Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), 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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.35 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.12 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.77972i | 1.02752i | 0.857933 | + | 0.513762i | \(0.171748\pi\) | ||||
−0.857933 | + | 0.513762i | \(0.828252\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.91545i | − | 0.856614i | −0.903633 | − | 0.428307i | \(-0.859110\pi\) | ||
0.903633 | − | 0.428307i | \(-0.140890\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.45686i | − | 0.928607i | −0.885676 | − | 0.464303i | \(-0.846305\pi\) | ||
0.885676 | − | 0.464303i | \(-0.153695\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.167415 | −0.0558049 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63017i | 0.491515i | 0.969331 | + | 0.245758i | \(0.0790367\pi\) | ||||
−0.969331 | + | 0.245758i | \(0.920963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.53859 | 0.704079 | 0.352040 | − | 0.935985i | \(-0.385488\pi\) | ||||
0.352040 | + | 0.935985i | \(0.385488\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.40896 | 0.880191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23137 | − | 2.56091i | −0.783722 | − | 0.621112i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.17325 | 0.498579 | 0.249289 | − | 0.968429i | \(-0.419803\pi\) | ||||
0.249289 | + | 0.968429i | \(0.419803\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.37253 | 0.954165 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.41510i | 0.503582i | 0.967782 | + | 0.251791i | \(0.0810196\pi\) | ||||
−0.967782 | + | 0.251791i | \(0.918980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.33107 | 0.266213 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.04122i | 0.970183i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.33492i | − | 0.804974i | −0.915426 | − | 0.402487i | \(-0.868146\pi\) | ||
0.915426 | − | 0.402487i | \(-0.131854\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.11391i | − | 0.918485i | −0.888311 | − | 0.459242i | \(-0.848121\pi\) | ||
0.888311 | − | 0.459242i | \(-0.151879\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.90125 | −0.505043 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.70599 | −0.795457 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.50693i | − | 0.740935i | −0.928845 | − | 0.370467i | \(-0.879198\pi\) | ||
0.928845 | − | 0.370467i | \(-0.120802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.51800i | 0.723458i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47471i | 0.698833i | 0.936968 | + | 0.349416i | \(0.113620\pi\) | ||||
−0.936968 | + | 0.349416i | \(0.886380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.13699 | −0.630884 | −0.315442 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.320674i | 0.0478032i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7078 | 1.70775 | 0.853876 | − | 0.520476i | \(-0.174246\pi\) | ||||
0.853876 | + | 0.520476i | \(0.174246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.963830 | 0.137690 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.55771 | − | 5.75094i | 0.638208 | − | 0.805293i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.4131 | −1.97979 | −0.989897 | − | 0.141791i | \(-0.954714\pi\) | ||||
−0.989897 | + | 0.141791i | \(0.954714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.12250 | 0.421038 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.86779i | 0.512301i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.02775i | 0.387664i | 0.981035 | + | 0.193832i | \(0.0620917\pi\) | ||||
−0.981035 | + | 0.193832i | \(0.937908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.411315i | 0.0518208i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.86254i | − | 0.603124i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.34987 | 0.775760 | 0.387880 | − | 0.921710i | \(-0.373208\pi\) | ||||
0.387880 | + | 0.921710i | \(0.373208\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.29820 | −0.517443 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.97310i | − | 0.827555i | −0.910378 | − | 0.413778i | \(-0.864209\pi\) | ||
0.910378 | − | 0.413778i | \(-0.135791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.10446i | − | 1.06560i | −0.846242 | − | 0.532798i | \(-0.821140\pi\) | ||
0.846242 | − | 0.532798i | \(-0.178860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.36893i | 0.273540i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00511 | 0.456424 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.05009i | 0.455670i | 0.973700 | + | 0.227835i | \(0.0731647\pi\) | ||||
−0.973700 | + | 0.227835i | \(0.926835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.47422 | −1.05269 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8812 | −1.63342 | −0.816712 | − | 0.577045i | \(-0.804206\pi\) | ||||
−0.816712 | + | 0.577045i | \(0.804206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.90529 | + | 6.18951i | −0.532053 | + | 0.671347i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.71496 | 0.827130 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.92912 | 0.628485 | 0.314243 | − | 0.949343i | \(-0.398249\pi\) | ||||
0.314243 | + | 0.949343i | \(0.398249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.23698i | − | 0.653813i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.10134 | 0.943765 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.16275i | − | 0.427089i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.7962i | − | 1.19773i | −0.800851 | − | 0.598863i | \(-0.795619\pi\) | ||
0.800851 | − | 0.598863i | \(-0.204381\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.272914i | − | 0.0274289i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.17839 | 0.813780 | 0.406890 | − | 0.913477i | \(-0.366613\pi\) | ||||
0.406890 | + | 0.913477i | \(0.366613\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.16265 | 0.902822 | 0.451411 | − | 0.892316i | \(-0.350921\pi\) | ||||
0.451411 | + | 0.892316i | \(0.350921\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 8.37535i | − | 0.817351i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.0224i | − | 0.968904i | −0.874818 | − | 0.484452i | \(-0.839019\pi\) | ||
0.874818 | − | 0.484452i | \(-0.160981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.4574i | − | 1.00164i | −0.865553 | − | 0.500818i | \(-0.833033\pi\) | ||
0.865553 | − | 0.500818i | \(-0.166967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.02109 | 0.761328 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.100302i | 0.00943565i | 0.999989 | + | 0.00471783i | \(0.00150174\pi\) | ||||
−0.999989 | + | 0.00471783i | \(0.998498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.62599 | 0.431375 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.424998 | −0.0392911 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.29181 | + | 7.93902i | −0.576769 | + | 0.727769i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.34254 | 0.758413 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.96375 | −0.718067 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1268i | − | 1.08466i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.30255 | 0.647997 | 0.323998 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323998 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.36269i | − | 0.648249i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 18.0951i | − | 1.58098i | −0.612475 | − | 0.790490i | \(-0.709826\pi\) | ||
0.612475 | − | 0.790490i | \(-0.290174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.33938i | − | 0.462983i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.65618 | 0.831072 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.0065 | −1.36752 | −0.683762 | − | 0.729705i | \(-0.739657\pi\) | ||||
−0.683762 | + | 0.729705i | \(0.739657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.4708i | − | 1.31222i | −0.754667 | − | 0.656108i | \(-0.772201\pi\) | ||
0.754667 | − | 0.656108i | \(-0.227799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.8366i | 1.75476i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.13834i | 0.346066i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.30330 | −0.689552 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.71535i | 0.141480i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.70814 | 0.795322 | 0.397661 | − | 0.917532i | \(-0.369822\pi\) | ||||
0.397661 | + | 0.917532i | \(0.369822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5573 | −1.18466 | −0.592330 | − | 0.805696i | \(-0.701792\pi\) | ||||
−0.592330 | + | 0.805696i | \(0.701792\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.540978 | + | 0.428734i | 0.0437355 | + | 0.0346611i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.79541 | −0.786787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0953 | 1.44416 | 0.722080 | − | 0.691810i | \(-0.243186\pi\) | ||||
0.722080 | + | 0.691810i | \(0.243186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 25.6514i | − | 2.03428i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.93356 | 0.467630 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.15635i | 0.717180i | 0.933495 | + | 0.358590i | \(0.116742\pi\) | ||||
−0.933495 | + | 0.358590i | \(0.883258\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.55719i | 0.432627i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.3032i | 1.72587i | 0.505314 | + | 0.862935i | \(0.331377\pi\) | ||||
−0.505314 | + | 0.862935i | \(0.668623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.55554 | −0.504272 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.363834 | −0.0278231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.25558i | − | 0.475603i | −0.971314 | − | 0.237802i | \(-0.923573\pi\) | ||
0.971314 | − | 0.237802i | \(-0.0764268\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.27025i | − | 0.247207i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.77972i | 0.133772i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.4193 | 1.82518 | 0.912590 | − | 0.408875i | \(-0.134079\pi\) | ||||
0.912590 | + | 0.408875i | \(0.134079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.2410i | − | 0.984194i | −0.870540 | − | 0.492097i | \(-0.836230\pi\) | ||
0.870540 | − | 0.492097i | \(-0.163770\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.38856 | −0.398334 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.63278 | −0.634695 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.17472 | − | 5.26768i | 0.305286 | − | 0.385211i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.3856 | 0.900918 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.22406 | −0.595072 | −0.297536 | − | 0.954711i | \(-0.596165\pi\) | ||||
−0.297536 | + | 0.954711i | \(0.596165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.01119i | − | 0.288732i | −0.989524 | − | 0.144366i | \(-0.953886\pi\) | ||
0.989524 | − | 0.144366i | \(-0.0461142\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.65398 | 0.619724 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.07376i | − | 0.218996i | −0.993987 | − | 0.109498i | \(-0.965076\pi\) | ||
0.993987 | − | 0.109498i | \(-0.0349244\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.20338i | 0.652411i | 0.945299 | + | 0.326205i | \(0.105770\pi\) | ||||
−0.945299 | + | 0.326205i | \(0.894230\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3010i | 0.797112i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.6503 | −0.747504 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.57107 | 0.598629 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.404322i | − | 0.0281023i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.54278i | 0.245059i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.7010i | − | 1.28743i | −0.765265 | − | 0.643715i | \(-0.777392\pi\) | ||
0.765265 | − | 0.643715i | \(-0.222608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4102 | 0.850333 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.92417i | 0.540424i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5642 | −0.852911 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.2034 | 1.09493 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.20313 | − | 6.50112i | −0.551802 | − | 0.437312i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6784 | 1.18383 | 0.591917 | − | 0.805999i | \(-0.298371\pi\) | ||||
0.591917 | + | 0.805999i | \(0.298371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.222840 | −0.0148560 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.7808i | 1.31290i | 0.754369 | + | 0.656450i | \(0.227943\pi\) | ||||
−0.754369 | + | 0.656450i | \(0.772057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4331 | −1.21809 | −0.609046 | − | 0.793135i | \(-0.708448\pi\) | ||||
−0.609046 | + | 0.793135i | \(0.708448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.12798i | 0.468987i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.8125i | − | 0.904884i | −0.891794 | − | 0.452442i | \(-0.850553\pi\) | ||
0.891794 | − | 0.452442i | \(-0.149447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 22.4256i | − | 1.46288i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.20803 | −0.468212 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.4220 | 1.19162 | 0.595810 | − | 0.803125i | \(-0.296831\pi\) | ||||
0.595810 | + | 0.803125i | \(0.296831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5213i | 1.57955i | 0.613394 | + | 0.789777i | \(0.289804\pi\) | ||||
−0.613394 | + | 0.789777i | \(0.710196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.73783i | − | 0.111482i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.84616i | − | 0.117947i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.51701 | 0.351039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 26.4844i | − | 1.67838i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.5505 | 1.10777 | 0.553887 | − | 0.832592i | \(-0.313144\pi\) | ||||
0.553887 | + | 0.832592i | \(0.313144\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.93702 | −0.247518 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.0156 | − | 8.73005i | −0.689824 | − | 0.546697i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.3471 | −1.76825 | −0.884123 | − | 0.467255i | \(-0.845243\pi\) | ||||
−0.884123 | + | 0.467255i | \(0.845243\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0729 | −0.688037 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.725729i | 0.0449215i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.9897 | 1.72592 | 0.862961 | − | 0.505271i | \(-0.168607\pi\) | ||||
0.862961 | + | 0.505271i | \(0.168607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.6075i | 1.69592i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5522i | 0.645784i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.44275i | − | 0.392821i | −0.980522 | − | 0.196411i | \(-0.937071\pi\) | ||
0.980522 | − | 0.196411i | \(-0.0629285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9996 | 1.70085 | 0.850426 | − | 0.526094i | \(-0.176344\pi\) | ||||
0.850426 | + | 0.526094i | \(0.176344\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.1001 | 0.671808 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.16987i | 0.130848i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.48484i | − | 0.449720i | −0.974391 | − | 0.224860i | \(-0.927807\pi\) | ||
0.974391 | − | 0.224860i | \(-0.0721925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.856143i | 0.0512559i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.510434 | 0.0304499 | 0.0152250 | − | 0.999884i | \(-0.495154\pi\) | ||||
0.0152250 | + | 0.999884i | \(0.495154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 31.2509i | − | 1.85767i | −0.370489 | − | 0.928837i | \(-0.620810\pi\) | ||
0.370489 | − | 0.928837i | \(-0.379190\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.40854 | 0.438844 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.9937 | 0.648940 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.88347 | + | 16.5505i | 0.228439 | + | 0.973558i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.9940 | 1.23069 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.2697 | −0.658383 | −0.329192 | − | 0.944263i | \(-0.606776\pi\) | ||||
−0.329192 | + | 0.944263i | \(0.606776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.91545i | − | 0.111522i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.21805 | −0.476859 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.13095i | 0.354562i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1640i | 0.585843i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.5553i | 0.836178i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.79950 | 0.332078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.78761 | −0.159097 | −0.0795486 | − | 0.996831i | \(-0.525348\pi\) | ||||
−0.0795486 | + | 0.996831i | \(0.525348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.3070i | 0.927671i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.7573i | 1.57397i | 0.616969 | + | 0.786987i | \(0.288360\pi\) | ||||
−0.616969 | + | 0.786987i | \(0.711640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.64200i | 0.318905i | 0.987206 | + | 0.159452i | \(0.0509728\pi\) | ||||
−0.987206 | + | 0.159452i | \(0.949027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.787851 | 0.0443904 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.43933i | 0.305503i | 0.988265 | + | 0.152752i | \(0.0488134\pi\) | ||||
−0.988265 | + | 0.152752i | \(0.951187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.06666 | 0.395657 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.8371 | 0.995572 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.02258 | − | 5.56551i | −0.390747 | − | 0.309673i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.37904 | 0.187435 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.6113 | 1.02920 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 28.7644i | − | 1.58583i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.87894 | 0.433066 | 0.216533 | − | 0.976275i | \(-0.430525\pi\) | ||||
0.216533 | + | 0.976275i | \(0.430525\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.754526i | 0.0413478i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 12.1628i | − | 0.664526i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.0543i | 1.80058i | 0.435288 | + | 0.900291i | \(0.356647\pi\) | ||||
−0.435288 | + | 0.900291i | \(0.643353\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.178510 | −0.00969536 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.33654 | 0.451449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5660i | − | 1.05647i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.23297i | 0.443248i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.4162i | 1.95492i | 0.211110 | + | 0.977462i | \(0.432292\pi\) | ||||
−0.211110 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.1050 | −0.701496 | −0.350748 | − | 0.936470i | \(-0.614073\pi\) | ||||
−0.350748 | + | 0.936470i | \(0.614073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7976i | 0.683086i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.53985 | −0.241632 | −0.120816 | − | 0.992675i | \(-0.538551\pi\) | ||||
−0.120816 | + | 0.992675i | \(0.538551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.3566 | −0.708895 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.1293 | − | 11.1977i | −0.747800 | − | 0.592644i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.2595 | −0.541475 | −0.270738 | − | 0.962653i | \(-0.587268\pi\) | ||||
−0.270738 | + | 0.962653i | \(0.587268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2770 | −0.751419 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.8474i | 0.779287i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.4391 | −0.912804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5045i | 0.809331i | 0.914465 | + | 0.404665i | \(0.132612\pi\) | ||||
−0.914465 | + | 0.404665i | \(0.867388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.749132i | − | 0.0389983i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.4110i | 1.83845i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6689 | 0.604192 | 0.302096 | − | 0.953277i | \(-0.402314\pi\) | ||||
0.302096 | + | 0.953277i | \(0.402314\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.5824 | 1.11451 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.0046i | − | 0.566766i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1980i | 0.575203i | 0.957750 | + | 0.287601i | \(0.0928579\pi\) | ||||
−0.957750 | + | 0.287601i | \(0.907142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.9965i | 0.665832i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.55995 | −0.0797095 | −0.0398548 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398548 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7.67156i | − | 0.390979i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.692592 | 0.0352064 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.5522 | 1.09274 | 0.546369 | − | 0.837545i | \(-0.316010\pi\) | ||||
0.546369 | + | 0.837545i | \(0.316010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.18485 | − | 7.80406i | 0.312781 | − | 0.394668i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.2043 | 1.62449 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.75772 | 0.390333 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.56484i | − | 0.178914i | −0.995991 | − | 0.0894570i | \(-0.971487\pi\) | ||
0.995991 | − | 0.0894570i | \(-0.0285132\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.50263 | 0.475726 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.3067i | 1.86301i | 0.363729 | + | 0.931505i | \(0.381503\pi\) | ||||
−0.363729 | + | 0.931505i | \(0.618497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.9821i | − | 0.646686i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.1474i | 0.901749i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.34707 | 0.364181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3836 | 0.958457 | 0.479228 | − | 0.877690i | \(-0.340917\pi\) | ||||
0.479228 | + | 0.877690i | \(0.340917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 28.4871i | − | 1.40516i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.45686i | − | 0.120894i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.5041i | 1.39921i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.5338 | 1.34833 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.51292i | − | 0.269324i | −0.990892 | − | 0.134662i | \(-0.957005\pi\) | ||
0.990892 | − | 0.134662i | \(-0.0429948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7120 | −0.668282 | −0.334141 | − | 0.942523i | \(-0.608446\pi\) | ||||
−0.334141 | + | 0.942523i | \(0.608446\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.96005 | −0.0953009 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.30116 | − | 3.40874i | −0.208637 | − | 0.165348i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.43877 | 0.359988 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.36511 | −0.355591 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.4744i | − | 0.504533i | −0.967658 | − | 0.252267i | \(-0.918824\pi\) | ||
0.967658 | − | 0.252267i | \(-0.0811760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6141 | −0.846481 | −0.423240 | − | 0.906017i | \(-0.639107\pi\) | ||||
−0.423240 | + | 0.906017i | \(0.639107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 14.7776i | − | 0.708531i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.24862i | 0.251075i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.4576i | 1.02412i | 0.858951 | + | 0.512059i | \(0.171117\pi\) | ||||
−0.858951 | + | 0.512059i | \(0.828883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.161359 | −0.00768377 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.5184 | 1.11739 | 0.558696 | − | 0.829372i | \(-0.311302\pi\) | ||||
0.558696 | + | 0.829372i | \(0.311302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 11.3569i | − | 0.538369i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.2778i | 0.817212i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 37.1905i | − | 1.75513i | −0.479461 | − | 0.877563i | \(-0.659168\pi\) | ||
0.479461 | − | 0.877563i | \(-0.340832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.29455 | −0.343487 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 25.9080i | − | 1.21727i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.9466 | −0.560065 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0684 | 0.658094 | 0.329047 | − | 0.944314i | \(-0.393273\pi\) | ||||
0.329047 | + | 0.944314i | \(0.393273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.9101 | − | 16.2900i | 0.602592 | − | 0.760353i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.6177 | 1.19313 | 0.596567 | − | 0.802564i | \(-0.296531\pi\) | ||||
0.596567 | + | 0.802564i | \(0.296531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8828 | −0.691663 | −0.345832 | − | 0.938297i | \(-0.612403\pi\) | ||||
−0.345832 | + | 0.938297i | \(0.612403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 17.4331i | − | 0.808442i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1674 | −0.748139 | −0.374070 | − | 0.927401i | \(-0.622038\pi\) | ||||
−0.374070 | + | 0.927401i | \(0.622038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 15.6008i | − | 0.720376i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.2046i | 1.48391i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.74399i | − | 0.310089i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.89274 | 0.132728 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41297 | 0.110482 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 31.9120i | − | 1.45809i | −0.684463 | − | 0.729047i | \(-0.739963\pi\) | ||
0.684463 | − | 0.729047i | \(-0.260037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 11.4413i | − | 0.521677i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.5601i | 0.480501i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.5951 | −1.02599 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.32478i | − | 0.377232i | −0.982051 | − | 0.188616i | \(-0.939600\pi\) | ||
0.982051 | − | 0.188616i | \(-0.0604001\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2958 | −0.736920 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.6313 | −1.87880 | −0.939398 | − | 0.342830i | \(-0.888615\pi\) | ||||
−0.939398 | + | 0.342830i | \(0.888615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1013 | + | 14.0077i | −0.499979 | + | 0.630876i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.522753 | −0.0234960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.1320 | −0.768473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 44.1304i | − | 1.97555i | −0.155899 | − | 0.987773i | \(-0.549827\pi\) | ||
0.155899 | − | 0.987773i | \(-0.450173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.6935 | −1.77337 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.3377i | − | 0.550113i | −0.961428 | − | 0.275056i | \(-0.911303\pi\) | ||
0.961428 | − | 0.275056i | \(-0.0886966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 15.6653i | − | 0.697095i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.6670i | − | 0.518151i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.3709 | −1.47914 | −0.739570 | − | 0.673080i | \(-0.764971\pi\) | ||||
−0.739570 | + | 0.673080i | \(0.764971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.3684 | −0.989520 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.9558i | 0.483712i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 17.5506i | − | 0.773370i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.0857i | 0.839386i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1332 | 0.488694 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 34.9617i | − | 1.53170i | −0.643019 | − | 0.765850i | \(-0.722318\pi\) | ||
0.643019 | − | 0.765850i | \(-0.277682\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.28760 | −0.362391 | −0.181196 | − | 0.983447i | \(-0.557997\pi\) | ||||
−0.181196 | + | 0.983447i | \(0.557997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.82013 | 0.254011 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.0963 | + | 16.5249i | −0.570482 | + | 0.719836i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1673 | 0.746405 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.167415 | −0.00726518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3595i | 0.492034i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.1974 | −0.829977 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 43.4595i | 1.87542i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.57121i | 0.0676767i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.1610i | 1.59768i | 0.601547 | + | 0.798838i | \(0.294551\pi\) | ||||
−0.601547 | + | 0.798838i | \(0.705449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.5653 | 1.01128 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.0306 | −0.858015 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 36.8004i | − | 1.57347i | −0.617290 | − | 0.786736i | \(-0.711769\pi\) | ||
0.617290 | − | 0.786736i | \(-0.288231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 0.506890i | − | 0.0216336i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.42088i | − | 0.401343i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.95050 | 0.423138 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 15.3640i | − | 0.652164i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.5920 | 1.67757 | 0.838783 | − | 0.544466i | \(-0.183268\pi\) | ||||
0.838783 | + | 0.544466i | \(0.183268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.5021 | −0.444193 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.37501 | + | 7.42985i | 0.395813 | + | 0.313689i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.7253 | −0.957757 | −0.478879 | − | 0.877881i | \(-0.658957\pi\) | ||||
−0.478879 | + | 0.877881i | \(0.658957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.192124 | 0.00808271 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2768i | 0.977535i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.98876 | −0.251062 | −0.125531 | − | 0.992090i | \(-0.540063\pi\) | ||||
−0.125531 | + | 0.992090i | \(0.540063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.11101i | − | 0.172041i | −0.996293 | − | 0.0860203i | \(-0.972585\pi\) | ||
0.996293 | − | 0.0860203i | \(-0.0274150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 14.6365i | − | 0.611450i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.21465i | 0.134060i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.01381 | −0.333619 | −0.166810 | − | 0.985989i | \(-0.553347\pi\) | ||||
−0.166810 | + | 0.985989i | \(0.553347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.13881 | 0.296679 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.5611i | 1.51681i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 23.4958i | − | 0.973098i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.814060i | 0.0336573i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.3009 | −1.58085 | −0.790423 | − | 0.612562i | \(-0.790139\pi\) | ||||
−0.790423 | + | 0.612562i | \(0.790139\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.1138i | − | 0.457937i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.47044 | 0.225024 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.0545 | −0.700345 | −0.350172 | − | 0.936685i | \(-0.613877\pi\) | ||||
−0.350172 | + | 0.936685i | \(0.613877\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.2068 | + | 12.0516i | 0.623417 | + | 0.494068i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.3795 | −0.670367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.7691 | 1.46149 | 0.730743 | − | 0.682653i | \(-0.239174\pi\) | ||||
0.730743 | + | 0.682653i | \(0.239174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.22983i | 0.172538i | 0.996272 | + | 0.0862692i | \(0.0274945\pi\) | ||||
−0.996272 | + | 0.0862692i | \(0.972505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.06306 | −0.0432912 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 15.9797i | − | 0.649667i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5365i | 0.955316i | 0.878546 | + | 0.477658i | \(0.158514\pi\) | ||||
−0.878546 | + | 0.477658i | \(0.841486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 18.9546i | − | 0.768078i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.7213 | 1.20239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.4083 | −1.51091 | −0.755453 | − | 0.655202i | \(-0.772583\pi\) | ||||
−0.755453 | + | 0.655202i | \(0.772583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.2541i | 0.615106i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.09868i | 0.285782i | 0.989738 | + | 0.142891i | \(0.0456398\pi\) | ||||
−0.989738 | + | 0.142891i | \(0.954360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.14215i | 0.367454i | 0.982977 | + | 0.183727i | \(0.0588162\pi\) | ||||
−0.982977 | + | 0.183727i | \(0.941184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.1750 | −0.488567 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 14.5670i | − | 0.583616i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.5729 | −0.662917 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.30516 | −0.251804 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.5419 | + | 14.5635i | −0.460204 | + | 0.580687i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0906 | −0.759985 | −0.379992 | − | 0.924990i | \(-0.624073\pi\) | ||||
−0.379992 | + | 0.924990i | \(0.624073\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.2826 | 1.32287 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 13.9876i | − | 0.555083i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44677 | 0.0969447 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.16740i | 0.0461816i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.0504i | − | 0.554956i | −0.960732 | − | 0.277478i | \(-0.910501\pi\) | ||
0.960732 | − | 0.277478i | \(-0.0894985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8748i | 1.05984i | 0.848048 | + | 0.529919i | \(0.177778\pi\) | ||||
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.1028 | −0.555299 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.7167 | 1.12897 | 0.564485 | − | 0.825443i | \(-0.309075\pi\) | ||||
0.564485 | + | 0.825443i | \(0.309075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.63017i | 0.0639898i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 22.3607i | − | 0.876386i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 17.4582i | − | 0.683192i | −0.939847 | − | 0.341596i | \(-0.889032\pi\) | ||
0.939847 | − | 0.341596i | \(-0.110968\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.6603 | −1.35429 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.52422i | 0.0594655i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5925 | −0.763214 | −0.381607 | − | 0.924325i | \(-0.624629\pi\) | ||||
−0.381607 | + | 0.924325i | \(0.624629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.43303 | −0.366902 | −0.183451 | − | 0.983029i | \(-0.558727\pi\) | ||||
−0.183451 | + | 0.983029i | \(0.558727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.5702 | − | 14.5993i | 0.449349 | − | 0.566990i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.2273 | −0.396598 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4692 | 0.405371 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.4627i | 1.21642i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.93576 | −0.190543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 44.4240i | − | 1.71242i | −0.516627 | − | 0.856211i | \(-0.672813\pi\) | ||
0.516627 | − | 0.856211i | \(-0.327187\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.71019i | 0.258275i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6181i | 1.25361i | 0.779175 | + | 0.626807i | \(0.215639\pi\) | ||||
−0.779175 | + | 0.626807i | \(0.784361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.9817 | −1.11222 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.2044 | −1.34904 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.6943i | 0.677055i | 0.940956 | + | 0.338528i | \(0.109929\pi\) | ||||
−0.940956 | + | 0.338528i | \(0.890071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.6595i | 1.17144i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 32.8058i | − | 1.25162i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.5891 | −1.39393 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.6096i | 0.784027i | 0.919959 | + | 0.392013i | \(0.128221\pi\) | ||||
−0.919959 | + | 0.392013i | \(0.871779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.670513 | −0.0254707 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.6335 | −1.12406 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4593 | − | 14.4594i | 0.434053 | − | 0.547690i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.5824 | 0.929790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.1164 | −1.81733 | −0.908665 | − | 0.417525i | \(-0.862898\pi\) | ||||
−0.908665 | + | 0.417525i | \(0.862898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.79471i | − | 0.369414i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.9113 | 1.50315 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 20.0932i | − | 0.755681i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.20794i | − | 0.0829209i | −0.999140 | − | 0.0414605i | \(-0.986799\pi\) | ||
0.999140 | − | 0.0414605i | \(-0.0132011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.678043i | − | 0.0254286i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.3506 | 0.462533 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.92677 | 0.296445 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.7861i | 1.22442i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.7086i | 1.44359i | 0.692109 | + | 0.721793i | \(0.256682\pi\) | ||||
−0.692109 | + | 0.721793i | \(0.743318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 22.5114i | − | 0.838367i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43.6411 | −1.62303 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.77006i | − | 0.214295i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.8702 | 1.36744 | 0.683719 | − | 0.729745i | \(-0.260361\pi\) | ||||
0.683719 | + | 0.729745i | \(0.260361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3298 | −0.938141 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.3681 | + | 10.5945i | 0.494438 | + | 0.391850i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.96503 | −0.331131 | −0.165565 | − | 0.986199i | \(-0.552945\pi\) | ||||
−0.165565 | + | 0.986199i | \(0.552945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.28566 | 0.121193 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.3514i | 0.381298i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.4158 | −0.714221 | −0.357111 | − | 0.934062i | \(-0.616238\pi\) | ||||
−0.357111 | + | 0.934062i | \(0.616238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.81875i | 0.360701i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.08704i | − | 0.149939i | −0.997186 | − | 0.0749695i | \(-0.976114\pi\) | ||
0.997186 | − | 0.0749695i | \(-0.0238859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 18.5954i | − | 0.681284i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.49133 | 0.0911530 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.6237 | −0.899731 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38.1845i | − | 1.39337i | −0.717377 | − | 0.696685i | \(-0.754657\pi\) | ||
0.717377 | − | 0.696685i | \(-0.245343\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.2350i | 1.13826i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.8838i | 1.01480i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0495 | −0.728710 | −0.364355 | − | 0.931260i | \(-0.618710\pi\) | ||||
−0.364355 | + | 0.931260i | \(0.618710\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 7.00680i | − | 0.254331i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.504268 | −0.0182797 | −0.00913985 | − | 0.999958i | \(-0.502909\pi\) | ||||
−0.00913985 | + | 0.999958i | \(0.502909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.6924 | −0.930126 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.821217 | − | 1.03621i | 0.0296912 | − | 0.0374644i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.53859 | 0.0916633 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.3548 | −1.31099 | −0.655494 | − | 0.755200i | \(-0.727540\pi\) | ||||
−0.655494 | + | 0.755200i | \(0.727540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 50.4500i | − | 1.81691i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.4730 | −0.916202 | −0.458101 | − | 0.888900i | \(-0.651470\pi\) | ||||
−0.458101 | + | 0.888900i | \(0.651470\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.80695i | − | 0.244513i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 19.7067i | − | 0.706974i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.72468i | 0.348423i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3674 | 0.406756 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.8533 | 0.780972 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 34.6605i | − | 1.23709i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 11.0753i | − | 0.394791i | −0.980324 | − | 0.197396i | \(-0.936752\pi\) | ||
0.980324 | − | 0.197396i | \(-0.0632484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.8140i | 1.77343i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.246429 | 0.00876201 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.68624i | 0.272946i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −49.1338 | −1.74260 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.83717 | −0.348450 | −0.174225 | − | 0.984706i | \(-0.555742\pi\) | ||||
−0.174225 | + | 0.984706i | \(0.555742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.8321 | − | 29.9825i | −1.33840 | − | 1.06071i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.992621 | −0.0350725 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.8418 | 0.523757 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 11.3654i | − | 0.400578i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.4663 | 0.403633 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.0675i | 1.12743i | 0.825968 | + | 0.563717i | \(0.190629\pi\) | ||||
−0.825968 | + | 0.563717i | \(0.809371\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 26.9284i | − | 0.945582i | −0.881175 | − | 0.472791i | \(-0.843246\pi\) | ||
0.881175 | − | 0.472791i | \(-0.156754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 49.8315i | 1.74767i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5385 | 0.614347 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.99072 | −0.314545 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.04416i | 0.0364859i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.1629i | 0.808392i | 0.914672 | + | 0.404196i | \(0.132449\pi\) | ||||
−0.914672 | + | 0.404196i | \(0.867551\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.16307i | 0.319405i | 0.987165 | + | 0.159702i | \(0.0510534\pi\) | ||||
−0.987165 | + | 0.159702i | \(0.948947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.86176 | −0.134449 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.7676i | 1.45240i | 0.687482 | + | 0.726201i | \(0.258716\pi\) | ||||
−0.687482 | + | 0.726201i | \(0.741284\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.4668 | 1.85698 | 0.928490 | − | 0.371357i | \(-0.121108\pi\) | ||||
0.928490 | + | 0.371357i | \(0.121108\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.3209 | 0.462098 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.11449 | − | 2.46828i | −0.107911 | − | 0.0855209i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.7205 | 1.47840 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.7803 | 0.891098 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.11365i | − | 0.142019i | −0.997476 | − | 0.0710094i | \(-0.977378\pi\) | ||
0.997476 | − | 0.0710094i | \(-0.0226220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2085 | 0.352016 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.908431i | 0.0312880i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.5568i | 0.431966i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.4965i | − | 0.704267i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 55.6180 | 1.90880 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.8847 | 0.373122 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.8762i | 1.19414i | 0.802190 | + | 0.597069i | \(0.203668\pi\) | ||||
−0.802190 | + | 0.597069i | \(0.796332\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.696905i | 0.0238337i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.9312i | 0.544199i | 0.962269 | + | 0.272099i | \(0.0877179\pi\) | ||||
−0.962269 | + | 0.272099i | \(0.912282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.2313 | −0.895000 | −0.447500 | − | 0.894284i | \(-0.647686\pi\) | ||||
−0.447500 | + | 0.894284i | \(0.647686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.5658i | 0.666802i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.5634 | −0.904228 | −0.452114 | − | 0.891960i | \(-0.649330\pi\) | ||||
−0.452114 | + | 0.891960i | \(0.649330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.9822 | −0.407408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.4553 | + | 6.91149i | −1.00035 | + | 0.234727i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.60233 | −0.223969 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1197 | 0.546197 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.97486i | 0.0668390i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.7939 | −1.00722 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 17.5313i | − | 0.591990i | −0.955189 | − | 0.295995i | \(-0.904349\pi\) | ||
0.955189 | − | 0.295995i | \(-0.0956512\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 20.0570i | − | 0.676505i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.8560i | − | 1.00587i | −0.864323 | − | 0.502937i | \(-0.832253\pi\) | ||
0.864323 | − | 0.502937i | \(-0.167747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5774 | −0.557873 | −0.278937 | − | 0.960309i | \(-0.589982\pi\) | ||||
−0.278937 | + | 0.960309i | \(0.589982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.40896 | 0.114591 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 5.23541i | − | 0.175788i | −0.996130 | − | 0.0878939i | \(-0.971986\pi\) | ||
0.996130 | − | 0.0878939i | \(-0.0280136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 17.9414i | − | 0.601734i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 15.4446i | − | 0.517413i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.4439 | 0.851449 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 46.7738i | − | 1.56347i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.9114 | −0.364321 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.1684 | −0.739357 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.5741 | + | 36.9107i | 1.55161 | + | 1.22967i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.0891 | −0.601968 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.3624 | −0.843074 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 37.9018i | − | 1.25851i | −0.777199 | − | 0.629255i | \(-0.783360\pi\) | ||
0.777199 | − | 0.629255i | \(-0.216640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.36918 | −0.0454129 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.0157i | 1.49144i | 0.666262 | + | 0.745718i | \(0.267893\pi\) | ||||
−0.666262 | + | 0.745718i | \(0.732107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 24.2589i | − | 0.802853i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.3215i | 0.341218i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.4573 | −1.46811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.8548 | 1.05079 | 0.525397 | − | 0.850857i | \(-0.323917\pi\) | ||||
0.525397 | + | 0.850857i | \(0.323917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 4.96117i | − | 0.163476i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 17.7019i | − | 0.582665i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5.99902i | − | 0.197247i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.53396 | −0.0503819 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.9651i | 1.34402i | 0.740542 | + | 0.672010i | \(0.234569\pi\) | ||||
−0.740542 | + | 0.672010i | \(0.765431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.09465 | 0.0686493 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.4004 | −1.61730 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.0900 | − | 7.99646i | −0.329977 | − | 0.261512i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.1250 | 1.34350 | 0.671748 | − | 0.740780i | \(-0.265544\pi\) | ||||
0.671748 | + | 0.740780i | \(0.265544\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0412 | −0.327682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.9819i | 0.912184i | 0.889933 | + | 0.456092i | \(0.150751\pi\) | ||||
−0.889933 | + | 0.456092i | \(0.849249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.8069 | −0.351920 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 23.7239i | − | 0.771739i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 29.1771i | − | 0.948127i | −0.880491 | − | 0.474064i | \(-0.842787\pi\) | ||
0.880491 | − | 0.474064i | \(-0.157213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 23.1125i | − | 0.750265i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.68050 | −0.313912 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.70062 | −0.217054 | −0.108527 | − | 0.994093i | \(-0.534613\pi\) | ||||
−0.108527 | + | 0.994093i | \(0.534613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.7527i | 0.509747i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.5767i | 0.406547i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.3257i | 1.26989i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.84796 | 0.156386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.67790i | 0.0540696i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.68322 | −0.247332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.3201 | 1.58603 | 0.793013 | − | 0.609204i | \(-0.208511\pi\) | ||||
0.793013 | + | 0.609204i | \(0.208511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.90507 | − | 12.4983i | 0.318197 | − | 0.401502i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.6067 | 1.78451 | 0.892253 | − | 0.451536i | \(-0.149124\pi\) | ||||
0.892253 | + | 0.451536i | \(0.149124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.0096 | −1.21853 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.01375i | 0.192594i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.4637 | 1.55049 | 0.775246 | − | 0.631659i | \(-0.217626\pi\) | ||||
0.775246 | + | 0.631659i | \(0.217626\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.66548i | 0.308910i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.75072i | 0.0558962i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.0690i | 0.799575i | 0.916608 | + | 0.399788i | \(0.130916\pi\) | ||||
−0.916608 | + | 0.399788i | \(0.869084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.88762 | −0.187595 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.1926 | 1.62948 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.99121i | − | 0.317702i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.0435i | 1.04966i | 0.851206 | + | 0.524831i | \(0.175872\pi\) | ||||
−0.851206 | + | 0.524831i | \(0.824128\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.0223i | 0.444986i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.6286 | 0.558864 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 17.7066i | − | 0.560772i | −0.959887 | − | 0.280386i | \(-0.909537\pi\) | ||
0.959887 | − | 0.280386i | \(-0.0904625\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.7204 | 0.718842 |
(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 | 4012.2.b.b.237.35 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.12 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.12 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.35 | yes | 46 | 1.1 | even | 1 | trivial |