Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1279,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1279.2 | ||
Root | \(1.20036 - 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1279 |
Dual form | 2304.3.g.z.1279.1 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.98203 | −1.59641 | −0.798203 | − | 0.602388i | \(-0.794216\pi\) | ||||
−0.798203 | + | 0.602388i | \(0.794216\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.13878i | 0.305540i | 0.988262 | + | 0.152770i | \(0.0488193\pi\) | ||||
−0.988262 | + | 0.152770i | \(0.951181\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 8.00000i | − 0.727273i | −0.931541 | − | 0.363636i | \(-0.881535\pi\) | ||||
0.931541 | − | 0.363636i | \(-0.118465\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.6865 | 0.898962 | 0.449481 | − | 0.893290i | \(-0.351609\pi\) | ||||
0.449481 | + | 0.893290i | \(0.351609\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.8564 | −0.697436 | −0.348718 | − | 0.937228i | \(-0.613383\pi\) | ||||
−0.348718 | + | 0.937228i | \(0.613383\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.9282i | 0.785695i | 0.919604 | + | 0.392847i | \(0.128510\pi\) | ||||
−0.919604 | + | 0.392847i | \(0.871490\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.27756i | 0.185981i | 0.995667 | + | 0.0929904i | \(0.0296426\pi\) | ||||
−0.995667 | + | 0.0929904i | \(0.970357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38.7128 | 1.54851 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.573084 | −0.0197615 | −0.00988076 | − | 0.999951i | \(-0.503145\pi\) | ||||
−0.00988076 | + | 0.999951i | \(0.503145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.4399i | 1.85290i | 0.376417 | + | 0.926450i | \(0.377156\pi\) | ||||
−0.376417 | + | 0.926450i | \(0.622844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 17.0718i | − 0.487766i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.6506 | −0.747313 | −0.373656 | − | 0.927567i | \(-0.621896\pi\) | ||||
−0.373656 | + | 0.927567i | \(0.621896\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −31.5692 | −0.769981 | −0.384990 | − | 0.922921i | \(-0.625795\pi\) | ||||
−0.384990 | + | 0.922921i | \(0.625795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 28.7846i | − 0.669410i | −0.942323 | − | 0.334705i | \(-0.891363\pi\) | ||||
0.942323 | − | 0.334705i | \(-0.108637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 59.5787i | 1.26763i | 0.773484 | + | 0.633816i | \(0.218512\pi\) | ||||
−0.773484 | + | 0.633816i | \(0.781488\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.4256 | 0.906645 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 31.3550 | 0.591604 | 0.295802 | − | 0.955249i | \(-0.404413\pi\) | ||||
0.295802 | + | 0.955249i | \(0.404413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.8562i | 1.16102i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 52.7846i | − 0.894654i | −0.894370 | − | 0.447327i | \(-0.852376\pi\) | ||||
0.894370 | − | 0.447327i | \(-0.147624\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −59.5787 | −0.976700 | −0.488350 | − | 0.872648i | \(-0.662401\pi\) | ||||
−0.488350 | + | 0.872648i | \(0.662401\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −93.2820 | −1.43511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 84.7846i | − 1.26544i | −0.774380 | − | 0.632721i | \(-0.781938\pi\) | ||||
0.774380 | − | 0.632721i | \(-0.218062\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42.4685i | 0.598147i | 0.954230 | + | 0.299074i | \(0.0966776\pi\) | ||||
−0.954230 | + | 0.299074i | \(0.903322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.42563 | 0.0743236 | 0.0371618 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371618 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.1102 | 0.222211 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 44.6072i | − 0.564649i | −0.959319 | − | 0.282324i | \(-0.908895\pi\) | ||||
0.959319 | − | 0.282324i | \(-0.0911054\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 67.7128i | − 0.815817i | −0.913023 | − | 0.407909i | \(-0.866258\pi\) | ||||
0.913023 | − | 0.407909i | \(-0.133742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 94.6382 | 1.11339 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −133.138 | −1.49594 | −0.747969 | − | 0.663734i | \(-0.768971\pi\) | ||||
−0.747969 | + | 0.663734i | \(0.768971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.9948i | 0.274669i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 119.157i | − 1.25429i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 97.1384 | 1.00143 | 0.500714 | − | 0.865613i | \(-0.333071\pi\) | ||||
0.500714 | + | 0.865613i | \(0.333071\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −62.1370 | −0.615218 | −0.307609 | − | 0.951513i | \(-0.599529\pi\) | ||||
−0.307609 | + | 0.951513i | \(0.599529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 27.8041i | − 0.269943i | −0.990849 | − | 0.134971i | \(-0.956906\pi\) | ||||
0.990849 | − | 0.134971i | \(-0.0430943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 37.7795i | 0.353079i | 0.984294 | + | 0.176540i | \(0.0564903\pi\) | ||||
−0.984294 | + | 0.176540i | \(0.943510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 141.691 | 1.29992 | 0.649960 | − | 0.759968i | \(-0.274786\pi\) | ||||
0.649960 | + | 0.759968i | \(0.274786\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58.2872 | 0.515816 | 0.257908 | − | 0.966170i | \(-0.416967\pi\) | ||||
0.257908 | + | 0.966170i | \(0.416967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 34.1436i | − 0.296901i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 25.3582i | − 0.213094i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 57.0000 | 0.471074 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −109.456 | −0.875649 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 185.152i | − 1.45789i | −0.684571 | − | 0.728946i | \(-0.740010\pi\) | ||||
0.684571 | − | 0.728946i | \(-0.259990\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 125.359i | − 0.956939i | −0.878104 | − | 0.478469i | \(-0.841192\pi\) | ||||
0.878104 | − | 0.478469i | \(-0.158808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.9281 | −0.240061 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 99.5692 | 0.726783 | 0.363391 | − | 0.931637i | \(-0.381619\pi\) | ||||
0.363391 | + | 0.931637i | \(0.381619\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 177.492i | − 1.27692i | −0.769654 | − | 0.638461i | \(-0.779571\pi\) | ||||
0.769654 | − | 0.638461i | \(-0.220429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 93.4920i | − 0.653790i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.57437 | 0.0315474 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 87.8023 | 0.589277 | 0.294639 | − | 0.955609i | \(-0.404801\pi\) | ||||
0.294639 | + | 0.955609i | \(0.404801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 219.066i | − 1.45077i | −0.688345 | − | 0.725383i | \(-0.741663\pi\) | ||||
0.688345 | − | 0.725383i | \(-0.258337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 458.487i | − 2.95798i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −253.440 | −1.61427 | −0.807133 | − | 0.590370i | \(-0.798982\pi\) | ||||
−0.807133 | + | 0.590370i | \(0.798982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.14875 | −0.0568245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 102.354i | − 0.627938i | −0.949433 | − | 0.313969i | \(-0.898341\pi\) | ||||
0.949433 | − | 0.313969i | \(-0.101659\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 281.090i | − 1.68318i | −0.540120 | − | 0.841588i | \(-0.681621\pi\) | ||||
0.540120 | − | 0.841588i | \(-0.318379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −32.4256 | −0.191868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 242.858 | 1.40381 | 0.701903 | − | 0.712273i | \(-0.252334\pi\) | ||||
0.701903 | + | 0.712273i | \(0.252334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 82.7981i | 0.473132i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 318.354i | − 1.77851i | −0.457409 | − | 0.889257i | \(-0.651222\pi\) | ||||
0.457409 | − | 0.889257i | \(-0.348778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −79.5132 | −0.439299 | −0.219650 | − | 0.975579i | \(-0.570491\pi\) | ||||
−0.219650 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 220.708 | 1.19301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 94.8513i | 0.507226i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 352.887i | 1.84758i | 0.382902 | + | 0.923789i | \(0.374925\pi\) | ||||
−0.382902 | + | 0.923789i | \(0.625075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −284.277 | −1.47294 | −0.736469 | − | 0.676472i | \(-0.763508\pi\) | ||||
−0.736469 | + | 0.676472i | \(0.763508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 75.8087 | 0.384816 | 0.192408 | − | 0.981315i | \(-0.438370\pi\) | ||||
0.192408 | + | 0.981315i | \(0.438370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 104.186i | − 0.523547i | −0.965129 | − | 0.261774i | \(-0.915693\pi\) | ||||
0.965129 | − | 0.261774i | \(-0.0843074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.22570i | − 0.00603793i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 251.986 | 1.22920 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 119.426 | 0.571414 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 136.918i | 0.648900i | 0.945903 | + | 0.324450i | \(0.105179\pi\) | ||||
−0.945903 | + | 0.324450i | \(0.894821\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 229.760i | 1.06865i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −122.851 | −0.566135 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −138.560 | −0.626968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 53.1624i | 0.238396i | 0.992870 | + | 0.119198i | \(0.0380324\pi\) | ||||
−0.992870 | + | 0.119198i | \(0.961968\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 119.846i | 0.527956i | 0.964529 | + | 0.263978i | \(0.0850347\pi\) | ||||
−0.964529 | + | 0.263978i | \(0.914965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −214.103 | −0.934946 | −0.467473 | − | 0.884007i | \(-0.654836\pi\) | ||||
−0.467473 | + | 0.884007i | \(0.654836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −127.436 | −0.546935 | −0.273468 | − | 0.961881i | \(-0.588171\pi\) | ||||
−0.273468 | + | 0.961881i | \(0.588171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 475.559i | − 2.02365i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 319.281i | − 1.33590i | −0.744204 | − | 0.667952i | \(-0.767171\pi\) | ||||
0.744204 | − | 0.667952i | \(-0.232829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −247.415 | −1.02662 | −0.513310 | − | 0.858203i | \(-0.671581\pi\) | ||||
−0.513310 | + | 0.858203i | \(0.671581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −354.607 | −1.44737 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 174.459i | 0.706310i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 214.851i | − 0.855981i | −0.903783 | − | 0.427991i | \(-0.859222\pi\) | ||||
0.903783 | − | 0.427991i | \(-0.140778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.2205 | 0.135259 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 84.2769 | 0.327926 | 0.163963 | − | 0.986467i | \(-0.447572\pi\) | ||||
0.163963 | + | 0.986467i | \(0.447572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 59.1384i | − 0.228334i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 277.120i | 1.05369i | 0.849962 | + | 0.526844i | \(0.176625\pi\) | ||||
−0.849962 | + | 0.526844i | \(0.823375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −250.277 | −0.944441 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −123.701 | −0.459855 | −0.229927 | − | 0.973208i | \(-0.573849\pi\) | ||||
−0.229927 | + | 0.973208i | \(0.573849\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 197.985i | 0.730572i | 0.930895 | + | 0.365286i | \(0.119029\pi\) | ||||
−0.930895 | + | 0.365286i | \(0.880971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 309.703i | − 1.12619i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 247.709 | 0.894256 | 0.447128 | − | 0.894470i | \(-0.352447\pi\) | ||||
0.447128 | + | 0.894470i | \(0.352447\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 443.128 | 1.57697 | 0.788484 | − | 0.615055i | \(-0.210866\pi\) | ||||
0.788484 | + | 0.615055i | \(0.210866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 294.620i | 1.04106i | 0.853843 | + | 0.520531i | \(0.174266\pi\) | ||||
−0.853843 | + | 0.520531i | \(0.825734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 67.5196i | − 0.235260i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −148.426 | −0.513583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −66.7217 | −0.227719 | −0.113859 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113859 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 421.328i | 1.42823i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 49.9897i | 0.167190i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61.5639 | 0.204531 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 475.559 | 1.55921 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 524.210i | − 1.70753i | −0.520662 | − | 0.853763i | \(-0.674315\pi\) | ||||
0.520662 | − | 0.853763i | \(-0.325685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 362.057i | − 1.16417i | −0.813128 | − | 0.582085i | \(-0.802237\pi\) | ||||
0.813128 | − | 0.582085i | \(-0.197763\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −252.277 | −0.805996 | −0.402998 | − | 0.915201i | \(-0.632032\pi\) | ||||
−0.402998 | + | 0.915201i | \(0.632032\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 80.3934 | 0.253607 | 0.126803 | − | 0.991928i | \(-0.459528\pi\) | ||||
0.126803 | + | 0.991928i | \(0.459528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.58467i | 0.0143720i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 176.995i | − 0.547972i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 452.417 | 1.39205 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −127.426 | −0.387312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 172.056i | − 0.519808i | −0.965635 | − | 0.259904i | \(-0.916309\pi\) | ||||
0.965635 | − | 0.259904i | \(-0.0836909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 676.753i | 2.02016i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 564.277 | 1.67441 | 0.837206 | − | 0.546888i | \(-0.184187\pi\) | ||||
0.837206 | + | 0.546888i | \(0.184187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 459.519 | 1.34756 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 199.817i | 0.582556i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 286.123i | − 0.824562i | −0.911057 | − | 0.412281i | \(-0.864732\pi\) | ||||
0.911057 | − | 0.412281i | \(-0.135268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −421.021 | −1.20636 | −0.603182 | − | 0.797603i | \(-0.706101\pi\) | ||||
−0.603182 | + | 0.797603i | \(0.706101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −429.138 | −1.21569 | −0.607845 | − | 0.794056i | \(-0.707966\pi\) | ||||
−0.607845 | + | 0.794056i | \(0.707966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 338.985i | − 0.954886i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 263.673i | 0.734465i | 0.930129 | + | 0.367233i | \(0.119695\pi\) | ||||
−0.930129 | + | 0.367233i | \(0.880305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 138.149 | 0.382684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.3075 | −0.118651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 129.544i | − 0.352981i | −0.984302 | − | 0.176491i | \(-0.943525\pi\) | ||||
0.984302 | − | 0.176491i | \(-0.0564745\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 67.0615i | 0.180759i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −302.478 | −0.810933 | −0.405467 | − | 0.914110i | \(-0.632891\pi\) | ||||
−0.405467 | + | 0.914110i | \(0.632891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.69735 | −0.0177649 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 116.210i | 0.306623i | 0.988178 | + | 0.153312i | \(0.0489938\pi\) | ||||
−0.988178 | + | 0.153312i | \(0.951006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 566.151i | − 1.47820i | −0.673595 | − | 0.739101i | \(-0.735251\pi\) | ||||
0.673595 | − | 0.739101i | \(-0.264749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −136.574 | −0.354739 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 350.104 | 0.900011 | 0.450006 | − | 0.893026i | \(-0.351422\pi\) | ||||
0.450006 | + | 0.893026i | \(0.351422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 50.7165i | − 0.129710i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 356.056i | 0.901408i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −544.149 | −1.37065 | −0.685326 | − | 0.728236i | \(-0.740340\pi\) | ||||
−0.685326 | + | 0.728236i | \(0.740340\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 296.431 | 0.739229 | 0.369614 | − | 0.929185i | \(-0.379490\pi\) | ||||
0.369614 | + | 0.929185i | \(0.379490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 671.272i | 1.66569i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 221.205i | 0.543500i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 247.415 | 0.604927 | 0.302464 | − | 0.953161i | \(-0.402191\pi\) | ||||
0.302464 | + | 0.953161i | \(0.402191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 112.895 | 0.273353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 540.486i | 1.30238i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 92.1333i | 0.219889i | 0.993938 | + | 0.109944i | \(0.0350672\pi\) | ||||
−0.993938 | + | 0.109944i | \(0.964933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −445.540 | −1.05829 | −0.529145 | − | 0.848531i | \(-0.677487\pi\) | ||||
−0.529145 | + | 0.848531i | \(0.677487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −458.995 | −1.07999 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 127.426i | − 0.298421i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 186.677i | 0.433125i | 0.976269 | + | 0.216563i | \(0.0694845\pi\) | ||||
−0.976269 | + | 0.216563i | \(0.930515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 291.128 | 0.672351 | 0.336176 | − | 0.941799i | \(-0.390866\pi\) | ||||
0.336176 | + | 0.941799i | \(0.390866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −63.8562 | −0.146124 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 87.6899i | − 0.199749i | −0.995000 | − | 0.0998746i | \(-0.968156\pi\) | ||||
0.995000 | − | 0.0998746i | \(-0.0318442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7077i | 0.0467441i | 0.999727 | + | 0.0233721i | \(0.00744024\pi\) | ||||
−0.999727 | + | 0.0233721i | \(0.992560\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1062.72 | 2.38812 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −584.410 | −1.30158 | −0.650791 | − | 0.759257i | \(-0.725563\pi\) | ||||
−0.650791 | + | 0.759257i | \(0.725563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 252.554i | 0.559986i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 199.510i | − 0.438483i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 269.692 | 0.590136 | 0.295068 | − | 0.955476i | \(-0.404658\pi\) | ||||
0.295068 | + | 0.955476i | \(0.404658\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −44.4948 | −0.0965181 | −0.0482590 | − | 0.998835i | \(-0.515367\pi\) | ||||
−0.0482590 | + | 0.998835i | \(0.515367\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 611.065i | − 1.31980i | −0.751355 | − | 0.659898i | \(-0.770600\pi\) | ||||
0.751355 | − | 0.659898i | \(-0.229400\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 146.410i | − 0.313512i | −0.987637 | − | 0.156756i | \(-0.949896\pi\) | ||||
0.987637 | − | 0.156756i | \(-0.0501036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 181.336 | 0.386643 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −230.277 | −0.486843 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 577.913i | 1.21666i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 191.876i | 0.400576i | 0.979737 | + | 0.200288i | \(0.0641878\pi\) | ||||
−0.979737 | + | 0.200288i | \(0.935812\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −323.138 | −0.671805 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −775.362 | −1.59868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 610.758i | − 1.25412i | −0.778969 | − | 0.627062i | \(-0.784257\pi\) | ||||
0.778969 | − | 0.627062i | \(-0.215743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 142.354i | − 0.289926i | −0.989437 | − | 0.144963i | \(-0.953694\pi\) | ||||
0.989437 | − | 0.144963i | \(-0.0463064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.79472 | 0.0137824 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −90.8306 | −0.182758 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 91.3693i | 0.183105i | 0.995800 | + | 0.0915524i | \(0.0291829\pi\) | ||||
−0.995800 | + | 0.0915524i | \(0.970817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 230.067i | − 0.457389i | −0.973498 | − | 0.228695i | \(-0.926554\pi\) | ||||
0.973498 | − | 0.228695i | \(-0.0734457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 495.979 | 0.982137 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 527.387 | 1.03612 | 0.518062 | − | 0.855343i | \(-0.326654\pi\) | ||||
0.518062 | + | 0.855343i | \(0.326654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6042i | 0.0227088i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 221.933i | 0.430939i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 476.630 | 0.921914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 191.856 | 0.368246 | 0.184123 | − | 0.982903i | \(-0.441055\pi\) | ||||
0.184123 | + | 0.982903i | \(0.441055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 105.492i | − 0.201706i | −0.994901 | − | 0.100853i | \(-0.967843\pi\) | ||||
0.994901 | − | 0.100853i | \(-0.0321572\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 681.031i | − 1.29228i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 510.703 | 0.965411 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −368.934 | −0.692184 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 301.557i | − 0.563658i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 355.405i | − 0.659378i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 459.744 | 0.849804 | 0.424902 | − | 0.905239i | \(-0.360309\pi\) | ||||
0.424902 | + | 0.905239i | \(0.360309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1130.98 | −2.07520 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 67.3693i | 0.123161i | 0.998102 | + | 0.0615807i | \(0.0196142\pi\) | ||||
−0.998102 | + | 0.0615807i | \(0.980386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 8.55511i | − 0.0155265i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 95.4050 | 0.172523 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −476.671 | −0.855782 | −0.427891 | − | 0.903830i | \(-0.640743\pi\) | ||||
−0.427891 | + | 0.903830i | \(0.640743\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 336.391i | − 0.601774i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 910.123i | 1.61656i | 0.588799 | + | 0.808280i | \(0.299601\pi\) | ||||
−0.588799 | + | 0.808280i | \(0.700399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −465.250 | −0.823452 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −124.123 | −0.218142 | −0.109071 | − | 0.994034i | \(-0.534788\pi\) | ||||
−0.109071 | + | 0.994034i | \(0.534788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 945.031i | − 1.65504i | −0.561433 | − | 0.827522i | \(-0.689750\pi\) | ||||
0.561433 | − | 0.827522i | \(-0.310250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 165.596i | 0.287994i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 215.682 | 0.373799 | 0.186899 | − | 0.982379i | \(-0.440156\pi\) | ||||
0.186899 | + | 0.982379i | \(0.440156\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 144.823 | 0.249265 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 250.840i | − 0.430258i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 900.785i | 1.53456i | 0.641314 | + | 0.767278i | \(0.278389\pi\) | ||||
−0.641314 | + | 0.767278i | \(0.721611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −857.475 | −1.45581 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 508.585 | 0.857647 | 0.428824 | − | 0.903388i | \(-0.358928\pi\) | ||||
0.428824 | + | 0.903388i | \(0.358928\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 202.410i | 0.340185i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 846.934i | − 1.41391i | −0.707257 | − | 0.706957i | \(-0.750067\pi\) | ||||
0.707257 | − | 0.706957i | \(-0.249933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 406.000 | 0.675541 | 0.337770 | − | 0.941229i | \(-0.390327\pi\) | ||||
0.337770 | + | 0.941229i | \(0.390327\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −454.976 | −0.752026 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 771.156i | − 1.27044i | −0.772332 | − | 0.635219i | \(-0.780910\pi\) | ||||
0.772332 | − | 0.635219i | \(-0.219090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 696.267i | 1.13955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −336.699 | −0.549264 | −0.274632 | − | 0.961549i | \(-0.588556\pi\) | ||||
−0.274632 | + | 0.961549i | \(0.588556\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −908.831 | −1.47298 | −0.736492 | − | 0.676447i | \(-0.763519\pi\) | ||||
−0.736492 | + | 0.676447i | \(0.763519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1047.77i | 1.69268i | 0.532643 | + | 0.846340i | \(0.321199\pi\) | ||||
−0.532643 | + | 0.846340i | \(0.678801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 284.754i | − 0.457068i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −94.1384 | −0.150622 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 327.836 | 0.521202 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 610.758i | − 0.967921i | −0.875090 | − | 0.483961i | \(-0.839198\pi\) | ||||
0.875090 | − | 0.483961i | \(-0.160802\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1477.89i | 2.32739i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 519.180 | 0.815040 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.60015 | −0.0149768 | −0.00748842 | − | 0.999972i | \(-0.502384\pi\) | ||||
−0.00748842 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 86.1999i | 0.134059i | 0.997751 | + | 0.0670295i | \(0.0213522\pi\) | ||||
−0.997751 | + | 0.0670295i | \(0.978648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 352.580i | − 0.544946i | −0.962163 | − | 0.272473i | \(-0.912158\pi\) | ||||
0.962163 | − | 0.272473i | \(-0.0878416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −422.277 | −0.650658 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −319.322 | −0.489008 | −0.244504 | − | 0.969648i | \(-0.578625\pi\) | ||||
−0.244504 | + | 0.969648i | \(0.578625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1000.62i | 1.52766i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 275.328i | − 0.417797i | −0.977937 | − | 0.208898i | \(-0.933012\pi\) | ||||
0.977937 | − | 0.208898i | \(-0.0669878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −133.668 | −0.202221 | −0.101111 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101111 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 254.851 | 0.383235 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.45140i | − 0.00367526i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 476.630i | 0.710327i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 187.703 | 0.278904 | 0.139452 | − | 0.990229i | \(-0.455466\pi\) | ||||
0.139452 | + | 0.990229i | \(0.455466\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1169.84 | 1.72797 | 0.863986 | − | 0.503515i | \(-0.167960\pi\) | ||||
0.863986 | + | 0.503515i | \(0.167960\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 207.758i | 0.305976i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 89.4566i | 0.130976i | 0.997853 | + | 0.0654880i | \(0.0208604\pi\) | ||||
−0.997853 | + | 0.0654880i | \(0.979140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −794.765 | −1.16024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 366.431 | 0.531830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 139.103i | 0.201306i | 0.994922 | + | 0.100653i | \(0.0320933\pi\) | ||||
−0.994922 | + | 0.100653i | \(0.967907\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1416.75i | 2.03849i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 374.297 | 0.537012 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1218.34 | 1.73801 | 0.869004 | − | 0.494804i | \(-0.164760\pi\) | ||||
0.869004 | + | 0.494804i | \(0.164760\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 412.773i | − 0.587160i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 132.897i | − 0.187974i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1080.13 | 1.52346 | 0.761730 | − | 0.647895i | \(-0.224351\pi\) | ||||
0.761730 | + | 0.647895i | \(0.224351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −245.703 | −0.344604 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 746.256i | 1.04372i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 20.7736i | − 0.0288923i | −0.999896 | − | 0.0144461i | \(-0.995401\pi\) | ||||
0.999896 | − | 0.0144461i | \(-0.00459851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.4669 | 0.0824783 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.1857 | −0.0306010 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1031.17i | 1.41838i | 0.705015 | + | 0.709192i | \(0.250940\pi\) | ||||
−0.705015 | + | 0.709192i | \(0.749060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 341.282i | 0.466870i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −881.072 | −1.20201 | −0.601004 | − | 0.799246i | \(-0.705233\pi\) | ||||
−0.601004 | + | 0.799246i | \(0.705233\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −678.277 | −0.920321 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 671.195i | − 0.908247i | −0.890939 | − | 0.454124i | \(-0.849952\pi\) | ||||
0.890939 | − | 0.454124i | \(-0.150048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 254.197i | 0.342122i | 0.985260 | + | 0.171061i | \(0.0547195\pi\) | ||||
−0.985260 | + | 0.171061i | \(0.945281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −700.841 | −0.940726 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −80.8019 | −0.107880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 728.994i | 0.970698i | 0.874320 | + | 0.485349i | \(0.161307\pi\) | ||||
−0.874320 | + | 0.485349i | \(0.838693\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1748.59i | 2.31601i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −372.679 | −0.492311 | −0.246155 | − | 0.969230i | \(-0.579167\pi\) | ||||
−0.246155 | + | 0.969230i | \(0.579167\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1257.80 | 1.65283 | 0.826416 | − | 0.563060i | \(-0.190376\pi\) | ||||
0.826416 | + | 0.563060i | \(0.190376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 303.046i | 0.397177i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 616.868i | − 0.804260i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 247.703 | 0.322110 | 0.161055 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161055 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −587.805 | −0.760420 | −0.380210 | − | 0.924900i | \(-0.624148\pi\) | ||||
−0.380210 | + | 0.924900i | \(0.624148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2223.66i | 2.86924i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 471.272i | − 0.604970i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 339.748 | 0.435016 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2022.96 | 2.57702 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 31.0821i | − 0.0394944i | −0.999805 | − | 0.0197472i | \(-0.993714\pi\) | ||||
0.999805 | − | 0.0197472i | \(-0.00628614\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 124.663i | 0.157602i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −696.267 | −0.878016 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −490.260 | −0.615132 | −0.307566 | − | 0.951527i | \(-0.599514\pi\) | ||||
−0.307566 | + | 0.951527i | \(0.599514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 706.389i | − 0.884092i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 43.4050i | − 0.0540536i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 73.0256 | 0.0907150 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 676.102 | 0.835726 | 0.417863 | − | 0.908510i | \(-0.362779\pi\) | ||||
0.417863 | + | 0.908510i | \(0.362779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 74.1793i | 0.0914665i | 0.998954 | + | 0.0457332i | \(0.0145624\pi\) | ||||
−0.998954 | + | 0.0457332i | \(0.985438\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 816.991i | 1.00244i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 429.703 | 0.525952 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1130.58 | −1.37708 | −0.688540 | − | 0.725198i | \(-0.741748\pi\) | ||||
−0.688540 | + | 0.725198i | \(0.741748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 82.1839i | − 0.0998589i | −0.998753 | − | 0.0499295i | \(-0.984100\pi\) | ||||
0.998753 | − | 0.0499295i | \(-0.0158997\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1504.57i | 1.81931i | 0.415365 | + | 0.909655i | \(0.363654\pi\) | ||||
−0.415365 | + | 0.909655i | \(0.636346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1409.65 | 1.70042 | 0.850209 | − | 0.526445i | \(-0.176475\pi\) | ||||
0.850209 | + | 0.526445i | \(0.176475\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −526.728 | −0.632327 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2243.67i | 2.68703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 288.110i | 0.343397i | 0.985150 | + | 0.171698i | \(0.0549254\pi\) | ||||
−0.985150 | + | 0.171698i | \(0.945075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −840.672 | −0.999609 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 258.822 | 0.306299 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 121.910i | 0.143932i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 118.277i | − 0.138986i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 645.132 | 0.756310 | 0.378155 | − | 0.925742i | \(-0.376559\pi\) | ||||
0.378155 | + | 0.925742i | \(0.376559\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −995.549 | −1.16167 | −0.580833 | − | 0.814022i | \(-0.697273\pi\) | ||||
−0.580833 | + | 0.814022i | \(0.697273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 774.354i | 0.901460i | 0.892660 | + | 0.450730i | \(0.148836\pi\) | ||||
−0.892660 | + | 0.450730i | \(0.851164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1007.33i | 1.16724i | 0.812025 | + | 0.583622i | \(0.198365\pi\) | ||||
−0.812025 | + | 0.583622i | \(0.801635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1938.50 | −2.24104 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −356.858 | −0.410654 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 990.836i | − 1.13758i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 234.102i | − 0.267546i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 681.645 | 0.777246 | 0.388623 | − | 0.921397i | \(-0.372951\pi\) | ||||
0.388623 | + | 0.921397i | \(0.372951\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 679.108 | 0.770837 | 0.385419 | − | 0.922742i | \(-0.374057\pi\) | ||||
0.385419 | + | 0.922742i | \(0.374057\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1059.44i | − 1.19982i | −0.800068 | − | 0.599910i | \(-0.795203\pi\) | ||||
0.800068 | − | 0.599910i | \(-0.204797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 856.411i | 0.965514i | 0.875754 | + | 0.482757i | \(0.160365\pi\) | ||||
−0.875754 | + | 0.482757i | \(0.839635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 396.000 | 0.445444 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −889.403 | −0.995972 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2541.11i | 2.83923i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 32.9179i | − 0.0366161i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −371.758 | −0.412606 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 634.677 | 0.701300 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 761.492i | 0.839573i | 0.907623 | + | 0.419786i | \(0.137895\pi\) | ||||
−0.907623 | + | 0.419786i | \(0.862105\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 897.344i | − 0.985009i | −0.870310 | − | 0.492505i | \(-0.836081\pi\) | ||||
0.870310 | − | 0.492505i | \(-0.163919\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −541.703 | −0.593321 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 268.115 | 0.292383 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 62.6388i | 0.0681598i | 0.999419 | + | 0.0340799i | \(0.0108501\pi\) | ||||
−0.999419 | + | 0.0340799i | \(0.989150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 496.308i | 0.537712i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1070.43 | −1.15722 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −253.313 | −0.272673 | −0.136336 | − | 0.990663i | \(-0.543533\pi\) | ||||
−0.136336 | + | 0.990663i | \(0.543533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 663.195i | 0.712347i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 757.106i | − 0.809739i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.5538 | 0.0326081 | 0.0163040 | − | 0.999867i | \(-0.494810\pi\) | ||||
0.0163040 | + | 0.999867i | \(0.494810\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 388.745 | 0.413119 | 0.206559 | − | 0.978434i | \(-0.433773\pi\) | ||||
0.206559 | + | 0.978434i | \(0.433773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 135.039i | − 0.143202i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 263.615i | 0.278369i | 0.990266 | + | 0.139184i | \(0.0444481\pi\) | ||||
−0.990266 | + | 0.139184i | \(0.955552\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.4066 | 0.0668141 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1292.41 | 1.35615 | 0.678075 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678075 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2816.76i | − 2.94949i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 212.957i | 0.222061i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2338.34 | −2.43324 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2269.11 | 2.35141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1110.00i | − 1.14788i | −0.818896 | − | 0.573942i | \(-0.805413\pi\) | ||||
0.818896 | − | 0.573942i | \(-0.194587\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1341.66i | − 1.38173i | −0.722983 | − | 0.690866i | \(-0.757230\pi\) | ||||
0.722983 | − | 0.690866i | \(-0.242770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 379.617 | 0.390151 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 920.431 | 0.942099 | 0.471050 | − | 0.882107i | \(-0.343875\pi\) | ||||
0.471050 | + | 0.882107i | \(0.343875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1065.11i | 1.08795i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1697.84i | − 1.72720i | −0.504176 | − | 0.863601i | \(-0.668204\pi\) | ||||
0.504176 | − | 0.863601i | \(-0.331796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −605.108 | −0.614322 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 123.128 | 0.124497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 284.765i | − 0.287351i | −0.989625 | − | 0.143675i | \(-0.954108\pi\) | ||||
0.989625 | − | 0.143675i | \(-0.0458921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 831.615i | 0.835794i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1093.80 | −1.09710 | −0.548548 | − | 0.836119i | \(-0.684819\pi\) | ||||
−0.548548 | + | 0.836119i | \(0.684819\pi\) | |||||||
\(998\) | 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 | 2304.3.g.z.1279.2 | 8 | ||
3.2 | odd | 2 | 768.3.g.h.511.4 | 8 | |||
4.3 | odd | 2 | inner | 2304.3.g.z.1279.1 | 8 | ||
8.3 | odd | 2 | inner | 2304.3.g.z.1279.7 | 8 | ||
8.5 | even | 2 | inner | 2304.3.g.z.1279.8 | 8 | ||
12.11 | even | 2 | 768.3.g.h.511.8 | 8 | |||
16.3 | odd | 4 | 72.3.b.b.19.1 | 4 | |||
16.5 | even | 4 | 72.3.b.b.19.2 | 4 | |||
16.11 | odd | 4 | 288.3.b.b.271.1 | 4 | |||
16.13 | even | 4 | 288.3.b.b.271.4 | 4 | |||
24.5 | odd | 2 | 768.3.g.h.511.5 | 8 | |||
24.11 | even | 2 | 768.3.g.h.511.1 | 8 | |||
48.5 | odd | 4 | 24.3.b.a.19.3 | ✓ | 4 | ||
48.11 | even | 4 | 96.3.b.a.79.4 | 4 | |||
48.29 | odd | 4 | 96.3.b.a.79.3 | 4 | |||
48.35 | even | 4 | 24.3.b.a.19.4 | yes | 4 | ||
240.29 | odd | 4 | 2400.3.g.a.751.2 | 4 | |||
240.53 | even | 4 | 600.3.p.a.499.3 | 8 | |||
240.59 | even | 4 | 2400.3.g.a.751.1 | 4 | |||
240.77 | even | 4 | 2400.3.p.a.1999.3 | 8 | |||
240.83 | odd | 4 | 600.3.p.a.499.5 | 8 | |||
240.107 | odd | 4 | 2400.3.p.a.1999.2 | 8 | |||
240.149 | odd | 4 | 600.3.g.a.451.2 | 4 | |||
240.173 | even | 4 | 2400.3.p.a.1999.6 | 8 | |||
240.179 | even | 4 | 600.3.g.a.451.1 | 4 | |||
240.197 | even | 4 | 600.3.p.a.499.6 | 8 | |||
240.203 | odd | 4 | 2400.3.p.a.1999.7 | 8 | |||
240.227 | odd | 4 | 600.3.p.a.499.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.3.b.a.19.3 | ✓ | 4 | 48.5 | odd | 4 | ||
24.3.b.a.19.4 | yes | 4 | 48.35 | even | 4 | ||
72.3.b.b.19.1 | 4 | 16.3 | odd | 4 | |||
72.3.b.b.19.2 | 4 | 16.5 | even | 4 | |||
96.3.b.a.79.3 | 4 | 48.29 | odd | 4 | |||
96.3.b.a.79.4 | 4 | 48.11 | even | 4 | |||
288.3.b.b.271.1 | 4 | 16.11 | odd | 4 | |||
288.3.b.b.271.4 | 4 | 16.13 | even | 4 | |||
600.3.g.a.451.1 | 4 | 240.179 | even | 4 | |||
600.3.g.a.451.2 | 4 | 240.149 | odd | 4 | |||
600.3.p.a.499.3 | 8 | 240.53 | even | 4 | |||
600.3.p.a.499.4 | 8 | 240.227 | odd | 4 | |||
600.3.p.a.499.5 | 8 | 240.83 | odd | 4 | |||
600.3.p.a.499.6 | 8 | 240.197 | even | 4 | |||
768.3.g.h.511.1 | 8 | 24.11 | even | 2 | |||
768.3.g.h.511.4 | 8 | 3.2 | odd | 2 | |||
768.3.g.h.511.5 | 8 | 24.5 | odd | 2 | |||
768.3.g.h.511.8 | 8 | 12.11 | even | 2 | |||
2304.3.g.z.1279.1 | 8 | 4.3 | odd | 2 | inner | ||
2304.3.g.z.1279.2 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.g.z.1279.7 | 8 | 8.3 | odd | 2 | inner | ||
2304.3.g.z.1279.8 | 8 | 8.5 | even | 2 | inner | ||
2400.3.g.a.751.1 | 4 | 240.59 | even | 4 | |||
2400.3.g.a.751.2 | 4 | 240.29 | odd | 4 | |||
2400.3.p.a.1999.2 | 8 | 240.107 | odd | 4 | |||
2400.3.p.a.1999.3 | 8 | 240.77 | even | 4 | |||
2400.3.p.a.1999.6 | 8 | 240.173 | even | 4 | |||
2400.3.p.a.1999.7 | 8 | 240.203 | odd | 4 |