Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), not 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 16x^{14} + 174x^{12} + 1012x^{10} + 4243x^{8} + 9708x^{6} + 15858x^{4} + 12150x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(0.733987 + 1.27130i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.449 |
Dual form | 2736.2.dc.c.1889.1 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.12320 | + | 1.80318i | −1.39674 | + | 0.806407i | −0.994049 | − | 0.108930i | \(-0.965258\pi\) |
−0.402689 | + | 0.915337i | \(0.631924\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.25512 | 1.23032 | 0.615159 | − | 0.788403i | \(-0.289092\pi\) | ||||
0.615159 | + | 0.788403i | \(0.289092\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41128i | 0.727029i | 0.931589 | + | 0.363514i | \(0.118423\pi\) | ||||
−0.931589 | + | 0.363514i | \(0.881577\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.29789 | − | 1.90404i | −0.914671 | − | 0.528086i | −0.0327401 | − | 0.999464i | \(-0.510423\pi\) |
−0.881931 | + | 0.471378i | \(0.843757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.21143 | − | 3.00882i | 1.26396 | − | 0.729747i | 0.290120 | − | 0.956990i | \(-0.406305\pi\) |
0.973838 | + | 0.227244i | \(0.0729714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.75219 | − | 3.99122i | 0.401980 | − | 0.915649i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.58600 | + | 0.915680i | 0.330705 | + | 0.190932i | 0.656154 | − | 0.754627i | \(-0.272182\pi\) |
−0.325449 | + | 0.945559i | \(0.605516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00293 | − | 6.93327i | 0.800586 | − | 1.38665i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.46797 | + | 2.54261i | −0.272596 | + | 0.472150i | −0.969526 | − | 0.244989i | \(-0.921216\pi\) |
0.696930 | + | 0.717139i | \(0.254549\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.11969i | − | 0.201103i | −0.994932 | − | 0.100551i | \(-0.967939\pi\) | ||
0.994932 | − | 0.100551i | \(-0.0320606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.1664 | + | 5.86957i | −1.71843 | + | 0.992138i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.5658i | − | 1.73701i | −0.495683 | − | 0.868503i | \(-0.665082\pi\) | ||
0.495683 | − | 0.868503i | \(-0.334918\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.433003 | + | 0.749984i | 0.0676238 | + | 0.117128i | 0.897855 | − | 0.440292i | \(-0.145125\pi\) |
−0.830231 | + | 0.557419i | \(0.811792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.875369 | + | 1.51618i | 0.133493 | + | 0.231216i | 0.925021 | − | 0.379917i | \(-0.124047\pi\) |
−0.791528 | + | 0.611133i | \(0.790714\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.51672 | + | 3.18508i | 0.804696 | + | 0.464591i | 0.845110 | − | 0.534592i | \(-0.179535\pi\) |
−0.0404148 | + | 0.999183i | \(0.512868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.59579 | 0.513684 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.08823 | + | 3.61692i | −0.286841 | + | 0.496822i | −0.973054 | − | 0.230578i | \(-0.925938\pi\) |
0.686213 | + | 0.727400i | \(0.259272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.34798 | − | 7.53092i | −0.586281 | − | 1.01547i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.55621 | + | 6.15953i | 0.462979 | + | 0.801902i | 0.999108 | − | 0.0422336i | \(-0.0134474\pi\) |
−0.536129 | + | 0.844136i | \(0.680114\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.59286 | + | 6.22302i | −0.460019 | + | 0.796776i | −0.998961 | − | 0.0455667i | \(-0.985491\pi\) |
0.538943 | + | 0.842342i | \(0.318824\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.7333 | 1.70341 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5936 | + | 7.84825i | 1.66072 | + | 0.958816i | 0.972373 | + | 0.233433i | \(0.0749960\pi\) |
0.688345 | + | 0.725383i | \(0.258337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.502227 | + | 0.869883i | 0.0596034 | + | 0.103236i | 0.894287 | − | 0.447493i | \(-0.147683\pi\) |
−0.834684 | + | 0.550729i | \(0.814350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.05594 | + | 12.2212i | 0.825835 | + | 1.43039i | 0.901279 | + | 0.433239i | \(0.142629\pi\) |
−0.0754440 | + | 0.997150i | \(0.524037\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.84900i | 0.894477i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.03032 | − | 1.17221i | 0.228429 | − | 0.131883i | −0.381418 | − | 0.924403i | \(-0.624564\pi\) |
0.609847 | + | 0.792519i | \(0.291231\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.8931i | − | 1.85426i | −0.374743 | − | 0.927129i | \(-0.622269\pi\) | ||
0.374743 | − | 0.927129i | \(-0.377731\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8509 | + | 18.7943i | −1.17695 | + | 2.03853i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.62097 | − | 4.53966i | 0.277823 | − | 0.481203i | −0.693021 | − | 0.720918i | \(-0.743721\pi\) |
0.970843 | + | 0.239715i | \(0.0770539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.7350 | − | 6.19787i | −1.12534 | − | 0.649714i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.72445 | + | 15.6249i | 0.176925 | + | 1.60308i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.737257 | + | 0.425655i | −0.0748571 | + | 0.0432188i | −0.536961 | − | 0.843607i | \(-0.680428\pi\) |
0.462104 | + | 0.886826i | \(0.347095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.87118 | − | 2.23503i | −0.385197 | − | 0.222393i | 0.294880 | − | 0.955534i | \(-0.404720\pi\) |
−0.680077 | + | 0.733141i | \(0.738054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.34778i | 0.723998i | 0.932178 | + | 0.361999i | \(0.117906\pi\) | ||||
−0.932178 | + | 0.361999i | \(0.882094\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.41841 | 0.910512 | 0.455256 | − | 0.890361i | \(-0.349548\pi\) | ||||
0.455256 | + | 0.890361i | \(0.349548\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8524 | − | 8.57501i | 1.42260 | − | 0.821337i | 0.426077 | − | 0.904687i | \(-0.359895\pi\) |
0.996520 | + | 0.0833495i | \(0.0265618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.69989 | −0.253984 | −0.126992 | − | 0.991904i | \(-0.540532\pi\) | ||||
−0.126992 | + | 0.991904i | \(0.540532\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.60455 | −0.615877 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.9638 | − | 9.79407i | 1.55507 | − | 0.897821i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.18572 | 0.471429 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8402i | 0.969578i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.65025 | + | 4.41687i | 0.678850 | + | 0.391934i | 0.799422 | − | 0.600770i | \(-0.205139\pi\) |
−0.120572 | + | 0.992705i | \(0.538473\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.3246 | + | 8.27029i | −1.25154 | + | 0.722579i | −0.971416 | − | 0.237384i | \(-0.923710\pi\) |
−0.280127 | + | 0.959963i | \(0.590377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.70358 | − | 12.9919i | 0.494563 | − | 1.12654i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.66978 | − | 1.54140i | −0.228095 | − | 0.131691i | 0.381598 | − | 0.924328i | \(-0.375374\pi\) |
−0.609693 | + | 0.792638i | \(0.708707\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.27050 | + | 7.39673i | −0.362219 | + | 0.627382i | −0.988326 | − | 0.152355i | \(-0.951314\pi\) |
0.626106 | + | 0.779738i | \(0.284648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.59118 | − | 7.95215i | 0.383933 | − | 0.664992i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.5881i | − | 0.879294i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.747978 | + | 0.431845i | −0.0612767 | + | 0.0353781i | −0.530325 | − | 0.847794i | \(-0.677930\pi\) |
0.469049 | + | 0.883172i | \(0.344597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.75435i | − | 0.142767i | −0.997449 | − | 0.0713835i | \(-0.977259\pi\) | ||
0.997449 | − | 0.0713835i | \(-0.0227414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.01901 | + | 3.49702i | 0.162171 | + | 0.280888i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.41445 | + | 12.8422i | 0.591737 | + | 1.02492i | 0.993998 | + | 0.109394i | \(0.0348910\pi\) |
−0.402261 | + | 0.915525i | \(0.631776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.16263 | + | 2.98064i | 0.406872 | + | 0.234908i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.63532 | 0.519718 | 0.259859 | − | 0.965647i | \(-0.416324\pi\) | ||||
0.259859 | + | 0.965647i | \(0.416324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.59118 | + | 7.95215i | −0.355276 | + | 0.615356i | −0.987165 | − | 0.159703i | \(-0.948946\pi\) |
0.631889 | + | 0.775059i | \(0.282280\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.750738 | + | 1.30032i | 0.0577491 | + | 0.100024i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.18235 | + | 15.9043i | 0.698121 | + | 1.20918i | 0.969117 | + | 0.246601i | \(0.0793138\pi\) |
−0.270996 | + | 0.962581i | \(0.587353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0300 | − | 22.5686i | 0.984975 | − | 1.70603i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.6796 | 1.69515 | 0.847577 | − | 0.530672i | \(-0.178061\pi\) | ||||
0.847577 | + | 0.530672i | \(0.178061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.16348 | − | 2.40379i | −0.309469 | − | 0.178672i | 0.337220 | − | 0.941426i | \(-0.390513\pi\) |
−0.646689 | + | 0.762754i | \(0.723847\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.0521 | + | 32.9991i | 1.40074 | + | 2.42614i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.25512 | + | 12.5662i | 0.530547 | + | 0.918934i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.26376i | 0.308515i | 0.988031 | + | 0.154257i | \(0.0492985\pi\) | ||||
−0.988031 | + | 0.154257i | \(0.950702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4675 | − | 7.19809i | 0.897427 | − | 0.518130i | 0.0210626 | − | 0.999778i | \(-0.493295\pi\) |
0.876365 | + | 0.481648i | \(0.159962\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.14399i | − | 0.508988i | −0.967074 | − | 0.254494i | \(-0.918091\pi\) | ||
0.967074 | − | 0.254494i | \(-0.0819089\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.92983 | + | 5.07462i | −0.207690 | + | 0.359730i | −0.950987 | − | 0.309232i | \(-0.899928\pi\) |
0.743296 | + | 0.668962i | \(0.233261\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.77843 | + | 8.27648i | −0.335380 | + | 0.580895i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.70471 | − | 1.56157i | −0.188905 | − | 0.109065i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.62395 | + | 4.22502i | 0.665703 | + | 0.292251i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9872 | − | 10.9623i | 1.30714 | − | 0.754675i | 0.325519 | − | 0.945536i | \(-0.394461\pi\) |
0.981617 | + | 0.190860i | \(0.0611277\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.46791 | − | 3.15690i | −0.372908 | − | 0.215299i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.64473i | − | 0.247420i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.9157 | −1.54148 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.87215 | − | 4.54499i | 0.527158 | − | 0.304355i | −0.212700 | − | 0.977117i | \(-0.568226\pi\) |
0.739858 | + | 0.672763i | \(0.234892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.58898 | 0.570071 | 0.285035 | − | 0.958517i | \(-0.407995\pi\) | ||||
0.285035 | + | 0.958517i | \(0.407995\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2361 | −1.07291 | −0.536454 | − | 0.843929i | \(-0.680237\pi\) | ||||
−0.536454 | + | 0.843929i | \(0.680237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.27065 | + | 4.19771i | −0.476316 | + | 0.275001i | −0.718880 | − | 0.695134i | \(-0.755345\pi\) |
0.242564 | + | 0.970135i | \(0.422012\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.9731 | −1.49860 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.75382i | 0.307499i | 0.988110 | + | 0.153750i | \(0.0491349\pi\) | ||||
−0.988110 | + | 0.153750i | \(0.950865\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.80668 | + | 2.77514i | 0.309625 | + | 0.178762i | 0.646759 | − | 0.762695i | \(-0.276124\pi\) |
−0.337133 | + | 0.941457i | \(0.609457\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2304 | + | 6.48386i | −0.717482 | + | 0.414239i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3780 | + | 9.82638i | −0.851220 | + | 0.625238i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.48174 | + | 2.58754i | 0.282885 | + | 0.163324i | 0.634729 | − | 0.772735i | \(-0.281112\pi\) |
−0.351844 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.20796 | + | 3.82430i | −0.138813 | + | 0.240432i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9047 | − | 18.8875i | 0.680215 | − | 1.17817i | −0.294700 | − | 0.955590i | \(-0.595220\pi\) |
0.974915 | − | 0.222577i | \(-0.0714469\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 34.3929i | − | 2.13707i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.2691 | + | 9.97032i | −1.06486 | + | 0.614797i | −0.926772 | − | 0.375624i | \(-0.877429\pi\) |
−0.138087 | + | 0.990420i | \(0.544095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.0618i | − | 0.925241i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2408 | − | 22.9337i | −0.807305 | − | 1.39829i | −0.914724 | − | 0.404079i | \(-0.867592\pi\) |
0.107419 | − | 0.994214i | \(-0.465741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.92030 | + | 11.9863i | 0.420378 | + | 0.728117i | 0.995976 | − | 0.0896161i | \(-0.0285640\pi\) |
−0.575598 | + | 0.817733i | \(0.695231\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.7181 | + | 9.65219i | 1.00814 | + | 0.582049i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.98475 | 0.479757 | 0.239879 | − | 0.970803i | \(-0.422892\pi\) | ||||
0.239879 | + | 0.970803i | \(0.422892\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.23116 | + | 15.9888i | −0.550685 | + | 0.953814i | 0.447541 | + | 0.894264i | \(0.352300\pi\) |
−0.998225 | + | 0.0595503i | \(0.981033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.30990 | + | 4.00086i | 0.137309 | + | 0.237827i | 0.926477 | − | 0.376351i | \(-0.122821\pi\) |
−0.789168 | + | 0.614177i | \(0.789488\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.40948 | + | 2.44129i | 0.0831988 | + | 0.144105i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.60602 | − | 16.6381i | 0.565060 | − | 0.978713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.727559 | −0.0425045 | −0.0212522 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212522 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.2135 | − | 12.8250i | −1.29332 | − | 0.746699i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.48698 | − | 6.03963i | −0.201657 | − | 0.349281i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.84943 | + | 4.93536i | 0.164238 | + | 0.284469i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 25.9143i | − | 1.48385i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3269 | − | 9.42632i | 0.931824 | − | 0.537989i | 0.0444359 | − | 0.999012i | \(-0.485851\pi\) |
0.887388 | + | 0.461024i | \(0.152518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.9565i | − | 0.791401i | −0.918380 | − | 0.395700i | \(-0.870502\pi\) | ||
0.918380 | − | 0.395700i | \(-0.129498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.03222 | + | 1.78786i | −0.0583447 | + | 0.101056i | −0.893722 | − | 0.448620i | \(-0.851916\pi\) |
0.835378 | + | 0.549676i | \(0.185249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.96013 | − | 13.7873i | 0.447085 | − | 0.774375i | −0.551109 | − | 0.834433i | \(-0.685795\pi\) |
0.998195 | + | 0.0600583i | \(0.0191287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.13094 | − | 3.53970i | −0.343267 | − | 0.198185i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.87745 | − | 26.0720i | −0.160106 | − | 1.45068i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.4025 | + | 15.2435i | −1.46455 | + | 0.845556i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.9576 | + | 10.3678i | 0.990032 | + | 0.571595i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.6561i | 1.35522i | 0.735420 | + | 0.677612i | \(0.236985\pi\) | ||||
−0.735420 | + | 0.677612i | \(0.763015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −56.6073 | −3.09279 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.6046 | + | 9.00930i | −0.850035 | + | 0.490768i | −0.860663 | − | 0.509175i | \(-0.829950\pi\) |
0.0106275 | + | 0.999944i | \(0.496617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.69989 | 0.146207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0811 | −0.598324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.8051 | + | 15.4760i | −1.43898 | + | 0.830793i | −0.997779 | − | 0.0666174i | \(-0.978779\pi\) |
−0.441197 | + | 0.897410i | \(0.645446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.3181 | 1.24819 | 0.624094 | − | 0.781349i | \(-0.285468\pi\) | ||||
0.624094 | + | 0.781349i | \(0.285468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.5917i | − | 0.563738i | −0.959453 | − | 0.281869i | \(-0.909046\pi\) | ||
0.959453 | − | 0.281869i | \(-0.0909544\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.13711 | − | 1.81121i | −0.166501 | − | 0.0961293i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.67800 | + | 5.01024i | −0.458007 | + | 0.264431i | −0.711206 | − | 0.702984i | \(-0.751851\pi\) |
0.253199 | + | 0.967414i | \(0.418517\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8597 | − | 13.9867i | −0.676824 | − | 0.736144i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −44.0743 | − | 25.4463i | −2.30695 | − | 1.33192i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.6806 | − | 18.4993i | 0.557521 | − | 0.965655i | −0.440181 | − | 0.897909i | \(-0.645086\pi\) |
0.997703 | − | 0.0677462i | \(-0.0215808\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.79744 | + | 11.7735i | −0.352905 | + | 0.611250i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.27182i | 0.117631i | 0.998269 | + | 0.0588153i | \(0.0187323\pi\) | ||||
−0.998269 | + | 0.0588153i | \(0.981268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.68245 | − | 5.59017i | 0.498672 | − | 0.287908i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.1937i | − | 0.831814i | −0.909407 | − | 0.415907i | \(-0.863464\pi\) | ||
0.909407 | − | 0.415907i | \(-0.136536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.8160 | − | 32.5903i | −0.961453 | − | 1.66528i | −0.718858 | − | 0.695157i | \(-0.755335\pi\) |
−0.242595 | − | 0.970128i | \(-0.577999\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.1532 | − | 24.5140i | −0.721313 | − | 1.24935i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.15532 | − | 1.24438i | −0.109279 | − | 0.0630924i | 0.444364 | − | 0.895846i | \(-0.353430\pi\) |
−0.553643 | + | 0.832754i | \(0.686763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0205 | 0.557329 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.22740 | + | 7.32207i | −0.212703 | + | 0.368413i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.14294 | + | 15.8360i | 0.458871 | + | 0.794788i | 0.998902 | − | 0.0468572i | \(-0.0149206\pi\) |
−0.540030 | + | 0.841646i | \(0.681587\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.14886 | + | 3.72193i | 0.107309 | + | 0.185864i | 0.914679 | − | 0.404181i | \(-0.132443\pi\) |
−0.807370 | + | 0.590045i | \(0.799110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.13194 | + | 3.69262i | −0.106199 | + | 0.183943i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4771 | 1.26285 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0826 | − | 9.28527i | −0.795231 | − | 0.459127i | 0.0465697 | − | 0.998915i | \(-0.485171\pi\) |
−0.841801 | + | 0.539788i | \(0.818504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.5759 | + | 20.0500i | 0.569611 | + | 0.986595i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.4613 | + | 52.7605i | 1.49529 | + | 2.58991i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.6142i | − | 1.00707i | −0.863976 | − | 0.503534i | \(-0.832033\pi\) | ||
0.863976 | − | 0.503534i | \(-0.167967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.45259 | − | 2.57071i | 0.217006 | − | 0.125289i | −0.387557 | − | 0.921846i | \(-0.626681\pi\) |
0.604563 | + | 0.796557i | \(0.293348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 48.1764i | − | 2.33690i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.6952 | + | 20.2567i | −0.565970 | + | 0.980288i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.83621 | + | 4.91246i | −0.136615 | + | 0.236625i | −0.926213 | − | 0.377000i | \(-0.876956\pi\) |
0.789598 | + | 0.613624i | \(0.210289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8444 | − | 15.4986i | −1.29006 | − | 0.744817i | −0.311396 | − | 0.950280i | \(-0.600797\pi\) |
−0.978665 | + | 0.205463i | \(0.934130\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.43366 | − | 4.72564i | 0.307764 | − | 0.226058i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.2376 | + | 15.7257i | −1.29998 | + | 0.750545i | −0.980401 | − | 0.197014i | \(-0.936876\pi\) |
−0.319581 | + | 0.947559i | \(0.603542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.3895 | + | 16.9681i | 1.39634 | + | 0.806177i | 0.994007 | − | 0.109317i | \(-0.0348663\pi\) |
0.402332 | + | 0.915494i | \(0.368200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.9044i | 0.896153i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.7937 | 1.64201 | 0.821007 | − | 0.570918i | \(-0.193413\pi\) | ||||
0.821007 | + | 0.570918i | \(0.193413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.80842 | + | 1.04409i | −0.0851553 | + | 0.0491644i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 44.7036 | 2.09574 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.0849 | −0.752421 | −0.376210 | − | 0.926534i | \(-0.622773\pi\) | ||||
−0.376210 | + | 0.926534i | \(0.622773\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0278 | + | 10.4084i | −0.839639 | + | 0.484766i | −0.857141 | − | 0.515081i | \(-0.827762\pi\) |
0.0175025 | + | 0.999847i | \(0.494428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.27622 | −0.291681 | −0.145840 | − | 0.989308i | \(-0.546589\pi\) | ||||
−0.145840 | + | 0.989308i | \(0.546589\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 27.3684i | − | 1.26646i | −0.773964 | − | 0.633229i | \(-0.781729\pi\) | ||
0.773964 | − | 0.633229i | \(-0.218271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44.2486 | + | 25.5470i | 2.04321 | + | 1.17965i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.65595 | + | 2.11076i | −0.168101 | + | 0.0970529i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.6583 | − | 28.1250i | −0.947869 | − | 1.29046i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.44232 | − | 1.41007i | −0.111592 | − | 0.0644279i | 0.443165 | − | 0.896440i | \(-0.353856\pi\) |
−0.554757 | + | 0.832012i | \(0.687189\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.1177 | + | 34.8449i | −0.917289 | + | 1.58879i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.53507 | − | 2.65882i | 0.0697039 | − | 0.120731i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.78930i | − | 0.126395i | −0.998001 | − | 0.0631976i | \(-0.979870\pi\) | ||
0.998001 | − | 0.0631976i | \(-0.0201298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2780 | − | 5.93398i | 0.463838 | − | 0.267797i | −0.249819 | − | 0.968293i | \(-0.580371\pi\) |
0.713656 | + | 0.700496i | \(0.247038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.6675i | 0.795704i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.63481 | + | 2.83157i | 0.0733312 | + | 0.127013i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.396132 | − | 0.686120i | −0.0177333 | − | 0.0307150i | 0.857023 | − | 0.515279i | \(-0.172312\pi\) |
−0.874756 | + | 0.484564i | \(0.838978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8589 | + | 8.00145i | 0.617938 | + | 0.356767i | 0.776066 | − | 0.630652i | \(-0.217212\pi\) |
−0.158128 | + | 0.987419i | \(0.550546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.1206 | 0.717359 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.75277 | + | 9.96410i | −0.254987 | + | 0.441651i | −0.964892 | − | 0.262647i | \(-0.915405\pi\) |
0.709905 | + | 0.704298i | \(0.248738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.9679 | + | 39.7816i | 1.01604 | + | 1.75983i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2494 | − | 22.9486i | −0.583838 | − | 1.01124i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.68012 | + | 13.3024i | −0.337771 | + | 0.585037i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.3968 | −0.762169 | −0.381084 | − | 0.924540i | \(-0.624449\pi\) | ||||
−0.381084 | + | 0.924540i | \(0.624449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.1876 | + | 10.5006i | 0.795289 | + | 0.459161i | 0.841821 | − | 0.539756i | \(-0.181484\pi\) |
−0.0465320 | + | 0.998917i | \(0.514817\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.36895 | − | 5.83520i | −0.146754 | − | 0.254185i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.82306 | − | 17.0140i | −0.427090 | − | 0.739741i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.29782i | − | 0.142845i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.4156 | + | 16.9831i | −1.27175 | + | 0.734244i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.67046i | 0.373463i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.1857 | + | 31.4985i | −0.781862 | + | 1.35423i | 0.148993 | + | 0.988838i | \(0.452397\pi\) |
−0.930856 | + | 0.365387i | \(0.880937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.9246 | + | 53.5630i | −1.32466 | + | 2.29439i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.3308 | − | 18.6662i | −1.38237 | − | 0.798109i | −0.389927 | − | 0.920846i | \(-0.627500\pi\) |
−0.992439 | + | 0.122736i | \(0.960833\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.57593 | + | 10.3141i | 0.322746 | + | 0.439397i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.60893 | − | 3.81567i | 0.281040 | − | 0.162259i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.04479 | − | 3.48996i | −0.256126 | − | 0.147874i | 0.366440 | − | 0.930442i | \(-0.380576\pi\) |
−0.622566 | + | 0.782567i | \(0.713910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.66695i | − | 0.281982i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3463 | 0.646768 | 0.323384 | − | 0.946268i | \(-0.395179\pi\) | ||||
0.323384 | + | 0.946268i | \(0.395179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.43231 | − | 4.86839i | 0.354750 | − | 0.204815i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.5078 | 0.859732 | 0.429866 | − | 0.902893i | \(-0.358561\pi\) | ||||
0.429866 | + | 0.902893i | \(0.358561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.8357 | 1.79262 | 0.896308 | − | 0.443432i | \(-0.146239\pi\) | ||||
0.896308 | + | 0.443432i | \(0.146239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.6973 | − | 7.33080i | 0.529515 | − | 0.305715i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.56592 | 0.0651903 | 0.0325951 | − | 0.999469i | \(-0.489623\pi\) | ||||
0.0325951 | + | 0.999469i | \(0.489623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 54.9890i | − | 2.28133i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.72142 | − | 5.03531i | −0.361204 | − | 0.208541i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0867 | + | 6.97825i | −0.498871 | + | 0.288023i | −0.728247 | − | 0.685315i | \(-0.759665\pi\) |
0.229376 | + | 0.973338i | \(0.426331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.46893 | − | 1.96191i | −0.184139 | − | 0.0808392i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.7031 | + | 14.8397i | 1.05550 | + | 0.609393i | 0.924184 | − | 0.381948i | \(-0.124747\pi\) |
0.131315 | + | 0.991341i | \(0.458080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.3210 | + | 61.1777i | −1.44802 | + | 2.50804i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.56765 | + | 9.64345i | −0.227488 | + | 0.394021i | −0.957063 | − | 0.289880i | \(-0.906385\pi\) |
0.729575 | + | 0.683901i | \(0.239718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 42.1221i | − | 1.71820i | −0.511809 | − | 0.859099i | \(-0.671025\pi\) | ||
0.511809 | − | 0.859099i | \(-0.328975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.1961 | + | 9.35080i | −0.658463 | + | 0.380164i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.0336i | − | 1.09726i | −0.836066 | − | 0.548629i | \(-0.815150\pi\) | ||
0.836066 | − | 0.548629i | \(-0.184850\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1290 | − | 21.0081i | −0.490688 | − | 0.849897i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4631 | + | 18.1226i | 0.422600 | + | 0.731964i | 0.996193 | − | 0.0871761i | \(-0.0277843\pi\) |
−0.573593 | + | 0.819140i | \(0.694451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7102 | + | 10.8023i | 0.753244 | + | 0.434886i | 0.826865 | − | 0.562401i | \(-0.190122\pi\) |
−0.0736207 | + | 0.997286i | \(0.523455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.24636 | −0.331449 | −0.165725 | − | 0.986172i | \(-0.552996\pi\) | ||||
−0.165725 | + | 0.986172i | \(0.552996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.53158 | − | 14.7771i | 0.341811 | − | 0.592033i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.467776 | + | 0.810213i | 0.0187111 | + | 0.0324085i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.7906 | − | 55.0630i | −1.26757 | − | 2.19550i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.72187 | + | 15.1067i | −0.347212 | + | 0.601389i | −0.985753 | − | 0.168199i | \(-0.946205\pi\) |
0.638541 | + | 0.769588i | \(0.279538\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.8577 | −1.26423 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.8585 | − | 6.84653i | −0.469852 | − | 0.271269i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5620 | − | 21.7581i | −0.496170 | − | 0.859392i | 0.503820 | − | 0.863809i | \(-0.331928\pi\) |
−0.999990 | + | 0.00441635i | \(0.998594\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.48464 | − | 2.57147i | −0.0585485 | − | 0.101409i | 0.835266 | − | 0.549847i | \(-0.185314\pi\) |
−0.893814 | + | 0.448438i | \(0.851981\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0704751i | 0.00277066i | 0.999999 | + | 0.00138533i | \(0.000440965\pi\) | ||||
−0.999999 | + | 0.00138533i | \(0.999559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.8524 | + | 8.57501i | −0.583006 | + | 0.336599i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19.9759i | − | 0.781717i | −0.920451 | − | 0.390858i | \(-0.872178\pi\) | ||
0.920451 | − | 0.390858i | \(-0.127822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.8257 | − | 51.6596i | 1.16539 | − | 2.01851i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.3916 | − | 31.8552i | 0.716435 | − | 1.24090i | −0.245969 | − | 0.969278i | \(-0.579106\pi\) |
0.962404 | − | 0.271624i | \(-0.0875606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.578222 | + | 0.333836i | 0.0224902 | + | 0.0129847i | 0.511203 | − | 0.859460i | \(-0.329200\pi\) |
−0.488713 | + | 0.872445i | \(0.662533\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.61329 | + | 50.8609i | 0.217674 | + | 1.97230i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.65643 | + | 2.68839i | −0.180298 | + | 0.104095i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0054 | − | 8.66340i | −0.579279 | − | 0.334447i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.3752i | − | 0.669767i | −0.942260 | − | 0.334883i | \(-0.891303\pi\) | ||
0.942260 | − | 0.334883i | \(-0.108697\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.63427 | −0.370275 | −0.185138 | − | 0.982713i | \(-0.559273\pi\) | ||||
−0.185138 | + | 0.982713i | \(0.559273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.39986 | + | 1.38556i | −0.0920981 | + | 0.0531729i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.6304 | −1.24857 | −0.624283 | − | 0.781198i | \(-0.714609\pi\) | ||||
−0.624283 | + | 0.781198i | \(0.714609\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.1177 | 0.424785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7735 | − | 7.95215i | 0.524730 | − | 0.302953i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.14755 | −0.0436548 | −0.0218274 | − | 0.999762i | \(-0.506948\pi\) | ||||
−0.0218274 | + | 0.999762i | \(0.506948\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 30.8020i | − | 1.16839i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.51314 | + | 2.60566i | 0.170947 | + | 0.0986964i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.40173 | + | 4.85074i | −0.317329 | + | 0.183210i | −0.650201 | − | 0.759762i | \(-0.725315\pi\) |
0.332872 | + | 0.942972i | \(0.391982\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.1704 | − | 18.5133i | −1.59049 | − | 0.698242i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.6011 | − | 7.27527i | −0.473915 | − | 0.273615i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.37142 | + | 2.37537i | −0.0515047 | + | 0.0892087i | −0.890628 | − | 0.454732i | \(-0.849735\pi\) |
0.839124 | + | 0.543941i | \(0.183068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.02528 | − | 1.77583i | 0.0383970 | − | 0.0665055i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.1149i | 1.23843i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5543 | + | 11.2897i | −0.729252 | + | 0.421034i | −0.818148 | − | 0.575007i | \(-0.804999\pi\) |
0.0888966 | + | 0.996041i | \(0.471666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9179i | 0.890749i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.7524 | + | 20.3557i | 0.436473 | + | 0.755993i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.909044 | + | 1.57451i | 0.0337146 | + | 0.0583953i | 0.882390 | − | 0.470518i | \(-0.155933\pi\) |
−0.848676 | + | 0.528913i | \(0.822600\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.12386 | + | 5.26766i | 0.337458 | + | 0.194831i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.71411 | −0.174120 | −0.0870598 | − | 0.996203i | \(-0.527747\pi\) | ||||
−0.0870598 | + | 0.996203i | \(0.527747\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.9243 | + | 32.7779i | −0.697087 | + | 1.20739i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3144 | − | 35.1856i | −0.747279 | − | 1.29432i | −0.949123 | − | 0.314907i | \(-0.898027\pi\) |
0.201844 | − | 0.979418i | \(-0.435307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.86525 | − | 15.3551i | −0.325234 | − | 0.563323i | 0.656325 | − | 0.754478i | \(-0.272110\pi\) |
−0.981560 | + | 0.191155i | \(0.938777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.55739 | − | 2.69748i | 0.0570584 | − | 0.0988280i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.6580 | 1.12022 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6639 | − | 12.5076i | −0.790526 | − | 0.456410i | 0.0496218 | − | 0.998768i | \(-0.484198\pi\) |
−0.840148 | + | 0.542358i | \(0.817532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.16341 | + | 5.47919i | 0.115128 | + | 0.199408i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.6740 | + | 30.6122i | 0.642371 | + | 1.11262i | 0.984902 | + | 0.173113i | \(0.0553826\pi\) |
−0.342531 | + | 0.939507i | \(0.611284\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.2068i | − | 0.949997i | −0.879987 | − | 0.474998i | \(-0.842449\pi\) | ||
0.879987 | − | 0.474998i | \(-0.157551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.3462 | − | 27.9127i | 1.75025 | − | 1.01051i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 27.0846i | − | 0.977969i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.58555 | + | 2.74626i | −0.0571765 | + | 0.0990327i | −0.893197 | − | 0.449666i | \(-0.851543\pi\) |
0.836020 | + | 0.548698i | \(0.184876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.9192 | + | 20.6447i | −0.428705 | + | 0.742539i | −0.996758 | − | 0.0804531i | \(-0.974363\pi\) |
0.568054 | + | 0.822992i | \(0.307697\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.76313 | − | 4.48204i | −0.278860 | − | 0.161000i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.75205 | − | 0.414098i | 0.134431 | − | 0.0148366i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.09753 | + | 1.21101i | −0.0750556 | + | 0.0433334i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.3136 | − | 26.7392i | −1.65300 | − | 0.954362i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.1185i | 0.645855i | 0.946424 | + | 0.322928i | \(0.104667\pi\) | ||||
−0.946424 | + | 0.322928i | \(0.895333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.78846 | −0.312482 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.6978 | − | 13.6819i | 0.841532 | − | 0.485859i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.1831 | −1.21083 | −0.605414 | − | 0.795911i | \(-0.706992\pi\) | ||||
−0.605414 | + | 0.795911i | \(0.706992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.3333 | 1.35614 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.4689 | + | 17.0139i | −1.03993 | + | 0.600406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.4986 | −0.757725 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.3496i | − | 1.13735i | −0.822562 | − | 0.568675i | \(-0.807456\pi\) | ||
0.822562 | − | 0.568675i | \(-0.192544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.70299 | − | 5.60202i | −0.340718 | − | 0.196714i | 0.319872 | − | 0.947461i | \(-0.396360\pi\) |
−0.660589 | + | 0.750747i | \(0.729694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.7234 | + | 11.9647i | −0.725911 | + | 0.419105i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.58524 | − | 0.837149i | 0.265374 | − | 0.0292881i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.549531 | − | 0.317272i | −0.0191788 | − | 0.0110729i | 0.490380 | − | 0.871509i | \(-0.336858\pi\) |
−0.509559 | + | 0.860436i | \(0.670191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.07938 | − | 5.33364i | 0.107340 | − | 0.185919i | −0.807352 | − | 0.590071i | \(-0.799100\pi\) |
0.914692 | + | 0.404152i | \(0.132433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.740416 | − | 1.28244i | 0.0257468 | − | 0.0445947i | −0.852865 | − | 0.522132i | \(-0.825137\pi\) |
0.878612 | + | 0.477537i | \(0.158470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.23512i | − | 0.286017i | −0.989721 | − | 0.143009i | \(-0.954322\pi\) | ||
0.989721 | − | 0.143009i | \(-0.0456777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.7392 | − | 10.8191i | 0.649275 | − | 0.374859i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 33.1149i | − | 1.14599i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.6827 | + | 37.5556i | 0.748571 | + | 1.29656i | 0.948508 | + | 0.316754i | \(0.102593\pi\) |
−0.199937 | + | 0.979809i | \(0.564074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1901 | + | 17.6498i | 0.351383 | + | 0.608613i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.68942 | − | 2.70744i | −0.161321 | − | 0.0931386i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.8801 | 0.580008 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.67489 | − | 16.7574i | 0.331651 | − | 0.574436i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.4171 | − | 44.0237i | −0.870264 | − | 1.50734i | −0.861723 | − | 0.507378i | \(-0.830615\pi\) |
−0.00854088 | − | 0.999964i | \(-0.502719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.3175 | − | 47.3152i | −0.933147 | − | 1.61626i | −0.777905 | − | 0.628381i | \(-0.783718\pi\) |
−0.155242 | − | 0.987877i | \(-0.549616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9342 | + | 29.3310i | −0.577789 | + | 1.00076i | 0.417944 | + | 0.908473i | \(0.362751\pi\) |
−0.995732 | + | 0.0922865i | \(0.970582\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.1330 | 1.33210 | 0.666052 | − | 0.745905i | \(-0.267983\pi\) | ||||
0.666052 | + | 0.745905i | \(0.267983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.3567 | − | 33.1149i | −1.95019 | − | 1.12594i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.82652 | + | 4.89567i | 0.0958830 | + | 0.166074i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.8868 | − | 51.7654i | −1.01267 | − | 1.75400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.2861i | 1.19289i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3022 | − | 8.83476i | 0.516720 | − | 0.298329i | −0.218872 | − | 0.975754i | \(-0.570238\pi\) |
0.735592 | + | 0.677425i | \(0.236904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.6545i | − | 0.999086i | −0.866289 | − | 0.499543i | \(-0.833501\pi\) | ||
0.866289 | − | 0.499543i | \(-0.166499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.7052 | + | 35.8624i | −0.696784 | + | 1.20687i | 0.272791 | + | 0.962073i | \(0.412053\pi\) |
−0.969575 | + | 0.244793i | \(0.921280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.1366 | − | 21.0212i | 0.407507 | − | 0.705823i | −0.587103 | − | 0.809512i | \(-0.699732\pi\) |
0.994610 | + | 0.103690i | \(0.0330649\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.9025 | + | 14.3774i | 0.835202 | + | 0.482204i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.3787 | − | 16.4376i | 0.748874 | − | 0.550062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −70.8330 | + | 40.8955i | −2.36769 | + | 1.36698i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.84694 | + | 1.64368i | 0.0949506 | + | 0.0548198i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1325i | 0.837284i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.3379 | 0.576330 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.80842 | − | 1.04409i | 0.0600477 | − | 0.0346685i | −0.469676 | − | 0.882839i | \(-0.655629\pi\) |
0.529723 | + | 0.848171i | \(0.322296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.8978 | 1.18935 | 0.594673 | − | 0.803967i | \(-0.297281\pi\) | ||||
0.594673 | + | 0.803967i | \(0.297281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.7340 | 1.34810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.6281 | + | 26.9208i | −1.53980 | + | 0.889002i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.9710 | 1.51644 | 0.758221 | − | 0.651998i | \(-0.226069\pi\) | ||||
0.758221 | + | 0.651998i | \(0.226069\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 3.82504i | − | 0.125903i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −73.2556 | − | 42.2941i | −2.40863 | − | 1.39062i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.46164 | − | 3.73063i | 0.211999 | − | 0.122398i | −0.390241 | − | 0.920713i | \(-0.627608\pi\) |
0.602240 | + | 0.798315i | \(0.294275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.30050 | − | 14.3516i | 0.206491 | − | 0.470354i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.3184 | − | 26.1646i | −1.48207 | − | 0.855674i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.68304 | + | 8.11127i | −0.152988 | + | 0.264984i | −0.932325 | − | 0.361622i | \(-0.882223\pi\) |
0.779336 | + | 0.626606i | \(0.215556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.6883 | − | 25.4410i | 0.478826 | − | 0.829351i | −0.520879 | − | 0.853631i | \(-0.674396\pi\) |
0.999705 | + | 0.0242791i | \(0.00772904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.58597i | 0.0516463i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.7430 | + | 18.9042i | −1.06401 | + | 0.614304i | −0.926538 | − | 0.376202i | \(-0.877230\pi\) |
−0.137468 | + | 0.990506i | \(0.543896\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 53.7392i | − | 1.74445i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7307 | + | 41.1029i | 0.768714 | + | 1.33145i | 0.938260 | + | 0.345930i | \(0.112437\pi\) |
−0.169546 | + | 0.985522i | \(0.554230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.68833 | − | 13.3166i | −0.248789 | − | 0.430914i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.69045 | − | 5.01743i | −0.280629 | − | 0.162021i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7463 | 0.959558 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.9589 | + | 44.9622i | −0.835647 | + | 1.44738i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3557 | + | 28.3290i | 0.525965 | + | 0.910998i | 0.999542 | + | 0.0302461i | \(0.00962909\pi\) |
−0.473577 | + | 0.880752i | \(0.657038\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.502227 | + | 0.869883i | 0.0161172 | + | 0.0279159i | 0.873972 | − | 0.485977i | \(-0.161536\pi\) |
−0.857854 | + | 0.513893i | \(0.828203\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.9010 | + | 24.0772i | −0.445645 | + | 0.771880i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.57637 | 0.0504327 | 0.0252163 | − | 0.999682i | \(-0.491973\pi\) | ||||
0.0252163 | + | 0.999682i | \(0.491973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.9464 | + | 6.31991i | 0.349849 | + | 0.201985i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1511 | − | 29.7065i | −0.547034 | − | 0.947491i | −0.998476 | − | 0.0551907i | \(-0.982423\pi\) |
0.451441 | − | 0.892301i | \(-0.350910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8819 | + | 22.3121i | 0.410452 | + | 0.710923i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.20623i | 0.101952i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.2588 | − | 11.1191i | 0.611776 | − | 0.353209i | −0.161884 | − | 0.986810i | \(-0.551757\pi\) |
0.773660 | + | 0.633601i | \(0.218424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 21.1321i | − | 0.669932i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.6060 | − | 20.1022i | 0.367566 | − | 0.636644i | −0.621618 | − | 0.783321i | \(-0.713524\pi\) |
0.989184 | + | 0.146677i | \(0.0468577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2736.2.dc.c.449.1 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.c.449.8 | 16 | ||
4.3 | odd | 2 | 171.2.m.a.107.3 | yes | 16 | ||
12.11 | even | 2 | 171.2.m.a.107.6 | yes | 16 | ||
19.8 | odd | 6 | inner | 2736.2.dc.c.1889.8 | 16 | ||
57.8 | even | 6 | inner | 2736.2.dc.c.1889.1 | 16 | ||
76.27 | even | 6 | 171.2.m.a.8.6 | yes | 16 | ||
228.179 | odd | 6 | 171.2.m.a.8.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.m.a.8.3 | ✓ | 16 | 228.179 | odd | 6 | ||
171.2.m.a.8.6 | yes | 16 | 76.27 | even | 6 | ||
171.2.m.a.107.3 | yes | 16 | 4.3 | odd | 2 | ||
171.2.m.a.107.6 | yes | 16 | 12.11 | even | 2 | ||
2736.2.dc.c.449.1 | 16 | 1.1 | even | 1 | trivial | ||
2736.2.dc.c.449.8 | 16 | 3.2 | odd | 2 | inner | ||
2736.2.dc.c.1889.1 | 16 | 57.8 | even | 6 | inner | ||
2736.2.dc.c.1889.8 | 16 | 19.8 | odd | 6 | inner |