Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.18 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.g.3025.7 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.58470i | 0.708700i | 0.935113 | + | 0.354350i | \(0.115298\pi\) | ||||
−0.935113 | + | 0.354350i | \(0.884702\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.790533i | 0.238355i | 0.992873 | + | 0.119177i | \(0.0380257\pi\) | ||||
−0.992873 | + | 0.119177i | \(0.961974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.494366i | 0.137112i | 0.997647 | + | 0.0685562i | \(0.0218392\pi\) | ||||
−0.997647 | + | 0.0685562i | \(0.978161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.46962 | −1.08404 | −0.542021 | − | 0.840365i | \(-0.682340\pi\) | ||||
−0.542021 | + | 0.840365i | \(0.682340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.55705i | − 1.73371i | −0.498564 | − | 0.866853i | \(-0.666139\pi\) | ||||
0.498564 | − | 0.866853i | \(-0.333861\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.839644 | 0.175078 | 0.0875390 | − | 0.996161i | \(-0.472100\pi\) | ||||
0.0875390 | + | 0.996161i | \(0.472100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.48872 | 0.497744 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.76437i | 0.513331i | 0.966500 | + | 0.256665i | \(0.0826238\pi\) | ||||
−0.966500 | + | 0.256665i | \(0.917376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.568664 | 0.102135 | 0.0510675 | − | 0.998695i | \(-0.483738\pi\) | ||||
0.0510675 | + | 0.998695i | \(0.483738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.58470i | − 0.267864i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.343650i | 0.0564957i | 0.999601 | + | 0.0282479i | \(0.00899277\pi\) | ||||
−0.999601 | + | 0.0282479i | \(0.991007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.93014 | 0.926132 | 0.463066 | − | 0.886324i | \(-0.346749\pi\) | ||||
0.463066 | + | 0.886324i | \(0.346749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.16166i | − 0.482149i | −0.970507 | − | 0.241074i | \(-0.922500\pi\) | ||||
0.970507 | − | 0.241074i | \(-0.0774998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.80964 | 0.701558 | 0.350779 | − | 0.936458i | \(-0.385917\pi\) | ||||
0.350779 | + | 0.936458i | \(0.385917\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.36792i | − 0.599980i | −0.953942 | − | 0.299990i | \(-0.903017\pi\) | ||||
0.953942 | − | 0.299990i | \(-0.0969833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.25276 | −0.168922 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50798i | 0.586889i | 0.955976 | + | 0.293445i | \(0.0948016\pi\) | ||||
−0.955976 | + | 0.293445i | \(0.905198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.40103i | 0.691531i | 0.938321 | + | 0.345766i | \(0.112381\pi\) | ||||
−0.938321 | + | 0.345766i | \(0.887619\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.783423 | −0.0971716 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.57396i | 0.925307i | 0.886539 | + | 0.462653i | \(0.153103\pi\) | ||||
−0.886539 | + | 0.462653i | \(0.846897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.52886 | 1.13087 | 0.565434 | − | 0.824794i | \(-0.308709\pi\) | ||||
0.565434 | + | 0.824794i | \(0.308709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1344 | 1.65431 | 0.827155 | − | 0.561975i | \(-0.189958\pi\) | ||||
0.827155 | + | 0.561975i | \(0.189958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.790533i | − 0.0900896i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.71341 | 0.417791 | 0.208896 | − | 0.977938i | \(-0.433013\pi\) | ||||
0.208896 | + | 0.977938i | \(0.433013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.30905i | − 0.802273i | −0.916018 | − | 0.401136i | \(-0.868615\pi\) | ||||
0.916018 | − | 0.401136i | \(-0.131385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 7.08301i | − 0.768260i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.5305 | −1.22223 | −0.611114 | − | 0.791543i | \(-0.709278\pi\) | ||||
−0.611114 | + | 0.791543i | \(0.709278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.494366i | − 0.0518236i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.9757 | 1.22868 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.75839 | 0.178538 | 0.0892689 | − | 0.996008i | \(-0.471547\pi\) | ||||
0.0892689 | + | 0.996008i | \(0.471547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5623i | 1.74752i | 0.486362 | + | 0.873758i | \(0.338324\pi\) | ||||
−0.486362 | + | 0.873758i | \(0.661676\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.30641 | −0.818454 | −0.409227 | − | 0.912432i | \(-0.634202\pi\) | ||||
−0.409227 | + | 0.912432i | \(0.634202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.7750i | 1.81505i | 0.419996 | + | 0.907526i | \(0.362032\pi\) | ||||
−0.419996 | + | 0.907526i | \(0.637968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 0.165074i | − 0.0158113i | −0.999969 | − | 0.00790563i | \(-0.997484\pi\) | ||||
0.999969 | − | 0.00790563i | \(-0.00251646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.8486 | 1.02055 | 0.510275 | − | 0.860012i | \(-0.329544\pi\) | ||||
0.510275 | + | 0.860012i | \(0.329544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.33059i | 0.124078i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.46962 | 0.409729 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3751 | 0.943187 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8674i | 1.06145i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.0320 | −1.86629 | −0.933145 | − | 0.359499i | \(-0.882948\pi\) | ||||
−0.933145 | + | 0.359499i | \(0.882948\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.17978i | − 0.452560i | −0.974062 | − | 0.226280i | \(-0.927344\pi\) | ||||
0.974062 | − | 0.226280i | \(-0.0726564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.55705i | 0.655279i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.19905 | 0.700492 | 0.350246 | − | 0.936658i | \(-0.386098\pi\) | ||||
0.350246 | + | 0.936658i | \(0.386098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.89763i | − 0.330593i | −0.986244 | − | 0.165296i | \(-0.947142\pi\) | ||||
0.986244 | − | 0.165296i | \(-0.0528581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.390813 | −0.0326814 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.38070 | −0.363798 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.71034i | 0.303963i | 0.988383 | + | 0.151981i | \(0.0485654\pi\) | ||||
−0.988383 | + | 0.151981i | \(0.951435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.08172 | 0.332165 | 0.166083 | − | 0.986112i | \(-0.446888\pi\) | ||||
0.166083 | + | 0.986112i | \(0.446888\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.901163i | 0.0723832i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.64250i | − 0.769555i | −0.923009 | − | 0.384778i | \(-0.874278\pi\) | ||||
0.923009 | − | 0.384778i | \(-0.125722\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.839644 | −0.0661732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.79301i | − 0.532069i | −0.963963 | − | 0.266035i | \(-0.914286\pi\) | ||||
0.963963 | − | 0.266035i | \(-0.0857136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.35614 | 0.414471 | 0.207235 | − | 0.978291i | \(-0.433553\pi\) | ||||
0.207235 | + | 0.978291i | \(0.433553\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7556 | 0.981200 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.3862i | 1.16979i | 0.811110 | + | 0.584894i | \(0.198864\pi\) | ||||
−0.811110 | + | 0.584894i | \(0.801136\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.48872 | −0.188129 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5360i | 1.46019i | 0.683347 | + | 0.730094i | \(0.260524\pi\) | ||||
−0.683347 | + | 0.730094i | \(0.739476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.07045i | 0.0795657i | 0.999208 | + | 0.0397828i | \(0.0126666\pi\) | ||||
−0.999208 | + | 0.0397828i | \(0.987333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.544583 | −0.0400386 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.53338i | − 0.258386i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7019 | −1.28086 | −0.640431 | − | 0.768016i | \(-0.721244\pi\) | ||||
−0.640431 | + | 0.768016i | \(0.721244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5405 | −0.758719 | −0.379359 | − | 0.925249i | \(-0.623856\pi\) | ||||
−0.379359 | + | 0.925249i | \(0.623856\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1573i | 1.07991i | 0.841692 | + | 0.539957i | \(0.181560\pi\) | ||||
−0.841692 | + | 0.539957i | \(0.818440\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8834 | −1.40950 | −0.704750 | − | 0.709456i | \(-0.748941\pi\) | ||||
−0.704750 | + | 0.709456i | \(0.748941\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.76437i | − 0.194021i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.39751i | 0.656350i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.97410 | 0.413237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0319i | 1.79211i | 0.443942 | + | 0.896055i | \(0.353580\pi\) | ||||
−0.443942 | + | 0.896055i | \(0.646420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.01029 | 0.341699 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.568664 | −0.0386034 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.20963i | − 0.148635i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.1231 | −1.41451 | −0.707255 | − | 0.706959i | \(-0.750067\pi\) | ||||
−0.707255 | + | 0.706959i | \(0.750067\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.07343i | 0.602224i | 0.953589 | + | 0.301112i | \(0.0973579\pi\) | ||||
−0.953589 | + | 0.301112i | \(0.902642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 15.8950i | − 1.05037i | −0.850987 | − | 0.525187i | \(-0.823995\pi\) | ||||
0.850987 | − | 0.525187i | \(-0.176005\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2633 | 1.65505 | 0.827527 | − | 0.561426i | \(-0.189747\pi\) | ||||
0.827527 | + | 0.561426i | \(0.189747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.62185i | 0.497194i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.13797 | 0.202979 | 0.101489 | − | 0.994837i | \(-0.467639\pi\) | ||||
0.101489 | + | 0.994837i | \(0.467639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.05736 | 0.454604 | 0.227302 | − | 0.973824i | \(-0.427009\pi\) | ||||
0.227302 | + | 0.973824i | \(0.427009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.58470i | 0.101243i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.73595 | 0.237713 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8195i | 0.809158i | 0.914503 | + | 0.404579i | \(0.132582\pi\) | ||||
−0.914503 | + | 0.404579i | \(0.867418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.663767i | 0.0417307i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.1680 | 0.696639 | 0.348319 | − | 0.937376i | \(-0.386752\pi\) | ||||
0.348319 | + | 0.937376i | \(0.386752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.343650i | − 0.0213534i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.1277 | 0.932817 | 0.466408 | − | 0.884570i | \(-0.345548\pi\) | ||||
0.466408 | + | 0.884570i | \(0.345548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92185 | 0.425206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.70567i | 0.286910i | 0.989657 | + | 0.143455i | \(0.0458212\pi\) | ||||
−0.989657 | + | 0.143455i | \(0.954179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6194 | 1.19179 | 0.595897 | − | 0.803061i | \(-0.296797\pi\) | ||||
0.595897 | + | 0.803061i | \(0.296797\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.96742i | 0.118640i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0661i | 0.604811i | 0.953179 | + | 0.302406i | \(0.0977897\pi\) | ||||
−0.953179 | + | 0.302406i | \(0.902210\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6669 | 1.71013 | 0.855063 | − | 0.518525i | \(-0.173519\pi\) | ||||
0.855063 | + | 0.518525i | \(0.173519\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.69308i | − 0.516750i | −0.966045 | − | 0.258375i | \(-0.916813\pi\) | ||||
0.966045 | − | 0.258375i | \(-0.0831870\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.93014 | −0.350045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.97746 | 0.175145 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 23.9254i | − 1.39774i | −0.715250 | − | 0.698868i | \(-0.753687\pi\) | ||||
0.715250 | − | 0.698868i | \(-0.246313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.14381 | −0.415928 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.415091i | 0.0240054i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.16166i | 0.182235i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.55903 | −0.490089 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.88720i | − 0.450146i | −0.974342 | − | 0.225073i | \(-0.927738\pi\) | ||||
0.974342 | − | 0.225073i | \(-0.0722621\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.7041 | 1.96789 | 0.983944 | − | 0.178480i | \(-0.0571179\pi\) | ||||
0.983944 | + | 0.178480i | \(0.0571179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2387 | −0.635249 | −0.317624 | − | 0.948217i | \(-0.602885\pi\) | ||||
−0.317624 | + | 0.948217i | \(0.602885\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 30.2902i | − 1.70127i | −0.525761 | − | 0.850633i | \(-0.676219\pi\) | ||||
0.525761 | − | 0.850633i | \(-0.323781\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.18533 | −0.122355 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.7771i | 1.87941i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23034i | 0.0682469i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.80964 | −0.265164 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 20.2855i | − 1.11499i | −0.830180 | − | 0.557495i | \(-0.811763\pi\) | ||||
0.830180 | − | 0.557495i | \(-0.188237\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0025 | −0.655765 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.73774 | 0.149134 | 0.0745671 | − | 0.997216i | \(-0.476242\pi\) | ||||
0.0745671 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.449548i | 0.0243444i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.91592i | 0.317583i | 0.987312 | + | 0.158792i | \(0.0507598\pi\) | ||||
−0.987312 | + | 0.158792i | \(0.949240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.5968i | 1.42370i | 0.702333 | + | 0.711848i | \(0.252142\pi\) | ||||
−0.702333 | + | 0.711848i | \(0.747858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.8800 | 1.16455 | 0.582277 | − | 0.812990i | \(-0.302162\pi\) | ||||
0.582277 | + | 0.812990i | \(0.302162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1004i | 0.801446i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4834 | −0.975519 | −0.487759 | − | 0.872978i | \(-0.662186\pi\) | ||||
−0.487759 | + | 0.872978i | \(0.662186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −38.1090 | −2.00573 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.3989i | 1.17241i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.8686 | 1.71573 | 0.857863 | − | 0.513878i | \(-0.171792\pi\) | ||||
0.857863 | + | 0.513878i | \(0.171792\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.36792i | 0.226771i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.11202i | − 0.212912i | −0.994317 | − | 0.106456i | \(-0.966050\pi\) | ||||
0.994317 | − | 0.106456i | \(-0.0339504\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.36661 | −0.0703840 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6063i | 0.544811i | 0.962183 | + | 0.272406i | \(0.0878192\pi\) | ||||
−0.962183 | + | 0.272406i | \(0.912181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.193380 | −0.00988125 | −0.00494063 | − | 0.999988i | \(-0.501573\pi\) | ||||
−0.00494063 | + | 0.999988i | \(0.501573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.25276 | 0.0638466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.2102i | 1.53172i | 0.643008 | + | 0.765859i | \(0.277686\pi\) | ||||
−0.643008 | + | 0.765859i | \(0.722314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.75289 | −0.189792 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.88465i | 0.296089i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1773i | 0.962480i | 0.876589 | + | 0.481240i | \(0.159814\pi\) | ||||
−0.876589 | + | 0.481240i | \(0.840186\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.6813 | 1.68196 | 0.840981 | − | 0.541065i | \(-0.181979\pi\) | ||||
0.840981 | + | 0.541065i | \(0.181979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.281128i | 0.0140040i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.271667 | −0.0134660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.0414 | 0.743751 | 0.371876 | − | 0.928283i | \(-0.378715\pi\) | ||||
0.371876 | + | 0.928283i | \(0.378715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.50798i | − 0.221823i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.5827 | 0.568571 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8239i | 0.773048i | 0.922279 | + | 0.386524i | \(0.126324\pi\) | ||||
−0.922279 | + | 0.386524i | \(0.873676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.62118i | 0.127748i | 0.997958 | + | 0.0638742i | \(0.0203457\pi\) | ||||
−0.997958 | + | 0.0638742i | \(0.979654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.1236 | −0.539575 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.40103i | − 0.261374i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.5464 | −1.03785 | −0.518927 | − | 0.854819i | \(-0.673668\pi\) | ||||
−0.518927 | + | 0.854819i | \(0.673668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4258 | 0.597145 | 0.298572 | − | 0.954387i | \(-0.403490\pi\) | ||||
0.298572 | + | 0.954387i | \(0.403490\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.34523i | − 0.303534i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.2735 | 1.15851 | 0.579256 | − | 0.815146i | \(-0.303343\pi\) | ||||
0.579256 | + | 0.815146i | \(0.303343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 0.931584i | − 0.0442609i | −0.999755 | − | 0.0221304i | \(-0.992955\pi\) | ||||
0.999755 | − | 0.0221304i | \(-0.00704492\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 18.2724i | − 0.866193i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8693 | −0.984883 | −0.492441 | − | 0.870346i | \(-0.663895\pi\) | ||||
−0.492441 | + | 0.870346i | \(0.663895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.68797i | 0.220748i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.783423 | 0.0367274 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.3346 | −1.46577 | −0.732885 | − | 0.680353i | \(-0.761827\pi\) | ||||
−0.732885 | + | 0.680353i | \(0.761827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.90910i | 0.0889156i | 0.999011 | + | 0.0444578i | \(0.0141560\pi\) | ||||
−0.999011 | + | 0.0444578i | \(0.985844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6081 | −0.864793 | −0.432397 | − | 0.901683i | \(-0.642332\pi\) | ||||
−0.432397 | + | 0.901683i | \(0.642332\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 17.7972i | − 0.823554i | −0.911285 | − | 0.411777i | \(-0.864908\pi\) | ||||
0.911285 | − | 0.411777i | \(-0.135092\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7.57396i | − 0.349733i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.49940 | 0.114922 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 18.8074i | − 0.862941i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.6737 | 0.990294 | 0.495147 | − | 0.868809i | \(-0.335114\pi\) | ||||
0.495147 | + | 0.868809i | \(0.335114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.169889 | −0.00774627 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.78653i | 0.126530i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.6259 | 1.75030 | 0.875152 | − | 0.483848i | \(-0.160761\pi\) | ||||
0.875152 | + | 0.483848i | \(0.160761\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.9010i | 0.807863i | 0.914789 | + | 0.403931i | \(0.132357\pi\) | ||||
−0.914789 | + | 0.403931i | \(0.867643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 12.3557i | − 0.556472i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.52886 | −0.427428 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.3201i | 1.08872i | 0.838853 | + | 0.544359i | \(0.183227\pi\) | ||||
−0.838853 | + | 0.544359i | \(0.816773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.3076 | −1.61888 | −0.809438 | − | 0.587205i | \(-0.800228\pi\) | ||||
−0.809438 | + | 0.587205i | \(0.800228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.8310 | −1.23846 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 3.12375i | − 0.138458i | −0.997601 | − | 0.0692290i | \(-0.977946\pi\) | ||||
0.997601 | − | 0.0692290i | \(-0.0220539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.1344 | −0.625270 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 13.1632i | − 0.580039i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.80218i | 0.167220i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.68044 | −0.0736213 | −0.0368107 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368107 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 26.5738i | − 1.16199i | −0.813906 | − | 0.580996i | \(-0.802663\pi\) | ||||
0.813906 | − | 0.580996i | \(-0.197337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.54171 | −0.110719 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2950 | −0.969348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.93166i | 0.126984i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.7529 | −1.28633 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.790533i | 0.0340507i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 26.0022i | − 1.11792i | −0.829194 | − | 0.558962i | \(-0.811200\pi\) | ||||
0.829194 | − | 0.558962i | \(-0.188800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.261594 | 0.0112054 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 13.4108i | − 0.573406i | −0.958019 | − | 0.286703i | \(-0.907441\pi\) | ||||
0.958019 | − | 0.286703i | \(-0.0925594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.8905 | 0.889964 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.71341 | −0.157910 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9728i | 1.65133i | 0.564161 | + | 0.825665i | \(0.309200\pi\) | ||||
−0.564161 | + | 0.825665i | \(0.690800\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.56302 | 0.0661086 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 15.8415i | − 0.667642i | −0.942637 | − | 0.333821i | \(-0.891662\pi\) | ||||
0.942637 | − | 0.333821i | \(-0.108338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.1918i | 0.723264i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.4790 | −0.732758 | −0.366379 | − | 0.930466i | \(-0.619403\pi\) | ||||
−0.366379 | + | 0.930466i | \(0.619403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 11.4195i | − 0.477893i | −0.971033 | − | 0.238946i | \(-0.923198\pi\) | ||||
0.971033 | − | 0.238946i | \(-0.0768020\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.08964 | 0.0871439 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.4108 | 1.14113 | 0.570564 | − | 0.821253i | \(-0.306725\pi\) | ||||
0.570564 | + | 0.821253i | \(0.306725\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.30905i | 0.303231i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.45299 | 0.143008 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 23.8334i | − 0.983709i | −0.870677 | − | 0.491855i | \(-0.836319\pi\) | ||||
0.870677 | − | 0.491855i | \(-0.163681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4.29742i | − 0.177072i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.0780 | −1.15302 | −0.576512 | − | 0.817088i | \(-0.695587\pi\) | ||||
−0.576512 | + | 0.817088i | \(0.695587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.08301i | 0.290375i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.6780 | 0.885738 | 0.442869 | − | 0.896586i | \(-0.353961\pi\) | ||||
0.442869 | + | 0.896586i | \(0.353961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.83369 | 0.237961 | 0.118981 | − | 0.992897i | \(-0.462037\pi\) | ||||
0.118981 | + | 0.992897i | \(0.462037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.4414i | 0.668437i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.5358 | 1.19882 | 0.599410 | − | 0.800442i | \(-0.295402\pi\) | ||||
0.599410 | + | 0.800442i | \(0.295402\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.37772i | 0.0961923i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 19.5561i | − 0.789861i | −0.918711 | − | 0.394931i | \(-0.870769\pi\) | ||||
0.918711 | − | 0.394931i | \(-0.129231\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.8435 | 1.36249 | 0.681244 | − | 0.732056i | \(-0.261439\pi\) | ||||
0.681244 | + | 0.732056i | \(0.261439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 20.6581i | − 0.830320i | −0.909748 | − | 0.415160i | \(-0.863726\pi\) | ||||
0.909748 | − | 0.415160i | \(-0.136274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5305 | 0.461959 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.36268 | −0.254507 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.53598i | − 0.0612437i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.3648 | 1.68651 | 0.843257 | − | 0.537510i | \(-0.180635\pi\) | ||||
0.843257 | + | 0.537510i | \(0.180635\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 33.3295i | − 1.32264i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.494366i | 0.0195875i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.6219 | 0.459039 | 0.229519 | − | 0.973304i | \(-0.426285\pi\) | ||||
0.229519 | + | 0.973304i | \(0.426285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.4455i | 1.59502i | 0.603309 | + | 0.797508i | \(0.293849\pi\) | ||||
−0.603309 | + | 0.797508i | \(0.706151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.9913 | 1.17908 | 0.589540 | − | 0.807739i | \(-0.299309\pi\) | ||||
0.589540 | + | 0.807739i | \(0.299309\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.56371 | −0.139888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14.9263i | − 0.584110i | −0.956402 | − | 0.292055i | \(-0.905661\pi\) | ||||
0.956402 | − | 0.292055i | \(-0.0943390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.20842 | 0.320729 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.3581i | 1.06572i | 0.846204 | + | 0.532859i | \(0.178883\pi\) | ||||
−0.846204 | + | 0.532859i | \(0.821117\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 14.3560i | − 0.558385i | −0.960235 | − | 0.279192i | \(-0.909933\pi\) | ||||
0.960235 | − | 0.279192i | \(-0.0900667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.9757 | −0.464397 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.32109i | 0.0898729i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.26970 | −0.164830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.5132 | 0.790727 | 0.395364 | − | 0.918525i | \(-0.370619\pi\) | ||||
0.395364 | + | 0.918525i | \(0.370619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 43.5656i | − 1.67436i | −0.546926 | − | 0.837181i | \(-0.684202\pi\) | ||||
0.546926 | − | 0.837181i | \(-0.315798\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.75839 | −0.0674810 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 16.9585i | − 0.648898i | −0.945903 | − | 0.324449i | \(-0.894821\pi\) | ||||
0.945903 | − | 0.324449i | \(-0.105179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9931i | 0.496439i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.15935 | 0.0822647 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7324i | 1.05499i | 0.849558 | + | 0.527495i | \(0.176869\pi\) | ||||
−0.849558 | + | 0.527495i | \(0.823131\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.17659 | 0.234291 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.5054 | −1.00397 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5427i | 1.11581i | 0.829905 | + | 0.557905i | \(0.188395\pi\) | ||||
−0.829905 | + | 0.557905i | \(0.811605\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.59698 | 0.0979470 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 17.5623i | − 0.660499i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 45.9348i | − 1.72512i | −0.505955 | − | 0.862560i | \(-0.668860\pi\) | ||||
0.505955 | − | 0.862560i | \(-0.331140\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.477476 | 0.0178816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 0.619322i | − 0.0231613i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.3756 | −0.610708 | −0.305354 | − | 0.952239i | \(-0.598775\pi\) | ||||
−0.305354 | + | 0.952239i | \(0.598775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.30641 | 0.309347 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.87974i | 0.255507i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.43696 | −0.127470 | −0.0637348 | − | 0.997967i | \(-0.520301\pi\) | ||||
−0.0637348 | + | 0.997967i | \(0.520301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1314i | 0.522669i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 35.3171i | − 1.30447i | −0.758019 | − | 0.652233i | \(-0.773833\pi\) | ||||
0.758019 | − | 0.652233i | \(-0.226167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.98747 | −0.220551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.3212i | 1.52003i | 0.649908 | + | 0.760013i | \(0.274807\pi\) | ||||
−0.649908 | + | 0.760013i | \(0.725193\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.9110 | 0.840524 | 0.420262 | − | 0.907403i | \(-0.361938\pi\) | ||||
0.420262 | + | 0.907403i | \(0.361938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.87978 | −0.215418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 18.7750i | − 0.686025i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.2764 | 1.76163 | 0.880815 | − | 0.473461i | \(-0.156995\pi\) | ||||
0.880815 | + | 0.473461i | \(0.156995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.46830i | 0.235406i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.9389i | 0.979112i | 0.871972 | + | 0.489556i | \(0.162841\pi\) | ||||
−0.871972 | + | 0.489556i | \(0.837159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.98366 | −0.108158 | −0.0540789 | − | 0.998537i | \(-0.517222\pi\) | ||||
−0.0540789 | + | 0.998537i | \(0.517222\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.165074i | 0.00597609i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.22859 | −0.0804698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.13907 | 0.0410760 | 0.0205380 | − | 0.999789i | \(-0.493462\pi\) | ||||
0.0205380 | + | 0.999789i | \(0.493462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.40051i | 0.302145i | 0.988523 | + | 0.151073i | \(0.0482728\pi\) | ||||
−0.988523 | + | 0.151073i | \(0.951727\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.41525 | 0.0508371 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 44.8143i | − 1.60564i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.53288i | 0.269548i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.2805 | 0.545384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.6837i | − 0.487771i | −0.969804 | − | 0.243886i | \(-0.921578\pi\) | ||||
0.969804 | − | 0.243886i | \(-0.0784222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.8486 | −0.385731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67009 | −0.0948175 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 43.1786i | − 1.52946i | −0.644349 | − | 0.764731i | \(-0.722872\pi\) | ||||
0.644349 | − | 0.764731i | \(-0.277128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.4972 | −0.760518 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.1737i | 0.394312i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.33059i | − 0.0468970i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.5341 | −0.862573 | −0.431287 | − | 0.902215i | \(-0.641940\pi\) | ||||
−0.431287 | + | 0.902215i | \(0.641940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 0.566589i | − 0.0198956i | −0.999951 | − | 0.00994781i | \(-0.996833\pi\) | ||||
0.999951 | − | 0.00994781i | \(-0.00316654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7649 | 0.377078 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.8928 | −0.835904 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.22205i | 0.0426499i | 0.999773 | + | 0.0213250i | \(0.00678846\pi\) | ||||
−0.999773 | + | 0.0213250i | \(0.993212\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.7218 | 1.62862 | 0.814309 | − | 0.580431i | \(-0.197116\pi\) | ||||
0.814309 | + | 0.580431i | \(0.197116\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2221i | 1.22479i | 0.790551 | + | 0.612396i | \(0.209794\pi\) | ||||
−0.790551 | + | 0.612396i | \(0.790206\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.09826i | 0.0381443i | 0.999818 | + | 0.0190721i | \(0.00607122\pi\) | ||||
−0.999818 | + | 0.0190721i | \(0.993929\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.46962 | −0.154863 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.48789i | 0.293735i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.78246 | 0.268680 | 0.134340 | − | 0.990935i | \(-0.457109\pi\) | ||||
0.134340 | + | 0.990935i | \(0.457109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3583 | 0.736492 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.2138i | 0.695377i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3751 | −0.356491 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.288544i | 0.00989116i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 35.3178i | − 1.20926i | −0.796507 | − | 0.604630i | \(-0.793321\pi\) | ||||
0.796507 | − | 0.604630i | \(-0.206679\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.1812 | −1.64584 | −0.822919 | − | 0.568159i | \(-0.807656\pi\) | ||||
−0.822919 | + | 0.568159i | \(0.807656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.2897i | 0.794633i | 0.917682 | + | 0.397317i | \(0.130059\pi\) | ||||
−0.917682 | + | 0.397317i | \(0.869941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.2727 | −0.758173 | −0.379086 | − | 0.925361i | \(-0.623762\pi\) | ||||
−0.379086 | + | 0.925361i | \(0.623762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.3825 | −0.829029 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.93557i | 0.0995825i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.74431 | −0.126871 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11.8674i | − 0.401191i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.5939i | 1.77597i | 0.459872 | + | 0.887985i | \(0.347895\pi\) | ||||
−0.459872 | + | 0.887985i | \(0.652105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.9486 | −0.874229 | −0.437115 | − | 0.899406i | \(-0.644000\pi\) | ||||
−0.437115 | + | 0.899406i | \(0.644000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.37782i | − 0.214631i | −0.994225 | − | 0.107315i | \(-0.965775\pi\) | ||||
0.994225 | − | 0.107315i | \(-0.0342255\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.60567 | −0.255373 | −0.127687 | − | 0.991815i | \(-0.540755\pi\) | ||||
−0.127687 | + | 0.991815i | \(0.540755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.0320 | 0.705392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 36.3467i | − 1.21629i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.9587 | −1.03484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.57200i | 0.0524291i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.5229i | 0.650403i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.69634 | −0.0563882 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 21.2861i | − 0.706794i | −0.935473 | − | 0.353397i | \(-0.885026\pi\) | ||||
0.935473 | − | 0.353397i | \(-0.114974\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0894 | 1.59327 | 0.796637 | − | 0.604458i | \(-0.206610\pi\) | ||||
0.796637 | + | 0.604458i | \(0.206610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.77805 | 0.191226 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.17978i | 0.171052i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.6403 | −1.10969 | −0.554846 | − | 0.831953i | \(-0.687223\pi\) | ||||
−0.554846 | + | 0.831953i | \(0.687223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.71074i | 0.155056i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.855249i | 0.0281204i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.9109 | −1.17820 | −0.589100 | − | 0.808060i | \(-0.700517\pi\) | ||||
−0.589100 | + | 0.808060i | \(0.700517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 7.55705i | − 0.247672i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.59936 | 0.183119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.70862 | 0.219161 | 0.109581 | − | 0.993978i | \(-0.465049\pi\) | ||||
0.109581 | + | 0.993978i | \(0.465049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.81896i | 0.189693i | 0.995492 | + | 0.0948464i | \(0.0302360\pi\) | ||||
−0.995492 | + | 0.0948464i | \(0.969764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.97921 | 0.162145 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.8143i | 0.741365i | 0.928760 | + | 0.370682i | \(0.120876\pi\) | ||||
−0.928760 | + | 0.370682i | \(0.879124\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.98758i | 0.226826i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.659700 | 0.0213698 | 0.0106849 | − | 0.999943i | \(-0.496599\pi\) | ||||
0.0106849 | + | 0.999943i | \(0.496599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 28.0522i | − 0.907747i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.19905 | −0.264761 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6766 | −0.989568 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 16.7035i | − 0.537704i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.46722 | 0.111498 | 0.0557491 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557491 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.84056i | 0.0911580i | 0.998961 | + | 0.0455790i | \(0.0145133\pi\) | ||||
−0.998961 | + | 0.0455790i | \(0.985487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.89763i | 0.124952i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3811 | −0.556071 | −0.278035 | − | 0.960571i | \(-0.589683\pi\) | ||||
−0.278035 | + | 0.960571i | \(0.589683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 9.11522i | − 0.291324i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.8615 | −1.74981 | −0.874905 | − | 0.484294i | \(-0.839076\pi\) | ||||
−0.874905 | + | 0.484294i | \(0.839076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0198 | −0.765336 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.65467i | − 0.0844136i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.9952 | 0.666933 | 0.333467 | − | 0.942762i | \(-0.391782\pi\) | ||||
0.333467 | + | 0.942762i | \(0.391782\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 31.5093i | − 0.998913i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0239i | 1.39425i | 0.716950 | + | 0.697125i | \(0.245538\pi\) | ||||
−0.716950 | + | 0.697125i | \(0.754462\pi\) | |||||||
\(998\) | 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 | 6048.2.c.g.3025.18 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.g.3025.8 | 24 | ||
4.3 | odd | 2 | 1512.2.c.f.757.20 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.f.757.19 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.g.3025.7 | 24 | ||
12.11 | even | 2 | 1512.2.c.f.757.5 | ✓ | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.g.3025.17 | 24 | ||
24.11 | even | 2 | 1512.2.c.f.757.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.5 | ✓ | 24 | 12.11 | even | 2 | ||
1512.2.c.f.757.6 | yes | 24 | 24.11 | even | 2 | ||
1512.2.c.f.757.19 | yes | 24 | 8.3 | odd | 2 | ||
1512.2.c.f.757.20 | yes | 24 | 4.3 | odd | 2 | ||
6048.2.c.g.3025.7 | 24 | 8.5 | even | 2 | inner | ||
6048.2.c.g.3025.8 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.g.3025.17 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.g.3025.18 | 24 | 1.1 | even | 1 | trivial |