Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(949,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.g (of order \(2\), degree \(1\), 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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Character | \(\chi\) | \(=\) | 1900.949 |
Dual form | 1900.3.g.c.949.1 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −4.83157 | −1.61052 | −0.805262 | − | 0.592919i | \(-0.797975\pi\) | ||||
−0.805262 | + | 0.592919i | \(0.797975\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.72856i | − | 0.532651i | −0.963883 | − | 0.266326i | \(-0.914190\pi\) | ||
0.963883 | − | 0.266326i | \(-0.0858096\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.3441 | 1.59379 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.8938 | −1.26308 | −0.631539 | − | 0.775344i | \(-0.717576\pi\) | ||||
−0.631539 | + | 0.775344i | \(0.717576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.10699 | 0.315922 | 0.157961 | − | 0.987445i | \(-0.449508\pi\) | ||||
0.157961 | + | 0.987445i | \(0.449508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15.3087i | − | 0.900510i | −0.892900 | − | 0.450255i | \(-0.851333\pi\) | ||
0.892900 | − | 0.450255i | \(-0.148667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.4588 | + | 9.49250i | 0.866253 | + | 0.499605i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.0148i | 0.857847i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 17.4452i | − | 0.758486i | −0.925297 | − | 0.379243i | \(-0.876184\pi\) | ||
0.925297 | − | 0.379243i | \(-0.123816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −25.8203 | −0.956307 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.3924i | 0.565254i | 0.959230 | + | 0.282627i | \(0.0912059\pi\) | ||||
−0.959230 | + | 0.282627i | \(0.908794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 15.9121i | − | 0.513292i | −0.966505 | − | 0.256646i | \(-0.917383\pi\) | ||
0.966505 | − | 0.256646i | \(-0.0826175\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 67.1291 | 2.03422 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.14304 | −0.139001 | −0.0695005 | − | 0.997582i | \(-0.522141\pi\) | ||||
−0.0695005 | + | 0.997582i | \(0.522141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.8432 | −0.508800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.2785i | 1.03118i | 0.856835 | + | 0.515591i | \(0.172428\pi\) | ||||
−0.856835 | + | 0.515591i | \(0.827572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.56664i | − | 0.0364334i | −0.999834 | − | 0.0182167i | \(-0.994201\pi\) | ||
0.999834 | − | 0.0182167i | \(-0.00579888\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 54.5821i | − | 1.16132i | −0.814146 | − | 0.580660i | \(-0.802794\pi\) | ||
0.814146 | − | 0.580660i | \(-0.197206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.0979 | 0.716283 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 73.9649i | 1.45029i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.9822 | 1.05627 | 0.528134 | − | 0.849161i | \(-0.322892\pi\) | ||||
0.528134 | + | 0.849161i | \(0.322892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −79.5219 | − | 45.8637i | −1.39512 | − | 0.804626i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 101.822i | 1.72580i | 0.505376 | + | 0.862899i | \(0.331354\pi\) | ||||
−0.505376 | + | 0.862899i | \(0.668646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 80.5719 | 1.32085 | 0.660426 | − | 0.750892i | \(-0.270376\pi\) | ||||
0.660426 | + | 0.750892i | \(0.270376\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 53.4827i | − | 0.848932i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.8838 | −0.371400 | −0.185700 | − | 0.982606i | \(-0.559455\pi\) | ||||
−0.185700 | + | 0.982606i | \(0.559455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 84.2876i | 1.22156i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 121.245i | − | 1.70767i | −0.520545 | − | 0.853835i | \(-0.674271\pi\) | ||
0.520545 | − | 0.853835i | \(-0.325729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.9798i | 0.465476i | 0.972539 | + | 0.232738i | \(0.0747685\pi\) | ||||
−0.972539 | + | 0.232738i | \(0.925231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 51.8040i | 0.672779i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 102.623i | 1.29902i | 0.760351 | + | 0.649512i | \(0.225027\pi\) | ||||
−0.760351 | + | 0.649512i | \(0.774973\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.34417 | −0.0536317 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 80.3324i | − | 0.967860i | −0.875107 | − | 0.483930i | \(-0.839209\pi\) | ||
0.875107 | − | 0.483930i | \(-0.160791\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 79.2009i | − | 0.910355i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 12.0884i | − | 0.135824i | −0.997691 | − | 0.0679121i | \(-0.978366\pi\) | ||
0.997691 | − | 0.0679121i | \(-0.0216338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.3131i | − | 0.168276i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 76.8802i | 0.826669i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 161.837 | 1.66842 | 0.834210 | − | 0.551447i | \(-0.185924\pi\) | ||||
0.834210 | + | 0.551447i | \(0.185924\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −199.294 | −2.01308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.07921 | −0.0601901 | −0.0300951 | − | 0.999547i | \(-0.509581\pi\) | ||||
−0.0300951 | + | 0.999547i | \(0.509581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27.8929 | 0.270805 | 0.135402 | − | 0.990791i | \(-0.456767\pi\) | ||||
0.135402 | + | 0.990791i | \(0.456767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −61.4652 | −0.574441 | −0.287220 | − | 0.957865i | \(-0.592731\pi\) | ||||
−0.287220 | + | 0.957865i | \(0.592731\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 30.2310i | − | 0.277348i | −0.990338 | − | 0.138674i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138674i | \(-0.0442841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.8489 | 0.223864 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −178.939 | −1.58353 | −0.791765 | − | 0.610826i | \(-0.790837\pi\) | ||||
−0.791765 | + | 0.610826i | \(0.790837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 58.9109 | 0.503512 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −57.0793 | −0.479658 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 72.0390 | 0.595364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 204.272i | − | 1.66074i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −53.4071 | −0.420528 | −0.210264 | − | 0.977645i | \(-0.567432\pi\) | ||||
−0.210264 | + | 0.977645i | \(0.567432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.56932i | 0.0586769i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −109.035 | −0.832327 | −0.416163 | − | 0.909290i | \(-0.636626\pi\) | ||||
−0.416163 | + | 0.909290i | \(0.636626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 35.3933 | − | 61.3676i | 0.266115 | − | 0.461411i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 24.9987i | − | 0.182472i | −0.995829 | − | 0.0912362i | \(-0.970918\pi\) | ||
0.995829 | − | 0.0912362i | \(-0.0290818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −115.083 | −0.827936 | −0.413968 | − | 0.910291i | \(-0.635857\pi\) | ||||
−0.413968 | + | 0.910291i | \(0.635857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 263.717i | 1.87033i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −57.0619 | −0.399034 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −169.578 | −1.15359 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 141.364 | 0.948750 | 0.474375 | − | 0.880323i | \(-0.342674\pi\) | ||||
0.474375 | + | 0.880323i | \(0.342674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 250.107i | − | 1.65634i | −0.560478 | − | 0.828169i | \(-0.689383\pi\) | ||
0.560478 | − | 0.828169i | \(-0.310617\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 219.589i | − | 1.43522i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.5947i | − | 0.0929601i | −0.998919 | − | 0.0464801i | \(-0.985200\pi\) | ||
0.998919 | − | 0.0464801i | \(-0.0148004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −270.482 | −1.70115 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −65.0454 | −0.404009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.57924i | 0.0587684i | 0.999568 | + | 0.0293842i | \(0.00935462\pi\) | ||||
−0.999568 | + | 0.0293842i | \(0.990645\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −302.815 | −1.81326 | −0.906631 | − | 0.421923i | \(-0.861355\pi\) | ||||
−0.906631 | + | 0.421923i | \(0.861355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −152.133 | −0.900193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 236.086 | + | 136.161i | 1.38062 | + | 0.796264i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −111.084 | −0.642102 | −0.321051 | − | 0.947062i | \(-0.604036\pi\) | ||||
−0.321051 | + | 0.947062i | \(0.604036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 491.961i | − | 2.77944i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 247.724i | − | 1.38393i | −0.721929 | − | 0.691967i | \(-0.756744\pi\) | ||
0.721929 | − | 0.691967i | \(-0.243256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 234.560i | − | 1.29591i | −0.761678 | − | 0.647956i | \(-0.775624\pi\) | ||
0.761678 | − | 0.647956i | \(-0.224376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −389.289 | −2.12726 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 212.696i | 1.13741i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 96.2724i | 0.509378i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −250.384 | −1.31091 | −0.655455 | − | 0.755235i | \(-0.727523\pi\) | ||||
−0.655455 | + | 0.755235i | \(0.727523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −122.208 | −0.633204 | −0.316602 | − | 0.948558i | \(-0.602542\pi\) | ||||
−0.316602 | + | 0.948558i | \(0.602542\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 343.177i | − | 1.74201i | −0.491271 | − | 0.871007i | \(-0.663467\pi\) | ||
0.491271 | − | 0.871007i | \(-0.336533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −297.583 | −1.49539 | −0.747696 | − | 0.664042i | \(-0.768840\pi\) | ||||
−0.747696 | + | 0.664042i | \(0.768840\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 120.228 | 0.598148 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 61.1199 | 0.301083 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 250.235i | − | 1.20886i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −228.676 | − | 131.887i | −1.09414 | − | 0.631040i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 237.792i | − | 1.12698i | −0.826124 | − | 0.563488i | \(-0.809459\pi\) | ||
0.826124 | − | 0.563488i | \(-0.190541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 585.801i | 2.75024i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −59.3290 | −0.273406 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 164.176i | − | 0.749661i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 62.8725i | − | 0.284491i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −152.390 | −0.683365 | −0.341682 | − | 0.939815i | \(-0.610997\pi\) | ||||
−0.341682 | + | 0.939815i | \(0.610997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 205.814 | 0.906670 | 0.453335 | − | 0.891340i | \(-0.350234\pi\) | ||||
0.453335 | + | 0.891340i | \(0.350234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −135.060 | −0.589783 | −0.294892 | − | 0.955531i | \(-0.595284\pi\) | ||||
−0.294892 | + | 0.955531i | \(0.595284\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 250.295i | − | 1.08353i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 100.593i | − | 0.431728i | −0.976423 | − | 0.215864i | \(-0.930743\pi\) | ||
0.976423 | − | 0.215864i | \(-0.0692567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 495.830i | − | 2.09211i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 328.565 | 1.37475 | 0.687373 | − | 0.726304i | \(-0.258764\pi\) | ||||
0.687373 | + | 0.726304i | \(0.258764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 144.249i | 0.598543i | 0.954168 | + | 0.299272i | \(0.0967437\pi\) | ||||
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 253.372 | 1.04268 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 67.5961 | + | 38.9856i | 0.273669 | + | 0.157836i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 388.132i | 1.55876i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 66.0565 | 0.263173 | 0.131587 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131587 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 242.381i | 0.958027i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −268.255 | −1.04379 | −0.521896 | − | 0.853009i | \(-0.674775\pi\) | ||||
−0.521896 | + | 0.853009i | \(0.674775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.1761i | 0.0740390i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 235.133i | 0.900895i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 241.131i | 0.916848i | 0.888734 | + | 0.458424i | \(0.151586\pi\) | ||||
−0.888734 | + | 0.458424i | \(0.848414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 58.4058i | 0.218748i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 270.274i | − | 1.00473i | −0.864654 | − | 0.502367i | \(-0.832462\pi\) | ||
0.864654 | − | 0.502367i | \(-0.167538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 159.872 | 0.589934 | 0.294967 | − | 0.955507i | \(-0.404691\pi\) | ||||
0.294967 | + | 0.955507i | \(0.404691\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73.9865i | 0.271013i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 480.862i | 1.73596i | 0.496597 | + | 0.867981i | \(0.334583\pi\) | ||||
−0.496597 | + | 0.867981i | \(0.665417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 228.244i | − | 0.818078i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 125.506i | − | 0.446639i | −0.974745 | − | 0.223320i | \(-0.928311\pi\) | ||
0.974745 | − | 0.223320i | \(-0.0716894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 169.824i | 0.600086i | 0.953926 | + | 0.300043i | \(0.0970011\pi\) | ||||
−0.953926 | + | 0.300043i | \(0.902999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 157.638 | 0.549261 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 54.6445 | 0.189081 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −781.925 | −2.68703 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 103.213 | 0.352263 | 0.176131 | − | 0.984367i | \(-0.443642\pi\) | ||||
0.176131 | + | 0.984367i | \(0.443642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 358.743 | 1.20789 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 71.6472i | − | 0.239623i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.84130 | −0.0194063 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.3721 | 0.0969377 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −470.447 | −1.53240 | −0.766200 | − | 0.642602i | \(-0.777855\pi\) | ||||
−0.766200 | + | 0.642602i | \(0.777855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −134.767 | −0.436138 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −104.966 | −0.337511 | −0.168756 | − | 0.985658i | \(-0.553975\pi\) | ||||
−0.168756 | + | 0.985658i | \(0.553975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 358.845i | − | 1.14647i | −0.819392 | − | 0.573234i | \(-0.805689\pi\) | ||
0.819392 | − | 0.573234i | \(-0.194311\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −367.285 | −1.15863 | −0.579314 | − | 0.815104i | \(-0.696680\pi\) | ||||
−0.579314 | + | 0.815104i | \(0.696680\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 227.753i | − | 0.713960i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 296.973 | 0.925150 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 145.318 | − | 251.963i | 0.449900 | − | 0.780070i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 146.063i | 0.446676i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −203.512 | −0.618579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 496.428i | 1.49978i | 0.661561 | + | 0.749892i | \(0.269894\pi\) | ||||
−0.661561 | + | 0.749892i | \(0.730106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −73.7721 | −0.221538 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −52.5036 | −0.155797 | −0.0778986 | − | 0.996961i | \(-0.524821\pi\) | ||||
−0.0778986 | + | 0.996961i | \(0.524821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 864.556 | 2.55031 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 221.080i | 0.648328i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 313.564i | − | 0.914180i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 409.556i | 1.18028i | 0.807302 | + | 0.590138i | \(0.200927\pi\) | ||||
−0.807302 | + | 0.590138i | \(0.799073\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −562.063 | −1.61050 | −0.805248 | − | 0.592938i | \(-0.797968\pi\) | ||||
−0.805248 | + | 0.592938i | \(0.797968\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −106.044 | −0.302118 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 252.453i | − | 0.715165i | −0.933881 | − | 0.357583i | \(-0.883601\pi\) | ||
0.933881 | − | 0.357583i | \(-0.116399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 275.783 | 0.772500 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 119.344 | 0.332433 | 0.166217 | − | 0.986089i | \(-0.446845\pi\) | ||||
0.166217 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 180.785 | + | 312.470i | 0.500789 | + | 0.865569i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −348.062 | −0.958848 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 690.635i | − | 1.88184i | −0.338629 | − | 0.940920i | \(-0.609963\pi\) | ||
0.338629 | − | 0.940920i | \(-0.390037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 606.446i | 1.64349i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 208.733i | − | 0.562623i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 491.052 | 1.31649 | 0.658246 | − | 0.752803i | \(-0.271299\pi\) | ||||
0.658246 | + | 0.752803i | \(0.271299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 67.3233i | 0.178576i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 691.775i | 1.82526i | 0.408782 | + | 0.912632i | \(0.365954\pi\) | ||||
−0.408782 | + | 0.912632i | \(0.634046\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 258.040 | 0.677271 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −252.889 | −0.660285 | −0.330142 | − | 0.943931i | \(-0.607097\pi\) | ||||
−0.330142 | + | 0.943931i | \(0.607097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 22.4720i | − | 0.0580671i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 504.764 | 1.29759 | 0.648797 | − | 0.760961i | \(-0.275272\pi\) | ||||
0.648797 | + | 0.760961i | \(0.275272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −267.063 | −0.683025 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 526.809 | 1.34048 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 313.581i | 0.789876i | 0.918708 | + | 0.394938i | \(0.129234\pi\) | ||||
−0.918708 | + | 0.394938i | \(0.870766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −171.005 | + | 296.502i | −0.428585 | + | 0.743113i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 561.838i | 1.40109i | 0.713607 | + | 0.700546i | \(0.247060\pi\) | ||||
−0.713607 | + | 0.700546i | \(0.752940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 65.3506i | − | 0.162160i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 71.4566 | 0.175569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 165.613i | 0.404921i | 0.979290 | + | 0.202460i | \(0.0648937\pi\) | ||||
−0.979290 | + | 0.202460i | \(0.935106\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 120.783i | 0.293876i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 379.650 | 0.919249 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 556.032 | 1.33341 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 440.399 | 1.05107 | 0.525536 | − | 0.850771i | \(-0.323865\pi\) | ||||
0.525536 | + | 0.850771i | \(0.323865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 786.831i | − | 1.86896i | −0.356018 | − | 0.934479i | \(-0.615866\pi\) | ||
0.356018 | − | 0.934479i | \(-0.384134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 782.929i | − | 1.85090i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 300.417i | − | 0.703553i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 275.698 | 0.642654 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 219.539i | − | 0.509372i | −0.967024 | − | 0.254686i | \(-0.918028\pi\) | ||
0.967024 | − | 0.254686i | \(-0.0819721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −450.900 | −1.04134 | −0.520670 | − | 0.853758i | \(-0.674318\pi\) | ||||
−0.520670 | + | 0.853758i | \(0.674318\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 165.598 | − | 287.127i | 0.378944 | − | 0.657041i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 319.069i | − | 0.726808i | −0.931632 | − | 0.363404i | \(-0.881615\pi\) | ||
0.931632 | − | 0.363404i | \(-0.118385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 503.446 | 1.14160 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 780.776i | − | 1.76247i | −0.472674 | − | 0.881237i | \(-0.656711\pi\) | ||
0.472674 | − | 0.881237i | \(-0.343289\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −683.009 | −1.52798 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 523.244i | 1.16535i | 0.812704 | + | 0.582677i | \(0.197995\pi\) | ||||
−0.812704 | + | 0.582677i | \(0.802005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 587.411i | − | 1.30246i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1208.41i | 2.66757i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 874.643i | 1.91388i | 0.290285 | + | 0.956940i | \(0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 395.274i | 0.861164i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 120.368 | 0.261102 | 0.130551 | − | 0.991442i | \(-0.458325\pi\) | ||||
0.130551 | + | 0.991442i | \(0.458325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 256.911i | − | 0.554883i | −0.960743 | − | 0.277441i | \(-0.910514\pi\) | ||
0.960743 | − | 0.277441i | \(-0.0894864\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 490.911i | 1.05120i | 0.850731 | + | 0.525601i | \(0.176160\pi\) | ||||
−0.850731 | + | 0.525601i | \(0.823840\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 92.7807i | 0.197827i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 70.5155i | 0.149714i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7666i | 0.0460182i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 803.014 | 1.68347 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −545.752 | −1.13936 | −0.569679 | − | 0.821868i | \(-0.692932\pi\) | ||||
−0.569679 | + | 0.821868i | \(0.692932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.1224 | −0.0439135 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 314.271 | 0.650665 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 243.032 | 0.499039 | 0.249519 | − | 0.968370i | \(-0.419727\pi\) | ||||
0.249519 | + | 0.968370i | \(0.419727\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 46.2828i | − | 0.0946479i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −555.332 | −1.13102 | −0.565511 | − | 0.824740i | \(-0.691321\pi\) | ||||
−0.565511 | + | 0.824740i | \(0.691321\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 250.946 | 0.509017 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −452.067 | −0.909592 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 231.235 | 0.463397 | 0.231698 | − | 0.972788i | \(-0.425572\pi\) | ||||
0.231698 | + | 0.972788i | \(0.425572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1463.07 | 2.92030 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 206.048i | 0.409638i | 0.978800 | + | 0.204819i | \(0.0656605\pi\) | ||||
−0.978800 | + | 0.204819i | \(0.934340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 735.040 | 1.44978 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 398.832i | − | 0.783560i | −0.920059 | − | 0.391780i | \(-0.871859\pi\) | ||
0.920059 | − | 0.391780i | \(-0.128141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 126.696 | 0.247936 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −424.971 | − | 245.099i | −0.828404 | − | 0.477776i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 758.355i | 1.46684i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 536.708 | 1.03412 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 262.617i | − | 0.504064i | −0.967719 | − | 0.252032i | \(-0.918901\pi\) | ||
0.967719 | − | 0.252032i | \(-0.0810988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 814.031 | 1.55646 | 0.778232 | − | 0.627977i | \(-0.216117\pi\) | ||||
0.778232 | + | 0.627977i | \(0.216117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −243.592 | −0.462225 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 224.666 | 0.424699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1460.54i | 2.75055i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 173.637i | 0.325773i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1196.90i | 2.22886i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −487.644 | −0.904720 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −196.753 | −0.363684 | −0.181842 | − | 0.983328i | \(-0.558206\pi\) | ||||
−0.181842 | + | 0.983328i | \(0.558206\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1133.29i | 2.08710i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −759.052 | −1.38766 | −0.693832 | − | 0.720137i | \(-0.744079\pi\) | ||||
−0.693832 | + | 0.720137i | \(0.744079\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1155.73 | 2.10515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −155.605 | + | 269.799i | −0.282404 | + | 0.489653i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 382.636 | 0.691927 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 705.968i | 1.26745i | 0.773560 | + | 0.633723i | \(0.218474\pi\) | ||||
−0.773560 | + | 0.633723i | \(0.781526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.43416i | − | 0.0115101i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1027.66i | − | 1.83183i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 357.744 | 0.635424 | 0.317712 | − | 0.948187i | \(-0.397086\pi\) | ||||
0.317712 | + | 0.948187i | \(0.397086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.1975i | 0.0285670i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 448.411i | − | 0.788069i | −0.919096 | − | 0.394034i | \(-0.871079\pi\) | ||
0.919096 | − | 0.394034i | \(-0.128921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 203.672 | 0.356694 | 0.178347 | − | 0.983968i | \(-0.442925\pi\) | ||||
0.178347 | + | 0.983968i | \(0.442925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1209.75 | 2.11125 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 232.447i | 0.402854i | 0.979504 | + | 0.201427i | \(0.0645579\pi\) | ||||
−0.979504 | + | 0.201427i | \(0.935442\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 590.458 | 1.01979 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −299.524 | −0.515532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −777.809 | −1.33415 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1101.80i | − | 1.87701i | −0.345271 | − | 0.938503i | \(-0.612213\pi\) | ||
0.345271 | − | 0.938503i | \(-0.387787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 151.045 | − | 261.894i | 0.256443 | − | 0.444641i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1658.08i | 2.80555i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 387.409i | 0.653303i | 0.945145 | + | 0.326651i | \(0.105920\pi\) | ||||
−0.945145 | + | 0.326651i | \(0.894080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1437.79 | 2.40836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 649.288i | − | 1.08395i | −0.840393 | − | 0.541977i | \(-0.817676\pi\) | ||
0.840393 | − | 0.541977i | \(-0.182324\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 564.191i | − | 0.938754i | −0.882998 | − | 0.469377i | \(-0.844479\pi\) | ||
0.882998 | − | 0.469377i | \(-0.155521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −356.935 | −0.591932 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −431.505 | −0.710882 | −0.355441 | − | 0.934699i | \(-0.615669\pi\) | ||||
−0.355441 | + | 0.934699i | \(0.615669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −295.305 | −0.484902 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 224.168i | − | 0.366887i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 360.161i | − | 0.587539i | −0.955876 | − | 0.293769i | \(-0.905090\pi\) | ||
0.955876 | − | 0.293769i | \(-0.0949098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 255.900i | − | 0.414749i | −0.978262 | − | 0.207375i | \(-0.933508\pi\) | ||
0.978262 | − | 0.207375i | \(-0.0664919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 231.220 | 0.373538 | 0.186769 | − | 0.982404i | \(-0.440198\pi\) | ||||
0.186769 | + | 0.982404i | \(0.440198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 450.440i | 0.725346i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.0722 | −0.0723470 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1104.87 | + | 637.223i | 1.76215 | + | 1.01630i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 78.7331i | 0.125172i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 55.6688 | 0.0882232 | 0.0441116 | − | 0.999027i | \(-0.485954\pi\) | ||||
0.0441116 | + | 0.999027i | \(0.485954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1148.91i | 1.81502i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 144.146 | 0.226290 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1739.14i | − | 2.72166i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1086.58i | − | 1.69513i | −0.530692 | − | 0.847565i | \(-0.678068\pi\) | ||
0.530692 | − | 0.847565i | \(-0.321932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 132.021i | − | 0.205320i | −0.994717 | − | 0.102660i | \(-0.967265\pi\) | ||
0.994717 | − | 0.102660i | \(-0.0327353\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 139.001i | 0.214840i | 0.994214 | + | 0.107420i | \(0.0342589\pi\) | ||||
−0.994214 | + | 0.107420i | \(0.965741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1414.70i | − | 2.17982i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 286.652 | 0.440326 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.61433i | 0.00400356i | 0.999998 | + | 0.00200178i | \(0.000637187\pi\) | ||||
−0.999998 | + | 0.00200178i | \(0.999363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 487.408i | 0.741870i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1115.25i | 1.69234i | 0.532911 | + | 0.846171i | \(0.321098\pi\) | ||||
−0.532911 | + | 0.846171i | \(0.678902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1032.56i | − | 1.56212i | −0.624453 | − | 0.781062i | \(-0.714678\pi\) | ||
0.624453 | − | 0.781062i | \(-0.285322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 303.773i | 0.458180i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 285.968 | 0.428738 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 736.285 | 1.10058 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1119.45 | −1.66834 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −923.804 | −1.37267 | −0.686333 | − | 0.727288i | \(-0.740781\pi\) | ||||
−0.686333 | + | 0.727288i | \(0.740781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1144.25 | −1.69017 | −0.845086 | − | 0.534631i | \(-0.820451\pi\) | ||||
−0.845086 | + | 0.534631i | \(0.820451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 603.417i | − | 0.888686i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −994.406 | −1.46021 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −686.997 | −1.00585 | −0.502926 | − | 0.864330i | \(-0.667743\pi\) | ||||
−0.502926 | + | 0.864330i | \(0.667743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 652.554 | 0.949860 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 229.918 | 0.333699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1216.77 | −1.76088 | −0.880442 | − | 0.474154i | \(-0.842754\pi\) | ||||
−0.880442 | + | 0.474154i | \(0.842754\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 743.081i | 1.07227i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 647.228 | 0.928591 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 486.020i | 0.695308i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1082.00 | −1.54351 | −0.771753 | − | 0.635922i | \(-0.780620\pi\) | ||||
−0.771753 | + | 0.635922i | \(0.780620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −84.6482 | − | 48.8203i | −0.120410 | − | 0.0694456i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.6667i | 0.0320604i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 639.509 | 0.901987 | 0.450994 | − | 0.892527i | \(-0.351070\pi\) | ||||
0.450994 | + | 0.892527i | \(0.351070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1472.03i | 2.07037i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −277.589 | −0.389325 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1587.48 | −2.21406 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 95.9878 | 0.133502 | 0.0667509 | − | 0.997770i | \(-0.478737\pi\) | ||||
0.0667509 | + | 0.997770i | \(0.478737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 104.000i | − | 0.144245i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 696.949i | − | 0.963968i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 368.875i | − | 0.507394i | −0.967284 | − | 0.253697i | \(-0.918353\pi\) | ||
0.967284 | − | 0.253697i | \(-0.0816466\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1185.09 | −1.62563 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.9831 | −0.0328087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 865.251i | 1.18042i | 0.807248 | + | 0.590212i | \(0.200956\pi\) | ||||
−0.807248 | + | 0.590212i | \(0.799044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 345.732 | 0.469107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 934.331 | 1.26432 | 0.632159 | − | 0.774839i | \(-0.282169\pi\) | ||||
0.632159 | + | 0.774839i | \(0.282169\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −326.595 | − | 188.362i | −0.440750 | − | 0.254199i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −235.551 | −0.317027 | −0.158514 | − | 0.987357i | \(-0.550670\pi\) | ||||
−0.158514 | + | 0.987357i | \(0.550670\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1152.29i | − | 1.54256i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 229.176i | 0.305976i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 971.042i | − | 1.29300i | −0.762915 | − | 0.646499i | \(-0.776232\pi\) | ||
0.762915 | − | 0.646499i | \(-0.223768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −319.156 | −0.423847 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 177.074i | − | 0.233916i | −0.993137 | − | 0.116958i | \(-0.962686\pi\) | ||
0.993137 | − | 0.116958i | \(-0.0373143\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1171.08i | − | 1.54292i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −159.521 | −0.209621 | −0.104810 | − | 0.994492i | \(-0.533424\pi\) | ||||
−0.104810 | + | 0.994492i | \(0.533424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −112.718 | −0.147730 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 418.182i | 0.545218i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −707.134 | −0.919551 | −0.459775 | − | 0.888035i | \(-0.652070\pi\) | ||||
−0.459775 | + | 0.888035i | \(0.652070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1296.09 | 1.68105 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −799.572 | −1.03438 | −0.517188 | − | 0.855872i | \(-0.673021\pi\) | ||||
−0.517188 | + | 0.855872i | \(0.673021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 92.6507i | − | 0.119242i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −401.329 | + | 695.854i | −0.515184 | + | 0.893265i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1684.55i | 2.15692i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 423.256i | − | 0.540557i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1366.97 | 1.73693 | 0.868466 | − | 0.495749i | \(-0.165107\pi\) | ||||
0.868466 | + | 0.495749i | \(0.165107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1165.04i | − | 1.47661i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 667.184i | 0.843469i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 330.908 | 0.417286 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 121.258 | 0.152143 | 0.0760717 | − | 0.997102i | \(-0.475762\pi\) | ||||
0.0760717 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −835.579 | −1.04578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 173.396i | − | 0.216475i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 472.110i | − | 0.587933i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1305.85i | 1.61815i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −820.488 | −1.01420 | −0.507100 | − | 0.861887i | \(-0.669283\pi\) | ||||
−0.507100 | + | 0.861887i | \(0.669283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 537.722i | 0.663036i | 0.943449 | + | 0.331518i | \(0.107561\pi\) | ||||
−0.943449 | + | 0.331518i | \(0.892439\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −772.434 | −0.950103 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.8713 | − | 25.7850i | 0.0182023 | − | 0.0315606i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 219.653i | − | 0.268196i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.0424 | −0.0658250 | −0.0329125 | − | 0.999458i | \(-0.510478\pi\) | ||||
−0.0329125 | + | 0.999458i | \(0.510478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 599.052i | 0.727889i | 0.931421 | + | 0.363944i | \(0.118570\pi\) | ||||
−0.931421 | + | 0.363944i | \(0.881430\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −620.339 | −0.750108 | −0.375054 | − | 0.927003i | \(-0.622376\pi\) | ||||
−0.375054 | + | 0.927003i | \(0.622376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36.8107i | − | 0.0444038i | −0.999754 | − | 0.0222019i | \(-0.992932\pi\) | ||
0.999754 | − | 0.0222019i | \(-0.00706766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2323.32i | − | 2.79581i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 537.302i | − | 0.645020i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 410.854i | 0.490865i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 531.549i | − | 0.633551i | −0.948501 | − | 0.316776i | \(-0.897400\pi\) | ||
0.948501 | − | 0.316776i | \(-0.102600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 572.290 | 0.680488 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 606.389i | 0.719323i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 268.602i | − | 0.317121i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 820.519i | − | 0.966453i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 89.7212i | 0.105430i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.6518i | − | 0.0195214i | −0.999952 | − | 0.00976072i | \(-0.996893\pi\) | ||
0.999952 | − | 0.00976072i | \(-0.00310698\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −656.701 | −0.766279 | −0.383139 | − | 0.923691i | \(-0.625157\pi\) | ||||
−0.383139 | + | 0.923691i | \(0.625157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.72122 | 0.00898862 | 0.00449431 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449431 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −761.638 | −0.884597 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1132.71 | −1.31253 | −0.656266 | − | 0.754530i | \(-0.727865\pi\) | ||||
−0.656266 | + | 0.754530i | \(0.727865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −264.019 | −0.304520 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1425.83i | − | 1.64077i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −102.197 | −0.117333 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2321.40 | 2.65910 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −826.040 | −0.941893 | −0.470947 | − | 0.882162i | \(-0.656088\pi\) | ||||
−0.470947 | + | 0.882162i | \(0.656088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −498.681 | −0.567327 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 691.162 | 0.784520 | 0.392260 | − | 0.919854i | \(-0.371693\pi\) | ||||
0.392260 | + | 0.919854i | \(0.371693\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1339.08i | 1.51651i | 0.651958 | + | 0.758255i | \(0.273948\pi\) | ||||
−0.651958 | + | 0.758255i | \(0.726052\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1263.16 | 1.42408 | 0.712040 | − | 0.702139i | \(-0.247772\pi\) | ||||
0.712040 | + | 0.702139i | \(0.247772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 199.131i | 0.223995i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 60.3572 | 0.0677409 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 518.120 | − | 898.356i | 0.580202 | − | 1.00600i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 346.168i | 0.385918i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 260.836 | 0.290141 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 857.014i | − | 0.951181i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.2227 | 0.0312543 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −531.490 | −0.585987 | −0.292994 | − | 0.956114i | \(-0.594651\pi\) | ||||
−0.292994 | + | 0.956114i | \(0.594651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −87.2006 | −0.0959302 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 214.421i | − | 0.235368i | −0.993051 | − | 0.117684i | \(-0.962453\pi\) | ||
0.993051 | − | 0.117684i | \(-0.0375471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1116.13i | 1.22248i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 406.542i | 0.443340i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1523.80 | 1.65811 | 0.829055 | − | 0.559167i | \(-0.188879\pi\) | ||||
0.829055 | + | 0.559167i | \(0.188879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2273.00 | 2.46797 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 497.950i | − | 0.539490i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 400.098 | 0.431605 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 269.533 | 0.290132 | 0.145066 | − | 0.989422i | \(-0.453661\pi\) | ||||
0.145066 | + | 0.989422i | \(0.453661\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 577.669 | + | 333.166i | 0.620482 | + | 0.357859i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 507.151 | 0.543570 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 492.223i | − | 0.525318i | −0.964889 | − | 0.262659i | \(-0.915401\pi\) | ||
0.964889 | − | 0.262659i | \(-0.0845995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1733.78i | 1.84641i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1364.05i | − | 1.44958i | −0.688972 | − | 0.724788i | \(-0.741938\pi\) | ||
0.688972 | − | 0.724788i | \(-0.258062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 737.556 | 0.782138 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1082.40i | − | 1.14298i | −0.820609 | − | 0.571490i | \(-0.806366\pi\) | ||
0.820609 | − | 0.571490i | \(-0.193634\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 139.554i | 0.147054i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1774.56 | 1.86600 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 196.828 | 0.206535 | 0.103268 | − | 0.994654i | \(-0.467070\pi\) | ||||
0.103268 | + | 0.994654i | \(0.467070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1100.41i | 1.14985i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −93.2092 | −0.0971941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 707.806 | 0.736531 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −881.661 | −0.915536 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1381.14i | 1.42828i | 0.700005 | + | 0.714138i | \(0.253181\pi\) | ||||
−0.700005 | + | 0.714138i | \(0.746819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −702.112 | + | 1217.37i | −0.724574 | + | 1.25632i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1116.21i | 1.14954i | 0.818314 | + | 0.574771i | \(0.194909\pi\) | ||||
−0.818314 | + | 0.574771i | \(0.805091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 429.094i | 0.441001i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1784.43 | 1.82644 | 0.913218 | − | 0.407471i | \(-0.133589\pi\) | ||||
0.913218 | + | 0.407471i | \(0.133589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 167.954i | 0.171557i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 433.635i | − | 0.442034i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −600.203 | −0.610583 | −0.305291 | − | 0.952259i | \(-0.598754\pi\) | ||||
−0.305291 | + | 0.952259i | \(0.598754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 983.285 | 0.996236 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.3303 | −0.0276343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0179i | 0.0141452i | 0.999975 | + | 0.00707259i | \(0.00225129\pi\) | ||||
−0.999975 | + | 0.00707259i | \(0.997749\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2398.53i | − | 2.41544i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 137.727i | 0.138142i | 0.997612 | + | 0.0690708i | \(0.0220034\pi\) | ||||
−0.997612 | + | 0.0690708i | \(0.977997\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 132.795 | 0.132928 |
(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 | 1900.3.g.c.949.2 | 24 | ||
5.2 | odd | 4 | 1900.3.e.f.1101.12 | 12 | |||
5.3 | odd | 4 | 380.3.e.a.341.1 | ✓ | 12 | ||
5.4 | even | 2 | inner | 1900.3.g.c.949.23 | 24 | ||
15.8 | even | 4 | 3420.3.o.a.721.4 | 12 | |||
19.18 | odd | 2 | inner | 1900.3.g.c.949.24 | 24 | ||
20.3 | even | 4 | 1520.3.h.b.721.12 | 12 | |||
95.18 | even | 4 | 380.3.e.a.341.12 | yes | 12 | ||
95.37 | even | 4 | 1900.3.e.f.1101.1 | 12 | |||
95.94 | odd | 2 | inner | 1900.3.g.c.949.1 | 24 | ||
285.113 | odd | 4 | 3420.3.o.a.721.3 | 12 | |||
380.303 | odd | 4 | 1520.3.h.b.721.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.e.a.341.1 | ✓ | 12 | 5.3 | odd | 4 | ||
380.3.e.a.341.12 | yes | 12 | 95.18 | even | 4 | ||
1520.3.h.b.721.1 | 12 | 380.303 | odd | 4 | |||
1520.3.h.b.721.12 | 12 | 20.3 | even | 4 | |||
1900.3.e.f.1101.1 | 12 | 95.37 | even | 4 | |||
1900.3.e.f.1101.12 | 12 | 5.2 | odd | 4 | |||
1900.3.g.c.949.1 | 24 | 95.94 | odd | 2 | inner | ||
1900.3.g.c.949.2 | 24 | 1.1 | even | 1 | trivial | ||
1900.3.g.c.949.23 | 24 | 5.4 | even | 2 | inner | ||
1900.3.g.c.949.24 | 24 | 19.18 | odd | 2 | inner | ||
3420.3.o.a.721.3 | 12 | 285.113 | odd | 4 | |||
3420.3.o.a.721.4 | 12 | 15.8 | even | 4 |