | − | 0.799161i | \(-0.705277\pi\) | ||
0.601117 | − | 0.799161i | \(-0.294723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4670i | 0.674239i | 0.941462 | + | 0.337119i | \(0.109453\pi\) | ||||
−0.941462 | + | 0.337119i | \(0.890547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7941 | + | 15.7941i | 1.01319 | + | 1.01319i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.23367 | − | 0.526869i | 0.0788160 | − | 0.0336604i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.266283 | + | 0.266283i | 0.0169432 | + | 0.0169432i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.4752 | 1.42431 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 23.2669i | − | 1.46859i | −0.678829 | − | 0.734297i | \(-0.737512\pi\) | ||
0.678829 | − | 0.734297i | \(-0.262488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.24826 | − | 1.50475i | −0.267086 | − | 0.0946031i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.66597 | − | 1.13857i | 0.166949 | − | 0.0713001i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.11820 | + | 3.11820i | −0.194508 | + | 0.194508i | −0.797641 | − | 0.603133i | \(-0.793919\pi\) |
0.603133 | + | 0.797641i | \(0.293919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.30554i | 0.0811222i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.5936 | −1.70800 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.94773 | − | 2.94773i | 0.181765 | − | 0.181765i | −0.610360 | − | 0.792124i | \(-0.708975\pi\) |
0.792124 | + | 0.610360i | \(0.208975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.3852 | − | 7.38104i | −1.12939 | − | 0.453414i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.2611 | + | 30.2611i | 1.85195 | + | 1.85195i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 22.4439i | − | 1.36843i | −0.729280 | − | 0.684215i | \(-0.760145\pi\) | ||
0.729280 | − | 0.684215i | \(-0.239855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.7051 | −1.19700 | −0.598500 | − | 0.801123i | \(-0.704236\pi\) | ||||
−0.598500 | + | 0.801123i | \(0.704236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.7005 | − | 17.7005i | 1.07128 | − | 1.07128i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.39434 | − | 3.24910i | −0.204686 | − | 0.195928i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9674 | + | 11.9674i | −0.719051 | + | 0.719051i | −0.968411 | − | 0.249360i | \(-0.919780\pi\) |
0.249360 | + | 0.968411i | \(0.419780\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.43117i | 0.325156i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.1566i | − | 0.784859i | −0.919782 | − | 0.392429i | \(-0.871635\pi\) | ||
0.919782 | − | 0.392429i | \(-0.128365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.88725 | − | 8.88725i | 0.528292 | − | 0.528292i | −0.391771 | − | 0.920063i | \(-0.628137\pi\) |
0.920063 | + | 0.391771i | \(0.128137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.204858 | + | 0.510274i | −0.0121347 | + | 0.0302260i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.32865 | + | 1.32865i | 0.0784275 | + | 0.0784275i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.7399i | − | 0.984698i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.9644i | 1.40482i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.5379 | − | 21.5379i | 1.25826 | − | 1.25826i | 0.306336 | − | 0.951923i | \(-0.400897\pi\) |
0.951923 | − | 0.306336i | \(-0.0991032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.5246 | − | 12.6092i | 1.71899 | − | 0.734139i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.779138 | − | 0.779138i | −0.0452102 | − | 0.0452102i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.8507 | + | 8.03577i | −0.974500 | + | 0.464721i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9344 | −0.976083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4618 | + | 11.4618i | 0.658463 | + | 0.658463i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.7450 | − | 9.71386i | 1.30238 | − | 0.556214i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.95084 | + | 4.95084i | −0.282560 | + | 0.282560i | −0.834129 | − | 0.551569i | \(-0.814029\pi\) |
0.551569 | + | 0.834129i | \(0.314029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.426971 | 0.0242896 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.9472 | 1.30121 | 0.650607 | − | 0.759414i | \(-0.274514\pi\) | ||||
0.650607 | + | 0.759414i | \(0.274514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.758211 | + | 0.758211i | −0.0428566 | + | 0.0428566i | −0.728210 | − | 0.685354i | \(-0.759648\pi\) |
0.685354 | + | 0.728210i | \(0.259648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.1704 | + | 7.29481i | 1.02379 | + | 0.411016i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.33215 | + | 1.33215i | −0.0748213 | + | 0.0748213i | −0.743527 | − | 0.668706i | \(-0.766849\pi\) |
0.668706 | + | 0.743527i | \(0.266849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.49178 | −0.419459 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.9999i | 1.45117i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0348887 | − | 0.0348887i | −0.00194126 | − | 0.00194126i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.4588 | + | 0.425400i | −1.07938 | + | 0.0235969i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7385 | + | 19.7385i | 1.09154 | + | 1.09154i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.56072 | −0.527100 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.465793 | 0.0256023 | 0.0128011 | − | 0.999918i | \(-0.495925\pi\) | ||||
0.0128011 | + | 0.999918i | \(0.495925\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.26304 | − | 1.26304i | 0.0692142 | − | 0.0692142i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00339 | − | 7.48103i | 0.164092 | − | 0.408733i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4997 | − | 15.4997i | −0.844323 | − | 0.844323i | 0.145094 | − | 0.989418i | \(-0.453651\pi\) |
−0.989418 | + | 0.145094i | \(0.953651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −40.9081 | −2.22182 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.47459i | 0.0798533i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5952 | + | 13.5952i | −0.734074 | + | 0.734074i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.4540 | − | 18.0188i | −1.10121 | − | 0.970102i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.11658 | − | 4.11658i | 0.220990 | − | 0.220990i | −0.587925 | − | 0.808915i | \(-0.700055\pi\) |
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3428i | 0.821280i | 0.911798 | + | 0.410640i | \(0.134695\pi\) | ||||
−0.911798 | + | 0.410640i | \(0.865305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.56422 | −0.243620 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.359155 | + | 0.359155i | 0.0191159 | + | 0.0191159i | 0.716600 | − | 0.697484i | \(-0.245697\pi\) |
−0.697484 | + | 0.716600i | \(0.745697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.29542 | − | 17.0822i | −0.387200 | − | 0.906630i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.31915 | + | 2.31915i | −0.122742 | + | 0.122742i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.7510 | 0.936862 | 0.468431 | − | 0.883500i | \(-0.344819\pi\) | ||||
0.468431 | + | 0.883500i | \(0.344819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9906 | −0.999507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.1840 | + | 18.1840i | 0.954414 | + | 0.954414i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.99290 | − | 12.4366i | 0.261340 | − | 0.650963i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.58372 | − | 5.58372i | −0.291468 | − | 0.291468i | 0.546192 | − | 0.837660i | \(-0.316077\pi\) |
−0.837660 | + | 0.546192i | \(0.816077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.57079i | − | 0.133830i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.4143 | 1.16369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.41486 | + | 1.41486i | −0.0732588 | + | 0.0732588i | −0.742787 | − | 0.669528i | \(-0.766496\pi\) |
0.669528 | + | 0.742787i | \(0.266496\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.7305 | − | 25.8854i | −0.605759 | − | 1.33672i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.9436 | + | 21.9436i | −1.13015 | + | 1.13015i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.7521 | −1.63099 | −0.815497 | − | 0.578761i | \(-0.803537\pi\) | ||||
−0.815497 | + | 0.578761i | \(0.803537\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.344511 | −0.0176498 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.5180 | + | 12.5180i | −0.639638 | + | 0.639638i | −0.950466 | − | 0.310828i | \(-0.899394\pi\) |
0.310828 | + | 0.950466i | \(0.399394\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.93334 | + | 1.98057i | 0.251426 | + | 0.100939i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.3832 | + | 16.3832i | 0.832803 | + | 0.832803i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.9742 | −1.36765 | −0.683823 | − | 0.729647i | \(-0.739684\pi\) | ||||
−0.683823 | + | 0.729647i | \(0.739684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.20780 | − | 1.05286i | 0.111653 | − | 0.0532453i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.65478 | + | 7.65478i | 0.386133 | + | 0.386133i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.80642 | + | 6.57124i | 0.141207 | + | 0.330635i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5053 | + | 12.5053i | −0.627621 | + | 0.627621i | −0.947469 | − | 0.319848i | \(-0.896368\pi\) |
0.319848 | + | 0.947469i | \(0.396368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.622100i | − | 0.0311439i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 28.3962i | − | 1.41804i | −0.705189 | − | 0.709020i | \(-0.749138\pi\) | ||
0.705189 | − | 0.709020i | \(-0.250862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.31909 | + | 4.31909i | 0.215149 | + | 0.215149i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.50191 | + | 15.2242i | 0.323083 | + | 0.756498i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.342921 | − | 0.342921i | 0.0169980 | − | 0.0169980i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.4636i | − | 0.517392i | −0.965959 | − | 0.258696i | \(-0.916707\pi\) | ||
0.965959 | − | 0.258696i | \(-0.0832928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.65852i | − | 0.279114i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.6837 | + | 25.6837i | −1.26381 | + | 1.26381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3476 | + | 7.36596i | 0.900650 | + | 0.361581i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.5556 | − | 24.5556i | 1.20249 | − | 1.20249i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.01808 | 0.196296 | 0.0981480 | − | 0.995172i | \(-0.468708\pi\) | ||||
0.0981480 | + | 0.995172i | \(0.468708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.50020i | − | 0.414274i | −0.978312 | − | 0.207137i | \(-0.933585\pi\) | ||
0.978312 | − | 0.207137i | \(-0.0664146\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.24951 | + | 9.24951i | 0.449727 | + | 0.449727i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.54952 | − | 0.0557365i | 0.123670 | − | 0.00270362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.7861 | + | 19.7861i | −0.957516 | + | 0.957516i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.29866 | −0.448944 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.40012i | 0.115610i | 0.998328 | + | 0.0578048i | \(0.0184101\pi\) | ||||
−0.998328 | + | 0.0578048i | \(0.981590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4482 | − | 13.4482i | 0.646281 | − | 0.646281i | −0.305811 | − | 0.952092i | \(-0.598928\pi\) |
0.952092 | + | 0.305811i | \(0.0989277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −42.0502 | − | 16.8818i | −2.01615 | − | 0.809418i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.154904 | + | 0.437328i | −0.00741005 | + | 0.0209202i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.8506i | 1.23378i | 0.787049 | + | 0.616891i | \(0.211608\pi\) | ||||
−0.787049 | + | 0.616891i | \(0.788392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.07649 | 0.0988804 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.8114 | + | 16.8114i | 0.798735 | + | 0.798735i | 0.982896 | − | 0.184161i | \(-0.0589568\pi\) |
−0.184161 | + | 0.982896i | \(0.558957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.7860 | + | 34.6214i | 0.700922 | + | 1.64121i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.828032 | + | 0.828032i | 0.0391646 | + | 0.0391646i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1684i | 1.56532i | 0.622452 | + | 0.782658i | \(0.286136\pi\) | ||||
−0.622452 | + | 0.782658i | \(0.713864\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.697981i | − | 0.0328666i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.02916 | + | 5.02916i | 0.236291 | + | 0.236291i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.2510 | − | 8.64871i | 0.949380 | − | 0.405458i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.09465 | + | 8.09465i | 0.378652 | + | 0.378652i | 0.870616 | − | 0.491964i | \(-0.163721\pi\) |
−0.491964 | + | 0.870616i | \(0.663721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.598011 | 0.0279127 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.29745 | 0.339876 | 0.169938 | − | 0.985455i | \(-0.445643\pi\) | ||||
0.169938 | + | 0.985455i | \(0.445643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9813 | − | 24.9813i | −1.16098 | − | 1.16098i | −0.984261 | − | 0.176720i | \(-0.943451\pi\) |
−0.176720 | − | 0.984261i | \(-0.556549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.32279 | + | 8.27662i | −0.154090 | + | 0.383819i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.603738 | + | 0.603738i | 0.0279377 | + | 0.0279377i | 0.720938 | − | 0.693000i | \(-0.243711\pi\) |
−0.693000 | + | 0.720938i | \(0.743711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.12049i | 0.421145i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 59.2077i | 2.72815i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.44810 | + | 4.44810i | 0.204524 | + | 0.204524i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.334472 | + | 0.349423i | −0.0153466 | + | 0.0160326i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6847 | − | 21.6847i | −0.992873 | − | 0.992873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.4344 | 0.796598 | 0.398299 | − | 0.917256i | \(-0.369601\pi\) | ||||
0.398299 | + | 0.917256i | \(0.369601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 2.00884i | − | 0.0915954i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.0704 | + | 10.2969i | 1.32275 | + | 0.468524i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.85405 | + | 19.5634i | −0.356634 | + | 0.888328i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3954 | − | 16.3954i | 0.742947 | − | 0.742947i | −0.230197 | − | 0.973144i | \(-0.573937\pi\) |
0.973144 | + | 0.230197i | \(0.0739370\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 27.2747i | − | 1.23341i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2651 | −1.45610 | −0.728051 | − | 0.685522i | \(-0.759574\pi\) | ||||
−0.728051 | + | 0.685522i | \(0.759574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.87508 | − | 2.87508i | 0.129487 | − | 0.129487i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.85665 | − | 6.68886i | −0.128397 | − | 0.300642i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.8600 | + | 14.8600i | 0.666561 | + | 0.666561i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.4458i | 1.72107i | 0.509391 | + | 0.860535i | \(0.329871\pi\) | ||||
−0.509391 | + | 0.860535i | \(0.670129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.5026 | 1.67549 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.5636 | + | 25.5636i | −1.13982 | + | 1.13982i | −0.151344 | + | 0.988481i | \(0.548360\pi\) |
−0.988481 | + | 0.151344i | \(0.951640\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.60039 | + | 13.1133i | 0.249214 | + | 0.583535i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.86980 | + | 3.86980i | −0.171864 | + | 0.171864i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.7856i | 1.85211i | 0.377384 | + | 0.926057i | \(0.376824\pi\) | ||||
−0.377384 | + | 0.926057i | \(0.623176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1621i | 0.670732i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0802067 | + | 0.0802067i | −0.00354121 | + | 0.00354121i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.348559 | + | 0.139935i | 0.0153593 | + | 0.00616626i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.51128 | + | 2.51128i | 0.110446 | + | 0.110446i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.2415i | 1.10798i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.1834i | − | 0.796630i | −0.917249 | − | 0.398315i | \(-0.869595\pi\) | ||
0.917249 | − | 0.398315i | \(-0.130405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.4301 | + | 16.4301i | −0.718439 | + | 0.718439i | −0.968286 | − | 0.249846i | \(-0.919620\pi\) |
0.249846 | + | 0.968286i | \(0.419620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23.2271 | + | 22.2333i | 1.01371 | + | 0.970339i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.565893 | − | 0.565893i | −0.0246507 | − | 0.0246507i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8721 | − | 14.4771i | −0.777049 | − | 0.629440i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 49.6953 | 2.15659 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.04440 | − | 2.04440i | −0.0885528 | − | 0.0885528i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.52116 | + | 21.2251i | −0.368402 | + | 0.917640i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.24832 | − | 8.24832i | 0.355941 | − | 0.355941i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.563775 | 0.0242835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.2384 | 1.47202 | 0.736012 | − | 0.676968i | \(-0.236707\pi\) | ||||
0.736012 | + | 0.676968i | \(0.236707\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.0193 | − | 26.0193i | 1.11660 | − | 1.11660i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.64447 | + | 22.5825i | 0.413124 | + | 0.967330i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.3746 | + | 14.3746i | −0.614616 | + | 0.614616i | −0.944145 | − | 0.329530i | \(-0.893110\pi\) |
0.329530 | + | 0.944145i | \(0.393110\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 38.2841 | 1.63393 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.771226i | 0.0328553i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.71639 | − | 5.71639i | −0.243085 | − | 0.243085i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.69749 | − | 1.15203i | 0.114502 | − | 0.0489011i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8272 | + | 14.8272i | 0.628248 | + | 0.628248i | 0.947627 | − | 0.319379i | \(-0.103474\pi\) |
−0.319379 | + | 0.947627i | \(0.603474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.0571 | 1.10210 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.21832 | 0.0514377 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.4159 | + | 26.4159i | −1.11330 | + | 1.11330i | −0.120596 | + | 0.992702i | \(0.538481\pi\) |
−0.992702 | + | 0.120596i | \(0.961519\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.3953 | − | 13.4071i | −1.40495 | − | 0.564042i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.2437 | − | 13.2437i | −0.556183 | − | 0.556183i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.60059 | 0.318633 | 0.159317 | − | 0.987228i | \(-0.449071\pi\) | ||||
0.159317 | + | 0.987228i | \(0.449071\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.8517i | − | 0.872616i | −0.899797 | − | 0.436308i | \(-0.856286\pi\) | ||
0.899797 | − | 0.436308i | \(-0.143714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.0574 | + | 31.0574i | −1.29744 | + | 1.29744i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.7922 | − | 21.4133i | −0.450067 | − | 0.892995i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.6561 | − | 18.6561i | 0.776663 | − | 0.776663i | −0.202598 | − | 0.979262i | \(-0.564939\pi\) |
0.979262 | + | 0.202598i | \(0.0649386\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.98143i | 0.414814i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3685 | −0.928001 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.88748 | − | 5.88748i | −0.243834 | − | 0.243834i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.9590 | − | 11.2246i | −1.15596 | − | 0.464080i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.2734 | + | 17.2734i | −0.712950 | + | 0.712950i | −0.967151 | − | 0.254201i | \(-0.918187\pi\) |
0.254201 | + | 0.967151i | \(0.418187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.151798 | 0.00625473 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −49.8807 | −2.05182 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.17002 | + | 7.17002i | 0.294438 | + | 0.294438i | 0.838830 | − | 0.544393i | \(-0.183240\pi\) |
−0.544393 | + | 0.838830i | \(0.683240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.65331 | + | 1.13317i | −0.108775 | + | 0.0464553i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −45.7079 | − | 45.7079i | −1.87070 | − | 1.87070i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.9740i | − | 1.51072i | −0.655311 | − | 0.755359i | \(-0.727462\pi\) | ||
0.655311 | − | 0.755359i | \(-0.272538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7821 | −0.725348 | −0.362674 | − | 0.931916i | \(-0.618136\pi\) | ||||
−0.362674 | + | 0.931916i | \(0.618136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.82361 | − | 8.82361i | 0.359325 | − | 0.359325i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.88496 | + | 20.8042i | 0.361225 | + | 0.845809i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.3666 | + | 25.3666i | −1.02960 | + | 1.02960i | −0.0300509 | + | 0.999548i | \(0.509567\pi\) |
−0.999548 | + | 0.0300509i | \(0.990433\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51.2655 | 2.07738 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.7112 | 0.595150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0720 | − | 13.0720i | 0.527975 | − | 0.527975i | −0.391993 | − | 0.919968i | \(-0.628214\pi\) |
0.919968 | + | 0.391993i | \(0.128214\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.57281 | − | 3.91766i | 0.0634218 | − | 0.157975i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.31615 | − | 8.31615i | −0.334795 | − | 0.334795i | 0.519609 | − | 0.854404i | \(-0.326078\pi\) |
−0.854404 | + | 0.519609i | \(0.826078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.2423 | −0.411673 | −0.205836 | − | 0.978586i | \(-0.565991\pi\) | ||||
−0.205836 | + | 0.978586i | \(0.565991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.42045 | − | 5.07557i | −0.0971291 | − | 0.203676i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.1174 | − | 30.1174i | −1.20663 | − | 1.20663i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.09256 | − | 24.9761i | −0.0437023 | − | 0.999045i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.163405 | + | 0.163405i | −0.00652576 | + | 0.00652576i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.263202i | 0.0104945i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 32.8600i | − | 1.30814i | −0.756435 | − | 0.654068i | \(-0.773061\pi\) | ||
0.756435 | − | 0.654068i | \(-0.226939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.7496 | − | 26.7496i | −1.06320 | − | 1.06320i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.281242 | − | 0.112909i | −0.0111607 | − | 0.00448066i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.65131 | − | 1.65131i | 0.0654272 | − | 0.0654272i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 28.7526i | − | 1.13743i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9918i | 1.02662i | 0.858204 | + | 0.513308i | \(0.171580\pi\) | ||||
−0.858204 | + | 0.513308i | \(0.828420\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.7155 | − | 20.7155i | 0.816940 | − | 0.816940i | −0.168723 | − | 0.985663i | \(-0.553964\pi\) |
0.985663 | + | 0.168723i | \(0.0539644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.9433 | + | 34.9897i | 0.588391 | + | 1.37772i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.48231 | + | 1.48231i | −0.0582757 | + | 0.0582757i | −0.735644 | − | 0.677368i | \(-0.763120\pi\) |
0.677368 | + | 0.735644i | \(0.263120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4925 | 0.529626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 10.0904i | − | 0.395475i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.7750 | − | 25.7750i | −1.00865 | − | 1.00865i | −0.999962 | − | 0.00869217i | \(-0.997233\pi\) |
−0.00869217 | − | 0.999962i | \(-0.502767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.74023 | + | 8.75775i | 0.146143 | + | 0.342194i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6686 | − | 14.6686i | 0.572275 | − | 0.572275i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.6005 | 1.34785 | 0.673923 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673923 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 27.6795i | − | 1.07661i | −0.842750 | − | 0.538305i | \(-0.819065\pi\) | ||
0.842750 | − | 0.538305i | \(-0.180935\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.56850 | − | 3.56850i | 0.138589 | − | 0.138589i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.203886 | − | 0.507852i | 0.00790634 | − | 0.0196937i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0389 | − | 12.7652i | −1.39543 | − | 0.494269i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 21.8556i | − | 0.844987i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.3943 | 0.401267 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.8217 | + | 28.8217i | 1.11099 | + | 1.11099i | 0.993016 | + | 0.117977i | \(0.0376410\pi\) |
0.117977 | + | 0.993016i | \(0.462359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.128134 | − | 5.86116i | −0.00493189 | − | 0.225596i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0623 | − | 15.0623i | −0.578890 | − | 0.578890i | 0.355707 | − | 0.934597i | \(-0.384240\pi\) |
−0.934597 | + | 0.355707i | \(0.884240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 23.8507i | − | 0.915305i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 75.6570i | 2.89918i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.2791 | − | 21.2791i | −0.814220 | − | 0.814220i | 0.171043 | − | 0.985264i | \(-0.445286\pi\) |
−0.985264 | + | 0.171043i | \(0.945286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.85451 | − | 4.61934i | 0.0708572 | − | 0.176496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.4632 | − | 35.4632i | −1.35301 | − | 1.35301i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.4891 | −1.31393 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.3837 | −1.15585 | −0.577925 | − | 0.816090i | \(-0.696137\pi\) | ||||
−0.577925 | + | 0.816090i | \(0.696137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.81870 | + | 5.81870i | 0.221034 | + | 0.221034i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.0938 | − | 11.9982i | 1.06566 | − | 0.455117i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.267860 | + | 0.267860i | 0.0101459 | + | 0.0101459i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 16.3731i | − | 0.619287i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 49.3304i | − | 1.86318i | −0.363506 | − | 0.931592i | \(-0.618420\pi\) | ||
0.363506 | − | 0.931592i | \(-0.381580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0353013 | − | 0.0353013i | −0.00133141 | − | 0.00133141i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.43658 | + | 19.7543i | 0.317740 | + | 0.743989i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4074 | − | 11.4074i | −0.429019 | − | 0.429019i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7528 | 0.704274 | 0.352137 | − | 0.935948i | \(-0.385455\pi\) | ||||
0.352137 | + | 0.935948i | \(0.385455\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.0606i | 0.414806i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.51253 | + | 7.09343i | −0.0940950 | + | 0.265651i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.59097 | − | 3.04752i | −0.283886 | − | 0.113971i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.4127 | − | 44.4127i | 1.65862 | − | 1.65862i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.2558i | 0.680828i | 0.940276 | + | 0.340414i | \(0.110567\pi\) | ||||
−0.940276 | + | 0.340414i | \(0.889433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.424945 | −0.0158258 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.8134 | + | 18.8134i | −0.699676 | + | 0.699676i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.7950 | − | 27.5629i | −1.06942 | − | 1.02366i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5725 | + | 16.5725i | 0.614638 | + | 0.614638i | 0.944151 | − | 0.329513i | \(-0.106884\pi\) |
−0.329513 | + | 0.944151i | \(0.606884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.5664i | 1.28024i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.41404 | −0.126273 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.29943 | + | 2.29943i | −0.0849315 | + | 0.0849315i | −0.748296 | − | 0.663365i | \(-0.769128\pi\) |
0.663365 | + | 0.748296i | \(0.269128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.16438 | + | 1.27039i | 0.116720 | + | 0.0468591i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.39565 | − | 2.39565i | 0.0882448 | − | 0.0882448i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.44271i | − | 0.0898567i | −0.998990 | − | 0.0449284i | \(-0.985694\pi\) | ||
0.998990 | − | 0.0449284i | \(-0.0143060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.957231i | 0.0351648i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.8272 | + | 35.8272i | −1.31437 | + | 1.31437i | −0.396216 | + | 0.918157i | \(0.629677\pi\) |
−0.918157 | + | 0.396216i | \(0.870323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.404588 | + | 0.947343i | 0.0148229 | + | 0.0347079i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.6404 | + | 21.6404i | 0.791780 | + | 0.791780i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 25.8765i | − | 0.945507i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1199i | 0.880147i | 0.897962 | + | 0.440073i | \(0.145048\pi\) | ||||
−0.897962 | + | 0.440073i | \(0.854952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 41.8198 | − | 41.8198i | 1.52400 | − | 1.52400i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.45732 | + | 5.75381i | 0.0894309 | + | 0.209403i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.9249 | − | 31.9249i | −1.16033 | − | 1.16033i | −0.984403 | − | 0.175926i | \(-0.943708\pi\) |
−0.175926 | − | 0.984403i | \(-0.556292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.93116 | − | 10.3404i | −0.178990 | − | 0.375334i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.7758 | 1.51437 | 0.757186 | − | 0.653199i | \(-0.226574\pi\) | ||||
0.757186 | + | 0.653199i | \(0.226574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.6448 | − | 19.6448i | −0.711188 | − | 0.711188i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.66323 | + | 1.47066i | 0.132444 | + | 0.0531719i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.5197 | − | 39.5197i | 1.42697 | − | 1.42697i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.5466 | −1.13760 | −0.568800 | − | 0.822476i | \(-0.692592\pi\) | ||||
−0.568800 | + | 0.822476i | \(0.692592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2093 | −0.403693 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.3692 | + | 25.3692i | −0.912465 | + | 0.912465i | −0.996466 | − | 0.0840007i | \(-0.973230\pi\) |
0.0840007 | + | 0.996466i | \(0.473230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.42512 | + | 5.66762i | −0.194876 | + | 0.203587i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.34657 | + | 2.34657i | −0.0841827 | + | 0.0841827i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0718522 | −0.00257437 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 7.80643i | − | 0.279336i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.60960 | − | 6.60960i | −0.236208 | − | 0.236208i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.4046 | + | 48.3343i | −0.692580 | + | 1.72513i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.98641 | + | 4.98641i | 0.177746 | + | 0.177746i | 0.790373 | − | 0.612626i | \(-0.209887\pi\) |
−0.612626 | + | 0.790373i | \(0.709887\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5965 | 0.377245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.7139 | 1.44762 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.4451 | − | 30.4451i | 1.08114 | − | 1.08114i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.7788 | − | 46.3122i | −0.701483 | − | 1.64252i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.771307 | + | 0.771307i | 0.0273211 | + | 0.0273211i | 0.720635 | − | 0.693314i | \(-0.243850\pi\) |
−0.693314 | + | 0.720635i | \(0.743850\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.92748 | −0.0681893 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 58.2742i | 2.05902i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.98258 | − | 3.98258i | 0.140542 | − | 0.140542i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.3569 | + | 17.9333i | 0.717488 | + | 0.632066i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.3407 | − | 40.3407i | 1.42006 | − | 1.42006i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.1320i | 1.09454i | 0.836955 | + | 0.547272i | \(0.184334\pi\) | ||||
−0.836955 | + | 0.547272i | \(0.815666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0746 | 1.12629 | 0.563146 | − | 0.826357i | \(-0.309591\pi\) | ||||
0.563146 | + | 0.826357i | \(0.309591\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −35.4179 | − | 35.4179i | −1.24216 | − | 1.24216i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.93896 | − | 22.2658i | 0.313118 | − | 0.779936i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.457900 | − | 0.457900i | 0.0160199 | − | 0.0160199i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.0861 | 1.19107 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.3373 | −1.44268 | −0.721340 | − | 0.692581i | \(-0.756474\pi\) | ||||
−0.721340 | + | 0.692581i | \(0.756474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.7246 | + | 11.7246i | 0.408695 | + | 0.408695i | 0.881283 | − | 0.472589i | \(-0.156680\pi\) |
−0.472589 | + | 0.881283i | \(0.656680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.261047 | − | 11.9409i | −0.00908850 | − | 0.415729i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.7516 | + | 14.7516i | 0.512963 | + | 0.512963i | 0.915433 | − | 0.402470i | \(-0.131848\pi\) |
−0.402470 | + | 0.915433i | \(0.631848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.9157i | 0.379117i | 0.981869 | + | 0.189558i | \(0.0607056\pi\) | ||||
−0.981869 | + | 0.189558i | \(0.939294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.0203 | −1.49236 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.216357 | + | 0.216357i | −0.00749631 | + | 0.00749631i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.6153 | + | 12.2910i | 1.05949 | + | 0.425349i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.30095 | + | 1.30095i | −0.0449673 | + | 0.0449673i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.812978 | 0.0280671 | 0.0140336 | − | 0.999902i | \(-0.495533\pi\) | ||||
0.0140336 | + | 0.999902i | \(0.495533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.5545 | −1.19153 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.6477 | − | 23.6477i | 0.814470 | − | 0.814470i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.42739 | + | 1.89084i | −0.152307 | + | 0.0650467i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0977 | − | 18.0977i | −0.621845 | − | 0.621845i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.9478 | 1.09645 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.23391 | − | 1.06531i | 0.0765773 | − | 0.0365183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.1821 | + | 11.1821i | 0.382866 | + | 0.382866i | 0.872134 | − | 0.489267i | \(-0.162736\pi\) |
−0.489267 | + | 0.872134i | \(0.662736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.688570 | + | 0.294072i | −0.0235486 | + | 0.0100571i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0181 | + | 18.0181i | −0.615487 | + | 0.615487i | −0.944370 | − | 0.328884i | \(-0.893328\pi\) |
0.328884 | + | 0.944370i | \(0.393328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.153928i | − | 0.00525197i | −0.999997 | − | 0.00262598i | \(-0.999164\pi\) | ||
0.999997 | − | 0.00262598i | \(-0.000835878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.77621i | 0.162773i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8948 | + | 25.8948i | 0.881469 | + | 0.881469i | 0.993684 | − | 0.112215i | \(-0.0357945\pi\) |
−0.112215 | + | 0.993684i | \(0.535795\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.27260 | + | 20.6059i | −0.281277 | + | 0.700623i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.0882 | − | 30.0882i | 1.02185 | − | 1.02185i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00300i | 0.101870i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.0338i | − | 0.475517i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.0743 | + | 23.0743i | −0.780948 | + | 0.780948i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.6748 | + | 25.7626i | 0.394680 | + | 0.870933i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4985 | − | 21.4985i | 0.725954 | − | 0.725954i | −0.243857 | − | 0.969811i | \(-0.578413\pi\) |
0.969811 | + | 0.243857i | \(0.0784128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 77.4245 | 2.61146 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 0.629018i | − | 0.0211922i | −0.999944 | − | 0.0105961i | \(-0.996627\pi\) | ||
0.999944 | − | 0.0105961i | \(-0.00337290\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.22919 | + | 5.22919i | 0.175976 | + | 0.175976i | 0.789599 | − | 0.613623i | \(-0.210288\pi\) |
−0.613623 | + | 0.789599i | \(0.710288\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 75.7312 | + | 30.4035i | 2.54568 | + | 1.02200i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.8883 | + | 11.8883i | −0.399171 | + | 0.399171i | −0.877941 | − | 0.478770i | \(-0.841083\pi\) |
0.478770 | + | 0.877941i | \(0.341083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.342875 | 0.0114997 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.95735i | 0.233080i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.258518 | − | 0.258518i | 0.00865099 | − | 0.00865099i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.43681 | − | 4.03024i | 0.315438 | − | 0.134716i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.7308 | − | 15.8439i | −1.49352 | − | 0.529012i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5092i | 0.417206i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.51881 | 0.150543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.4378 | − | 30.4378i | −1.01291 | − | 1.01291i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.7684 | − | 12.7134i | 0.989536 | − | 0.422608i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.72698 | − | 5.72698i | −0.190161 | − | 0.190161i | 0.605605 | − | 0.795766i | \(-0.292931\pi\) |
−0.795766 | + | 0.605605i | \(0.792931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.0722i | 0.732087i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 31.0071i | − | 1.02731i | −0.857997 | − | 0.513655i | \(-0.828291\pi\) | ||
0.857997 | − | 0.513655i | \(-0.171709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.87545 | + | 5.87545i | 0.194449 | + | 0.194449i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 58.3415 | + | 23.4222i | 1.92871 | + | 0.774313i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.61845 | − | 7.61845i | −0.251583 | − | 0.251583i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.62320 | −0.152505 | −0.0762527 | − | 0.997089i | \(-0.524296\pi\) | ||||
−0.0762527 | + | 0.997089i | \(0.524296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7973 | −0.586440 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.8652 | − | 22.8652i | −0.752617 | − | 0.752617i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.57966 | − | 0.0563955i | 0.0848188 | − | 0.00185427i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.411112 | + | 0.411112i | 0.0135027 | + | 0.0135027i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 39.1876i | − | 1.28570i | −0.765990 | − | 0.642852i | \(-0.777751\pi\) | ||
0.765990 | − | 0.642852i | \(-0.222249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.0580366i | − | 0.00190207i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41.2452 | + | 41.2452i | 1.35031 | + | 1.35031i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.994581 | + | 0.399291i | 0.0325263 | + | 0.0130582i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3368 | − | 23.3368i | −0.762378 | − | 0.762378i | 0.214373 | − | 0.976752i | \(-0.431229\pi\) |
−0.976752 | + | 0.214373i | \(0.931229\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.72561 | −0.0889471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 43.2393i | − | 1.40956i | −0.709425 | − | 0.704781i | \(-0.751045\pi\) | ||
0.709425 | − | 0.704781i | \(-0.248955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.18928 | − | 3.35761i | 0.0387284 | − | 0.109339i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.60507 | + | 6.09977i | 0.0847429 | + | 0.198426i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7242 | − | 23.7242i | 0.770932 | − | 0.770932i | −0.207338 | − | 0.978269i | \(-0.566480\pi\) |
0.978269 | + | 0.207338i | \(0.0664799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 23.3301i | − | 0.757327i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.78882 | −0.155288 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.9642 | + | 34.9642i | −1.13260 | + | 1.13260i | −0.142859 | + | 0.989743i | \(0.545629\pi\) |
−0.989743 | + | 0.142859i | \(0.954371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.5324 | + | 15.1751i | −1.14980 | + | 0.491054i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.4657 | − | 13.4657i | −0.435285 | − | 0.435285i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.63166i | 0.181856i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5378 | −0.920576 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.0342 | + | 25.0342i | −0.806716 | + | 0.806716i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.27129 | + | 8.14836i | −0.105307 | + | 0.262305i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.13933 | + | 3.13933i | −0.100954 | + | 0.100954i | −0.755780 | − | 0.654826i | \(-0.772742\pi\) |
0.654826 | + | 0.755780i | \(0.272742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.125418i | − | 0.00402900i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.3061i | 1.77486i | 0.460945 | + | 0.887429i | \(0.347511\pi\) | ||||
−0.460945 | + | 0.887429i | \(0.652489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.4390 | + | 24.4390i | −0.783479 | + | 0.783479i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.7398 | − | 34.2105i | −1.14459 | − | 1.09561i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.9868 | + | 36.9868i | 1.18331 | + | 1.18331i | 0.978881 | + | 0.204433i | \(0.0655351\pi\) |
0.204433 | + | 0.978881i | \(0.434465\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.8217i | 0.505663i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.0106i | 1.21359i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.1670 | + | 38.1670i | −1.21734 | + | 1.21734i | −0.248777 | + | 0.968561i | \(0.580029\pi\) |
−0.968561 | + | 0.248777i | \(0.919971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.7202 | − | 16.3478i | −1.29745 | − | 0.520884i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.1844 | − | 17.1844i | −0.546986 | − | 0.546986i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.8183 | + | 28.9764i | 0.439397 | + | 0.921397i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3418 | 0.709711 | 0.354856 | − | 0.934921i | \(-0.384530\pi\) | ||||
0.354856 | + | 0.934921i | \(0.384530\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.837215 | + | 0.837215i | 0.0265682 | + | 0.0265682i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.3335 | − | 52.2939i | −0.708019 | − | 1.65783i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1162 | − | 43.1162i | 1.36550 | − | 1.36550i | 0.498766 | − | 0.866737i | \(-0.333787\pi\) |
0.866737 | − | 0.498766i | \(-0.166213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.605081 | 0.0191439 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 920.2.q.a.873.34 | yes | 72 | |
5.2 | odd | 4 | inner | 920.2.q.a.137.33 | ✓ | 72 | |
23.22 | odd | 2 | inner | 920.2.q.a.873.33 | yes | 72 | |
115.22 | even | 4 | inner | 920.2.q.a.137.34 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.q.a.137.33 | ✓ | 72 | 5.2 | odd | 4 | inner | |
920.2.q.a.137.34 | yes | 72 | 115.22 | even | 4 | inner | |
920.2.q.a.873.33 | yes | 72 | 23.22 | odd | 2 | inner | |
920.2.q.a.873.34 | yes | 72 | 1.1 | even | 1 | trivial |