Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(385,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.385");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.d (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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 385.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.385 |
Dual form | 768.4.d.b.385.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 14.0000i | − 1.25220i | −0.779744 | − | 0.626099i | \(-0.784651\pi\) | ||||
0.779744 | − | 0.626099i | \(-0.215349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.0000 | −1.29588 | −0.647939 | − | 0.761692i | \(-0.724369\pi\) | ||||
−0.647939 | + | 0.761692i | \(0.724369\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 28.0000i | − 0.767483i | −0.923440 | − | 0.383742i | \(-0.874635\pi\) | ||||
0.923440 | − | 0.383742i | \(-0.125365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 74.0000i | − 1.57876i | −0.613904 | − | 0.789381i | \(-0.710402\pi\) | ||||
0.613904 | − | 0.789381i | \(-0.289598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −42.0000 | −0.722957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82.0000 | 1.16988 | 0.584939 | − | 0.811077i | \(-0.301118\pi\) | ||||
0.584939 | + | 0.811077i | \(0.301118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 92.0000i | − 1.11086i | −0.831565 | − | 0.555428i | \(-0.812555\pi\) | ||||
0.831565 | − | 0.555428i | \(-0.187445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 72.0000i | 0.748176i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000 | 0.0725268 | 0.0362634 | − | 0.999342i | \(-0.488454\pi\) | ||||
0.0362634 | + | 0.999342i | \(0.488454\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −71.0000 | −0.568000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 138.000i | − 0.883654i | −0.897100 | − | 0.441827i | \(-0.854331\pi\) | ||||
0.897100 | − | 0.441827i | \(-0.145669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −80.0000 | −0.463498 | −0.231749 | − | 0.972776i | \(-0.574445\pi\) | ||||
−0.231749 | + | 0.972776i | \(0.574445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −84.0000 | −0.443107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 336.000i | 1.62270i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 30.0000i | − 0.133296i | −0.997777 | − | 0.0666482i | \(-0.978769\pi\) | ||||
0.997777 | − | 0.0666482i | \(-0.0212305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −222.000 | −0.911499 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −282.000 | −1.07417 | −0.537085 | − | 0.843528i | \(-0.680475\pi\) | ||||
−0.537085 | + | 0.843528i | \(0.680475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.0141859i | 0.999975 | + | 0.00709296i | \(0.00225778\pi\) | ||||
−0.999975 | + | 0.00709296i | \(0.997742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 126.000i | 0.417399i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −240.000 | −0.744843 | −0.372421 | − | 0.928064i | \(-0.621472\pi\) | ||||
−0.372421 | + | 0.928064i | \(0.621472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 233.000 | 0.679300 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 246.000i | − 0.675429i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 130.000i | 0.336922i | 0.985708 | + | 0.168461i | \(0.0538797\pi\) | ||||
−0.985708 | + | 0.168461i | \(0.946120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −392.000 | −0.961041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −276.000 | −0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 596.000i | 1.31513i | 0.753398 | + | 0.657564i | \(0.228413\pi\) | ||||
−0.753398 | + | 0.657564i | \(0.771587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 218.000i | − 0.457574i | −0.973476 | − | 0.228787i | \(-0.926524\pi\) | ||||
0.973476 | − | 0.228787i | \(-0.0734760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 216.000 | 0.431959 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1036.00 | −1.97692 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 436.000i | 0.795013i | 0.917599 | + | 0.397507i | \(0.130124\pi\) | ||||
−0.917599 | + | 0.397507i | \(0.869876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 24.0000i | − 0.0418733i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 856.000 | 1.43082 | 0.715412 | − | 0.698703i | \(-0.246239\pi\) | ||||
0.715412 | + | 0.698703i | \(0.246239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 998.000 | 1.60010 | 0.800048 | − | 0.599935i | \(-0.204807\pi\) | ||||
0.800048 | + | 0.599935i | \(0.204807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 213.000i | 0.327935i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 672.000i | 0.994565i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.0000 | 0.0455732 | 0.0227866 | − | 0.999740i | \(-0.492746\pi\) | ||||
0.0227866 | + | 0.999740i | \(0.492746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1508.00i | 1.99427i | 0.0756351 | + | 0.997136i | \(0.475902\pi\) | ||||
−0.0756351 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1148.00i | − 1.46492i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −414.000 | −0.510178 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 246.000 | 0.292988 | 0.146494 | − | 0.989212i | \(-0.453201\pi\) | ||||
0.146494 | + | 0.989212i | \(0.453201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1776.00i | 2.04588i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 240.000i | 0.267600i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1288.00 | −1.39101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 866.000 | 0.906484 | 0.453242 | − | 0.891387i | \(-0.350267\pi\) | ||||
0.453242 | + | 0.891387i | \(0.350267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 252.000i | 0.255828i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 270.000i | − 0.266000i | −0.991116 | − | 0.133000i | \(-0.957539\pi\) | ||||
0.991116 | − | 0.133000i | \(-0.0424610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1496.00 | −1.43112 | −0.715560 | − | 0.698552i | \(-0.753828\pi\) | ||||
−0.715560 | + | 0.698552i | \(0.753828\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1008.00 | 0.936864 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1692.00i | − 1.52871i | −0.644797 | − | 0.764354i | \(-0.723058\pi\) | ||||
0.644797 | − | 0.764354i | \(-0.276942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 406.000i | 0.356768i | 0.983961 | + | 0.178384i | \(0.0570870\pi\) | ||||
−0.983961 | + | 0.178384i | \(0.942913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −90.0000 | −0.0769588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 786.000 | 0.654342 | 0.327171 | − | 0.944965i | \(-0.393905\pi\) | ||||
0.327171 | + | 0.944965i | \(0.393905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 112.000i | − 0.0908179i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 666.000i | 0.526254i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1968.00 | −1.51602 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 547.000 | 0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 846.000i | 0.620173i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 756.000i | − 0.540950i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1744.00 | −1.21854 | −0.609272 | − | 0.792962i | \(-0.708538\pi\) | ||||
−0.609272 | + | 0.792962i | \(0.708538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 0.00819024 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 652.000i | − 0.434851i | −0.976077 | − | 0.217426i | \(-0.930234\pi\) | ||||
0.976077 | − | 0.217426i | \(-0.0697659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2208.00i | 1.43953i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 378.000 | 0.240986 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1530.00 | −0.954137 | −0.477068 | − | 0.878866i | \(-0.658301\pi\) | ||||
−0.477068 | + | 0.878866i | \(0.658301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 516.000i | 0.314867i | 0.987530 | + | 0.157434i | \(0.0503220\pi\) | ||||
−0.987530 | + | 0.157434i | \(0.949678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 720.000i | 0.430035i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2072.00 | −1.21167 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1932.00 | −1.10651 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 699.000i | − 0.392194i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1342.00i | − 0.737859i | −0.929457 | − | 0.368929i | \(-0.879724\pi\) | ||||
0.929457 | − | 0.368929i | \(-0.120276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −424.000 | −0.228507 | −0.114254 | − | 0.993452i | \(-0.536448\pi\) | ||||
−0.114254 | + | 0.993452i | \(0.536448\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −738.000 | −0.389959 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1120.00i | 0.580391i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 262.000i | 0.133184i | 0.997780 | + | 0.0665920i | \(0.0212126\pi\) | ||||
−0.997780 | + | 0.0665920i | \(0.978787\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 390.000 | 0.194522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.000 | −0.0939858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2292.00i | 1.10137i | 0.834713 | + | 0.550685i | \(0.185633\pi\) | ||||
−0.834713 | + | 0.550685i | \(0.814367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1176.00i | 0.554857i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1896.00 | −0.878544 | −0.439272 | − | 0.898354i | \(-0.644764\pi\) | ||||
−0.439272 | + | 0.898354i | \(0.644764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3279.00 | −1.49249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 828.000i | 0.370285i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2874.00i | − 1.26304i | −0.775359 | − | 0.631521i | \(-0.782431\pi\) | ||||
0.775359 | − | 0.631521i | \(-0.217569\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1704.00 | 0.736059 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1788.00 | 0.759290 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1188.00i | 0.496063i | 0.968752 | + | 0.248032i | \(0.0797837\pi\) | ||||
−0.968752 | + | 0.248032i | \(0.920216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3474.00i | 1.42663i | 0.700843 | + | 0.713316i | \(0.252808\pi\) | ||||
−0.700843 | + | 0.713316i | \(0.747192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −654.000 | −0.264181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −420.000 | −0.166914 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2296.00i | − 0.897862i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 648.000i | − 0.249392i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −192.000 | −0.0727363 | −0.0363681 | − | 0.999338i | \(-0.511579\pi\) | ||||
−0.0363681 | + | 0.999338i | \(0.511579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4802.00 | 1.79096 | 0.895481 | − | 0.445100i | \(-0.146832\pi\) | ||||
0.895481 | + | 0.445100i | \(0.146832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3108.00i | 1.14138i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1518.00i | − 0.549000i | −0.961587 | − | 0.274500i | \(-0.911488\pi\) | ||||
0.961587 | − | 0.274500i | \(-0.0885123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5128.00 | 1.82670 | 0.913352 | − | 0.407170i | \(-0.133484\pi\) | ||||
0.913352 | + | 0.407170i | \(0.133484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1308.00 | 0.459001 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3312.00i | 1.14511i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3948.00i | 1.34507i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −72.0000 | −0.0241756 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2576.00 | −0.852563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1084.00i | − 0.353676i | −0.984240 | − | 0.176838i | \(-0.943413\pi\) | ||||
0.984240 | − | 0.176838i | \(-0.0565869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2568.00i | − 0.826087i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 56.0000 | 0.0177636 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1920.00 | 0.600636 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2994.00i | − 0.923816i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6068.00i | − 1.84696i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −688.000 | −0.206600 | −0.103300 | − | 0.994650i | \(-0.532940\pi\) | ||||
−0.103300 | + | 0.994650i | \(0.532940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 639.000 | 0.189333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4812.00i | − 1.40698i | −0.710707 | − | 0.703488i | \(-0.751625\pi\) | ||||
0.710707 | − | 0.703488i | \(-0.248375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2494.00i | − 0.719686i | −0.933013 | − | 0.359843i | \(-0.882830\pi\) | ||||
0.933013 | − | 0.359843i | \(-0.117170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2016.00 | 0.574212 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −698.000 | −0.196255 | −0.0981277 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981277 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3360.00i | 0.932690i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 96.0000i | − 0.0263117i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6320.00 | 1.71049 | 0.855244 | − | 0.518225i | \(-0.173407\pi\) | ||||
0.855244 | + | 0.518225i | \(0.173407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6510.00 | −1.74002 | −0.870012 | − | 0.493030i | \(-0.835889\pi\) | ||||
−0.870012 | + | 0.493030i | \(0.835889\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3262.00i | − 0.850619i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6808.00 | −1.75378 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4524.00 | 1.15139 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 628.000i | 0.157924i | 0.996878 | + | 0.0789622i | \(0.0251606\pi\) | ||||
−0.996878 | + | 0.0789622i | \(0.974839\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 224.000i | − 0.0556631i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3444.00 | −0.845771 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4862.00 | −1.18009 | −0.590045 | − | 0.807370i | \(-0.700890\pi\) | ||||
−0.590045 | + | 0.807370i | \(0.700890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 720.000i | 0.172736i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1242.00i | 0.294551i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5816.00 | 1.36361 | 0.681806 | − | 0.731533i | \(-0.261195\pi\) | ||||
0.681806 | + | 0.731533i | \(0.261195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1820.00 | 0.421893 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 738.000i | − 0.169157i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3526.00i | 0.799197i | 0.916690 | + | 0.399599i | \(0.130850\pi\) | ||||
−0.916690 | + | 0.399599i | \(0.869150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 256.000 | 0.0573834 | 0.0286917 | − | 0.999588i | \(-0.490866\pi\) | ||||
0.0286917 | + | 0.999588i | \(0.490866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5328.00 | 1.18119 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1988.00i | 0.435931i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 142.000i | − 0.0308013i | −0.999881 | − | 0.0154006i | \(-0.995098\pi\) | ||||
0.999881 | − | 0.0154006i | \(-0.00490237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 720.000 | 0.154499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8842.00 | −1.87712 | −0.938558 | − | 0.345122i | \(-0.887838\pi\) | ||||
−0.938558 | + | 0.345122i | \(0.887838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7180.00i | − 1.50815i | −0.656788 | − | 0.754075i | \(-0.728085\pi\) | ||||
0.656788 | − | 0.754075i | \(-0.271915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3864.00i | 0.803100i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6768.00 | 1.39199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1811.00 | 0.368614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2598.00i | − 0.523359i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7374.00i | − 1.47029i | −0.677912 | − | 0.735143i | \(-0.737115\pi\) | ||||
0.677912 | − | 0.735143i | \(-0.262885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8344.00 | 1.64680 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 756.000 | 0.147702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 592.000i | − 0.114502i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 96.0000i | − 0.0183832i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −810.000 | −0.153575 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3052.00 | −0.572974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1500.00i | − 0.278858i | −0.990232 | − | 0.139429i | \(-0.955473\pi\) | ||||
0.990232 | − | 0.139429i | \(-0.0445268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4488.00i | 0.826257i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7608.00 | −1.38717 | −0.693585 | − | 0.720374i | \(-0.743970\pi\) | ||||
−0.693585 | + | 0.720374i | \(0.743970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4758.00 | 0.859227 | 0.429614 | − | 0.903013i | \(-0.358650\pi\) | ||||
0.429614 | + | 0.903013i | \(0.358650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 3024.00i | − 0.540899i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4374.00i | 0.774979i | 0.921874 | + | 0.387489i | \(0.126658\pi\) | ||||
−0.921874 | + | 0.387489i | \(0.873342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3864.00 | −0.678190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5076.00 | −0.882600 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7544.00i | − 1.29956i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5254.00i | 0.896737i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1218.00 | 0.205980 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5760.00 | 0.965225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7804.00i | − 1.29591i | −0.761678 | − | 0.647956i | \(-0.775624\pi\) | ||||
0.761678 | − | 0.647956i | \(-0.224376\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 270.000i | 0.0444322i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6104.00 | 0.995514 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5106.00 | 0.825346 | 0.412673 | − | 0.910879i | \(-0.364595\pi\) | ||||
0.412673 | + | 0.910879i | \(0.364595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2358.00i | − 0.377785i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2240.00i | 0.355727i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2640.00 | 0.415588 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −336.000 | −0.0524337 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4716.00i | − 0.729591i | −0.931088 | − | 0.364796i | \(-0.881139\pi\) | ||||
0.931088 | − | 0.364796i | \(-0.118861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7302.00i | 1.11996i | 0.828505 | + | 0.559982i | \(0.189192\pi\) | ||||
−0.828505 | + | 0.559982i | \(0.810808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1998.00 | 0.303833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4382.00 | −0.660709 | −0.330355 | − | 0.943857i | \(-0.607168\pi\) | ||||
−0.330355 | + | 0.943857i | \(0.607168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 11984.0i | − 1.79168i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5904.00i | 0.875274i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7224.00 | 1.06203 | 0.531014 | − | 0.847363i | \(-0.321811\pi\) | ||||
0.531014 | + | 0.847363i | \(0.321811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1605.00 | −0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1641.00i | − 0.237273i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 13972.0i | − 2.00364i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1408.00 | −0.200264 | −0.100132 | − | 0.994974i | \(-0.531927\pi\) | ||||
−0.100132 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2538.00 | 0.358057 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3120.00i | − 0.436610i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1714.00i | 0.237929i | 0.992899 | + | 0.118965i | \(0.0379575\pi\) | ||||
−0.992899 | + | 0.118965i | \(0.962043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2268.00 | −0.312317 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10212.0 | −1.39508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 884.000i | 0.119810i | 0.998204 | + | 0.0599051i | \(0.0190798\pi\) | ||||
−0.998204 | + | 0.0599051i | \(0.980920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5232.00i | 0.703526i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10368.0 | −1.38324 | −0.691619 | − | 0.722263i | \(-0.743102\pi\) | ||||
−0.691619 | + | 0.722263i | \(0.743102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9408.00 | 1.24539 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 36.0000i | − 0.00472864i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 398.000i | − 0.0518751i | −0.999664 | − | 0.0259375i | \(-0.991743\pi\) | ||||
0.999664 | − | 0.0259375i | \(-0.00825710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 656.000 | 0.0848474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1956.00 | −0.251061 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 448.000i | − 0.0570666i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5098.00i | − 0.644487i | −0.946657 | − | 0.322243i | \(-0.895563\pi\) | ||||
0.946657 | − | 0.322243i | \(-0.104437\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6624.00 | 0.831115 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10002.0 | 1.24558 | 0.622788 | − | 0.782391i | \(-0.286000\pi\) | ||||
0.622788 | + | 0.782391i | \(0.286000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5920.00i | 0.731752i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1134.00i | − 0.139133i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −840.000 | −0.102303 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9270.00 | 1.12071 | 0.560357 | − | 0.828251i | \(-0.310664\pi\) | ||||
0.560357 | + | 0.828251i | \(0.310664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4590.00i | 0.550871i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 14304.0i | − 1.70425i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21112.0 | 2.49722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1548.00 | 0.181789 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6516.00i | 0.759731i | 0.925042 | + | 0.379866i | \(0.124030\pi\) | ||||
−0.925042 | + | 0.379866i | \(0.875970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2626.00i | 0.303999i | 0.988381 | + | 0.151999i | \(0.0485711\pi\) | ||||
−0.988381 | + | 0.151999i | \(0.951429\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2160.00 | 0.248281 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5822.00 | −0.664491 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5232.00i | 0.592961i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6216.00i | 0.699560i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4304.00 | 0.481012 | 0.240506 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240506 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11794.0 | 1.30897 | 0.654484 | − | 0.756076i | \(-0.272886\pi\) | ||||
0.654484 | + | 0.756076i | \(0.272886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5796.00i | 0.638844i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 736.000i | − 0.0805667i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5544.00 | −0.602735 | −0.301368 | − | 0.953508i | \(-0.597443\pi\) | ||||
−0.301368 | + | 0.953508i | \(0.597443\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2097.00 | −0.226433 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 3788.00i | − 0.406260i | −0.979152 | − | 0.203130i | \(-0.934889\pi\) | ||||
0.979152 | − | 0.203130i | \(-0.0651115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 3444.00i | − 0.366879i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4026.00 | −0.426003 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13342.0 | −1.40233 | −0.701167 | − | 0.712997i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7896.00i | 0.824408i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1272.00i | 0.131929i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24864.0 | 2.56185 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4390.00 | 0.449356 | 0.224678 | − | 0.974433i | \(-0.427867\pi\) | ||||
0.224678 | + | 0.974433i | \(0.427867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2214.00i | 0.225143i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5798.00i | 0.585770i | 0.956148 | + | 0.292885i | \(0.0946152\pi\) | ||||
−0.956148 | + | 0.292885i | \(0.905385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14656.0 | 1.47111 | 0.735553 | − | 0.677467i | \(-0.236922\pi\) | ||||
0.735553 | + | 0.677467i | \(0.236922\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3360.00 | 0.335089 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8412.00i | − 0.833535i | −0.909013 | − | 0.416768i | \(-0.863163\pi\) | ||||
0.909013 | − | 0.416768i | \(-0.136837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10464.0i | − 1.03024i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 786.000 | 0.0768938 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 112.000 | 0.0108875 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6532.00i | 0.630966i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1170.00i | − 0.112307i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14848.0 | −1.41633 | −0.708165 | − | 0.706047i | \(-0.750477\pi\) | ||||
−0.708165 | + | 0.706047i | \(0.750477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2220.00 | −0.210443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 576.000i | 0.0542627i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 12124.0i | − 1.13510i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18568.0 | 1.72771 | 0.863857 | − | 0.503738i | \(-0.168042\pi\) | ||||
0.863857 | + | 0.503738i | \(0.168042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6876.00 | 0.635876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 14364.0i | − 1.32024i | −0.751160 | − | 0.660120i | \(-0.770505\pi\) | ||||
0.751160 | − | 0.660120i | \(-0.229495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 11316.0i | − 1.03377i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3528.00 | 0.320347 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20544.0 | −1.85417 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 21660.0i | − 1.94316i | −0.236720 | − | 0.971578i | \(-0.576072\pi\) | ||||
0.236720 | − | 0.971578i | \(-0.423928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5688.00i | 0.507228i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17112.0 | −1.51687 | −0.758436 | − | 0.651748i | \(-0.774036\pi\) | ||||
−0.758436 | + | 0.651748i | \(0.774036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3780.00 | −0.333085 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9837.00i | 0.861689i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11478.0i | 0.999516i | 0.866165 | + | 0.499758i | \(0.166578\pi\) | ||||
−0.866165 | + | 0.499758i | \(0.833422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23952.0 | −2.07353 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2484.00 | 0.213784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20944.0i | 1.79204i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6720.00i | 0.571654i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8622.00 | −0.729217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13114.0 | −1.10275 | −0.551377 | − | 0.834256i | \(-0.685897\pi\) | ||||
−0.551377 | + | 0.834256i | \(0.685897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4508.00i | − 0.376905i | −0.982082 | − | 0.188452i | \(-0.939653\pi\) | ||||
0.982082 | − | 0.188452i | \(-0.0603471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 5112.00i | − 0.424964i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6560.00 | −0.542235 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12103.0 | −0.994740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5364.00i | − 0.438376i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20868.0i | 1.69586i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23688.0 | −1.91425 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3564.00 | 0.286402 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 6524.00i | − 0.521352i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22950.0i | 1.82384i | 0.410368 | + | 0.911920i | \(0.365400\pi\) | ||||
−0.410368 | + | 0.911920i | \(0.634600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10422.0 | 0.823666 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5684.00 | 0.446745 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6580.00i | 0.514334i | 0.966367 | + | 0.257167i | \(0.0827890\pi\) | ||||
−0.966367 | + | 0.257167i | \(0.917211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1962.00i | 0.152525i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12696.0 | −0.981611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −768.000 | −0.0590573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1260.00i | 0.0963676i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7046.00i | 0.535994i | 0.963420 | + | 0.267997i | \(0.0863617\pi\) | ||||
−0.963420 | + | 0.267997i | \(0.913638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 296.000 | 0.0223962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6888.00 | −0.518381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8252.00i | − 0.617727i | −0.951106 | − | 0.308864i | \(-0.900051\pi\) | ||||
0.951106 | − | 0.308864i | \(-0.0999486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 11004.0i | − 0.819366i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1944.00 | −0.143986 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6838.00 | 0.503803 | 0.251901 | − | 0.967753i | \(-0.418944\pi\) | ||||
0.251901 | + | 0.967753i | \(0.418944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23316.0i | 1.70883i | 0.519588 | + | 0.854417i | \(0.326085\pi\) | ||||
−0.519588 | + | 0.854417i | \(0.673915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 576.000i | 0.0419943i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −568.000 | −0.0411952 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10558.0 | −0.761760 | −0.380880 | − | 0.924625i | \(-0.624379\pi\) | ||||
−0.380880 | + | 0.924625i | \(0.624379\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 14406.0i | − 1.03401i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 36192.0i | − 2.58433i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3640.00 | 0.258582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9324.00 | 0.658974 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1028.00i | 0.0722830i | 0.999347 | + | 0.0361415i | \(0.0115067\pi\) | ||||
−0.999347 | + | 0.0361415i | \(0.988493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7360.00i | 0.514879i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4554.00 | −0.316965 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1202.00 | 0.0832382 | 0.0416191 | − | 0.999134i | \(-0.486748\pi\) | ||||
0.0416191 | + | 0.999134i | \(0.486748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27552.0i | 1.89836i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 15384.0i | − 1.05465i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3576.00 | −0.243926 | −0.121963 | − | 0.992535i | \(-0.538919\pi\) | ||||
−0.121963 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8650.00 | −0.587090 | −0.293545 | − | 0.955945i | \(-0.594835\pi\) | ||||
−0.293545 | + | 0.955945i | \(0.594835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3924.00i | − 0.265004i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7658.00i | − 0.514615i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12656.0 | −0.846279 | −0.423139 | − | 0.906065i | \(-0.639072\pi\) | ||||
−0.423139 | + | 0.906065i | \(0.639072\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9936.00 | 0.661128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17760.0i | 1.17593i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3298.00i | 0.217300i | 0.994080 | + | 0.108650i | \(0.0346528\pi\) | ||||
−0.994080 | + | 0.108650i | \(0.965347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11844.0 | 0.776579 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5370.00 | −0.350386 | −0.175193 | − | 0.984534i | \(-0.556055\pi\) | ||||
−0.175193 | + | 0.984534i | \(0.556055\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 16220.0i | − 1.05321i | −0.850110 | − | 0.526605i | \(-0.823465\pi\) | ||||
0.850110 | − | 0.526605i | \(-0.176535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 216.000i | 0.0139578i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5904.00 | −0.379677 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7728.00i | 0.492227i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 2460.00i | − 0.155941i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20360.0 | −1.28450 | −0.642249 | − | 0.766496i | \(-0.721999\pi\) | ||||
−0.642249 | + | 0.766496i | \(0.721999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3252.00 | −0.204195 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24416.0i | 1.52586i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 17242.0i | − 1.07245i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7704.00 | −0.476941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14498.0 | 0.893349 | 0.446674 | − | 0.894697i | \(-0.352608\pi\) | ||||
0.446674 | + | 0.894697i | \(0.352608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 21612.0i | − 1.32550i | −0.748842 | − | 0.662748i | \(-0.769390\pi\) | ||||
0.748842 | − | 0.662748i | \(-0.230610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 168.000i | − 0.0102558i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12184.0 | 0.740344 | 0.370172 | − | 0.928963i | \(-0.379299\pi\) | ||||
0.370172 | + | 0.928963i | \(0.379299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16688.0 | 1.00934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 5760.00i | − 0.346778i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 28122.0i | − 1.68530i | −0.538464 | − | 0.842648i | \(-0.680995\pi\) | ||||
0.538464 | − | 0.842648i | \(-0.319005\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9128.00 | −0.544520 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8982.00 | −0.533366 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5700.00i | 0.336935i | 0.985707 | + | 0.168468i | \(0.0538819\pi\) | ||||
−0.985707 | + | 0.168468i | \(0.946118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29458.0i | 1.73341i | 0.498822 | + | 0.866705i | \(0.333766\pi\) | ||||
−0.498822 | + | 0.866705i | \(0.666234\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18204.0 | −1.06634 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30912.0 | 1.80258 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1104.00i | − 0.0640885i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2064.00i | 0.119281i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6104.00 | −0.351181 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19810.0 | 1.13465 | 0.567325 | − | 0.823494i | \(-0.307978\pi\) | ||||
0.567325 | + | 0.823494i | \(0.307978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1917.00i | − 0.109312i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10450.0i | 0.593244i | 0.954995 | + | 0.296622i | \(0.0958601\pi\) | ||||
−0.954995 | + | 0.296622i | \(0.904140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20784.0 | −1.17469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14436.0 | −0.812318 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23300.0i | 1.30534i | 0.757641 | + | 0.652672i | \(0.226352\pi\) | ||||
−0.757641 | + | 0.652672i | \(0.773648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21420.0i | 1.19477i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7482.00 | −0.415511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9620.00 | 0.531920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14212.0i | 0.782417i | 0.920302 | + | 0.391208i | \(0.127943\pi\) | ||||
−0.920302 | + | 0.391208i | \(0.872057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6048.00i | − 0.331522i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7224.00 | 0.394276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23124.0 | −1.25665 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2094.00i | 0.113308i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 15978.0i | − 0.860885i | −0.902618 | − | 0.430443i | \(-0.858357\pi\) | ||||
0.902618 | − | 0.430443i | \(-0.141643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2760.00 | −0.148073 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10080.0 | 0.538489 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6480.00i | 0.344704i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8866.00i | 0.469633i | 0.972040 | + | 0.234816i | \(0.0754489\pi\) | ||||
−0.972040 | + | 0.234816i | \(0.924551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −288.000 | −0.0151911 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −640.000 | −0.0336160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29008.0i | 1.51726i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 18960.0i | − 0.987551i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7760.00 | −0.402502 | −0.201251 | − | 0.979540i | \(-0.564501\pi\) | ||||
−0.201251 | + | 0.979540i | \(0.564501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35904.0 | 1.85456 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19530.0i | 1.00460i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9798.00i | 0.501915i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13080.0 | 0.667277 | 0.333638 | − | 0.942701i | \(-0.391724\pi\) | ||||
0.333638 | + | 0.942701i | \(0.391724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 328.000i | 0.0165958i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16934.0i | 0.853304i | 0.904416 | + | 0.426652i | \(0.140307\pi\) | ||||
−0.904416 | + | 0.426652i | \(0.859693\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9786.00 | −0.491105 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12208.0 | 0.610159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7060.00i | 0.351429i | 0.984441 | + | 0.175715i | \(0.0562236\pi\) | ||||
−0.984441 | + | 0.175715i | \(0.943776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20424.0i | 1.01254i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12520.0 | −0.618189 | −0.309094 | − | 0.951031i | \(-0.600026\pi\) | ||||
−0.309094 | + | 0.951031i | \(0.600026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18788.0 | −0.923945 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 13572.0i | − 0.664757i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40608.0i | 1.98102i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9792.00 | 0.475786 | 0.237893 | − | 0.971291i | \(-0.423543\pi\) | ||||
0.237893 | + | 0.971291i | \(0.423543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1884.00 | 0.0911777 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5936.00i | 0.286137i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 13166.0i | − 0.632135i | −0.948737 | − | 0.316068i | \(-0.897637\pi\) | ||||
0.948737 | − | 0.316068i | \(-0.102363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −672.000 | −0.0321371 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23222.0 | 1.10617 | 0.553086 | − | 0.833124i | \(-0.313450\pi\) | ||||
0.553086 | + | 0.833124i | \(0.313450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9744.00i | − 0.462328i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10332.0i | 0.488306i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44104.0 | 2.07628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39934.0 | −1.87264 | −0.936318 | − | 0.351154i | \(-0.885789\pi\) | ||||
−0.936318 | + | 0.351154i | \(0.885789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14586.0i | 0.681325i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17106.0i | 0.795938i | 0.917399 | + | 0.397969i | \(0.130285\pi\) | ||||
−0.917399 | + | 0.397969i | \(0.869715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5680.00 | 0.263267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2160.00 | 0.0997292 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25944.0i | 1.19325i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 23968.0i | − 1.09813i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3726.00 | 0.170059 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3668.00 | 0.166773 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9956.00i | 0.450944i | 0.974250 | + | 0.225472i | \(0.0723924\pi\) | ||||
−0.974250 | + | 0.225472i | \(0.927608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 17448.0i | − 0.787282i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18864.0 | −0.847948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16132.0 | −0.722401 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 5460.00i | − 0.243580i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9130.00i | − 0.405773i | −0.979202 | − | 0.202887i | \(-0.934968\pi\) | ||||
0.979202 | − | 0.202887i | \(-0.0650323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19680.0 | −0.871375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2214.00 | −0.0976627 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 27944.0i | − 1.22805i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2688.00i | 0.117689i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10578.0 | 0.461417 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11482.0 | −0.498993 | −0.249497 | − | 0.968376i | \(-0.580265\pi\) | ||||
−0.249497 | + | 0.968376i | \(0.580265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4612.00i | 0.199691i | 0.995003 | + | 0.0998454i | \(0.0318348\pi\) | ||||
−0.995003 | + | 0.0998454i | \(0.968165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 768.000i | − 0.0331303i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32088.0 | 1.37913 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 368.000 | 0.0157585 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 15984.0i | − 0.681961i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35010.0i | 1.48826i | 0.668038 | + | 0.744128i | \(0.267135\pi\) | ||||
−0.668038 | + | 0.744128i | \(0.732865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13688.0 | 0.579749 | 0.289875 | − | 0.957065i | \(-0.406386\pi\) | ||||
0.289875 | + | 0.957065i | \(0.406386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5964.00 | 0.251685 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11668.0i | 0.490612i | 0.969446 | + | 0.245306i | \(0.0788884\pi\) | ||||
−0.969446 | + | 0.245306i | \(0.921112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 29306.0i | − 1.22779i | −0.789387 | − | 0.613896i | \(-0.789601\pi\) | ||||
0.789387 | − | 0.613896i | \(-0.210399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −426.000 | −0.0177831 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19106.0 | 0.794698 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26544.0i | 1.10011i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2160.00i | − 0.0892001i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2664.00 | −0.109620 | −0.0548102 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548102 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5345.00 | 0.219156 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26526.0i | 1.08375i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45906.0i | 1.86889i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13128.0 | −0.532566 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21540.0 | −0.870731 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 240.000i | − 0.00966756i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 26030.0i | − 1.04484i | −0.852688 | − | 0.522421i | \(-0.825029\pi\) | ||||
0.852688 | − | 0.522421i | \(-0.174971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11592.0 | 0.463670 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44202.0 | −1.76186 | −0.880929 | − | 0.473249i | \(-0.843081\pi\) | ||||
−0.880929 | + | 0.473249i | \(0.843081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 32748.0i | − 1.30075i | −0.759612 | − | 0.650377i | \(-0.774611\pi\) | ||||
0.759612 | − | 0.650377i | \(-0.225389\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 20304.0i | − 0.803668i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45344.0 | −1.78856 | −0.894280 | − | 0.447507i | \(-0.852312\pi\) | ||||
−0.894280 | + | 0.447507i | \(0.852312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40236.0 | −1.58158 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 5433.00i | − 0.212819i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 896.000i | − 0.0349767i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32264.0 | 1.25514 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7794.00 | −0.302161 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18144.0i | 0.701005i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 8778.00i | − 0.337984i | −0.985617 | − | 0.168992i | \(-0.945949\pi\) | ||||
0.985617 | − | 0.168992i | \(-0.0540512\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22122.0 | −0.848870 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4142.00 | −0.158397 | −0.0791984 | − | 0.996859i | \(-0.525236\pi\) | ||||
−0.0791984 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 22076.0i | − 0.841355i | −0.907210 | − | 0.420678i | \(-0.861792\pi\) | ||||
0.907210 | − | 0.420678i | \(-0.138208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 25032.0i | − 0.950781i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40376.0 | −1.52840 | −0.764201 | − | 0.644978i | \(-0.776867\pi\) | ||||
−0.764201 | + | 0.644978i | \(0.776867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41856.0 | 1.57908 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2268.00i | − 0.0852759i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22080.0i | 0.827412i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16632.0 | 0.621169 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1776.00 | −0.0661080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11040.0i | 0.409571i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10660.0i | 0.394158i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −288.000 | −0.0106136 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48636.0 | 1.78643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 26396.0i | − 0.966334i | −0.875528 | − | 0.483167i | \(-0.839486\pi\) | ||||
0.875528 | − | 0.483167i | \(-0.160514\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2430.00i | 0.0886667i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24368.0 | −0.886222 | −0.443111 | − | 0.896467i | \(-0.646125\pi\) | ||||
−0.443111 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42224.0 | 1.53057 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9156.00i | 0.330807i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15648.0i | 0.563514i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5096.00 | −0.182918 | −0.0914589 | − | 0.995809i | \(-0.529153\pi\) | ||||
−0.0914589 | + | 0.995809i | \(0.529153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4500.00 | −0.160999 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 63344.0i | − 2.25893i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2130.00i | 0.0757124i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13464.0 | 0.477040 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18494.0 | −0.653142 | −0.326571 | − | 0.945173i | \(-0.605893\pi\) | ||||
−0.326571 | + | 0.945173i | \(0.605893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 21436.0i | − 0.754604i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22824.0i | 0.800883i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32144.0 | −1.12430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33222.0 | 1.15829 | 0.579144 | − | 0.815225i | \(-0.303387\pi\) | ||||
0.579144 | + | 0.815225i | \(0.303387\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 14274.0i | − 0.496075i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27846.0i | 0.964669i | 0.875987 | + | 0.482335i | \(0.160211\pi\) | ||||
−0.875987 | + | 0.482335i | \(0.839789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2256.00 | −0.0779061 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9072.00 | −0.312288 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 41052.0i | − 1.40867i | −0.709868 | − | 0.704335i | \(-0.751245\pi\) | ||||
0.709868 | − | 0.704335i | \(-0.248755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 73852.0i | − 2.52617i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13122.0 | 0.447434 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5706.00 | −0.193951 | −0.0969756 | − | 0.995287i | \(-0.530917\pi\) | ||||
−0.0969756 | + | 0.995287i | \(0.530917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2688.00i | 0.0910802i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11592.0i | 0.391553i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36720.0 | 1.23644 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23391.0 | −0.785170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15228.0i | 0.509570i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 67228.0i | − 2.24264i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39352.0 | −1.30866 | −0.654330 | − | 0.756209i | \(-0.727049\pi\) | ||||
−0.654330 | + | 0.756209i | \(0.727049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22632.0 | −0.750304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 33180.0i | − 1.09660i | −0.836282 | − | 0.548299i | \(-0.815276\pi\) | ||||
0.836282 | − | 0.548299i | \(-0.184724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12384.0i | − 0.408030i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15762.0 | 0.517731 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4014.00 | −0.131442 | −0.0657212 | − | 0.997838i | \(-0.520935\pi\) | ||||
−0.0657212 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 6888.00i | − 0.224864i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3654.00i | − 0.118923i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20328.0 | 0.659575 | 0.329788 | − | 0.944055i | \(-0.393023\pi\) | ||||
0.329788 | + | 0.944055i | \(0.393023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21252.0 | −0.687457 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 17280.0i | − 0.557273i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000i | 0.00102886i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11728.0 | −0.375936 | −0.187968 | − | 0.982175i | \(-0.560190\pi\) | ||||
−0.187968 | + | 0.982175i | \(0.560190\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23412.0 | −0.748195 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 71792.0i | − 2.28740i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 50974.0i | − 1.61922i | −0.586968 | − | 0.809610i | \(-0.699679\pi\) | ||||
0.586968 | − | 0.809610i | \(-0.300321\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 810.000 | 0.0256529 |
(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 | 768.4.d.b.385.1 | 2 | ||
4.3 | odd | 2 | 768.4.d.o.385.2 | 2 | |||
8.3 | odd | 2 | 768.4.d.o.385.1 | 2 | |||
8.5 | even | 2 | inner | 768.4.d.b.385.2 | 2 | ||
16.3 | odd | 4 | 192.4.a.a.1.1 | 1 | |||
16.5 | even | 4 | 48.4.a.b.1.1 | 1 | |||
16.11 | odd | 4 | 24.4.a.a.1.1 | ✓ | 1 | ||
16.13 | even | 4 | 192.4.a.g.1.1 | 1 | |||
48.5 | odd | 4 | 144.4.a.b.1.1 | 1 | |||
48.11 | even | 4 | 72.4.a.b.1.1 | 1 | |||
48.29 | odd | 4 | 576.4.a.v.1.1 | 1 | |||
48.35 | even | 4 | 576.4.a.u.1.1 | 1 | |||
80.27 | even | 4 | 600.4.f.b.49.1 | 2 | |||
80.37 | odd | 4 | 1200.4.f.p.49.2 | 2 | |||
80.43 | even | 4 | 600.4.f.b.49.2 | 2 | |||
80.53 | odd | 4 | 1200.4.f.p.49.1 | 2 | |||
80.59 | odd | 4 | 600.4.a.h.1.1 | 1 | |||
80.69 | even | 4 | 1200.4.a.u.1.1 | 1 | |||
112.27 | even | 4 | 1176.4.a.a.1.1 | 1 | |||
112.69 | odd | 4 | 2352.4.a.w.1.1 | 1 | |||
144.11 | even | 12 | 648.4.i.k.433.1 | 2 | |||
144.43 | odd | 12 | 648.4.i.b.433.1 | 2 | |||
144.59 | even | 12 | 648.4.i.k.217.1 | 2 | |||
144.139 | odd | 12 | 648.4.i.b.217.1 | 2 | |||
240.59 | even | 4 | 1800.4.a.bg.1.1 | 1 | |||
240.107 | odd | 4 | 1800.4.f.q.649.1 | 2 | |||
240.203 | odd | 4 | 1800.4.f.q.649.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.a.a.1.1 | ✓ | 1 | 16.11 | odd | 4 | ||
48.4.a.b.1.1 | 1 | 16.5 | even | 4 | |||
72.4.a.b.1.1 | 1 | 48.11 | even | 4 | |||
144.4.a.b.1.1 | 1 | 48.5 | odd | 4 | |||
192.4.a.a.1.1 | 1 | 16.3 | odd | 4 | |||
192.4.a.g.1.1 | 1 | 16.13 | even | 4 | |||
576.4.a.u.1.1 | 1 | 48.35 | even | 4 | |||
576.4.a.v.1.1 | 1 | 48.29 | odd | 4 | |||
600.4.a.h.1.1 | 1 | 80.59 | odd | 4 | |||
600.4.f.b.49.1 | 2 | 80.27 | even | 4 | |||
600.4.f.b.49.2 | 2 | 80.43 | even | 4 | |||
648.4.i.b.217.1 | 2 | 144.139 | odd | 12 | |||
648.4.i.b.433.1 | 2 | 144.43 | odd | 12 | |||
648.4.i.k.217.1 | 2 | 144.59 | even | 12 | |||
648.4.i.k.433.1 | 2 | 144.11 | even | 12 | |||
768.4.d.b.385.1 | 2 | 1.1 | even | 1 | trivial | ||
768.4.d.b.385.2 | 2 | 8.5 | even | 2 | inner | ||
768.4.d.o.385.1 | 2 | 8.3 | odd | 2 | |||
768.4.d.o.385.2 | 2 | 4.3 | odd | 2 | |||
1176.4.a.a.1.1 | 1 | 112.27 | even | 4 | |||
1200.4.a.u.1.1 | 1 | 80.69 | even | 4 | |||
1200.4.f.p.49.1 | 2 | 80.53 | odd | 4 | |||
1200.4.f.p.49.2 | 2 | 80.37 | odd | 4 | |||
1800.4.a.bg.1.1 | 1 | 240.59 | even | 4 | |||
1800.4.f.q.649.1 | 2 | 240.107 | odd | 4 | |||
1800.4.f.q.649.2 | 2 | 240.203 | odd | 4 | |||
2352.4.a.w.1.1 | 1 | 112.69 | odd | 4 |