Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(449,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.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: | \(85.8312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.9671731157401600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 7x^{12} + 753x^{8} + 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.10 | ||
Root | \(-2.08559 - 0.941471i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.449 |
Dual form | 3150.3.c.f.449.15 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.78840i | − 0.344400i | −0.985062 | − | 0.172200i | \(-0.944912\pi\) | ||||
0.985062 | − | 0.172200i | \(-0.0550875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 14.9496i | − 1.14997i | −0.818164 | − | 0.574985i | \(-0.805008\pi\) | ||||
0.818164 | − | 0.574985i | \(-0.194992\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 0.335699 | 0.0197470 | 0.00987351 | − | 0.999951i | \(-0.496857\pi\) | ||||
0.00987351 | + | 0.999951i | \(0.496857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.8955 | 1.57345 | 0.786723 | − | 0.617306i | \(-0.211776\pi\) | ||||
0.786723 | + | 0.617306i | \(0.211776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 5.35761i | − 0.243528i | ||||||||
\(23\) | −18.5255 | −0.805458 | −0.402729 | − | 0.915319i | \(-0.631938\pi\) | ||||
−0.402729 | + | 0.915319i | \(0.631938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 21.1419i | − 0.813151i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 5.29150i | − 0.188982i | ||||||||
\(29\) | − 11.1480i | − 0.384415i | −0.981354 | − | 0.192208i | \(-0.938435\pi\) | ||||
0.981354 | − | 0.192208i | \(-0.0615647\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.603437 | 0.0194657 | 0.00973286 | − | 0.999953i | \(-0.496902\pi\) | ||||
0.00973286 | + | 0.999953i | \(0.496902\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.474751 | 0.0139633 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.9826i | 1.13466i | 0.823489 | + | 0.567332i | \(0.192024\pi\) | ||||
−0.823489 | + | 0.567332i | \(0.807976\pi\) | |||||||
\(38\) | 42.2786 | 1.11259 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 35.7336i | − 0.871550i | −0.900056 | − | 0.435775i | \(-0.856474\pi\) | ||||
0.900056 | − | 0.435775i | \(-0.143526\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 24.2590i | − 0.564163i | −0.959391 | − | 0.282081i | \(-0.908975\pi\) | ||||
0.959391 | − | 0.282081i | \(-0.0910248\pi\) | |||||||
\(44\) | − 7.57680i | − 0.172200i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.1991 | −0.569545 | ||||||||
\(47\) | −50.3738 | −1.07178 | −0.535892 | − | 0.844287i | \(-0.680025\pi\) | ||||
−0.535892 | + | 0.844287i | \(0.680025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 29.8992i | − 0.574985i | ||||||||
\(53\) | 44.9810 | 0.848699 | 0.424349 | − | 0.905499i | \(-0.360503\pi\) | ||||
0.424349 | + | 0.905499i | \(0.360503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.48331i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 15.7657i | − 0.271823i | ||||||||
\(59\) | 16.1852i | 0.274326i | 0.990548 | + | 0.137163i | \(0.0437984\pi\) | ||||
−0.990548 | + | 0.137163i | \(0.956202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.189 | −1.67523 | −0.837615 | − | 0.546260i | \(-0.816051\pi\) | ||||
−0.837615 | + | 0.546260i | \(0.816051\pi\) | |||||||
\(62\) | 0.853389 | 0.0137643 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 17.8987i | − 0.267144i | −0.991039 | − | 0.133572i | \(-0.957355\pi\) | ||||
0.991039 | − | 0.133572i | \(-0.0426448\pi\) | |||||||
\(68\) | 0.671399 | 0.00987351 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 76.4296i | − 1.07647i | −0.842794 | − | 0.538237i | \(-0.819091\pi\) | ||||
0.842794 | − | 0.538237i | \(-0.180909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 63.2996i | − 0.867118i | −0.901125 | − | 0.433559i | \(-0.857258\pi\) | ||||
0.901125 | − | 0.433559i | \(-0.142742\pi\) | |||||||
\(74\) | 59.3723i | 0.802328i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 59.7910 | 0.786723 | ||||||||
\(77\) | −10.0232 | −0.130171 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 60.6925 | 0.768260 | 0.384130 | − | 0.923279i | \(-0.374501\pi\) | ||||
0.384130 | + | 0.923279i | \(0.374501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 50.5349i | − 0.616279i | ||||||||
\(83\) | −129.480 | −1.56001 | −0.780003 | − | 0.625776i | \(-0.784782\pi\) | ||||
−0.780003 | + | 0.625776i | \(0.784782\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 34.3074i | − 0.398923i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 10.7152i | − 0.121764i | ||||||||
\(89\) | − 15.0312i | − 0.168890i | −0.996428 | − | 0.0844451i | \(-0.973088\pi\) | ||||
0.996428 | − | 0.0844451i | \(-0.0269117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39.5529 | −0.434648 | ||||||||
\(92\) | −37.0511 | −0.402729 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −71.2394 | −0.757866 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 59.4802i | − 0.613197i | −0.951839 | − | 0.306599i | \(-0.900809\pi\) | ||||
0.951839 | − | 0.306599i | \(-0.0991910\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 34.9641i | − 0.346179i | −0.984906 | − | 0.173089i | \(-0.944625\pi\) | ||||
0.984906 | − | 0.173089i | \(-0.0553750\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 16.5291i | − 0.160476i | −0.996776 | − | 0.0802381i | \(-0.974432\pi\) | ||||
0.996776 | − | 0.0802381i | \(-0.0255681\pi\) | |||||||
\(104\) | − 42.2839i | − 0.406576i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 63.6128 | 0.600121 | ||||||||
\(107\) | 117.574 | 1.09883 | 0.549413 | − | 0.835551i | \(-0.314851\pi\) | ||||
0.549413 | + | 0.835551i | \(0.314851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.23755 | −0.0205280 | −0.0102640 | − | 0.999947i | \(-0.503267\pi\) | ||||
−0.0102640 | + | 0.999947i | \(0.503267\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 10.5830i | − 0.0944911i | ||||||||
\(113\) | −89.0131 | −0.787726 | −0.393863 | − | 0.919169i | \(-0.628862\pi\) | ||||
−0.393863 | + | 0.919169i | \(0.628862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 22.2961i | − 0.192208i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22.8894i | 0.193978i | ||||||||
\(119\) | − 0.888177i | − 0.00746367i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 106.648 | 0.881389 | ||||||||
\(122\) | −144.517 | −1.18457 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.20687 | 0.00973286 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 234.130i | − 1.84354i | −0.387732 | − | 0.921772i | \(-0.626741\pi\) | ||||
0.387732 | − | 0.921772i | \(-0.373259\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0511i | 0.130161i | 0.997880 | + | 0.0650805i | \(0.0207304\pi\) | ||||
−0.997880 | + | 0.0650805i | \(0.979270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 79.0960i | − 0.594707i | ||||||||
\(134\) | − 25.3125i | − 0.188900i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.949501 | 0.00698163 | ||||||||
\(137\) | −177.901 | −1.29855 | −0.649274 | − | 0.760554i | \(-0.724927\pi\) | ||||
−0.649274 | + | 0.760554i | \(0.724927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 192.255 | 1.38313 | 0.691563 | − | 0.722316i | \(-0.256922\pi\) | ||||
0.691563 | + | 0.722316i | \(0.256922\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 108.088i | − 0.761181i | ||||||||
\(143\) | −56.6351 | −0.396050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 89.5192i | − 0.613145i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 83.9651i | 0.567332i | ||||||||
\(149\) | − 231.696i | − 1.55501i | −0.628880 | − | 0.777503i | \(-0.716486\pi\) | ||||
0.628880 | − | 0.777503i | \(-0.283514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −238.478 | −1.57932 | −0.789661 | − | 0.613543i | \(-0.789744\pi\) | ||||
−0.789661 | + | 0.613543i | \(0.789744\pi\) | |||||||
\(152\) | 84.5572 | 0.556297 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.1749 | −0.0920448 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 226.506i | − 1.44271i | −0.692564 | − | 0.721356i | \(-0.743519\pi\) | ||||
0.692564 | − | 0.721356i | \(-0.256481\pi\) | |||||||
\(158\) | 85.8322 | 0.543242 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 49.0140i | 0.304435i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 38.9379i | 0.238883i | 0.992841 | + | 0.119441i | \(0.0381104\pi\) | ||||
−0.992841 | + | 0.119441i | \(0.961890\pi\) | |||||||
\(164\) | − 71.4671i | − 0.435775i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −183.113 | −1.10309 | ||||||||
\(167\) | 195.038 | 1.16789 | 0.583945 | − | 0.811793i | \(-0.301508\pi\) | ||||
0.583945 | + | 0.811793i | \(0.301508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −54.4907 | −0.322430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 48.5180i | − 0.282081i | ||||||||
\(173\) | 98.7868 | 0.571022 | 0.285511 | − | 0.958375i | \(-0.407837\pi\) | ||||
0.285511 | + | 0.958375i | \(0.407837\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 15.1536i | − 0.0861000i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 21.2574i | − 0.119423i | ||||||||
\(179\) | − 164.993i | − 0.921751i | −0.887465 | − | 0.460875i | \(-0.847536\pi\) | ||||
0.887465 | − | 0.460875i | \(-0.152464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 112.556 | 0.621854 | 0.310927 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310927 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(182\) | −55.9363 | −0.307342 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −52.3981 | −0.284772 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.27176i | − 0.00680088i | ||||||||
\(188\) | −100.748 | −0.535892 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 261.319i | 1.36816i | 0.729406 | + | 0.684081i | \(0.239796\pi\) | ||||
−0.729406 | + | 0.684081i | \(0.760204\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 268.372i | 1.39053i | 0.718754 | + | 0.695265i | \(0.244713\pi\) | ||||
−0.718754 | + | 0.695265i | \(0.755287\pi\) | |||||||
\(194\) | − 84.1176i | − 0.433596i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 51.9378 | 0.263644 | 0.131822 | − | 0.991273i | \(-0.457917\pi\) | ||||
0.131822 | + | 0.991273i | \(0.457917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 307.244 | 1.54394 | 0.771970 | − | 0.635659i | \(-0.219272\pi\) | ||||
0.771970 | + | 0.635659i | \(0.219272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 49.4466i | − 0.244785i | ||||||||
\(203\) | −29.4950 | −0.145295 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 23.3756i | − 0.113474i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 59.7984i | − 0.287492i | ||||||||
\(209\) | − 113.256i | − 0.541895i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −112.097 | −0.531265 | −0.265632 | − | 0.964074i | \(-0.585581\pi\) | ||||
−0.265632 | + | 0.964074i | \(0.585581\pi\) | |||||||
\(212\) | 89.9621 | 0.424349 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 166.275 | 0.776988 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.59654i | − 0.00735735i | ||||||||
\(218\) | −3.16437 | −0.0145155 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5.01857i | − 0.0227085i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 192.031i | − 0.861124i | −0.902561 | − | 0.430562i | \(-0.858315\pi\) | ||||
0.902561 | − | 0.430562i | \(-0.141685\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −125.883 | −0.557006 | ||||||||
\(227\) | 7.21336 | 0.0317769 | 0.0158885 | − | 0.999874i | \(-0.494942\pi\) | ||||
0.0158885 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 336.703 | 1.47032 | 0.735159 | − | 0.677894i | \(-0.237107\pi\) | ||||
0.735159 | + | 0.677894i | \(0.237107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 31.5314i | − 0.135911i | ||||||||
\(233\) | −255.652 | −1.09722 | −0.548609 | − | 0.836079i | \(-0.684842\pi\) | ||||
−0.548609 | + | 0.836079i | \(0.684842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.3705i | 0.137163i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 1.25607i | − 0.00527761i | ||||||||
\(239\) | 59.2293i | 0.247822i | 0.992293 | + | 0.123911i | \(0.0395437\pi\) | ||||
−0.992293 | + | 0.123911i | \(0.960456\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 67.0919 | 0.278390 | 0.139195 | − | 0.990265i | \(-0.455549\pi\) | ||||
0.139195 | + | 0.990265i | \(0.455549\pi\) | |||||||
\(242\) | 150.823 | 0.623236 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −204.378 | −0.837615 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 446.926i | − 1.80942i | ||||||||
\(248\) | 1.70678 | 0.00688217 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 303.866i | 1.21062i | 0.795990 | + | 0.605310i | \(0.206951\pi\) | ||||
−0.795990 | + | 0.605310i | \(0.793049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 70.1822i | 0.277400i | ||||||||
\(254\) | − 331.110i | − 1.30358i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −44.2141 | −0.172039 | −0.0860197 | − | 0.996293i | \(-0.527415\pi\) | ||||
−0.0860197 | + | 0.996293i | \(0.527415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 111.075 | 0.428863 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.1139i | 0.0920377i | ||||||||
\(263\) | −296.519 | −1.12745 | −0.563724 | − | 0.825963i | \(-0.690632\pi\) | ||||
−0.563724 | + | 0.825963i | \(0.690632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 111.859i | − 0.420521i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 35.7973i | − 0.133572i | ||||||||
\(269\) | − 6.16168i | − 0.0229059i | −0.999934 | − | 0.0114529i | \(-0.996354\pi\) | ||||
0.999934 | − | 0.0114529i | \(-0.00364566\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 71.3691 | 0.263355 | 0.131677 | − | 0.991293i | \(-0.457964\pi\) | ||||
0.131677 | + | 0.991293i | \(0.457964\pi\) | |||||||
\(272\) | 1.34280 | 0.00493676 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −251.590 | −0.918213 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 36.9936i | 0.133551i | 0.997768 | + | 0.0667754i | \(0.0212711\pi\) | ||||
−0.997768 | + | 0.0667754i | \(0.978729\pi\) | |||||||
\(278\) | 271.889 | 0.978018 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 74.7131i | − 0.265883i | −0.991124 | − | 0.132942i | \(-0.957558\pi\) | ||||
0.991124 | − | 0.132942i | \(-0.0424423\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 37.7485i | 0.133387i | 0.997774 | + | 0.0666934i | \(0.0212449\pi\) | ||||
−0.997774 | + | 0.0666934i | \(0.978755\pi\) | |||||||
\(284\) | − 152.859i | − 0.538237i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −80.0941 | −0.280049 | ||||||||
\(287\) | −94.5421 | −0.329415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.887 | −0.999610 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 126.599i | − 0.433559i | ||||||||
\(293\) | −343.619 | −1.17276 | −0.586381 | − | 0.810035i | \(-0.699448\pi\) | ||||
−0.586381 | + | 0.810035i | \(0.699448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 118.745i | 0.401164i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 327.667i | − 1.09955i | ||||||||
\(299\) | 276.949i | 0.926252i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −64.1833 | −0.213233 | ||||||||
\(302\) | −337.258 | −1.11675 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 119.582 | 0.393362 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 55.4240i | − 0.180534i | −0.995918 | − | 0.0902671i | \(-0.971228\pi\) | ||||
0.995918 | − | 0.0902671i | \(-0.0287721\pi\) | |||||||
\(308\) | −20.0463 | −0.0650855 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 452.240i | − 1.45415i | −0.686560 | − | 0.727074i | \(-0.740880\pi\) | ||||
0.686560 | − | 0.727074i | \(-0.259120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 232.943i | − 0.744228i | −0.928187 | − | 0.372114i | \(-0.878633\pi\) | ||||
0.928187 | − | 0.372114i | \(-0.121367\pi\) | |||||||
\(314\) | − 320.328i | − 1.02015i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 121.385 | 0.384130 | ||||||||
\(317\) | −389.212 | −1.22780 | −0.613899 | − | 0.789384i | \(-0.710400\pi\) | ||||
−0.613899 | + | 0.789384i | \(0.710400\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.2333 | −0.132393 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 69.3162i | 0.215268i | ||||||||
\(323\) | 10.0359 | 0.0310709 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 55.0665i | 0.168916i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 101.070i | − 0.308140i | ||||||||
\(329\) | 133.277i | 0.405096i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −201.361 | −0.608341 | −0.304170 | − | 0.952618i | \(-0.598379\pi\) | ||||
−0.304170 | + | 0.952618i | \(0.598379\pi\) | |||||||
\(332\) | −258.961 | −0.780003 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 275.825 | 0.825823 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 576.780i | − 1.71151i | −0.517379 | − | 0.855756i | \(-0.673092\pi\) | ||||
0.517379 | − | 0.855756i | \(-0.326908\pi\) | |||||||
\(338\) | −77.0615 | −0.227993 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.28606i | − 0.00670399i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − 68.6148i | − 0.199462i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 139.706 | 0.403773 | ||||||||
\(347\) | −395.628 | −1.14014 | −0.570069 | − | 0.821597i | \(-0.693083\pi\) | ||||
−0.570069 | + | 0.821597i | \(0.693083\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 378.937 | 1.08578 | 0.542890 | − | 0.839804i | \(-0.317330\pi\) | ||||
0.542890 | + | 0.839804i | \(0.317330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 21.4304i | − 0.0608819i | ||||||||
\(353\) | 610.300 | 1.72889 | 0.864447 | − | 0.502724i | \(-0.167669\pi\) | ||||
0.864447 | + | 0.502724i | \(0.167669\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 30.0624i | − 0.0844451i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 233.336i | − 0.651776i | ||||||||
\(359\) | − 493.501i | − 1.37466i | −0.726347 | − | 0.687328i | \(-0.758784\pi\) | ||||
0.726347 | − | 0.687328i | \(-0.241216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 532.740 | 1.47573 | ||||||||
\(362\) | 159.178 | 0.439717 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −79.1059 | −0.217324 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 384.894i | 1.04876i | 0.851485 | + | 0.524379i | \(0.175703\pi\) | ||||
−0.851485 | + | 0.524379i | \(0.824297\pi\) | |||||||
\(368\) | −74.1021 | −0.201365 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 119.009i | − 0.320778i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 659.925i | 1.76924i | 0.466316 | + | 0.884618i | \(0.345581\pi\) | ||||
−0.466316 | + | 0.884618i | \(0.654419\pi\) | |||||||
\(374\) | − 1.79855i | − 0.00480895i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −142.479 | −0.378933 | ||||||||
\(377\) | −166.659 | −0.442066 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 157.587 | 0.415796 | 0.207898 | − | 0.978150i | \(-0.433338\pi\) | ||||
0.207898 | + | 0.978150i | \(0.433338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 369.561i | 0.967436i | ||||||||
\(383\) | −6.80377 | −0.0177644 | −0.00888220 | − | 0.999961i | \(-0.502827\pi\) | ||||
−0.00888220 | + | 0.999961i | \(0.502827\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 379.536i | 0.983253i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 118.960i | − 0.306599i | ||||||||
\(389\) | 769.376i | 1.97783i | 0.148484 | + | 0.988915i | \(0.452561\pi\) | ||||
−0.148484 | + | 0.988915i | \(0.547439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.21901 | −0.0159054 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 73.4511 | 0.186424 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 533.930i | − 1.34491i | −0.740137 | − | 0.672456i | \(-0.765240\pi\) | ||||
0.740137 | − | 0.672456i | \(-0.234760\pi\) | |||||||
\(398\) | 434.509 | 1.09173 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 622.370i | 1.55204i | 0.630705 | + | 0.776022i | \(0.282766\pi\) | ||||
−0.630705 | + | 0.776022i | \(0.717234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.02115i | − 0.0223850i | ||||||||
\(404\) | − 69.9281i | − 0.173089i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −41.7122 | −0.102739 | ||||||||
\(407\) | 159.047 | 0.390778 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 754.068 | 1.84369 | 0.921843 | − | 0.387564i | \(-0.126683\pi\) | ||||
0.921843 | + | 0.387564i | \(0.126683\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 33.0581i | − 0.0802381i | ||||||||
\(413\) | 42.8221 | 0.103685 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 84.5677i | − 0.203288i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 160.168i | − 0.383178i | ||||||||
\(419\) | 312.486i | 0.745789i | 0.927874 | + | 0.372895i | \(0.121635\pi\) | ||||
−0.927874 | + | 0.372895i | \(0.878365\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −159.259 | −0.378287 | −0.189144 | − | 0.981949i | \(-0.560571\pi\) | ||||
−0.189144 | + | 0.981949i | \(0.560571\pi\) | |||||||
\(422\) | −158.529 | −0.375661 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 127.226 | 0.300060 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 270.367i | 0.633178i | ||||||||
\(428\) | 235.149 | 0.549413 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 610.194i | − 1.41576i | −0.706331 | − | 0.707882i | \(-0.749651\pi\) | ||||
0.706331 | − | 0.707882i | \(-0.250349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 179.507i | 0.414565i | 0.978281 | + | 0.207283i | \(0.0664620\pi\) | ||||
−0.978281 | + | 0.207283i | \(0.933538\pi\) | |||||||
\(434\) | − 2.25786i | − 0.00520243i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.47509 | −0.0102640 | ||||||||
\(437\) | −553.830 | −1.26734 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 385.194 | 0.877434 | 0.438717 | − | 0.898625i | \(-0.355433\pi\) | ||||
0.438717 | + | 0.898625i | \(0.355433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 7.09733i | − 0.0160573i | ||||||||
\(443\) | −98.2782 | −0.221847 | −0.110923 | − | 0.993829i | \(-0.535381\pi\) | ||||
−0.110923 | + | 0.993829i | \(0.535381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 271.572i | − 0.608907i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 21.1660i | − 0.0472456i | ||||||||
\(449\) | 345.416i | 0.769302i | 0.923062 | + | 0.384651i | \(0.125678\pi\) | ||||
−0.923062 | + | 0.384651i | \(0.874322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −135.373 | −0.300162 | ||||||||
\(452\) | −178.026 | −0.393863 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.2012 | 0.0224697 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 520.425i | − 1.13879i | −0.822066 | − | 0.569393i | \(-0.807178\pi\) | ||||
0.822066 | − | 0.569393i | \(-0.192822\pi\) | |||||||
\(458\) | 476.170 | 1.03967 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 131.936i | − 0.286196i | −0.989709 | − | 0.143098i | \(-0.954294\pi\) | ||||
0.989709 | − | 0.143098i | \(-0.0457064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 240.485i | − 0.519406i | −0.965688 | − | 0.259703i | \(-0.916375\pi\) | ||||
0.965688 | − | 0.259703i | \(-0.0836247\pi\) | |||||||
\(464\) | − 44.5922i | − 0.0961038i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −361.546 | −0.775850 | ||||||||
\(467\) | −524.985 | −1.12416 | −0.562082 | − | 0.827081i | \(-0.690000\pi\) | ||||
−0.562082 | + | 0.827081i | \(0.690000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −47.3554 | −0.100971 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 45.7787i | 0.0969888i | ||||||||
\(473\) | −91.9028 | −0.194298 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 1.77635i | − 0.00373184i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 83.7629i | 0.175236i | ||||||||
\(479\) | − 259.839i | − 0.542461i | −0.962514 | − | 0.271230i | \(-0.912569\pi\) | ||||
0.962514 | − | 0.271230i | \(-0.0874305\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 627.623 | 1.30483 | ||||||||
\(482\) | 94.8823 | 0.196851 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 213.296 | 0.440694 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 16.7084i | − 0.0343089i | −0.999853 | − | 0.0171544i | \(-0.994539\pi\) | ||||
0.999853 | − | 0.0171544i | \(-0.00546070\pi\) | |||||||
\(488\) | −289.034 | −0.592284 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 750.622i | 1.52876i | 0.644765 | + | 0.764381i | \(0.276955\pi\) | ||||
−0.644765 | + | 0.764381i | \(0.723045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3.74239i | − 0.00759106i | ||||||||
\(494\) | − 632.048i | − 1.27945i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.41375 | 0.00486643 | ||||||||
\(497\) | −202.214 | −0.406869 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 263.681 | 0.528419 | 0.264210 | − | 0.964465i | \(-0.414889\pi\) | ||||
0.264210 | + | 0.964465i | \(0.414889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 429.731i | 0.856038i | ||||||||
\(503\) | −383.069 | −0.761569 | −0.380784 | − | 0.924664i | \(-0.624346\pi\) | ||||
−0.380784 | + | 0.924664i | \(0.624346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 99.2526i | 0.196151i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 468.260i | − 0.921772i | ||||||||
\(509\) | 850.177i | 1.67029i | 0.550031 | + | 0.835144i | \(0.314616\pi\) | ||||
−0.550031 | + | 0.835144i | \(0.685384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −167.475 | −0.327740 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −62.5282 | −0.121650 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 190.836i | 0.369122i | ||||||||
\(518\) | 157.084 | 0.303252 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 435.203i | 0.835323i | 0.908603 | + | 0.417661i | \(0.137150\pi\) | ||||
−0.908603 | + | 0.417661i | \(0.862850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 350.756i | − 0.670662i | −0.942100 | − | 0.335331i | \(-0.891152\pi\) | ||||
0.942100 | − | 0.335331i | \(-0.108848\pi\) | |||||||
\(524\) | 34.1022i | 0.0650805i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −419.341 | −0.797226 | ||||||||
\(527\) | 0.202573 | 0.000384390 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −185.805 | −0.351237 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 158.192i | − 0.297353i | ||||||||
\(533\) | −534.203 | −1.00226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 50.6251i | − 0.0944498i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 8.71393i | − 0.0161969i | ||||||||
\(539\) | 26.5188i | 0.0492000i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 814.349 | 1.50527 | 0.752633 | − | 0.658440i | \(-0.228783\pi\) | ||||
0.752633 | + | 0.658440i | \(0.228783\pi\) | |||||||
\(542\) | 100.931 | 0.186220 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.89900 | 0.00349081 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 187.880i | 0.343474i | 0.985143 | + | 0.171737i | \(0.0549379\pi\) | ||||
−0.985143 | + | 0.171737i | \(0.945062\pi\) | |||||||
\(548\) | −355.802 | −0.649274 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 333.276i | − 0.604857i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 160.577i | − 0.290375i | ||||||||
\(554\) | 52.3168i | 0.0944346i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 384.509 | 0.691563 | ||||||||
\(557\) | −490.508 | −0.880624 | −0.440312 | − | 0.897845i | \(-0.645132\pi\) | ||||
−0.440312 | + | 0.897845i | \(0.645132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −362.662 | −0.648770 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 105.660i | − 0.188008i | ||||||||
\(563\) | −479.230 | −0.851207 | −0.425604 | − | 0.904910i | \(-0.639938\pi\) | ||||
−0.425604 | + | 0.904910i | \(0.639938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 53.3844i | 0.0943187i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 216.176i | − 0.380591i | ||||||||
\(569\) | 681.193i | 1.19718i | 0.801057 | + | 0.598588i | \(0.204271\pi\) | ||||
−0.801057 | + | 0.598588i | \(0.795729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 727.119 | 1.27341 | 0.636707 | − | 0.771106i | \(-0.280296\pi\) | ||||
0.636707 | + | 0.771106i | \(0.280296\pi\) | |||||||
\(572\) | −113.270 | −0.198025 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −133.703 | −0.232932 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 653.309i | 1.13225i | 0.824319 | + | 0.566125i | \(0.191558\pi\) | ||||
−0.824319 | + | 0.566125i | \(0.808442\pi\) | |||||||
\(578\) | −408.548 | −0.706831 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 342.573i | 0.589627i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 170.406i | − 0.292292i | ||||||||
\(584\) | − 179.038i | − 0.306572i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −485.951 | −0.829268 | ||||||||
\(587\) | 615.483 | 1.04852 | 0.524262 | − | 0.851557i | \(-0.324341\pi\) | ||||
0.524262 | + | 0.851557i | \(0.324341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0400 | 0.0306283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 167.930i | 0.283666i | ||||||||
\(593\) | 692.270 | 1.16740 | 0.583701 | − | 0.811968i | \(-0.301604\pi\) | ||||
0.583701 | + | 0.811968i | \(0.301604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 463.392i | − 0.777503i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 391.666i | 0.654959i | ||||||||
\(599\) | − 449.015i | − 0.749608i | −0.927104 | − | 0.374804i | \(-0.877710\pi\) | ||||
0.927104 | − | 0.374804i | \(-0.122290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 402.229 | 0.669266 | 0.334633 | − | 0.942348i | \(-0.391388\pi\) | ||||
0.334633 | + | 0.942348i | \(0.391388\pi\) | |||||||
\(602\) | −90.7688 | −0.150779 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −476.955 | −0.789661 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 473.443i | − 0.779971i | −0.920821 | − | 0.389986i | \(-0.872480\pi\) | ||||
0.920821 | − | 0.389986i | \(-0.127520\pi\) | |||||||
\(608\) | 169.114 | 0.278149 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 753.069i | 1.23252i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 830.537i | − 1.35487i | −0.735581 | − | 0.677437i | \(-0.763091\pi\) | ||||
0.735581 | − | 0.677437i | \(-0.236909\pi\) | |||||||
\(614\) | − 78.3813i | − 0.127657i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.3498 | −0.0460224 | ||||||||
\(617\) | 193.710 | 0.313954 | 0.156977 | − | 0.987602i | \(-0.449825\pi\) | ||||
0.156977 | + | 0.987602i | \(0.449825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 558.554 | 0.902349 | 0.451174 | − | 0.892436i | \(-0.351005\pi\) | ||||
0.451174 | + | 0.892436i | \(0.351005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 639.564i | − 1.02824i | ||||||||
\(623\) | −39.7689 | −0.0638345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 329.431i | − 0.526248i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 453.012i | − 0.721356i | ||||||||
\(629\) | 14.0935i | 0.0224062i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −653.265 | −1.03529 | −0.517643 | − | 0.855597i | \(-0.673190\pi\) | ||||
−0.517643 | + | 0.855597i | \(0.673190\pi\) | |||||||
\(632\) | 171.664 | 0.271621 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −550.429 | −0.868185 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 104.647i | 0.164281i | ||||||||
\(638\) | −59.7268 | −0.0936158 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 148.157i | 0.231134i | 0.993300 | + | 0.115567i | \(0.0368685\pi\) | ||||
−0.993300 | + | 0.115567i | \(0.963132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 449.684i | 0.699353i | 0.936870 | + | 0.349677i | \(0.113709\pi\) | ||||
−0.936870 | + | 0.349677i | \(0.886291\pi\) | |||||||
\(644\) | 98.0279i | 0.152217i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.1929 | 0.0219704 | ||||||||
\(647\) | −272.475 | −0.421137 | −0.210568 | − | 0.977579i | \(-0.567531\pi\) | ||||
−0.210568 | + | 0.977579i | \(0.567531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.3161 | 0.0944779 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 77.8758i | 0.119441i | ||||||||
\(653\) | −594.454 | −0.910343 | −0.455172 | − | 0.890404i | \(-0.650422\pi\) | ||||
−0.455172 | + | 0.890404i | \(0.650422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 142.934i | − 0.217888i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 188.482i | 0.286446i | ||||||||
\(659\) | 423.092i | 0.642022i | 0.947076 | + | 0.321011i | \(0.104023\pi\) | ||||
−0.947076 | + | 0.321011i | \(0.895977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −252.437 | −0.381901 | −0.190951 | − | 0.981600i | \(-0.561157\pi\) | ||||
−0.190951 | + | 0.981600i | \(0.561157\pi\) | |||||||
\(662\) | −284.767 | −0.430162 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −366.226 | −0.551545 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 206.523i | 0.309630i | ||||||||
\(668\) | 390.075 | 0.583945 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 387.133i | 0.576950i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 216.267i | − 0.321348i | −0.987008 | − | 0.160674i | \(-0.948633\pi\) | ||||
0.987008 | − | 0.160674i | \(-0.0513667\pi\) | |||||||
\(674\) | − 815.690i | − 1.21022i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −108.981 | −0.161215 | ||||||||
\(677\) | 828.658 | 1.22402 | 0.612008 | − | 0.790852i | \(-0.290362\pi\) | ||||
0.612008 | + | 0.790852i | \(0.290362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −157.370 | −0.231767 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 3.23298i | − 0.00474044i | ||||||||
\(683\) | 534.258 | 0.782223 | 0.391111 | − | 0.920343i | \(-0.372091\pi\) | ||||
0.391111 | + | 0.920343i | \(0.372091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 97.0360i | − 0.141041i | ||||||||
\(689\) | − 672.449i | − 0.975978i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −506.311 | −0.732723 | −0.366361 | − | 0.930473i | \(-0.619397\pi\) | ||||
−0.366361 | + | 0.930473i | \(0.619397\pi\) | |||||||
\(692\) | 197.574 | 0.285511 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −559.502 | −0.806199 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 11.9957i | − 0.0172105i | ||||||||
\(698\) | 535.898 | 0.767762 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 588.963i | 0.840176i | 0.907483 | + | 0.420088i | \(0.138001\pi\) | ||||
−0.907483 | + | 0.420088i | \(0.861999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1255.09i | 1.78533i | ||||||||
\(704\) | − 30.3072i | − 0.0430500i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 863.094 | 1.22251 | ||||||||
\(707\) | −92.5062 | −0.130843 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2232 | −0.0257027 | −0.0128513 | − | 0.999917i | \(-0.504091\pi\) | ||||
−0.0128513 | + | 0.999917i | \(0.504091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 42.5147i | − 0.0597117i | ||||||||
\(713\) | −11.1790 | −0.0156788 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 329.987i | − 0.460875i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 697.916i | − 0.972028i | ||||||||
\(719\) | 813.874i | 1.13195i | 0.824422 | + | 0.565976i | \(0.191501\pi\) | ||||
−0.824422 | + | 0.565976i | \(0.808499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.7318 | −0.0606543 | ||||||||
\(722\) | 753.408 | 1.04350 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 225.111 | 0.310927 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1003.37i | 1.38016i | 0.723734 | + | 0.690079i | \(0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(728\) | −111.873 | −0.153671 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 8.14373i | − 0.0111405i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1223.13i | 1.66867i | 0.551259 | + | 0.834334i | \(0.314148\pi\) | ||||
−0.551259 | + | 0.834334i | \(0.685852\pi\) | |||||||
\(734\) | 544.323i | 0.741584i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −104.796 | −0.142386 | ||||||||
\(737\) | −67.8073 | −0.0920045 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −639.556 | −0.865435 | −0.432717 | − | 0.901530i | \(-0.642445\pi\) | ||||
−0.432717 | + | 0.901530i | \(0.642445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 168.304i | − 0.226824i | ||||||||
\(743\) | −1325.46 | −1.78393 | −0.891964 | − | 0.452106i | \(-0.850673\pi\) | ||||
−0.891964 | + | 0.452106i | \(0.850673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 933.275i | 1.25104i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 2.54353i | − 0.00340044i | ||||||||
\(749\) | − 311.073i | − 0.415317i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1055.16 | 1.40501 | 0.702503 | − | 0.711681i | \(-0.252066\pi\) | ||||
0.702503 | + | 0.711681i | \(0.252066\pi\) | |||||||
\(752\) | −201.495 | −0.267946 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −235.691 | −0.312588 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 908.785i | 1.20051i | 0.799809 | + | 0.600254i | \(0.204934\pi\) | ||||
−0.799809 | + | 0.600254i | \(0.795066\pi\) | |||||||
\(758\) | 222.861 | 0.294012 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 218.340i | 0.286912i | 0.989657 | + | 0.143456i | \(0.0458216\pi\) | ||||
−0.989657 | + | 0.143456i | \(0.954178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.91999i | 0.00775884i | ||||||||
\(764\) | 522.638i | 0.684081i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.62198 | −0.0125613 | ||||||||
\(767\) | 241.963 | 0.315466 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −297.681 | −0.387102 | −0.193551 | − | 0.981090i | \(-0.562000\pi\) | ||||
−0.193551 | + | 0.981090i | \(0.562000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 536.744i | 0.695265i | ||||||||
\(773\) | 272.647 | 0.352713 | 0.176356 | − | 0.984326i | \(-0.443569\pi\) | ||||
0.176356 | + | 0.984326i | \(0.443569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 168.235i | − 0.216798i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1088.06i | 1.39854i | ||||||||
\(779\) | − 1068.27i | − 1.37134i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −289.546 | −0.370737 | ||||||||
\(782\) | −8.79501 | −0.0112468 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 164.051i | − 0.208451i | −0.994554 | − | 0.104226i | \(-0.966764\pi\) | ||||
0.994554 | − | 0.104226i | \(-0.0332364\pi\) | |||||||
\(788\) | 103.876 | 0.131822 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 235.506i | 0.297732i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1527.69i | 1.92646i | ||||||||
\(794\) | − 755.091i | − 0.950996i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 614.488 | 0.771970 | ||||||||
\(797\) | 416.976 | 0.523182 | 0.261591 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261591 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.9105 | −0.0211645 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 880.164i | 1.09746i | ||||||||
\(803\) | −239.804 | −0.298636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 12.7578i | − 0.0158286i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 98.8933i | − 0.122393i | ||||||||
\(809\) | 1237.84i | 1.53009i | 0.643975 | + | 0.765046i | \(0.277284\pi\) | ||||
−0.643975 | + | 0.765046i | \(0.722716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 87.6470 | 0.108073 | 0.0540363 | − | 0.998539i | \(-0.482791\pi\) | ||||
0.0540363 | + | 0.998539i | \(0.482791\pi\) | |||||||
\(812\) | −58.9899 | −0.0726477 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 224.926 | 0.276322 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 725.234i | − 0.887679i | ||||||||
\(818\) | 1066.41 | 1.30368 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1432.46i | − 1.74477i | −0.488818 | − | 0.872386i | \(-0.662572\pi\) | ||||
0.488818 | − | 0.872386i | \(-0.337428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 699.888i | 0.850410i | 0.905097 | + | 0.425205i | \(0.139798\pi\) | ||||
−0.905097 | + | 0.425205i | \(0.860202\pi\) | |||||||
\(824\) | − 46.7512i | − 0.0567369i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 60.5596 | 0.0733167 | ||||||||
\(827\) | 1538.24 | 1.86003 | 0.930015 | − | 0.367522i | \(-0.119794\pi\) | ||||
0.930015 | + | 0.367522i | \(0.119794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.3166 | −0.0510454 | −0.0255227 | − | 0.999674i | \(-0.508125\pi\) | ||||
−0.0255227 | + | 0.999674i | \(0.508125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 119.597i | − 0.143746i | ||||||||
\(833\) | −2.34990 | −0.00282100 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 226.512i | − 0.270948i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 441.922i | 0.527353i | ||||||||
\(839\) | − 652.708i | − 0.777959i | −0.921246 | − | 0.388980i | \(-0.872828\pi\) | ||||
0.921246 | − | 0.388980i | \(-0.127172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 716.721 | 0.852225 | ||||||||
\(842\) | −225.226 | −0.267490 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −224.194 | −0.265632 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 282.164i | − 0.333134i | ||||||||
\(848\) | 179.924 | 0.212175 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 777.749i | − 0.913924i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 348.369i | − 0.408404i | −0.978929 | − | 0.204202i | \(-0.934540\pi\) | ||||
0.978929 | − | 0.204202i | \(-0.0654600\pi\) | |||||||
\(854\) | 382.357i | 0.447724i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 332.551 | 0.388494 | ||||||||
\(857\) | 444.441 | 0.518601 | 0.259301 | − | 0.965797i | \(-0.416508\pi\) | ||||
0.259301 | + | 0.965797i | \(0.416508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 93.8325 | 0.109235 | 0.0546173 | − | 0.998507i | \(-0.482606\pi\) | ||||
0.0546173 | + | 0.998507i | \(0.482606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 862.945i | − 1.00110i | ||||||||
\(863\) | 1138.10 | 1.31877 | 0.659384 | − | 0.751806i | \(-0.270817\pi\) | ||||
0.659384 | + | 0.751806i | \(0.270817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 253.861i | 0.293142i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 3.19309i | − 0.00367867i | ||||||||
\(869\) | − 229.928i | − 0.264589i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −267.578 | −0.307208 | ||||||||
\(872\) | −6.32874 | −0.00725773 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −783.234 | −0.896148 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 965.193i | 1.10056i | 0.834980 | + | 0.550281i | \(0.185479\pi\) | ||||
−0.834980 | + | 0.550281i | \(0.814521\pi\) | |||||||
\(878\) | 544.746 | 0.620440 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 518.314i | − 0.588324i | −0.955756 | − | 0.294162i | \(-0.904959\pi\) | ||||
0.955756 | − | 0.294162i | \(-0.0950406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1525.69i | − 1.72785i | −0.503621 | − | 0.863925i | \(-0.667999\pi\) | ||||
0.503621 | − | 0.863925i | \(-0.332001\pi\) | |||||||
\(884\) | − 10.0371i | − 0.0113542i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −138.986 | −0.156869 | ||||||||
\(887\) | 1667.27 | 1.87967 | 0.939835 | − | 0.341629i | \(-0.110979\pi\) | ||||
0.939835 | + | 0.341629i | \(0.110979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −619.450 | −0.696794 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 384.061i | − 0.430562i | ||||||||
\(893\) | −1505.95 | −1.68639 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 29.9333i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 488.493i | 0.543978i | ||||||||
\(899\) | − 6.72714i | − 0.00748292i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.1001 | 0.0167593 | ||||||||
\(902\) | −191.446 | −0.212247 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −251.767 | −0.278503 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 214.983i | 0.237026i | 0.992952 | + | 0.118513i | \(0.0378127\pi\) | ||||
−0.992952 | + | 0.118513i | \(0.962187\pi\) | |||||||
\(908\) | 14.4267 | 0.0158885 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 515.038i | 0.565355i | 0.959215 | + | 0.282677i | \(0.0912226\pi\) | ||||
−0.959215 | + | 0.282677i | \(0.908777\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 490.524i | 0.537266i | ||||||||
\(914\) | − 735.992i | − 0.805243i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 673.406 | 0.735159 | ||||||||
\(917\) | 45.1129 | 0.0491962 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 157.043 | 0.170884 | 0.0854421 | − | 0.996343i | \(-0.472770\pi\) | ||||
0.0854421 | + | 0.996343i | \(0.472770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 186.586i | − 0.202371i | ||||||||
\(923\) | −1142.59 | −1.23791 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − 340.097i | − 0.367276i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 63.0629i | − 0.0679557i | ||||||||
\(929\) | 1002.16i | 1.07875i | 0.842065 | + | 0.539376i | \(0.181340\pi\) | ||||
−0.842065 | + | 0.539376i | \(0.818660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −209.268 | −0.224778 | ||||||||
\(932\) | −511.303 | −0.548609 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −742.441 | −0.794905 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 386.668i | 0.412666i | 0.978482 | + | 0.206333i | \(0.0661531\pi\) | ||||
−0.978482 | + | 0.206333i | \(0.933847\pi\) | |||||||
\(938\) | −66.9707 | −0.0713973 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 440.452i | 0.468068i | 0.972228 | + | 0.234034i | \(0.0751927\pi\) | ||||
−0.972228 | + | 0.234034i | \(0.924807\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 661.983i | 0.701997i | ||||||||
\(944\) | 64.7409i | 0.0685815i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −129.970 | −0.137389 | ||||||||
\(947\) | 255.582 | 0.269886 | 0.134943 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134943 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −946.304 | −0.997159 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 2.51214i | − 0.00263881i | ||||||||
\(953\) | 1609.14 | 1.68849 | 0.844247 | − | 0.535954i | \(-0.180048\pi\) | ||||
0.844247 | + | 0.535954i | \(0.180048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 118.459i | 0.123911i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 367.467i | − 0.383578i | ||||||||
\(959\) | 470.682i | 0.490805i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −960.636 | −0.999621 | ||||||||
\(962\) | 887.592 | 0.922653 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 134.184 | 0.139195 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 872.053i | 0.901812i | 0.892571 | + | 0.450906i | \(0.148899\pi\) | ||||
−0.892571 | + | 0.450906i | \(0.851101\pi\) | |||||||
\(968\) | 301.646 | 0.311618 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 829.279i | − 0.854046i | −0.904241 | − | 0.427023i | \(-0.859562\pi\) | ||||
0.904241 | − | 0.427023i | \(-0.140438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 508.658i | − 0.522773i | ||||||||
\(974\) | − 23.6293i | − 0.0242601i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −408.756 | −0.418808 | ||||||||
\(977\) | −115.891 | −0.118620 | −0.0593098 | − | 0.998240i | \(-0.518890\pi\) | ||||
−0.0593098 | + | 0.998240i | \(0.518890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.9443 | −0.0581658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1061.54i | 1.08100i | ||||||||
\(983\) | −854.970 | −0.869756 | −0.434878 | − | 0.900489i | \(-0.643209\pi\) | ||||
−0.434878 | + | 0.900489i | \(0.643209\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 5.29254i | − 0.00536769i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 893.851i | − 0.904708i | ||||||||
\(989\) | 449.411i | 0.454409i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1389.62 | −1.40224 | −0.701119 | − | 0.713045i | \(-0.747316\pi\) | ||||
−0.701119 | + | 0.713045i | \(0.747316\pi\) | |||||||
\(992\) | 3.41356 | 0.00344108 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −285.973 | −0.287700 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1331.86i | 1.33586i | 0.744222 | + | 0.667932i | \(0.232820\pi\) | ||||
−0.744222 | + | 0.667932i | \(0.767180\pi\) | |||||||
\(998\) | 372.902 | 0.373649 | ||||||||
\(999\) | 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 | 3150.3.c.f.449.10 | 16 | ||
3.2 | odd | 2 | inner | 3150.3.c.f.449.3 | 16 | ||
5.2 | odd | 4 | 630.3.e.b.71.8 | yes | 8 | ||
5.3 | odd | 4 | 3150.3.e.f.701.1 | 8 | |||
5.4 | even | 2 | inner | 3150.3.c.f.449.6 | 16 | ||
15.2 | even | 4 | 630.3.e.b.71.2 | ✓ | 8 | ||
15.8 | even | 4 | 3150.3.e.f.701.6 | 8 | |||
15.14 | odd | 2 | inner | 3150.3.c.f.449.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.3.e.b.71.2 | ✓ | 8 | 15.2 | even | 4 | ||
630.3.e.b.71.8 | yes | 8 | 5.2 | odd | 4 | ||
3150.3.c.f.449.3 | 16 | 3.2 | odd | 2 | inner | ||
3150.3.c.f.449.6 | 16 | 5.4 | even | 2 | inner | ||
3150.3.c.f.449.10 | 16 | 1.1 | even | 1 | trivial | ||
3150.3.c.f.449.15 | 16 | 15.14 | odd | 2 | inner | ||
3150.3.e.f.701.1 | 8 | 5.3 | odd | 4 | |||
3150.3.e.f.701.6 | 8 | 15.8 | even | 4 |