Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.i (of order \(3\), 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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.6 | ||
Root | \(-1.04556 + 0.339889i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.865 |
Dual form | 2268.2.i.n.2053.6 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.515559 | − | 0.892975i | 0.230565 | − | 0.399350i | −0.727409 | − | 0.686204i | \(-0.759276\pi\) |
0.957975 | + | 0.286853i | \(0.0926092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63118 | + | 0.277320i | −0.994492 | + | 0.104817i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.792879 | − | 1.37331i | −0.239062 | − | 0.414067i | 0.721383 | − | 0.692536i | \(-0.243507\pi\) |
−0.960445 | + | 0.278468i | \(0.910173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.52415 | − | 4.37196i | −0.700074 | − | 1.21256i | −0.968440 | − | 0.249246i | \(-0.919817\pi\) |
0.268366 | − | 0.963317i | \(-0.413516\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.58242 | − | 4.47288i | 0.626329 | − | 1.08483i | −0.361954 | − | 0.932196i | \(-0.617890\pi\) |
0.988282 | − | 0.152637i | \(-0.0487765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.392975 | − | 0.680652i | −0.0901546 | − | 0.156152i | 0.817421 | − | 0.576040i | \(-0.195403\pi\) |
−0.907576 | + | 0.419888i | \(0.862069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.93289 | + | 5.07991i | −0.611549 | + | 1.05923i | 0.379431 | + | 0.925220i | \(0.376120\pi\) |
−0.990980 | + | 0.134014i | \(0.957213\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96840 | + | 3.40936i | 0.393679 | + | 0.681873i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.44511 | + | 7.69915i | −0.825435 | + | 1.42970i | 0.0761506 | + | 0.997096i | \(0.475737\pi\) |
−0.901586 | + | 0.432600i | \(0.857596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.15085 | −0.206698 | −0.103349 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103349 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.10889 | + | 2.49255i | −0.187436 | + | 0.421318i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.07991 | + | 7.06661i | 0.670732 | + | 1.16174i | 0.977697 | + | 0.210022i | \(0.0673535\pi\) |
−0.306964 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.87206 | + | 6.70660i | 0.604714 | + | 1.04739i | 0.992097 | + | 0.125476i | \(0.0400458\pi\) |
−0.387383 | + | 0.921919i | \(0.626621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.26628 | − | 2.19326i | 0.193106 | − | 0.334470i | −0.753172 | − | 0.657824i | \(-0.771477\pi\) |
0.946278 | + | 0.323354i | \(0.104811\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.49189 | −1.23867 | −0.619335 | − | 0.785127i | \(-0.712598\pi\) | ||||
−0.619335 | + | 0.785127i | \(0.712598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.84619 | − | 1.45935i | 0.978027 | − | 0.208479i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.41270 | + | 4.17892i | −0.331410 | + | 0.574019i | −0.982789 | − | 0.184734i | \(-0.940858\pi\) |
0.651378 | + | 0.758753i | \(0.274191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.63510 | −0.220477 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.87245 | −0.504150 | −0.252075 | − | 0.967708i | \(-0.581113\pi\) | ||||
−0.252075 | + | 0.967708i | \(0.581113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.64407 | −1.23480 | −0.617398 | − | 0.786651i | \(-0.711813\pi\) | ||||
−0.617398 | + | 0.786651i | \(0.711813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.20540 | −0.645650 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.67444 | −0.204565 | −0.102283 | − | 0.994755i | \(-0.532615\pi\) | ||||
−0.102283 | + | 0.994755i | \(0.532615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2795 | −1.69467 | −0.847333 | − | 0.531062i | \(-0.821793\pi\) | ||||
−0.847333 | + | 0.531062i | \(0.821793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.04382 | − | 5.27205i | 0.356252 | − | 0.617047i | −0.631079 | − | 0.775718i | \(-0.717388\pi\) |
0.987331 | + | 0.158671i | \(0.0507211\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.46705 | + | 3.39353i | 0.281146 | + | 0.386729i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.31066 | −0.935022 | −0.467511 | − | 0.883987i | \(-0.654849\pi\) | ||||
−0.467511 | + | 0.883987i | \(0.654849\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.12095 | + | 12.3339i | −0.781626 | + | 1.35382i | 0.149368 | + | 0.988782i | \(0.452276\pi\) |
−0.930994 | + | 0.365034i | \(0.881057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.66278 | − | 4.61207i | −0.288819 | − | 0.500249i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.69272 | − | 11.5921i | −0.709426 | − | 1.22876i | −0.965070 | − | 0.261992i | \(-0.915621\pi\) |
0.255644 | − | 0.966771i | \(-0.417713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.85392 | + | 10.8034i | 0.823315 | + | 1.13250i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.810407 | −0.0831460 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.67500 | + | 4.63323i | −0.271605 | + | 0.470433i | −0.969273 | − | 0.245988i | \(-0.920888\pi\) |
0.697668 | + | 0.716421i | \(0.254221\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.59038 | − | 2.75462i | −0.158249 | − | 0.274095i | 0.775988 | − | 0.630747i | \(-0.217251\pi\) |
−0.934237 | + | 0.356652i | \(0.883918\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.70660 | − | 9.88412i | 0.562288 | − | 0.973911i | −0.435008 | − | 0.900426i | \(-0.643255\pi\) |
0.997296 | − | 0.0734850i | \(-0.0234121\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.311386 | + | 0.539337i | 0.0301028 | + | 0.0521396i | 0.880684 | − | 0.473704i | \(-0.157083\pi\) |
−0.850582 | + | 0.525843i | \(0.823750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.971921 | − | 1.68342i | 0.0930932 | − | 0.161242i | −0.815718 | − | 0.578450i | \(-0.803658\pi\) |
0.908811 | + | 0.417208i | \(0.136991\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.79416 | + | 3.10758i | 0.168781 | + | 0.292337i | 0.937991 | − | 0.346658i | \(-0.112684\pi\) |
−0.769211 | + | 0.638995i | \(0.779350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.02415 | + | 5.23798i | 0.282004 | + | 0.488445i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.55438 | + | 12.4851i | −0.509170 | + | 1.14451i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.24269 | − | 7.34855i | 0.385699 | − | 0.668050i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.21489 | 0.824205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6202 | 1.03113 | 0.515563 | − | 0.856852i | \(-0.327583\pi\) | ||||
0.515563 | + | 0.856852i | \(0.327583\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.07898 | + | 7.06501i | −0.356382 | + | 0.617272i | −0.987354 | − | 0.158534i | \(-0.949323\pi\) |
0.630971 | + | 0.775806i | \(0.282657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.22274 | + | 1.68194i | 0.106025 | + | 0.145842i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.28181 | − | 12.6125i | −0.622127 | − | 1.07756i | −0.989089 | − | 0.147320i | \(-0.952935\pi\) |
0.366962 | − | 0.930236i | \(-0.380398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.91713 | + | 10.2488i | 0.501884 | + | 0.869289i | 0.999998 | + | 0.00217698i | \(0.000692954\pi\) |
−0.498113 | + | 0.867112i | \(0.665974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00269 | + | 6.93287i | −0.334722 | + | 0.579756i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.58343 | + | 7.93873i | 0.380633 | + | 0.659276i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.02477 | + | 12.1673i | −0.575492 | + | 0.996781i | 0.420496 | + | 0.907294i | \(0.361856\pi\) |
−0.995988 | + | 0.0894868i | \(0.971477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24269 | − | 2.15240i | −0.101128 | − | 0.175159i | 0.811021 | − | 0.585016i | \(-0.198912\pi\) |
−0.912150 | + | 0.409857i | \(0.865579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.593329 | + | 1.02768i | −0.0476573 | + | 0.0825449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.03934 | −0.242565 | −0.121283 | − | 0.992618i | \(-0.538701\pi\) | ||||
−0.121283 | + | 0.992618i | \(0.538701\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.30818 | − | 14.1795i | 0.497154 | − | 1.11750i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.75883 | − | 15.1707i | −0.686045 | − | 1.18826i | −0.973107 | − | 0.230352i | \(-0.926012\pi\) |
0.287063 | − | 0.957912i | \(-0.407321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2738 | + | 21.2588i | 0.949775 | + | 1.64506i | 0.745897 | + | 0.666061i | \(0.232021\pi\) |
0.203877 | + | 0.978996i | \(0.434646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24269 | + | 10.8126i | −0.480207 | + | 0.831742i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0689138 | 0.00523942 | 0.00261971 | − | 0.999997i | \(-0.499166\pi\) | ||||
0.00261971 | + | 0.999997i | \(0.499166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.12469 | − | 8.42477i | −0.462983 | − | 0.636853i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.96086 | + | 6.86041i | −0.296049 | + | 0.512771i | −0.975228 | − | 0.221201i | \(-0.929002\pi\) |
0.679180 | + | 0.733972i | \(0.262336\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.59688 | 0.267354 | 0.133677 | − | 0.991025i | \(-0.457322\pi\) | ||||
0.133677 | + | 0.991025i | \(0.457322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.41373 | 0.618590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.19018 | −0.598925 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0492 | −1.16128 | −0.580638 | − | 0.814162i | \(-0.697197\pi\) | ||||
−0.580638 | + | 0.814162i | \(0.697197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5730 | −1.55286 | −0.776430 | − | 0.630204i | \(-0.782971\pi\) | ||||
−0.776430 | + | 0.630204i | \(0.782971\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4441 | 1.45659 | 0.728293 | − | 0.685266i | \(-0.240314\pi\) | ||||
0.728293 | + | 0.685266i | \(0.240314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50056 | + | 11.2593i | −0.460812 | + | 0.798150i | −0.999002 | − | 0.0446737i | \(-0.985775\pi\) |
0.538189 | + | 0.842824i | \(0.319109\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.56074 | − | 21.4905i | 0.671032 | − | 1.50834i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.98510 | 0.557703 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.623163 | + | 1.07935i | −0.0431051 | + | 0.0746602i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.11924 | − | 3.67064i | −0.145895 | − | 0.252697i | 0.783812 | − | 0.620999i | \(-0.213273\pi\) |
−0.929706 | + | 0.368302i | \(0.879939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.30569 | − | 2.26151i | −0.0890470 | − | 0.154234i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.02808 | − | 0.319152i | 0.205559 | − | 0.0216655i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.0737 | −1.75391 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.83329 | − | 10.1036i | 0.390626 | − | 0.676584i | −0.601906 | − | 0.798567i | \(-0.705592\pi\) |
0.992532 | + | 0.121982i | \(0.0389252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.08989 | + | 3.61980i | 0.138711 | + | 0.240255i | 0.927009 | − | 0.375039i | \(-0.122371\pi\) |
−0.788298 | + | 0.615294i | \(0.789037\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.19086 | − | 7.25878i | 0.276940 | − | 0.479674i | −0.693683 | − | 0.720280i | \(-0.744013\pi\) |
0.970623 | + | 0.240607i | \(0.0773464\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.499512 | − | 0.865180i | −0.0327241 | − | 0.0566798i | 0.849200 | − | 0.528072i | \(-0.177085\pi\) |
−0.881924 | + | 0.471392i | \(0.843752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.37807 | + | 7.58305i | −0.285594 | + | 0.494663i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.15412 | − | 10.6593i | −0.398077 | − | 0.689490i | 0.595411 | − | 0.803421i | \(-0.296989\pi\) |
−0.993489 | + | 0.113931i | \(0.963656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.23916 | − | 5.61039i | −0.208653 | − | 0.361397i | 0.742638 | − | 0.669694i | \(-0.233575\pi\) |
−0.951290 | + | 0.308296i | \(0.900241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.22645 | − | 6.86586i | 0.142243 | − | 0.438643i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.98386 | + | 3.43614i | −0.126230 | + | 0.218636i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.2236 | −0.771544 | −0.385772 | − | 0.922594i | \(-0.626065\pi\) | ||||
−0.385772 | + | 0.922594i | \(0.626065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.30169 | 0.584792 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.96355 | − | 13.7933i | 0.496753 | − | 0.860401i | −0.503240 | − | 0.864147i | \(-0.667859\pi\) |
0.999993 | + | 0.00374541i | \(0.00119220\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.6947 | − | 17.4621i | −0.788808 | − | 1.08504i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5305 | + | 19.9714i | 0.711002 | + | 1.23149i | 0.964481 | + | 0.264150i | \(0.0850916\pi\) |
−0.253480 | + | 0.967341i | \(0.581575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.48778 | + | 4.30897i | 0.152823 | + | 0.264698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.51107 | + | 9.54546i | −0.336016 | + | 0.581997i | −0.983679 | − | 0.179930i | \(-0.942413\pi\) |
0.647663 | + | 0.761927i | \(0.275746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74213 | + | 4.74951i | 0.166572 | + | 0.288512i | 0.937213 | − | 0.348759i | \(-0.113397\pi\) |
−0.770640 | + | 0.637271i | \(0.780063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.12140 | − | 5.40643i | 0.188228 | − | 0.326020i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0331 | + | 26.0381i | 0.903253 | + | 1.56448i | 0.823246 | + | 0.567685i | \(0.192161\pi\) |
0.0800068 | + | 0.996794i | \(0.474506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.90908 | − | 10.2348i | 0.352506 | − | 0.610559i | −0.634182 | − | 0.773184i | \(-0.718663\pi\) |
0.986688 | + | 0.162625i | \(0.0519961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.1210 | 1.25552 | 0.627758 | − | 0.778409i | \(-0.283973\pi\) | ||||
0.627758 | + | 0.778409i | \(0.283973\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0479 | − | 16.5725i | −0.711167 | − | 0.978241i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.83778 | − | 8.37928i | −0.284575 | − | 0.492899i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.15098 | + | 10.6538i | 0.359344 | + | 0.622402i | 0.987851 | − | 0.155401i | \(-0.0496671\pi\) |
−0.628507 | + | 0.777804i | \(0.716334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.99648 | + | 3.45800i | −0.116239 | + | 0.201332i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.6122 | 1.71252 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.72358 | + | 6.12203i | −0.156984 | + | 0.352868i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.97209 | + | 8.61191i | −0.284701 | + | 0.493117i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.5033 | −1.91213 | −0.956067 | − | 0.293147i | \(-0.905297\pi\) | ||||
−0.956067 | + | 0.293147i | \(0.905297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.6114 | −1.67911 | −0.839555 | − | 0.543275i | \(-0.817184\pi\) | ||||
−0.839555 | + | 0.543275i | \(0.817184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7149 | −0.662165 | −0.331082 | − | 0.943602i | \(-0.607414\pi\) | ||||
−0.331082 | + | 0.943602i | \(0.607414\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.16168 | −0.121412 | −0.0607061 | − | 0.998156i | \(-0.519335\pi\) | ||||
−0.0607061 | + | 0.998156i | \(0.519335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0977 | 0.789321 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.05930 | −0.225866 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.93707 | − | 17.2115i | 0.551209 | − | 0.954723i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.3437 | − | 2.35497i | 1.23185 | − | 0.129834i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.2003 | 1.71492 | 0.857461 | − | 0.514549i | \(-0.172041\pi\) | ||||
0.857461 | + | 0.514549i | \(0.172041\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.863273 | + | 1.49523i | −0.0471656 | + | 0.0816933i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.94425 | − | 3.36753i | −0.105910 | − | 0.183441i | 0.808200 | − | 0.588908i | \(-0.200442\pi\) |
−0.914110 | + | 0.405467i | \(0.867109\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.912481 | + | 1.58046i | 0.0494136 | + | 0.0855869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6088 | + | 5.73840i | −0.950787 | + | 0.309845i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.7566 | −0.899543 | −0.449771 | − | 0.893144i | \(-0.648495\pi\) | ||||
−0.449771 | + | 0.893144i | \(0.648495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9097 | − | 27.5564i | 0.851625 | − | 1.47506i | −0.0281152 | − | 0.999605i | \(-0.508951\pi\) |
0.879741 | − | 0.475454i | \(-0.157716\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.66867 | + | 6.35431i | 0.195263 | + | 0.338206i | 0.946987 | − | 0.321272i | \(-0.104111\pi\) |
−0.751723 | + | 0.659478i | \(0.770777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.36193 | + | 12.7512i | −0.390731 | + | 0.676765i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.16644 | + | 12.4126i | 0.378230 | + | 0.655114i | 0.990805 | − | 0.135299i | \(-0.0431994\pi\) |
−0.612574 | + | 0.790413i | \(0.709866\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.19114 | − | 15.9195i | 0.483744 | − | 0.837870i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.13854 | − | 5.43611i | −0.164279 | − | 0.284539i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7865 | − | 22.1469i | −0.667450 | − | 1.15606i | −0.978615 | − | 0.205702i | \(-0.934052\pi\) |
0.311165 | − | 0.950356i | \(-0.399281\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.18935 | − | 11.6646i | 0.269418 | − | 0.605595i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5734 | + | 26.9739i | −0.806361 | + | 1.39666i | 0.109008 | + | 0.994041i | \(0.465233\pi\) |
−0.915368 | + | 0.402617i | \(0.868101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.8805 | 2.31146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.72979 | −0.345686 | −0.172843 | − | 0.984949i | \(-0.555295\pi\) | ||||
−0.172843 | + | 0.984949i | \(0.555295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.7673 | − | 32.5060i | 0.958967 | − | 1.66098i | 0.233949 | − | 0.972249i | \(-0.424835\pi\) |
0.725018 | − | 0.688730i | \(-0.241832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.30225 | − | 0.453446i | 0.219263 | − | 0.0231098i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.3213 | − | 26.5372i | −0.776819 | − | 1.34549i | −0.933766 | − | 0.357883i | \(-0.883499\pi\) |
0.156947 | − | 0.987607i | \(-0.449835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1479 | + | 26.2369i | 0.766061 | + | 1.32686i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.28464 | + | 7.42121i | −0.215583 | + | 0.373401i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.65885 | − | 4.60527i | −0.133444 | − | 0.231132i | 0.791558 | − | 0.611094i | \(-0.209270\pi\) |
−0.925002 | + | 0.379962i | \(0.875937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.328399 | − | 0.568803i | 0.0163994 | − | 0.0284047i | −0.857709 | − | 0.514135i | \(-0.828113\pi\) |
0.874109 | + | 0.485730i | \(0.161446\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.90491 | + | 5.03145i | 0.144704 | + | 0.250634i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.46974 | − | 11.2059i | 0.320693 | − | 0.555457i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.5988 | −1.56246 | −0.781230 | − | 0.624243i | \(-0.785407\pi\) | ||||
−0.781230 | + | 0.624243i | \(0.785407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1891 | − | 1.07391i | 0.501373 | − | 0.0528435i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.34254 | + | 12.7177i | 0.360431 | + | 0.624285i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4424 | + | 18.0868i | 0.510146 | + | 0.883598i | 0.999931 | + | 0.0117550i | \(0.00374180\pi\) |
−0.489785 | + | 0.871843i | \(0.662925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.79788 | + | 11.7743i | −0.331309 | + | 0.573843i | −0.982769 | − | 0.184840i | \(-0.940823\pi\) |
0.651460 | + | 0.758683i | \(0.274157\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.3329 | 0.986291 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.3753 | − | 2.67449i | 1.22799 | − | 0.129428i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.9416 | + | 24.1475i | −0.671541 | + | 1.16314i | 0.305926 | + | 0.952055i | \(0.401034\pi\) |
−0.977467 | + | 0.211088i | \(0.932299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.7059 | −1.09118 | −0.545589 | − | 0.838053i | \(-0.683694\pi\) | ||||
−0.545589 | + | 0.838053i | \(0.683694\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.61020 | 0.220536 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.9016 | 1.52258 | 0.761290 | − | 0.648411i | \(-0.224566\pi\) | ||||
0.761290 | + | 0.648411i | \(0.224566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.1257 | 1.66887 | 0.834436 | − | 0.551104i | \(-0.185793\pi\) | ||||
0.834436 | + | 0.551104i | \(0.185793\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.8020 | −0.654276 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.0966532 | 0.00456135 | 0.00228067 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228067 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.14014 | − | 10.6350i | 0.289128 | − | 0.500785i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6963 | − | 1.44356i | 0.642094 | − | 0.0676751i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0185 | −0.796092 | −0.398046 | − | 0.917365i | \(-0.630312\pi\) | ||||
−0.398046 | + | 0.917365i | \(0.630312\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.08817 | − | 14.0091i | 0.376704 | − | 0.652470i | −0.613877 | − | 0.789402i | \(-0.710391\pi\) |
0.990580 | + | 0.136932i | \(0.0437242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.24297 | + | 10.8131i | 0.290135 | + | 0.502529i | 0.973842 | − | 0.227228i | \(-0.0729663\pi\) |
−0.683706 | + | 0.729757i | \(0.739633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.72717 | − | 11.6518i | −0.311296 | − | 0.539181i | 0.667347 | − | 0.744747i | \(-0.267430\pi\) |
−0.978643 | + | 0.205566i | \(0.934097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.40575 | − | 0.464355i | 0.203439 | − | 0.0214419i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.01603 | −0.184657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.54706 | − | 2.67959i | 0.0709840 | − | 0.122948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.98107 | − | 12.0916i | −0.318973 | − | 0.552478i | 0.661301 | − | 0.750121i | \(-0.270005\pi\) |
−0.980274 | + | 0.197643i | \(0.936671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5966 | − | 35.6744i | 0.939124 | − | 1.62661i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.75824 | + | 4.77741i | 0.125245 | + | 0.216931i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4858 | − | 25.0901i | 0.656413 | − | 1.13694i | −0.325124 | − | 0.945671i | \(-0.605406\pi\) |
0.981538 | − | 0.191270i | \(-0.0612605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.8775 | − | 36.1609i | −0.942189 | − | 1.63192i | −0.761283 | − | 0.648419i | \(-0.775430\pi\) |
−0.180906 | − | 0.983500i | \(-0.557903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.9583 | + | 39.7649i | 1.03399 | + | 1.79092i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.5719 | − | 3.95999i | 1.68533 | − | 0.177630i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7230 | + | 18.5728i | −0.480028 | + | 0.831433i | −0.999738 | − | 0.0229099i | \(-0.992707\pi\) |
0.519709 | + | 0.854343i | \(0.326040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.3098 | 1.26227 | 0.631135 | − | 0.775673i | \(-0.282589\pi\) | ||||
0.631135 | + | 0.775673i | \(0.282589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.27974 | −0.145947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.8142 | − | 27.3910i | 0.700951 | − | 1.21408i | −0.267182 | − | 0.963646i | \(-0.586092\pi\) |
0.968133 | − | 0.250437i | \(-0.0805743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.54679 | + | 14.7158i | −0.289613 | + | 0.650989i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.88418 | − | 10.1917i | −0.259288 | − | 0.449100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.73304 | + | 11.6620i | 0.296119 | + | 0.512893i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0364 | − | 26.0439i | 0.658759 | − | 1.14100i | −0.322179 | − | 0.946679i | \(-0.604415\pi\) |
0.980937 | − | 0.194325i | \(-0.0622515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.73793 | + | 13.4025i | 0.338356 | + | 0.586050i | 0.984124 | − | 0.177484i | \(-0.0567959\pi\) |
−0.645768 | + | 0.763534i | \(0.723463\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.97197 | + | 5.14760i | −0.129461 | + | 0.224233i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.70363 | − | 9.87898i | −0.247984 | − | 0.429521i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.5473 | − | 33.8570i | 0.846689 | − | 1.46651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.642152 | 0.0277626 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.43234 | − | 8.24482i | −0.320133 | − | 0.355130i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.11884 | − | 14.0622i | −0.349056 | − | 0.604583i | 0.637026 | − | 0.770842i | \(-0.280164\pi\) |
−0.986082 | + | 0.166259i | \(0.946831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.00217 | − | 1.73580i | −0.0429281 | − | 0.0743536i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4541 | − | 33.6954i | 0.831795 | − | 1.44071i | −0.0648180 | − | 0.997897i | \(-0.520647\pi\) |
0.896613 | − | 0.442815i | \(-0.146020\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.98726 | 0.297667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.8668 | − | 2.30471i | 0.929872 | − | 0.0980062i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.86210 | − | 4.95730i | 0.121271 | − | 0.210048i | −0.798998 | − | 0.601334i | \(-0.794636\pi\) |
0.920269 | + | 0.391286i | \(0.127970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.7851 | −0.540754 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.94667 | 0.208477 | 0.104239 | − | 0.994552i | \(-0.466759\pi\) | ||||
0.104239 | + | 0.994552i | \(0.466759\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.69999 | 0.155660 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.2194 | 0.679954 | 0.339977 | − | 0.940434i | \(-0.389581\pi\) | ||||
0.339977 | + | 0.940434i | \(0.389581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.6058 | −1.53191 | −0.765954 | − | 0.642896i | \(-0.777733\pi\) | ||||
−0.765954 | + | 0.642896i | \(0.777733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.0923 | −0.963017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.2684 | + | 31.6417i | −0.760522 | + | 1.31726i | 0.182060 | + | 0.983287i | \(0.441723\pi\) |
−0.942582 | + | 0.333975i | \(0.891610\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.3161 | − | 34.4273i | 0.635418 | − | 1.42829i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.65192 | 0.316910 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9237 | + | 20.6525i | −0.492144 | + | 0.852419i | −0.999959 | − | 0.00904721i | \(-0.997120\pi\) |
0.507815 | + | 0.861466i | \(0.330453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.452253 | + | 0.783325i | 0.0186348 | + | 0.0322764i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.54751 | − | 11.3406i | −0.268874 | − | 0.465704i | 0.699697 | − | 0.714439i | \(-0.253318\pi\) |
−0.968571 | + | 0.248736i | \(0.919985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.28526 | + | 11.3967i | 0.339663 | + | 0.467220i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.1539 | −1.51807 | −0.759034 | − | 0.651051i | \(-0.774328\pi\) | ||||
−0.759034 | + | 0.651051i | \(0.774328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.53133 | − | 14.7767i | 0.348000 | − | 0.602754i | −0.637894 | − | 0.770124i | \(-0.720194\pi\) |
0.985894 | + | 0.167370i | \(0.0535275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.37471 | − | 7.57722i | −0.177857 | − | 0.308058i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5973 | + | 20.0871i | −0.470719 | + | 0.815310i | −0.999439 | − | 0.0334867i | \(-0.989339\pi\) |
0.528720 | + | 0.848796i | \(0.322672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.4348 | + | 37.1262i | 0.867160 | + | 1.50197i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2875 | − | 38.6030i | 0.900182 | − | 1.55916i | 0.0729255 | − | 0.997337i | \(-0.476766\pi\) |
0.827257 | − | 0.561824i | \(-0.189900\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.12703 | − | 5.41618i | −0.125890 | − | 0.218047i | 0.796191 | − | 0.605046i | \(-0.206845\pi\) |
−0.922080 | + | 0.386999i | \(0.873512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.770208 | + | 1.33404i | 0.0309573 | + | 0.0536196i | 0.881089 | − | 0.472951i | \(-0.156811\pi\) |
−0.850132 | + | 0.526570i | \(0.823478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.8244 | + | 28.6449i | 0.834314 | + | 1.14763i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.09116 | + | 8.81816i | −0.203647 | + | 0.352726i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.1441 | 1.68040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.5148 | −1.77210 | −0.886052 | − | 0.463585i | \(-0.846563\pi\) | ||||
−0.886052 | + | 0.463585i | \(0.846563\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.99090 | − | 10.3765i | 0.237742 | − | 0.411781i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.6611 | − | 26.2476i | −0.937485 | − | 1.03997i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.87520 | − | 3.24794i | −0.0740660 | − | 0.128286i | 0.826614 | − | 0.562770i | \(-0.190264\pi\) |
−0.900680 | + | 0.434484i | \(0.856931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.818392 | − | 1.41750i | −0.0322742 | − | 0.0559006i | 0.849437 | − | 0.527690i | \(-0.176942\pi\) |
−0.881711 | + | 0.471789i | \(0.843608\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0748 | + | 17.4501i | −0.396082 | + | 0.686034i | −0.993239 | − | 0.116091i | \(-0.962964\pi\) |
0.597157 | + | 0.802125i | \(0.296297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.07038 | + | 5.31806i | 0.120523 | + | 0.208752i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.4570 | + | 37.1646i | −0.839677 | + | 1.45436i | 0.0504888 | + | 0.998725i | \(0.483922\pi\) |
−0.890165 | + | 0.455638i | \(0.849411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.20591 | + | 7.28486i | 0.164339 | + | 0.284643i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.8526 | + | 18.7973i | −0.422758 | + | 0.732238i | −0.996208 | − | 0.0870025i | \(-0.972271\pi\) |
0.573450 | + | 0.819240i | \(0.305605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.3815 | −0.987225 | −0.493613 | − | 0.869682i | \(-0.664324\pi\) | ||||
−0.493613 | + | 0.869682i | \(0.664324\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.13232 | − | 0.224742i | 0.0826880 | − | 0.00871511i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.0740 | − | 45.1614i | −1.00959 | − | 1.74866i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.64658 | + | 13.2443i | 0.295193 | + | 0.511289i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.88676 | − | 13.6603i | 0.304012 | − | 0.526565i | −0.673029 | − | 0.739616i | \(-0.735007\pi\) |
0.977041 | + | 0.213052i | \(0.0683403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.6506 | −0.409336 | −0.204668 | − | 0.978831i | \(-0.565612\pi\) | ||||
−0.204668 | + | 0.978831i | \(0.565612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.75351 | − | 12.9327i | 0.220799 | − | 0.496311i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3656 | + | 24.8819i | −0.549683 | + | 0.952078i | 0.448613 | + | 0.893726i | \(0.351918\pi\) |
−0.998296 | + | 0.0583524i | \(0.981415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0168 | −0.573763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.3601 | 0.928046 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.2272 | −1.49227 | −0.746136 | − | 0.665794i | \(-0.768093\pi\) | ||||
−0.746136 | + | 0.665794i | \(0.768093\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.2025 | 0.462868 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.9971 | 1.51500 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.1643 | −1.29037 | −0.645184 | − | 0.764028i | \(-0.723219\pi\) | ||||
−0.645184 | + | 0.764028i | \(0.723219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20660 | − | 5.55399i | 0.120939 | − | 0.209473i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.94848 | + | 6.80685i | 0.186107 | + | 0.255998i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.7070 | 0.740113 | 0.370057 | − | 0.929009i | \(-0.379338\pi\) | ||||
0.370057 | + | 0.929009i | \(0.379338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.37530 | − | 5.84619i | 0.126406 | − | 0.218941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.12725 | + | 7.14861i | 0.154350 | + | 0.267343i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.87829 | − | 10.1815i | −0.219223 | − | 0.379705i | 0.735348 | − | 0.677690i | \(-0.237019\pi\) |
−0.954571 | + | 0.297985i | \(0.903686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2740 | + | 27.5894i | −0.457108 | + | 1.02748i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.9989 | −1.29983 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8161 | − | 39.5186i | 0.846202 | − | 1.46567i | −0.0383705 | − | 0.999264i | \(-0.512217\pi\) |
0.884573 | − | 0.466402i | \(-0.154450\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.54014 | − | 11.3279i | −0.241896 | − | 0.418976i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4901 | + | 33.7579i | −0.719885 | + | 1.24688i | 0.241160 | + | 0.970485i | \(0.422472\pi\) |
−0.961045 | + | 0.276392i | \(0.910861\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.32763 | + | 2.29952i | 0.0489038 | + | 0.0847039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.7719 | + | 20.3895i | −0.433036 | + | 0.750040i | −0.997133 | − | 0.0756686i | \(-0.975891\pi\) |
0.564097 | + | 0.825708i | \(0.309224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.09612 | − | 7.09469i | −0.150272 | − | 0.260279i | 0.781055 | − | 0.624462i | \(-0.214682\pi\) |
−0.931327 | + | 0.364183i | \(0.881348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.24337 | + | 12.5459i | 0.265377 | + | 0.459646i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.968881 | − | 1.33274i | −0.0354021 | − | 0.0486971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0936 | − | 24.4109i | 0.514284 | − | 0.890766i | −0.485578 | − | 0.874193i | \(-0.661391\pi\) |
0.999863 | − | 0.0165733i | \(-0.00527570\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.56271 | −0.0932667 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.42352 | 0.269812 | 0.134906 | − | 0.990858i | \(-0.456927\pi\) | ||||
0.134906 | + | 0.990858i | \(0.456927\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.3534 | − | 26.5928i | 0.556559 | − | 0.963988i | −0.441222 | − | 0.897398i | \(-0.645455\pi\) |
0.997780 | − | 0.0665900i | \(-0.0212120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.09045 | + | 4.69890i | −0.0756795 | + | 0.170112i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.77465 | + | 16.9302i | 0.352942 | + | 0.611314i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0973 | + | 34.8095i | 0.724727 | + | 1.25526i | 0.959086 | + | 0.283113i | \(0.0913673\pi\) |
−0.234360 | + | 0.972150i | \(0.575299\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.69611 | − | 2.93775i | 0.0610050 | − | 0.105664i | −0.833910 | − | 0.551901i | \(-0.813903\pi\) |
0.894915 | + | 0.446237i | \(0.147236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.26532 | − | 3.92365i | −0.0813727 | − | 0.140942i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.04324 | − | 5.27105i | 0.109035 | − | 0.188855i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3219 | + | 19.6101i | 0.405130 | + | 0.701706i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.56696 | + | 2.71405i | −0.0559271 | + | 0.0968686i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.8331 | 0.386160 | 0.193080 | − | 0.981183i | \(-0.438152\pi\) | ||||
0.193080 | + | 0.981183i | \(0.438152\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.58256 | − | 7.67904i | −0.198493 | − | 0.273035i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.3431 | + | 42.1635i | 0.864449 | + | 1.49727i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.4982 | + | 40.7001i | 0.832350 | + | 1.44167i | 0.896170 | + | 0.443712i | \(0.146339\pi\) |
−0.0638193 | + | 0.997961i | \(0.520328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.9296 | + | 37.9832i | −0.775814 | + | 1.34375i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.65352 | −0.340665 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.40968 | − | 12.9434i | −0.331648 | − | 0.456195i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5052 | − | 25.1238i | 0.509977 | − | 0.883306i | −0.489957 | − | 0.871747i | \(-0.662987\pi\) |
0.999933 | − | 0.0115587i | \(-0.00367932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6805 | 1.21780 | 0.608899 | − | 0.793248i | \(-0.291612\pi\) | ||||
0.608899 | + | 0.793248i | \(0.291612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0628 | −0.632712 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.99047 | −0.0696376 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.3213 | −1.37232 | −0.686161 | − | 0.727450i | \(-0.740705\pi\) | ||||
−0.686161 | + | 0.727450i | \(0.740705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.6864 | −1.48796 | −0.743978 | − | 0.668204i | \(-0.767063\pi\) | ||||
−0.743978 | + | 0.668204i | \(0.767063\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5672 | −0.506551 | −0.253276 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253276 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6920 | − | 28.9113i | 0.579736 | − | 1.00413i | −0.415773 | − | 0.909468i | \(-0.636489\pi\) |
0.995509 | − | 0.0946641i | \(-0.0301777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.1522 | − | 34.3908i | 0.386401 | − | 1.19157i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.3115 | 0.875939 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.987290 | − | 1.71004i | 0.0340850 | − | 0.0590370i | −0.848480 | − | 0.529228i | \(-0.822482\pi\) |
0.882565 | + | 0.470191i | \(0.155815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0179 | − | 43.3323i | −0.862687 | − | 1.49422i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.43695 | + | 11.1491i | 0.221438 | + | 0.383541i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.12536 | + | 20.5119i | −0.313551 | + | 0.704798i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.8636 | −1.64074 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.68637 | − | 11.5811i | 0.228937 | − | 0.396531i | −0.728556 | − | 0.684986i | \(-0.759808\pi\) |
0.957493 | + | 0.288455i | \(0.0931417\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.4324 | + | 23.2656i | 0.458842 | + | 0.794738i | 0.998900 | − | 0.0468899i | \(-0.0149310\pi\) |
−0.540058 | + | 0.841628i | \(0.681598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9212 | − | 39.7007i | 0.782062 | − | 1.35457i | −0.148677 | − | 0.988886i | \(-0.547502\pi\) |
0.930739 | − | 0.365685i | \(-0.119165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.90612 | − | 10.2297i | −0.201047 | − | 0.348223i | 0.747819 | − | 0.663902i | \(-0.231101\pi\) |
−0.948866 | + | 0.315679i | \(0.897768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0355291 | − | 0.0615383i | 0.00120803 | − | 0.00209236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.58935 | + | 11.4131i | 0.223528 | + | 0.387162i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.22654 | + | 7.32059i | 0.143211 | + | 0.248049i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.2460 | + | 2.55547i | −0.819665 | + | 0.0863907i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6046 | − | 21.8318i | 0.425628 | − | 0.737209i | −0.570851 | − | 0.821054i | \(-0.693387\pi\) |
0.996479 | + | 0.0838449i | \(0.0267200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.268589 | 0.00904898 | 0.00452449 | − | 0.999990i | \(-0.498560\pi\) | ||||
0.00452449 | + | 0.999990i | \(0.498560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.8915 | 0.871319 | 0.435660 | − | 0.900112i | \(-0.356515\pi\) | ||||
0.435660 | + | 0.900112i | \(0.356515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.8396 | − | 37.8274i | 0.733303 | − | 1.27012i | −0.222160 | − | 0.975010i | \(-0.571311\pi\) |
0.955464 | − | 0.295109i | \(-0.0953558\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.5748 | + | 3.22251i | −1.02545 | + | 0.108080i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.33710 | + | 5.78003i | 0.111672 | + | 0.193421i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.08412 | + | 7.07390i | 0.136517 | + | 0.236454i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.11563 | − | 8.86053i | 0.170616 | − | 0.295515i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4612 | + | 21.5835i | 0.415143 | + | 0.719050i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.85441 | − | 3.21192i | 0.0616425 | − | 0.106768i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0146274 | + | 0.0253355i | 0.000485696 | + | 0.000841251i | 0.866268 | − | 0.499579i | \(-0.166512\pi\) |
−0.865782 | + | 0.500421i | \(0.833179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0048 | − | 24.2569i | 0.463998 | − | 0.803668i | −0.535158 | − | 0.844752i | \(-0.679748\pi\) |
0.999156 | + | 0.0410839i | \(0.0130811\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5842 | 0.747428 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.77326 | − | 19.7205i | 0.289719 | − | 0.651227i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.11476 | − | 10.5911i | −0.201707 | − | 0.349367i | 0.747371 | − | 0.664407i | \(-0.231316\pi\) |
−0.949079 | + | 0.315039i | \(0.897982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0436 | + | 62.4294i | 1.18639 | + | 2.05489i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0618 | + | 27.8198i | −0.528107 | + | 0.914709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.96405 | 0.261292 | 0.130646 | − | 0.991429i | \(-0.458295\pi\) | ||||
0.130646 | + | 0.991429i | \(0.458295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.68369 | − | 4.08638i | −0.120728 | − | 0.133926i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.22252 | + | 7.31363i | −0.138091 | + | 0.239181i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0407 | −0.491358 | −0.245679 | − | 0.969351i | \(-0.579011\pi\) | ||||
−0.245679 | + | 0.969351i | \(0.579011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.9119 | −1.88787 | −0.943936 | − | 0.330128i | \(-0.892908\pi\) | ||||
−0.943936 | + | 0.330128i | \(0.892908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.4252 | −1.47925 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.6883 | −0.769767 | −0.384883 | − | 0.922965i | \(-0.625758\pi\) | ||||
−0.384883 | + | 0.922965i | \(0.625758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.7323 | −0.997611 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.2226 | −0.460716 | −0.230358 | − | 0.973106i | \(-0.573990\pi\) | ||||
−0.230358 | + | 0.973106i | \(0.573990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.27429 | + | 14.3315i | −0.267750 | + | 0.463756i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.6574 | + | 31.1663i | 0.731646 | + | 1.00641i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6756 | −0.957276 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.1222 | + | 19.2642i | −0.358035 | + | 0.620135i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3665 | + | 17.9554i | 0.333365 | + | 0.577405i | 0.983169 | − | 0.182696i | \(-0.0584825\pi\) |
−0.649804 | + | 0.760102i | \(0.725149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.39847 | − | 14.5466i | −0.269520 | − | 0.466822i | 0.699218 | − | 0.714908i | \(-0.253532\pi\) |
−0.968738 | + | 0.248087i | \(0.920198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.4112 | − | 25.3254i | −0.590236 | − | 0.811894i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.4327 | 1.19758 | 0.598788 | − | 0.800907i | \(-0.295649\pi\) | ||||
0.598788 | + | 0.800907i | \(0.295649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6130 | + | 18.3823i | −0.339194 | + | 0.587501i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.8389 | − | 44.7543i | −0.824132 | − | 1.42744i | −0.902581 | − | 0.430521i | \(-0.858330\pi\) |
0.0784482 | − | 0.996918i | \(-0.475003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5402 | − | 18.2561i | 0.335838 | − | 0.581688i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.42771 | + | 12.8652i | 0.236188 | + | 0.409089i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.5452 | − | 49.4418i | 0.906769 | − | 1.57057i | 0.0882435 | − | 0.996099i | \(-0.471875\pi\) |
0.818525 | − | 0.574471i | \(-0.194792\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.70284 | + | 11.6097i | 0.212494 | + | 0.368051i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.00745 | + | 1.74496i | 0.0319063 | + | 0.0552633i | 0.881538 | − | 0.472114i | \(-0.156509\pi\) |
−0.849631 | + | 0.527377i | \(0.823176\pi\) | |||||||
\(998\) | 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 | 2268.2.i.n.865.6 | 16 | ||
3.2 | odd | 2 | inner | 2268.2.i.n.865.3 | 16 | ||
7.2 | even | 3 | 2268.2.l.n.541.3 | 16 | |||
9.2 | odd | 6 | 2268.2.k.g.1621.3 | yes | 16 | ||
9.4 | even | 3 | 2268.2.l.n.109.3 | 16 | |||
9.5 | odd | 6 | 2268.2.l.n.109.6 | 16 | |||
9.7 | even | 3 | 2268.2.k.g.1621.6 | yes | 16 | ||
21.2 | odd | 6 | 2268.2.l.n.541.6 | 16 | |||
63.2 | odd | 6 | 2268.2.k.g.1297.3 | ✓ | 16 | ||
63.16 | even | 3 | 2268.2.k.g.1297.6 | yes | 16 | ||
63.23 | odd | 6 | inner | 2268.2.i.n.2053.3 | 16 | ||
63.58 | even | 3 | inner | 2268.2.i.n.2053.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.n.865.3 | 16 | 3.2 | odd | 2 | inner | ||
2268.2.i.n.865.6 | 16 | 1.1 | even | 1 | trivial | ||
2268.2.i.n.2053.3 | 16 | 63.23 | odd | 6 | inner | ||
2268.2.i.n.2053.6 | 16 | 63.58 | even | 3 | inner | ||
2268.2.k.g.1297.3 | ✓ | 16 | 63.2 | odd | 6 | ||
2268.2.k.g.1297.6 | yes | 16 | 63.16 | even | 3 | ||
2268.2.k.g.1621.3 | yes | 16 | 9.2 | odd | 6 | ||
2268.2.k.g.1621.6 | yes | 16 | 9.7 | even | 3 | ||
2268.2.l.n.109.3 | 16 | 9.4 | even | 3 | |||
2268.2.l.n.109.6 | 16 | 9.5 | odd | 6 | |||
2268.2.l.n.541.3 | 16 | 7.2 | even | 3 | |||
2268.2.l.n.541.6 | 16 | 21.2 | odd | 6 |