Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [228,3,Mod(5,228)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(228, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 16]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("228.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 228.s (of order \(18\), degree \(6\), 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: | \(6.21255002741\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(0.939693 - 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 228.5 |
Dual form | 228.3.s.a.137.1 |
$q$-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 \(\left(\mathbb{Z}/228\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) | \(115\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.520945 | + | 2.95442i | −0.173648 | + | 0.984808i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.99660 | − | 12.1185i | −0.999514 | − | 1.73121i | −0.526760 | − | 0.850014i | \(-0.676593\pi\) |
−0.472754 | − | 0.881194i | \(-0.656740\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.45723 | − | 3.07818i | −0.939693 | − | 0.342020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37985 | − | 7.82553i | −0.106142 | − | 0.601964i | −0.990758 | − | 0.135642i | \(-0.956690\pi\) |
0.884615 | − | 0.466321i | \(-0.154421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 39.4479 | − | 14.3579i | 1.87847 | − | 0.683708i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.7217 | − | 49.7474i | −0.926506 | − | 1.60476i | −0.789121 | − | 0.614238i | \(-0.789464\pi\) |
−0.137385 | − | 0.990518i | \(-0.543870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.1279 | −1.30075 | −0.650376 | − | 0.759612i | \(-0.725389\pi\) | ||||
−0.650376 | + | 0.759612i | \(0.725389\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 23.8388 | 0.611250 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.94587 | − | 4.98918i | −0.138276 | − | 0.116027i | 0.571026 | − | 0.820932i | \(-0.306545\pi\) |
−0.709302 | + | 0.704904i | \(0.750990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −73.4047 | + | 127.141i | −1.49806 | + | 2.59471i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 50.8655 | + | 25.7235i | 0.892378 | + | 0.451290i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 91.1856 | − | 76.5138i | 1.49485 | − | 1.25432i | 0.606557 | − | 0.795040i | \(-0.292550\pi\) |
0.888289 | − | 0.459285i | \(-0.151894\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.8690 | + | 124.025i | 0.347127 | + | 1.96866i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −71.1993 | − | 25.9144i | −1.06268 | − | 0.386782i | −0.249243 | − | 0.968441i | \(-0.580182\pi\) |
−0.813433 | + | 0.581659i | \(0.802404\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.5854 | + | 122.417i | −0.295690 | + | 1.67694i | 0.368693 | + | 0.929551i | \(0.379805\pi\) |
−0.664384 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −1.00000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.56610 | − | 42.9095i | 0.0957734 | − | 0.543158i | −0.898734 | − | 0.438494i | \(-0.855512\pi\) |
0.994508 | − | 0.104664i | \(-0.0333768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 62.0496 | + | 52.0658i | 0.766044 | + | 0.642788i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −85.1791 | + | 71.4738i | −0.936034 | + | 0.785426i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 161.937 | − | 58.9404i | 1.74126 | − | 0.633767i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 158.808 | − | 57.8014i | 1.63720 | − | 0.595891i | 0.650651 | − | 0.759377i | \(-0.274496\pi\) |
0.986546 | + | 0.163486i | \(0.0522740\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −96.5731 | + | 167.270i | −0.937603 | + | 1.62398i | −0.167678 | + | 0.985842i | \(0.553627\pi\) |
−0.769925 | + | 0.638135i | \(0.779706\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 54.3892 | + | 45.6379i | 0.498983 | + | 0.418697i | 0.857233 | − | 0.514929i | \(-0.172182\pi\) |
−0.358250 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.0719 | − | 142.190i | 0.225873 | − | 1.28099i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.4187 | + | 70.4298i | −0.106142 | + | 0.601964i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.5000 | − | 104.789i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −43.9330 | − | 249.156i | −0.345929 | − | 1.96186i | −0.260266 | − | 0.965537i | \(-0.583810\pi\) |
−0.0856630 | − | 0.996324i | \(-0.527301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.8376 | − | 14.9675i | 0.138276 | − | 0.116027i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −258.874 | + | 60.5923i | −1.94642 | + | 0.455581i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 28.0062 | + | 158.831i | 0.201484 | + | 1.14267i | 0.902878 | + | 0.429898i | \(0.141450\pi\) |
−0.701394 | + | 0.712774i | \(0.747439\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −337.388 | − | 283.102i | −2.29515 | − | 1.92586i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 227.000 | 1.50331 | 0.751656 | − | 0.659556i | \(-0.229256\pi\) | ||||
0.751656 | + | 0.659556i | \(0.229256\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −235.217 | − | 197.371i | −1.49820 | − | 1.25714i | −0.883549 | − | 0.468338i | \(-0.844853\pi\) |
−0.614650 | − | 0.788800i | \(-0.710703\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 162.699 | − | 281.803i | 0.998153 | − | 1.72885i | 0.446462 | − | 0.894802i | \(-0.352684\pi\) |
0.551690 | − | 0.834049i | \(-0.313983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 99.4731 | − | 36.2053i | 0.588598 | − | 0.214232i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −102.496 | + | 136.878i | −0.599393 | + | 0.800455i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 267.985 | − | 224.866i | 1.53134 | − | 1.28495i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 294.124 | + | 107.052i | 1.62499 | + | 0.591449i | 0.984324 | − | 0.176368i | \(-0.0564349\pi\) |
0.640669 | + | 0.767817i | \(0.278657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 178.552 | + | 309.260i | 0.975692 | + | 1.68995i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −377.816 | −1.99903 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 59.0414 | − | 334.840i | 0.305914 | − | 1.73492i | −0.313257 | − | 0.949668i | \(-0.601420\pi\) |
0.619171 | − | 0.785256i | \(-0.287469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 372.020 | + | 135.404i | 1.86945 | + | 0.680423i | 0.969849 | + | 0.243706i | \(0.0783631\pi\) |
0.899599 | + | 0.436718i | \(0.143859\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 113.653 | − | 196.853i | 0.565438 | − | 0.979367i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.8875 | + | 7.96641i | −0.103732 | + | 0.0377555i | −0.393365 | − | 0.919382i | \(-0.628689\pi\) |
0.289633 | + | 0.957138i | \(0.406467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −401.908 | + | 696.125i | −1.85211 | + | 3.20795i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −350.426 | − | 127.545i | −1.60012 | − | 0.582396i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −174.559 | − | 146.472i | −0.782776 | − | 0.656827i | 0.161170 | − | 0.986927i | \(-0.448473\pi\) |
−0.943946 | + | 0.330099i | \(0.892918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 39.0708 | − | 221.582i | 0.173648 | − | 0.984808i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 131.961 | 0.576247 | 0.288124 | − | 0.957593i | \(-0.406969\pi\) | ||||
0.288124 | + | 0.957593i | \(0.406969\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 122.831 | + | 44.7069i | 0.518275 | + | 0.188637i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 57.7244 | + | 327.371i | 0.239520 | + | 1.35839i | 0.832881 | + | 0.553451i | \(0.186690\pi\) |
−0.593361 | + | 0.804936i | \(0.702199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −186.149 | + | 156.197i | −0.766044 | + | 0.642788i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −149.908 | − | 17.9457i | −0.606917 | − | 0.0726546i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 336.731 | + | 583.236i | 1.30012 | + | 2.25187i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 229.047 | + | 192.193i | 0.845193 | + | 0.709201i | 0.958726 | − | 0.284333i | \(-0.0917722\pi\) |
−0.113533 | + | 0.993534i | \(0.536217\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −166.790 | − | 288.889i | −0.610953 | − | 1.05820i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −203.500 | + | 352.472i | −0.734657 | + | 1.27246i | 0.220217 | + | 0.975451i | \(0.429324\pi\) |
−0.954874 | + | 0.297012i | \(0.904010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 89.7744 | + | 509.136i | 0.321772 | + | 1.82486i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −55.4419 | + | 20.1792i | −0.195908 | + | 0.0713046i | −0.438111 | − | 0.898921i | \(-0.644352\pi\) |
0.242203 | + | 0.970226i | \(0.422130\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 221.387 | − | 185.766i | 0.766044 | − | 0.642788i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 88.0396 | + | 499.298i | 0.302542 | + | 1.71580i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.8603 | + | 106.962i | −0.0626588 | + | 0.355356i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 106.099 | − | 601.718i | 0.345599 | − | 1.95999i | 0.0755672 | − | 0.997141i | \(-0.475923\pi\) |
0.270032 | − | 0.962851i | \(-0.412966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −443.876 | − | 372.456i | −1.43649 | − | 1.20536i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −562.876 | − | 204.870i | −1.79833 | − | 0.654537i | −0.998526 | − | 0.0542693i | \(-0.982717\pi\) |
−0.799799 | − | 0.600268i | \(-0.795061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 186.676 | − | 67.9445i | 0.574387 | − | 0.209060i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −163.167 | + | 136.914i | −0.498983 | + | 0.418697i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 75.3010 | − | 130.425i | 0.227495 | − | 0.394034i | −0.729570 | − | 0.683906i | \(-0.760280\pi\) |
0.957065 | + | 0.289873i | \(0.0936130\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 407.029 | + | 148.146i | 1.22231 | + | 0.444884i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 50.8690 | + | 42.6841i | 0.150946 | + | 0.126659i | 0.715134 | − | 0.698988i | \(-0.246366\pi\) |
−0.564187 | + | 0.825647i | \(0.690810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1368.67 | 3.99028 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −152.927 | − | 264.878i | −0.438187 | − | 0.758963i | 0.559362 | − | 0.828923i | \(-0.311046\pi\) |
−0.997550 | + | 0.0699605i | \(0.977713\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −201.610 | − | 73.3800i | −0.574387 | − | 0.209060i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −300.500 | − | 200.052i | −0.832410 | − | 0.554160i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 341.108 | − | 124.153i | 0.939693 | − | 0.342020i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 108.108 | + | 613.110i | 0.294572 | + | 1.67060i | 0.668937 | + | 0.743319i | \(0.266749\pi\) |
−0.374365 | + | 0.927281i | \(0.622139\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −349.000 | − | 604.486i | −0.935657 | − | 1.62061i | −0.773458 | − | 0.633847i | \(-0.781475\pi\) |
−0.162198 | − | 0.986758i | \(-0.551858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −727.583 | −1.91974 | −0.959872 | − | 0.280439i | \(-0.909520\pi\) | ||||
−0.959872 | + | 0.280439i | \(0.909520\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 759.000 | 1.99213 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.9280 | + | 60.4971i | 0.0902533 | + | 0.156323i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 166.264 | − | 60.5153i | 0.418802 | − | 0.152432i | −0.124019 | − | 0.992280i | \(-0.539578\pi\) |
0.542821 | + | 0.839848i | \(0.317356\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −44.1563 | − | 796.389i | −0.110667 | − | 1.99596i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −349.668 | + | 293.406i | −0.867663 | + | 0.728056i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −588.248 | − | 214.105i | −1.43826 | − | 0.523483i | −0.498972 | − | 0.866618i | \(-0.666289\pi\) |
−0.939286 | + | 0.343135i | \(0.888511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −483.845 | −1.16030 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 145.691 | − | 826.254i | 0.346059 | − | 1.96260i | 0.0899710 | − | 0.995944i | \(-0.471323\pi\) |
0.256088 | − | 0.966653i | \(-0.417566\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1565.22 | − | 569.693i | −3.66562 | − | 1.33418i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −51.9450 | + | 43.5870i | −0.119965 | + | 0.100663i | −0.700797 | − | 0.713361i | \(-0.747172\pi\) |
0.580831 | + | 0.814024i | \(0.302728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −459.618 | + | 167.287i | −1.04697 | + | 0.381065i | −0.807517 | − | 0.589844i | \(-0.799189\pi\) |
−0.239449 | + | 0.970909i | \(0.576967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1012.16 | − | 849.306i | 2.29515 | − | 1.92586i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −118.254 | + | 670.654i | −0.261047 | + | 1.48047i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 268.027 | 0.586493 | 0.293246 | − | 0.956037i | \(-0.405264\pi\) | ||||
0.293246 | + | 0.956037i | \(0.405264\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −43.4653 | − | 75.2841i | −0.0938775 | − | 0.162601i | 0.815262 | − | 0.579092i | \(-0.196593\pi\) |
−0.909140 | + | 0.416492i | \(0.863260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 184.110 | + | 1044.14i | 0.392558 | + | 2.22631i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 705.652 | − | 592.112i | 1.49820 | − | 1.25714i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 471.633 | + | 56.4596i | 0.992911 | + | 0.118862i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 66.4093 | + | 376.626i | 0.138065 | + | 0.783006i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 174.500 | + | 302.243i | 0.358316 | + | 0.620622i | 0.987680 | − | 0.156489i | \(-0.0500176\pi\) |
−0.629363 | + | 0.777111i | \(0.716684\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 747.808 | + | 627.485i | 1.52926 | + | 1.28320i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −475.995 | − | 399.407i | −0.953897 | − | 0.800415i | 0.0260521 | − | 0.999661i | \(-0.491706\pi\) |
−0.979950 | + | 0.199246i | \(0.936151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 55.1457 | + | 312.747i | 0.108769 | + | 0.616857i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1634.53 | − | 594.919i | 3.19868 | − | 1.16423i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −351.000 | − | 374.123i | −0.684211 | − | 0.729285i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −751.340 | − | 273.466i | −1.43660 | − | 0.522879i | −0.497783 | − | 0.867302i | \(-0.665852\pi\) |
−0.938815 | + | 0.344423i | \(0.888075\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 524.745 | + | 908.885i | 0.999514 | + | 1.73121i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 91.8599 | − | 520.963i | 0.173648 | − | 0.984808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −463.652 | − | 168.755i | −0.857027 | − | 0.311932i | −0.124125 | − | 0.992267i | \(-0.539612\pi\) |
−0.732902 | + | 0.680334i | \(0.761835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −469.500 | + | 813.198i | −0.864641 | + | 1.49760i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −664.426 | + | 557.520i | −1.21467 | + | 1.01923i | −0.215587 | + | 0.976485i | \(0.569167\pi\) |
−0.999086 | + | 0.0427471i | \(0.986389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1006.70 | + | 366.409i | −1.83370 | + | 0.667412i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −572.934 | + | 208.531i | −1.03605 | + | 0.377090i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.8385 | + | 53.4139i | −0.0551673 | + | 0.0955526i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 196.821 | − | 1116.23i | 0.347127 | − | 1.96866i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1079.00 | 1.88968 | 0.944838 | − | 0.327539i | \(-0.106219\pi\) | ||||
0.944838 | + | 0.327539i | \(0.106219\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 516.500 | + | 894.604i | 0.895147 | + | 1.55044i | 0.833622 | + | 0.552335i | \(0.186263\pi\) |
0.0615251 | + | 0.998106i | \(0.480404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 958.503 | + | 348.867i | 1.65545 | + | 0.602533i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1062.70 | + | 248.737i | −1.80425 | + | 0.422304i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −593.843 | + | 1028.57i | −0.994712 | + | 1.72289i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 548.832 | + | 950.605i | 0.913198 | + | 1.58171i | 0.809518 | + | 0.587095i | \(0.199728\pi\) |
0.103680 | + | 0.994611i | \(0.466938\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 522.379 | + | 438.328i | 0.866301 | + | 0.726913i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1028.33 | −1.69412 | −0.847062 | − | 0.531495i | \(-0.821631\pi\) | ||||
−0.847062 | + | 0.531495i | \(0.821631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 753.022 | + | 631.860i | 1.22842 | + | 1.03077i | 0.998340 | + | 0.0575954i | \(0.0183434\pi\) |
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 619.000 | − | 1072.14i | 1.00000 | − | 1.73205i | 0.499306 | − | 0.866426i | \(-0.333588\pi\) |
0.500693 | − | 0.865625i | \(-0.333078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −587.308 | + | 213.763i | −0.939693 | + | 0.342020i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −764.718 | + | 641.675i | −1.21191 | + | 1.01692i | −0.212707 | + | 0.977116i | \(0.568228\pi\) |
−0.999208 | + | 0.0398015i | \(0.987327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.1340 | − | 68.8151i | −0.0191690 | − | 0.108713i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1096.23 | + | 398.995i | 1.72093 | + | 0.626367i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −203.794 | + | 1155.78i | −0.316943 | + | 1.79747i | 0.244168 | + | 0.969733i | \(0.421485\pi\) |
−0.561111 | + | 0.827741i | \(0.689626\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1847.28 | − | 1550.05i | −2.83760 | − | 2.38103i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 559.374 | − | 968.864i | 0.851406 | − | 1.47468i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 93.4574 | − | 78.4201i | 0.141388 | − | 0.118639i | −0.569351 | − | 0.822095i | \(-0.692805\pi\) |
0.710739 | + | 0.703456i | \(0.248361\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 523.677 | − | 439.417i | 0.782776 | − | 0.656827i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 240.952 | − | 417.342i | 0.358027 | − | 0.620122i | −0.629604 | − | 0.776916i | \(-0.716783\pi\) |
0.987631 | + | 0.156795i | \(0.0501161\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 634.293 | + | 230.864i | 0.939693 | + | 0.342020i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1811.58 | − | 1520.10i | −2.66801 | − | 2.23873i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −68.7442 | + | 389.867i | −0.100064 | + | 0.567493i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −509.500 | − | 882.480i | −0.737337 | − | 1.27711i | −0.953690 | − | 0.300790i | \(-0.902750\pi\) |
0.216353 | − | 0.976315i | \(-0.430584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −264.703 | + | 875.279i | −0.376534 | + | 1.24506i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.15172 | − | 29.2169i | −0.00726618 | − | 0.0412085i | 0.980959 | − | 0.194214i | \(-0.0622158\pi\) |
−0.988225 | + | 0.153006i | \(0.951105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −196.071 | + | 339.606i | −0.275769 | + | 0.477645i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2702.73 | 3.74859 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −997.265 | −1.37934 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 958.321 | + | 804.127i | 1.31819 | + | 1.10609i | 0.986687 | + | 0.162634i | \(0.0519989\pi\) |
0.331499 | + | 0.943455i | \(0.392446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −364.500 | − | 631.333i | −0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 708.500 | − | 1227.16i | 0.966576 | − | 1.67416i | 0.261255 | − | 0.965270i | \(-0.415864\pi\) |
0.705321 | − | 0.708888i | \(-0.250803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 968.778 | − | 352.606i | 1.31093 | − | 0.477140i | 0.410390 | − | 0.911910i | \(-0.365393\pi\) |
0.900541 | + | 0.434771i | \(0.143171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 131.113 | − | 433.544i | 0.176941 | − | 0.585080i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −321.232 | − | 116.919i | −0.427739 | − | 0.155684i | 0.119174 | − | 0.992873i | \(-0.461975\pi\) |
−0.546914 | + | 0.837189i | \(0.684197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 211.630 | − | 1200.21i | 0.279564 | − | 1.58548i | −0.444518 | − | 0.895770i | \(-0.646625\pi\) |
0.724082 | − | 0.689714i | \(-0.242264\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 172.522 | − | 978.423i | 0.226111 | − | 1.28234i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1171.20 | + | 426.282i | 1.52302 | + | 0.554333i | 0.961900 | − | 0.273402i | \(-0.0881490\pi\) |
0.561118 | + | 0.827736i | \(0.310371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1100.10 | − | 923.097i | 1.41949 | − | 1.19109i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1898.54 | + | 691.013i | −2.44343 | + | 0.889335i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −535.934 | + | 928.264i | −0.680983 | + | 1.17950i | 0.293698 | + | 0.955898i | \(0.405114\pi\) |
−0.974681 | + | 0.223599i | \(0.928219\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −724.584 | − | 607.998i | −0.913725 | − | 0.766706i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.9330 | − | 249.156i | −0.0541714 | − | 0.307221i | 0.945668 | − | 0.325133i | \(-0.105409\pi\) |
−0.999840 | + | 0.0179122i | \(0.994298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −687.142 | + | 576.580i | −0.845193 | + | 0.709201i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −123.438 | + | 80.6943i | −0.151087 | + | 0.0987690i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 940.389 | − | 342.274i | 1.14822 | − | 0.417916i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −281.484 | − | 1596.37i | −0.342022 | − | 1.93970i | −0.341999 | − | 0.939700i | \(-0.611104\pi\) |
−2.25276e−5 | − | 1.00000i | \(-0.500007\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −824.404 | − | 1427.91i | −0.994457 | − | 1.72245i | −0.588289 | − | 0.808650i | \(-0.700198\pi\) |
−0.406167 | − | 0.913799i | \(-0.633135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −935.340 | − | 784.844i | −1.12556 | − | 0.944457i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1550.97 | −1.85301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 644.243 | + | 540.584i | 0.766044 | + | 0.642788i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −846.588 | + | 1466.33i | −0.999514 | + | 1.73121i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.7357 | − | 174.311i | −0.0362023 | − | 0.205313i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1334.90 | − | 485.865i | 1.56495 | − | 0.569596i | 0.593087 | − | 0.805138i | \(-0.297909\pi\) |
0.971864 | + | 0.235543i | \(0.0756867\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −543.110 | + | 455.723i | −0.632258 | + | 0.530528i | −0.901630 | − | 0.432509i | \(-0.857629\pi\) |
0.269371 | + | 0.963036i | \(0.413184\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 433.500 | + | 750.844i | 0.500000 | + | 0.866025i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −104.550 | + | 592.930i | −0.120034 | + | 0.680746i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1521.00 | −1.74227 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 263.949 | − | 1496.93i | 0.300968 | − | 1.70687i | −0.340935 | − | 0.940087i | \(-0.610744\pi\) |
0.641903 | − | 0.766786i | \(-0.278145\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 713.706 | + | 259.768i | 0.808274 | + | 0.294188i | 0.712911 | − | 0.701255i | \(-0.247377\pi\) |
0.0953631 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2712.01 | + | 2275.65i | −3.05063 | + | 2.55978i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −306.186 | − | 111.443i | −0.339076 | − | 0.123414i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1277.00 | + | 1071.53i | 1.40793 | + | 1.18140i | 0.957445 | + | 0.288615i | \(0.0931946\pi\) |
0.450489 | + | 0.892782i | \(0.351250\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 129.645 | + | 224.553i | 0.141072 | + | 0.244344i | 0.927901 | − | 0.372827i | \(-0.121612\pi\) |
−0.786828 | + | 0.617172i | \(0.788278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1722.46 | + | 626.923i | 1.87020 | + | 0.680698i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −208.933 | − | 1184.92i | −0.225873 | − | 1.28099i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1331.63 | − | 1117.37i | 1.43649 | − | 1.20536i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1908.52 | + | 2034.25i | 2.04997 | + | 2.18502i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 210.313 | + | 1192.74i | 0.224453 | + | 1.27294i | 0.863728 | + | 0.503959i | \(0.168124\pi\) |
−0.639274 | + | 0.768979i | \(0.720765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 898.500 | − | 1556.25i | 0.956869 | − | 1.65735i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 987.761 | 1.04084 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1169.37 | + | 2025.41i | −1.21683 | + | 2.10761i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −976.020 | + | 355.242i | −1.00933 | + | 0.367365i | −0.793175 | − | 0.608994i | \(-0.791573\pi\) |
−0.216153 | + | 0.976359i | \(0.569351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1728.84 | − | 1450.67i | 1.77682 | − | 1.49093i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 103.489 | + | 586.915i | 0.106142 | + | 0.601964i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −319.500 | − | 553.390i | −0.325688 | − | 0.564108i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −227.288 | + | 1289.01i | −0.229352 | + | 1.30072i | 0.624835 | + | 0.780756i | \(0.285166\pi\) |
−0.854188 | + | 0.519965i | \(0.825945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 346.103 | + | 290.415i | 0.348543 | + | 0.292462i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1472.04 | − | 535.780i | −1.47647 | − | 0.537392i | −0.526623 | − | 0.850099i | \(-0.676542\pi\) |
−0.949850 | + | 0.312707i | \(0.898764\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −649.726 | + | 1125.36i | −0.650376 | + | 1.12649i |
(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 | 228.3.s.a.5.1 | ✓ | 6 | |
3.2 | odd | 2 | CM | 228.3.s.a.5.1 | ✓ | 6 | |
19.4 | even | 9 | inner | 228.3.s.a.137.1 | yes | 6 | |
57.23 | odd | 18 | inner | 228.3.s.a.137.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.s.a.5.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
228.3.s.a.5.1 | ✓ | 6 | 3.2 | odd | 2 | CM | |
228.3.s.a.137.1 | yes | 6 | 19.4 | even | 9 | inner | |
228.3.s.a.137.1 | yes | 6 | 57.23 | odd | 18 | inner |