Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,3,Mod(1889,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.1889");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.c (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: | \(58.8557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-11}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 15x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.2 | ||
Root | \(3.83776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1889 |
Dual form | 2160.3.c.l.1889.1 |
$q$-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 \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −2.86421 | + | 4.09833i | −0.572842 | + | 0.819666i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.15439i | 1.02206i | 0.859564 | + | 0.511028i | \(0.170735\pi\) | ||||
−0.859564 | + | 0.511028i | \(0.829265\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.06984i | − | 0.460894i | −0.973085 | − | 0.230447i | \(-0.925981\pi\) | ||
0.973085 | − | 0.230447i | \(-0.0740189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.12682i | − | 0.240525i | −0.992742 | − | 0.120262i | \(-0.961626\pi\) | ||
0.992742 | − | 0.120262i | \(-0.0383736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.72842 | 0.513436 | 0.256718 | − | 0.966486i | \(-0.417359\pi\) | ||||
0.256718 | + | 0.966486i | \(0.417359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.1852 | 1.06238 | 0.531191 | − | 0.847252i | \(-0.321745\pi\) | ||||
0.531191 | + | 0.847252i | \(0.321745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.7284 | 0.640366 | 0.320183 | − | 0.947356i | \(-0.396256\pi\) | ||||
0.320183 | + | 0.947356i | \(0.396256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.59262 | − | 23.4769i | −0.343705 | − | 0.939078i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 39.7995i | − | 1.37240i | −0.727415 | − | 0.686198i | \(-0.759278\pi\) | ||
0.727415 | − | 0.686198i | \(-0.240722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.3705 | 1.27002 | 0.635008 | − | 0.772506i | \(-0.280997\pi\) | ||||
0.635008 | + | 0.772506i | \(0.280997\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −29.3210 | − | 20.4917i | −0.837744 | − | 0.585476i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 34.8712i | − | 0.942465i | −0.882009 | − | 0.471232i | \(-0.843809\pi\) | ||
0.882009 | − | 0.471232i | \(-0.156191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 13.2665i | − | 0.323573i | −0.986826 | − | 0.161787i | \(-0.948274\pi\) | ||
0.986826 | − | 0.161787i | \(-0.0517256\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66.6156i | 1.54920i | 0.632452 | + | 0.774600i | \(0.282049\pi\) | ||||
−0.632452 | + | 0.774600i | \(0.717951\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.9137 | 0.359865 | 0.179933 | − | 0.983679i | \(-0.442412\pi\) | ||||
0.179933 | + | 0.983679i | \(0.442412\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.18525 | −0.0445969 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.62950 | −0.0873491 | −0.0436746 | − | 0.999046i | \(-0.513906\pi\) | ||||
−0.0436746 | + | 0.999046i | \(0.513906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.7779 | + | 14.5211i | 0.377780 | + | 0.264019i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 25.7738i | 0.436844i | 0.975854 | + | 0.218422i | \(0.0700909\pi\) | ||||
−0.975854 | + | 0.218422i | \(0.929909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.1852 | −0.199758 | −0.0998791 | − | 0.995000i | \(-0.531846\pi\) | ||||
−0.0998791 | + | 0.995000i | \(0.531846\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.8148 | + | 8.95587i | 0.197150 | + | 0.137783i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 106.415i | 1.58828i | 0.607732 | + | 0.794142i | \(0.292080\pi\) | ||||
−0.607732 | + | 0.794142i | \(0.707920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 101.487i | − | 1.42939i | −0.699436 | − | 0.714695i | \(-0.746565\pi\) | ||
0.699436 | − | 0.714695i | \(-0.253435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 23.2646i | − | 0.318694i | −0.987223 | − | 0.159347i | \(-0.949061\pi\) | ||
0.987223 | − | 0.159347i | \(-0.0509388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 36.2716 | 0.471060 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 66.5557 | 0.842478 | 0.421239 | − | 0.906950i | \(-0.361595\pi\) | ||||
0.421239 | + | 0.906950i | \(0.361595\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 144.284 | 1.73836 | 0.869182 | − | 0.494493i | \(-0.164646\pi\) | ||||
0.869182 | + | 0.494493i | \(0.164646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.0000 | + | 35.7719i | −0.294118 | + | 0.420846i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 154.553i | 1.73655i | 0.496085 | + | 0.868274i | \(0.334770\pi\) | ||||
−0.496085 | + | 0.868274i | \(0.665230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.3705 | 0.245830 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −57.8148 | + | 82.7258i | −0.608576 | + | 0.870798i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 175.733i | 1.81168i | 0.423621 | + | 0.905839i | \(0.360759\pi\) | ||||
−0.423621 | + | 0.905839i | \(0.639241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 149.483i | − | 1.48003i | −0.672591 | − | 0.740014i | \(-0.734819\pi\) | ||
0.672591 | − | 0.740014i | \(-0.265181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 28.6175i | 0.277840i | 0.990304 | + | 0.138920i | \(0.0443631\pi\) | ||||
−0.990304 | + | 0.138920i | \(0.955637\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −156.297 | −1.46072 | −0.730359 | − | 0.683064i | \(-0.760647\pi\) | ||||
−0.730359 | + | 0.683064i | \(0.760647\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.55575 | 0.0784931 | 0.0392465 | − | 0.999230i | \(-0.487504\pi\) | ||||
0.0392465 | + | 0.999230i | \(0.487504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −184.370 | −1.63160 | −0.815799 | − | 0.578336i | \(-0.803702\pi\) | ||||
−0.815799 | + | 0.578336i | \(0.803702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −42.1852 | + | 60.3619i | −0.366828 | + | 0.524886i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 62.4465i | 0.524760i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 95.2967 | 0.787576 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 120.827 | + | 32.0274i | 0.966619 | + | 0.256219i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 40.7002i | 0.320474i | 0.987079 | + | 0.160237i | \(0.0512259\pi\) | ||||
−0.987079 | + | 0.160237i | \(0.948774\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 80.0236i | 0.610867i | 0.952213 | + | 0.305434i | \(0.0988014\pi\) | ||||
−0.952213 | + | 0.305434i | \(0.901199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 144.413i | 1.08581i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0738 | 0.0954289 | 0.0477144 | − | 0.998861i | \(-0.484806\pi\) | ||||
0.0477144 | + | 0.998861i | \(0.484806\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −144.370 | −1.03864 | −0.519318 | − | 0.854581i | \(-0.673814\pi\) | ||||
−0.519318 | + | 0.854581i | \(0.673814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.8525 | −0.110857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 163.111 | + | 113.994i | 1.12491 | + | 0.786166i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 54.2498i | 0.364093i | 0.983290 | + | 0.182046i | \(0.0582721\pi\) | ||||
−0.983290 | + | 0.182046i | \(0.941728\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.1852 | −0.140300 | −0.0701498 | − | 0.997536i | \(-0.522348\pi\) | ||||
−0.0701498 | + | 0.997536i | \(0.522348\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −112.765 | + | 161.353i | −0.727518 | + | 1.04099i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 105.939i | 0.674770i | 0.941367 | + | 0.337385i | \(0.109542\pi\) | ||||
−0.941367 | + | 0.337385i | \(0.890458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 105.373i | 0.654489i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 154.746i | − | 0.949361i | −0.880158 | − | 0.474680i | \(-0.842564\pi\) | ||
0.880158 | − | 0.474680i | \(-0.157436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 151.667 | 0.908187 | 0.454094 | − | 0.890954i | \(-0.349963\pi\) | ||||
0.454094 | + | 0.890954i | \(0.349963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 159.223 | 0.942148 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −311.198 | −1.79883 | −0.899416 | − | 0.437094i | \(-0.856008\pi\) | ||||
−0.899416 | + | 0.437094i | \(0.856008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 167.963 | − | 61.4750i | 0.959789 | − | 0.351285i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 211.170i | − | 1.17972i | −0.807505 | − | 0.589861i | \(-0.799183\pi\) | ||
0.807505 | − | 0.589861i | \(-0.200817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 149.297 | 0.824844 | 0.412422 | − | 0.910993i | \(-0.364683\pi\) | ||||
0.412422 | + | 0.910993i | \(0.364683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 142.914 | + | 99.8783i | 0.772506 | + | 0.539883i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 44.2517i | − | 0.236640i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.1654i | − | 0.126520i | −0.997997 | − | 0.0632602i | \(-0.979850\pi\) | ||
0.997997 | − | 0.0632602i | \(-0.0201498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 332.653i | 1.72359i | 0.507255 | + | 0.861796i | \(0.330660\pi\) | ||||
−0.507255 | + | 0.861796i | \(0.669340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 279.568 | 1.41913 | 0.709564 | − | 0.704641i | \(-0.248892\pi\) | ||||
0.709564 | + | 0.704641i | \(0.248892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 161.185 | 0.809976 | 0.404988 | − | 0.914322i | \(-0.367276\pi\) | ||||
0.404988 | + | 0.914322i | \(0.367276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 284.741 | 1.40266 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54.3705 | + | 37.9980i | 0.265222 | + | 0.185356i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 102.336i | − | 0.489646i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 92.1852 | 0.436897 | 0.218448 | − | 0.975848i | \(-0.429900\pi\) | ||||
0.218448 | + | 0.975848i | \(0.429900\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −273.013 | − | 190.801i | −1.26983 | − | 0.887446i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 281.672i | 1.29803i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.2922i | − | 0.123494i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 197.672i | 0.886422i | 0.896417 | + | 0.443211i | \(0.146161\pi\) | ||||
−0.896417 | + | 0.443211i | \(0.853839\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −32.7284 | −0.144178 | −0.0720890 | − | 0.997398i | \(-0.522967\pi\) | ||||
−0.0720890 | + | 0.997398i | \(0.522967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 350.926 | 1.53243 | 0.766215 | − | 0.642585i | \(-0.222138\pi\) | ||||
0.766215 | + | 0.642585i | \(0.222138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −399.827 | −1.71600 | −0.857999 | − | 0.513652i | \(-0.828292\pi\) | ||||
−0.857999 | + | 0.513652i | \(0.828292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −48.4443 | + | 69.3178i | −0.206146 | + | 0.294969i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 363.690i | 1.52172i | 0.648919 | + | 0.760858i | \(0.275221\pi\) | ||||
−0.648919 | + | 0.760858i | \(0.724779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 227.667 | 0.944677 | 0.472339 | − | 0.881417i | \(-0.343410\pi\) | ||||
0.472339 | + | 0.881417i | \(0.343410\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.25901 | − | 8.95587i | 0.0255470 | − | 0.0365546i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 63.1157i | − | 0.255529i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 227.988i | − | 0.908319i | −0.890920 | − | 0.454160i | \(-0.849940\pi\) | ||
0.890920 | − | 0.454160i | \(-0.150060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 74.6707i | − | 0.295141i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 456.038 | 1.77447 | 0.887233 | − | 0.461322i | \(-0.152625\pi\) | ||||
0.887233 | + | 0.461322i | \(0.152625\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 249.482 | 0.963251 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 186.543 | 0.709290 | 0.354645 | − | 0.935001i | \(-0.384602\pi\) | ||||
0.354645 | + | 0.935001i | \(0.384602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.2599 | − | 18.9732i | 0.0500372 | − | 0.0715971i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 337.157i | − | 1.25337i | −0.779272 | − | 0.626686i | \(-0.784411\pi\) | ||
0.779272 | − | 0.626686i | \(-0.215589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −58.2590 | −0.214978 | −0.107489 | − | 0.994206i | \(-0.534281\pi\) | ||||
−0.107489 | + | 0.994206i | \(0.534281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −119.024 | + | 43.5632i | −0.432816 | + | 0.158412i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 332.229i | − | 1.19938i | −0.800232 | − | 0.599691i | \(-0.795290\pi\) | ||
0.800232 | − | 0.599691i | \(-0.204710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 112.296i | − | 0.399629i | −0.979834 | − | 0.199814i | \(-0.935966\pi\) | ||
0.979834 | − | 0.199814i | \(-0.0640339\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 325.975i | 1.15185i | 0.817501 | + | 0.575927i | \(0.195359\pi\) | ||||
−0.817501 | + | 0.575927i | \(0.804641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 94.9137 | 0.330710 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −212.815 | −0.736383 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −71.9623 | −0.245605 | −0.122803 | − | 0.992431i | \(-0.539188\pi\) | ||||
−0.122803 | + | 0.992431i | \(0.539188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −105.630 | − | 73.8215i | −0.358066 | − | 0.250242i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 46.0531i | − | 0.154024i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −476.593 | −1.58337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.9011 | − | 49.9392i | 0.114430 | − | 0.163735i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 245.900i | 0.800977i | 0.916302 | + | 0.400488i | \(0.131159\pi\) | ||||
−0.916302 | + | 0.400488i | \(0.868841\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 69.3693i | − | 0.223053i | −0.993761 | − | 0.111526i | \(-0.964426\pi\) | ||
0.993761 | − | 0.111526i | \(-0.0355739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 218.659i | 0.698592i | 0.937013 | + | 0.349296i | \(0.113579\pi\) | ||||
−0.937013 | + | 0.349296i | \(0.886421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 74.4317 | 0.234800 | 0.117400 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117400 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −201.777 | −0.632530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 176.185 | 0.545465 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −73.4082 | + | 26.8676i | −0.225871 | + | 0.0826696i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 121.007i | 0.367802i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 220.223 | 0.665326 | 0.332663 | − | 0.943046i | \(-0.392053\pi\) | ||||
0.332663 | + | 0.943046i | \(0.392053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −436.124 | − | 304.795i | −1.30186 | − | 0.909835i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.6415i | − | 0.0731203i | −0.999331 | − | 0.0365601i | \(-0.988360\pi\) | ||
0.999331 | − | 0.0365601i | \(-0.0116400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 199.602i | − | 0.585343i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 334.931i | 0.976475i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 147.556 | 0.425233 | 0.212616 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212616 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −503.149 | −1.44169 | −0.720844 | − | 0.693097i | \(-0.756246\pi\) | ||||
−0.720844 | + | 0.693097i | \(0.756246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −236.716 | −0.670583 | −0.335292 | − | 0.942114i | \(-0.608835\pi\) | ||||
−0.335292 | + | 0.942114i | \(0.608835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 415.926 | + | 290.679i | 1.17162 | + | 0.818815i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 195.871i | − | 0.545601i | −0.962071 | − | 0.272800i | \(-0.912050\pi\) | ||
0.962071 | − | 0.272800i | \(-0.0879499\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.4443 | 0.128654 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 95.3462 | + | 66.6348i | 0.261222 | + | 0.182561i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 339.756i | 0.925766i | 0.886419 | + | 0.462883i | \(0.153185\pi\) | ||||
−0.886419 | + | 0.462883i | \(0.846815\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 33.1213i | − | 0.0892756i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 540.980i | − | 1.45035i | −0.688566 | − | 0.725174i | \(-0.741759\pi\) | ||
0.688566 | − | 0.725174i | \(-0.258241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −124.446 | −0.330095 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 432.926 | 1.14229 | 0.571143 | − | 0.820851i | \(-0.306500\pi\) | ||||
0.571143 | + | 0.820851i | \(0.306500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 478.977 | 1.25059 | 0.625296 | − | 0.780388i | \(-0.284978\pi\) | ||||
0.625296 | + | 0.780388i | \(0.284978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −103.889 | + | 148.653i | −0.269843 | + | 0.386112i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 339.190i | 0.871954i | 0.899958 | + | 0.435977i | \(0.143597\pi\) | ||||
−0.899958 | + | 0.435977i | \(0.856403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 128.556 | 0.328787 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −190.630 | + | 272.767i | −0.482606 | + | 0.690550i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 113.042i | − | 0.284740i | −0.989814 | − | 0.142370i | \(-0.954528\pi\) | ||
0.989814 | − | 0.142370i | \(-0.0454723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 477.774i | 1.19146i | 0.803186 | + | 0.595728i | \(0.203136\pi\) | ||||
−0.803186 | + | 0.595728i | \(0.796864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 123.105i | − | 0.305470i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −176.791 | −0.434377 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 677.370 | 1.65616 | 0.828081 | − | 0.560608i | \(-0.189433\pi\) | ||||
0.828081 | + | 0.560608i | \(0.189433\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −184.396 | −0.446479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −413.260 | + | 591.324i | −0.995807 | + | 1.42488i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 344.170i | − | 0.821408i | −0.911769 | − | 0.410704i | \(-0.865283\pi\) | ||
0.911769 | − | 0.410704i | \(-0.134717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5918 | 0.0702892 | 0.0351446 | − | 0.999382i | \(-0.488811\pi\) | ||||
0.0351446 | + | 0.999382i | \(0.488811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −75.0000 | − | 204.917i | −0.176471 | − | 0.482157i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 87.1780i | − | 0.204164i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 724.253i | 1.68040i | 0.542276 | + | 0.840201i | \(0.317563\pi\) | ||||
−0.542276 | + | 0.840201i | \(0.682437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 96.6100i | − | 0.223118i | −0.993758 | − | 0.111559i | \(-0.964416\pi\) | ||
0.993758 | − | 0.111559i | \(-0.0355844\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 297.297 | 0.680313 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −101.223 | −0.230576 | −0.115288 | − | 0.993332i | \(-0.536779\pi\) | ||||
−0.115288 | + | 0.993332i | \(0.536779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −377.520 | −0.852189 | −0.426094 | − | 0.904679i | \(-0.640111\pi\) | ||||
−0.426094 | + | 0.904679i | \(0.640111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −633.408 | − | 442.671i | −1.42339 | − | 0.994767i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 654.974i | − | 1.45874i | −0.684120 | − | 0.729369i | \(-0.739814\pi\) | ||
0.684120 | − | 0.729369i | \(-0.260186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −67.2590 | −0.149133 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −64.0738 | + | 91.6817i | −0.140821 | + | 0.201498i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 321.574i | − | 0.703664i | −0.936063 | − | 0.351832i | \(-0.885559\pi\) | ||
0.936063 | − | 0.351832i | \(-0.114441\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 465.511i | 1.00979i | 0.863182 | + | 0.504893i | \(0.168468\pi\) | ||||
−0.863182 | + | 0.504893i | \(0.831532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 250.880i | − | 0.541857i | −0.962600 | − | 0.270928i | \(-0.912669\pi\) | ||
0.962600 | − | 0.270928i | \(-0.0873307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 246.259 | 0.527321 | 0.263661 | − | 0.964616i | \(-0.415070\pi\) | ||||
0.263661 | + | 0.964616i | \(0.415070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −761.334 | −1.62331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 337.730 | 0.714017 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −173.444 | − | 473.888i | −0.365146 | − | 0.997659i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 175.012i | − | 0.365370i | −0.983172 | − | 0.182685i | \(-0.941521\pi\) | ||
0.983172 | − | 0.182685i | \(-0.0584788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −109.036 | −0.226686 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −720.211 | − | 503.335i | −1.48497 | − | 1.03781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 28.9906i | − | 0.0595289i | −0.999557 | − | 0.0297645i | \(-0.990524\pi\) | ||
0.999557 | − | 0.0297645i | \(-0.00947573\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 974.373i | 1.98447i | 0.124388 | + | 0.992234i | \(0.460303\pi\) | ||||
−0.124388 | + | 0.992234i | \(0.539697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 347.387i | − | 0.704638i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 726.075 | 1.46092 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −626.185 | −1.25488 | −0.627440 | − | 0.778665i | \(-0.715897\pi\) | ||||
−0.627440 | + | 0.778665i | \(0.715897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 71.5197 | 0.142186 | 0.0710932 | − | 0.997470i | \(-0.477351\pi\) | ||||
0.0710932 | + | 0.997470i | \(0.477351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 612.630 | + | 428.150i | 1.21313 | + | 0.847822i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 932.296i | 1.83162i | 0.401608 | + | 0.915812i | \(0.368451\pi\) | ||||
−0.401608 | + | 0.915812i | \(0.631549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 166.444 | 0.325723 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −117.284 | − | 81.9666i | −0.227736 | − | 0.159158i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 85.7495i | − | 0.165860i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 373.070i | − | 0.716066i | −0.933709 | − | 0.358033i | \(-0.883448\pi\) | ||
0.933709 | − | 0.358033i | \(-0.116552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 828.480i | − | 1.58409i | −0.610461 | − | 0.792046i | \(-0.709016\pi\) | ||
0.610461 | − | 0.792046i | \(-0.290984\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 343.642 | 0.652072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −312.074 | −0.589931 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.4820 | −0.0778274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 447.666 | − | 640.556i | 0.836760 | − | 1.19730i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0789i | 0.0205545i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −50.5935 | −0.0935184 | −0.0467592 | − | 0.998906i | \(-0.514889\pi\) | ||||
−0.0467592 | + | 0.998906i | \(0.514889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.5054 | + | 35.0643i | −0.0449641 | + | 0.0643381i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 485.070i | − | 0.886782i | −0.896328 | − | 0.443391i | \(-0.853775\pi\) | ||
0.896328 | − | 0.443391i | \(-0.146225\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 803.363i | − | 1.45801i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 476.166i | 0.861059i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −198.372 | −0.356144 | −0.178072 | − | 0.984017i | \(-0.556986\pi\) | ||||
−0.178072 | + | 0.984017i | \(0.556986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 208.295 | 0.372621 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −660.840 | −1.17378 | −0.586892 | − | 0.809666i | \(-0.699649\pi\) | ||||
−0.586892 | + | 0.809666i | \(0.699649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 528.075 | − | 755.611i | 0.934647 | − | 1.33736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 162.994i | − | 0.286457i | −0.989690 | − | 0.143229i | \(-0.954252\pi\) | ||
0.989690 | − | 0.143229i | \(-0.0457484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −262.631 | −0.459950 | −0.229975 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229975 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −126.556 | − | 345.778i | −0.220097 | − | 0.601353i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 532.551i | 0.922966i | 0.887149 | + | 0.461483i | \(0.152682\pi\) | ||||
−0.887149 | + | 0.461483i | \(0.847318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1032.26i | 1.77670i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.4708i | 0.0402587i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 927.593 | 1.58023 | 0.790114 | − | 0.612960i | \(-0.210021\pi\) | ||||
0.790114 | + | 0.612960i | \(0.210021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 794.703 | 1.34924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −890.336 | −1.50141 | −0.750705 | − | 0.660638i | \(-0.770286\pi\) | ||||
−0.750705 | + | 0.660638i | \(0.770286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −255.926 | − | 178.860i | −0.430128 | − | 0.300604i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1036.76i | 1.73081i | 0.501073 | + | 0.865405i | \(0.332939\pi\) | ||||
−0.501073 | + | 0.865405i | \(0.667061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 865.816 | 1.44063 | 0.720313 | − | 0.693649i | \(-0.243998\pi\) | ||||
0.720313 | + | 0.693649i | \(0.243998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −272.950 | + | 390.558i | −0.451157 | + | 0.645550i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 708.606i | − | 1.16739i | −0.811973 | − | 0.583695i | \(-0.801606\pi\) | ||
0.811973 | − | 0.583695i | \(-0.198394\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 52.8860i | − | 0.0865565i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 677.814i | − | 1.10573i | −0.833270 | − | 0.552866i | \(-0.813534\pi\) | ||
0.833270 | − | 0.552866i | \(-0.186466\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 474.063 | 0.768335 | 0.384168 | − | 0.923263i | \(-0.374488\pi\) | ||||
0.384168 | + | 0.923263i | \(0.374488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −323.187 | −0.522111 | −0.261056 | − | 0.965324i | \(-0.584071\pi\) | ||||
−0.261056 | + | 0.965324i | \(0.584071\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1105.73 | −1.77485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −477.334 | + | 403.457i | −0.763734 | + | 0.645531i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 304.370i | − | 0.483896i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −977.669 | −1.54940 | −0.774698 | − | 0.632331i | \(-0.782098\pi\) | ||||
−0.774698 | + | 0.632331i | \(0.782098\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −166.803 | − | 116.574i | −0.262682 | − | 0.183581i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.83288i | 0.0107267i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 245.231i | − | 0.382575i | −0.981534 | − | 0.191288i | \(-0.938734\pi\) | ||
0.981534 | − | 0.191288i | \(-0.0612663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 244.471i | − | 0.380204i | −0.981764 | − | 0.190102i | \(-0.939118\pi\) | ||
0.981764 | − | 0.190102i | \(-0.0608819\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 866.779 | 1.33969 | 0.669844 | − | 0.742501i | \(-0.266361\pi\) | ||||
0.669844 | + | 0.742501i | \(0.266361\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 130.669 | 0.201339 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 641.198 | 0.981926 | 0.490963 | − | 0.871180i | \(-0.336645\pi\) | ||||
0.490963 | + | 0.871180i | \(0.336645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −327.963 | − | 229.204i | −0.500707 | − | 0.349930i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 771.490i | − | 1.17070i | −0.810781 | − | 0.585349i | \(-0.800958\pi\) | ||
0.810781 | − | 0.585349i | \(-0.199042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −796.075 | −1.20435 | −0.602175 | − | 0.798364i | \(-0.705699\pi\) | ||||
−0.602175 | + | 0.798364i | \(0.705699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −591.852 | − | 413.629i | −0.890004 | − | 0.621999i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 586.184i | − | 0.878836i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 61.7772i | 0.0920674i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 698.325i | 1.03763i | 0.854887 | + | 0.518815i | \(0.173627\pi\) | ||||
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 433.655 | 0.640553 | 0.320277 | − | 0.947324i | \(-0.396224\pi\) | ||||
0.320277 | + | 0.947324i | \(0.396224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1257.26 | −1.85164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1112.83 | −1.62933 | −0.814663 | − | 0.579935i | \(-0.803078\pi\) | ||||
−0.814663 | + | 0.579935i | \(0.803078\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4460 | + | 53.5806i | −0.0546656 | + | 0.0782198i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4756i | 0.0210096i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −497.743 | −0.720322 | −0.360161 | − | 0.932890i | \(-0.617278\pi\) | ||||
−0.360161 | + | 0.932890i | \(0.617278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 413.507 | − | 591.678i | 0.594974 | − | 0.851335i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 115.796i | − | 0.166134i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 660.713i | − | 0.942529i | −0.881992 | − | 0.471264i | \(-0.843798\pi\) | ||
0.881992 | − | 0.471264i | \(-0.156202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 703.884i | − | 1.00126i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1069.46 | 1.51267 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1013.56 | −1.42956 | −0.714780 | − | 0.699350i | \(-0.753473\pi\) | ||||
−0.714780 | + | 0.699350i | \(0.753473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 579.865 | 0.813275 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.4048 | − | 64.9687i | 0.0635032 | − | 0.0908653i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1067.57i | 1.48480i | 0.669955 | + | 0.742402i | \(0.266313\pi\) | ||||
−0.669955 | + | 0.742402i | \(0.733687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −204.741 | −0.283968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −934.370 | + | 341.982i | −1.28879 | + | 0.471699i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 878.561i | − | 1.20847i | −0.796804 | − | 0.604237i | \(-0.793478\pi\) | ||
0.796804 | − | 0.604237i | \(-0.206522\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 581.448i | 0.795415i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 76.9483i | − | 0.104977i | −0.998622 | − | 0.0524886i | \(-0.983285\pi\) | ||
0.998622 | − | 0.0524886i | \(-0.0167153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 539.507 | 0.732031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 613.815 | 0.830602 | 0.415301 | − | 0.909684i | \(-0.363676\pi\) | ||||
0.415301 | + | 0.909684i | \(0.363676\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −331.036 | −0.445540 | −0.222770 | − | 0.974871i | \(-0.571510\pi\) | ||||
−0.222770 | + | 0.974871i | \(0.571510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −222.334 | − | 155.383i | −0.298434 | − | 0.208567i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1118.21i | − | 1.49293i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 496.852 | 0.661588 | 0.330794 | − | 0.943703i | \(-0.392683\pi\) | ||||
0.330794 | + | 0.943703i | \(0.392683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 60.6790 | − | 86.8241i | 0.0803695 | − | 0.114999i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1234.26i | − | 1.63046i | −0.579135 | − | 0.815232i | \(-0.696610\pi\) | ||
0.579135 | − | 0.815232i | \(-0.303390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 69.3693i | 0.0911555i | 0.998961 | + | 0.0455777i | \(0.0145129\pi\) | ||||
−0.998961 | + | 0.0455777i | \(0.985487\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 61.2111i | 0.0802243i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 80.5901 | 0.105072 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1110.85 | 1.44454 | 0.722271 | − | 0.691610i | \(-0.243098\pi\) | ||||
0.722271 | + | 0.691610i | \(0.243098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 733.074 | 0.948349 | 0.474174 | − | 0.880431i | \(-0.342747\pi\) | ||||
0.474174 | + | 0.880431i | \(0.342747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −338.296 | − | 924.299i | −0.436511 | − | 1.19264i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 267.788i | − | 0.343758i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −514.521 | −0.658798 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −434.173 | − | 303.431i | −0.553086 | − | 0.386536i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1004.84i | 1.27680i | 0.769703 | + | 0.638402i | \(0.220404\pi\) | ||||
−0.769703 | + | 0.638402i | \(0.779596\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1319.06i | − | 1.66758i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.1011i | 0.0480468i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 621.101 | 0.779298 | 0.389649 | − | 0.920963i | \(-0.372596\pi\) | ||||
0.389649 | + | 0.920963i | \(0.372596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 147.630 | 0.184768 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −117.948 | −0.146884 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −431.852 | − | 301.810i | −0.536463 | − | 0.374919i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 276.049i | 0.341222i | 0.985338 | + | 0.170611i | \(0.0545742\pi\) | ||||
−0.985338 | + | 0.170611i | \(0.945426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1024.08 | −1.26273 | −0.631366 | − | 0.775485i | \(-0.717505\pi\) | ||||
−0.631366 | + | 0.775485i | \(0.717505\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 634.200 | + | 443.224i | 0.778159 | + | 0.543833i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1344.65i | 1.64584i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.43362i | 0.00783632i | 0.999992 | + | 0.00391816i | \(0.00124719\pi\) | ||||
−0.999992 | + | 0.00391816i | \(0.998753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 282.727i | − | 0.343532i | −0.985138 | − | 0.171766i | \(-0.945053\pi\) | ||
0.985138 | − | 0.171766i | \(-0.0549474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 223.567 | 0.270334 | 0.135167 | − | 0.990823i | \(-0.456843\pi\) | ||||
0.135167 | + | 0.990823i | \(0.456843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1355.63 | −1.63526 | −0.817631 | − | 0.575742i | \(-0.804713\pi\) | ||||
−0.817631 | + | 0.575742i | \(0.804713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.0738 | −0.0228977 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −434.407 | + | 621.582i | −0.520247 | + | 0.744410i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 643.715i | − | 0.767241i | −0.923491 | − | 0.383620i | \(-0.874677\pi\) | ||
0.923491 | − | 0.383620i | \(-0.125323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −743.000 | −0.883472 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −456.048 | + | 652.548i | −0.539701 | + | 0.772247i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 681.790i | 0.804947i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 513.597i | − | 0.603522i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 964.735i | − | 1.13099i | −0.824751 | − | 0.565495i | \(-0.808685\pi\) | ||
0.824751 | − | 0.565495i | \(-0.191315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −455.077 | −0.531012 | −0.265506 | − | 0.964109i | \(-0.585539\pi\) | ||||
−0.265506 | + | 0.964109i | \(0.585539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1086.78 | −1.26517 | −0.632584 | − | 0.774492i | \(-0.718006\pi\) | ||||
−0.632584 | + | 0.774492i | \(0.718006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1273.67 | −1.47586 | −0.737930 | − | 0.674877i | \(-0.764197\pi\) | ||||
−0.737930 | + | 0.674877i | \(0.764197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 891.335 | − | 1275.39i | 1.03045 | − | 1.47444i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 337.427i | − | 0.388293i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 332.741 | 0.382022 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −229.137 | + | 864.445i | −0.261870 | + | 0.987938i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1169.03i | − | 1.33299i | −0.745509 | − | 0.666496i | \(-0.767793\pi\) | ||
0.745509 | − | 0.666496i | \(-0.232207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 547.812i | − | 0.621808i | −0.950441 | − | 0.310904i | \(-0.899368\pi\) | ||
0.950441 | − | 0.310904i | \(-0.100632\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 494.077i | 0.559544i | 0.960066 | + | 0.279772i | \(0.0902589\pi\) | ||||
−0.960066 | + | 0.279772i | \(0.909741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 919.667 | 1.03683 | 0.518414 | − | 0.855129i | \(-0.326522\pi\) | ||||
0.518414 | + | 0.855129i | \(0.326522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −291.185 | −0.327542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 341.407 | 0.382314 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 865.445 | + | 604.835i | 0.966978 | + | 0.675794i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1566.93i | − | 1.74297i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.4082 | −0.0448482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −427.617 | + | 611.867i | −0.472505 | + | 0.676097i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 142.135i | 0.156709i | 0.996926 | + | 0.0783547i | \(0.0249667\pi\) | ||||
−0.996926 | + | 0.0783547i | \(0.975033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.6341i | 0.0171615i | 0.999963 | + | 0.00858074i | \(0.00273137\pi\) | ||||
−0.999963 | + | 0.00858074i | \(0.997269\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 731.497i | − | 0.801202i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −572.520 | −0.624340 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1549.48 | 1.68605 | 0.843027 | − | 0.537871i | \(-0.180771\pi\) | ||||
0.843027 | + | 0.537871i | \(0.180771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −317.331 | −0.343804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −818.669 | + | 299.635i | −0.885048 | + | 0.323930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 982.480i | 1.05757i | 0.848757 | + | 0.528784i | \(0.177352\pi\) | ||||
−0.848757 | + | 0.528784i | \(0.822648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.1098 | −0.0473789 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 181.358 | + | 126.746i | 0.193966 | + | 0.135557i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 329.526i | 0.351682i | 0.984419 | + | 0.175841i | \(0.0562645\pi\) | ||||
−0.984419 | + | 0.175841i | \(0.943735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 939.888i | − | 0.998819i | −0.866366 | − | 0.499409i | \(-0.833550\pi\) | ||
0.866366 | − | 0.499409i | \(-0.166450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 195.395i | − | 0.207205i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1456.78 | 1.53831 | 0.769155 | − | 0.639062i | \(-0.220677\pi\) | ||||
0.769155 | + | 0.639062i | \(0.220677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −72.7444 | −0.0766538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1391.14 | 1.45975 | 0.729874 | − | 0.683582i | \(-0.239579\pi\) | ||||
0.729874 | + | 0.683582i | \(0.239579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 99.0377 | + | 69.2147i | 0.103704 | + | 0.0724761i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 93.5347i | 0.0975336i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 589.036 | 0.612941 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1363.32 | − | 952.788i | −1.41277 | − | 0.987345i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.9796i | − | 0.0123884i | −0.999981 | − | 0.00619421i | \(-0.998028\pi\) | ||
0.999981 | − | 0.00619421i | \(-0.00197169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 504.732i | − | 0.519806i | −0.965635 | − | 0.259903i | \(-0.916309\pi\) | ||
0.965635 | − | 0.259903i | \(-0.0836906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1032.88i | − | 1.06154i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 529.554 | 0.542021 | 0.271010 | − | 0.962576i | \(-0.412642\pi\) | ||||
0.271010 | + | 0.962576i | \(0.412642\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 783.557 | 0.800365 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1110.66 | −1.12986 | −0.564932 | − | 0.825137i | \(-0.691098\pi\) | ||||
−0.564932 | + | 0.825137i | \(0.691098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −800.742 | + | 1145.76i | −0.812936 | + | 1.16321i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 981.142i | 0.992054i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1048.11 | 1.05763 | 0.528817 | − | 0.848736i | \(-0.322636\pi\) | ||||
0.528817 | + | 0.848736i | \(0.322636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −461.668 | + | 660.590i | −0.463988 | + | 0.663910i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1596.81i | − | 1.60161i | −0.598925 | − | 0.800805i | \(-0.704405\pi\) | ||
0.598925 | − | 0.800805i | \(-0.295595\pi\) | |||||||
\(998\) | 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 | 2160.3.c.l.1889.2 | 4 | ||
3.2 | odd | 2 | 2160.3.c.h.1889.3 | 4 | |||
4.3 | odd | 2 | 540.3.b.b.269.2 | yes | 4 | ||
5.4 | even | 2 | 2160.3.c.h.1889.4 | 4 | |||
12.11 | even | 2 | 540.3.b.a.269.3 | ✓ | 4 | ||
15.14 | odd | 2 | inner | 2160.3.c.l.1889.1 | 4 | ||
20.3 | even | 4 | 2700.3.g.s.701.2 | 8 | |||
20.7 | even | 4 | 2700.3.g.s.701.8 | 8 | |||
20.19 | odd | 2 | 540.3.b.a.269.4 | yes | 4 | ||
36.7 | odd | 6 | 1620.3.t.a.1349.2 | 8 | |||
36.11 | even | 6 | 1620.3.t.d.1349.3 | 8 | |||
36.23 | even | 6 | 1620.3.t.d.269.1 | 8 | |||
36.31 | odd | 6 | 1620.3.t.a.269.4 | 8 | |||
60.23 | odd | 4 | 2700.3.g.s.701.1 | 8 | |||
60.47 | odd | 4 | 2700.3.g.s.701.7 | 8 | |||
60.59 | even | 2 | 540.3.b.b.269.1 | yes | 4 | ||
180.59 | even | 6 | 1620.3.t.a.269.2 | 8 | |||
180.79 | odd | 6 | 1620.3.t.d.1349.1 | 8 | |||
180.119 | even | 6 | 1620.3.t.a.1349.4 | 8 | |||
180.139 | odd | 6 | 1620.3.t.d.269.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.3.b.a.269.3 | ✓ | 4 | 12.11 | even | 2 | ||
540.3.b.a.269.4 | yes | 4 | 20.19 | odd | 2 | ||
540.3.b.b.269.1 | yes | 4 | 60.59 | even | 2 | ||
540.3.b.b.269.2 | yes | 4 | 4.3 | odd | 2 | ||
1620.3.t.a.269.2 | 8 | 180.59 | even | 6 | |||
1620.3.t.a.269.4 | 8 | 36.31 | odd | 6 | |||
1620.3.t.a.1349.2 | 8 | 36.7 | odd | 6 | |||
1620.3.t.a.1349.4 | 8 | 180.119 | even | 6 | |||
1620.3.t.d.269.1 | 8 | 36.23 | even | 6 | |||
1620.3.t.d.269.3 | 8 | 180.139 | odd | 6 | |||
1620.3.t.d.1349.1 | 8 | 180.79 | odd | 6 | |||
1620.3.t.d.1349.3 | 8 | 36.11 | even | 6 | |||
2160.3.c.h.1889.3 | 4 | 3.2 | odd | 2 | |||
2160.3.c.h.1889.4 | 4 | 5.4 | even | 2 | |||
2160.3.c.l.1889.1 | 4 | 15.14 | odd | 2 | inner | ||
2160.3.c.l.1889.2 | 4 | 1.1 | even | 1 | trivial | ||
2700.3.g.s.701.1 | 8 | 60.23 | odd | 4 | |||
2700.3.g.s.701.2 | 8 | 20.3 | even | 4 | |||
2700.3.g.s.701.7 | 8 | 60.47 | odd | 4 | |||
2700.3.g.s.701.8 | 8 | 20.7 | even | 4 |