Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6020,2,Mod(1,6020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6020 = 2^{2} \cdot 5 \cdot 7 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6020.a (trivial) |
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: | yes |
Analytic conductor: | \(48.0699420168\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - x^{12} - 28 x^{11} + 26 x^{10} + 286 x^{9} - 235 x^{8} - 1298 x^{7} + 895 x^{6} + 2571 x^{5} - 1548 x^{4} - 1833 x^{3} + 1119 x^{2} + 342 x - 216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.700922\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −0.700922 | −0.404677 | −0.202339 | − | 0.979316i | \(-0.564854\pi\) | ||||
−0.202339 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50871 | −0.836236 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.50079 | −1.65855 | −0.829276 | − | 0.558840i | \(-0.811247\pi\) | ||||
−0.829276 | + | 0.558840i | \(0.811247\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.90479 | 1.36034 | 0.680171 | − | 0.733053i | \(-0.261905\pi\) | ||||
0.680171 | + | 0.733053i | \(0.261905\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.700922 | 0.180977 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.01768 | −0.974431 | −0.487215 | − | 0.873282i | \(-0.661987\pi\) | ||||
−0.487215 | + | 0.873282i | \(0.661987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.12968 | 1.63566 | 0.817830 | − | 0.575460i | \(-0.195177\pi\) | ||||
0.817830 | + | 0.575460i | \(0.195177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.700922 | 0.152954 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.84223 | −1.00967 | −0.504837 | − | 0.863215i | \(-0.668447\pi\) | ||||
−0.504837 | + | 0.863215i | \(0.668447\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.86117 | 0.743083 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.850146 | −0.157868 | −0.0789341 | − | 0.996880i | \(-0.525152\pi\) | ||||
−0.0789341 | + | 0.996880i | \(0.525152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.51909 | −1.70968 | −0.854840 | − | 0.518892i | \(-0.826345\pi\) | ||||
−0.854840 | + | 0.518892i | \(0.826345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.85563 | 0.671178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.77907 | −1.44327 | −0.721635 | − | 0.692274i | \(-0.756609\pi\) | ||||
−0.721635 | + | 0.692274i | \(0.756609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.43787 | −0.550500 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.93687 | 1.23953 | 0.619766 | − | 0.784787i | \(-0.287228\pi\) | ||||
0.619766 | + | 0.784787i | \(0.287228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.50871 | 0.373976 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.69012 | 1.26758 | 0.633792 | − | 0.773504i | \(-0.281498\pi\) | ||||
0.633792 | + | 0.773504i | \(0.281498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.81608 | 0.394330 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.3811 | −1.70068 | −0.850341 | − | 0.526233i | \(-0.823604\pi\) | ||||
−0.850341 | + | 0.526233i | \(0.823604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.50079 | 0.741727 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.99735 | −0.661915 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2176 | −1.59060 | −0.795301 | − | 0.606215i | \(-0.792687\pi\) | ||||
−0.795301 | + | 0.606215i | \(0.792687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3673 | −1.58346 | −0.791732 | − | 0.610868i | \(-0.790820\pi\) | ||||
−0.791732 | + | 0.610868i | \(0.790820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50871 | 0.316068 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.90479 | −0.608364 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.41256 | 0.294742 | 0.147371 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147371 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.39402 | 0.408593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.30283 | −1.10404 | −0.552021 | − | 0.833830i | \(-0.686143\pi\) | ||||
−0.552021 | + | 0.833830i | \(0.686143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.44040 | 0.519709 | 0.259855 | − | 0.965648i | \(-0.416325\pi\) | ||||
0.259855 | + | 0.965648i | \(0.416325\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.700922 | −0.0809355 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.50079 | 0.626873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.91718 | −1.11577 | −0.557885 | − | 0.829918i | \(-0.688387\pi\) | ||||
−0.557885 | + | 0.829918i | \(0.688387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.81974 | 0.535527 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9630 | 1.64241 | 0.821203 | − | 0.570636i | \(-0.193303\pi\) | ||||
0.821203 | + | 0.570636i | \(0.193303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.01768 | 0.435779 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.595886 | 0.0638857 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9581 | 1.16155 | 0.580776 | − | 0.814063i | \(-0.302749\pi\) | ||||
0.580776 | + | 0.814063i | \(0.302749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.90479 | −0.514161 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.67214 | 0.691869 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.12968 | −0.731489 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.86462 | 0.798531 | 0.399266 | − | 0.916835i | \(-0.369265\pi\) | ||||
0.399266 | + | 0.916835i | \(0.369265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.7999 | 1.38694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.60449 | 0.756675 | 0.378338 | − | 0.925668i | \(-0.376496\pi\) | ||||
0.378338 | + | 0.925668i | \(0.376496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.00896932 | 0.000883773 0 | 0.000441887 | − | 1.00000i | \(-0.499859\pi\) | ||||
0.000441887 | 1.00000i | \(0.499859\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.700922 | −0.0684030 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.5317 | −1.59818 | −0.799088 | − | 0.601214i | \(-0.794684\pi\) | ||||
−0.799088 | + | 0.601214i | \(0.794684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.5225 | 1.86991 | 0.934957 | − | 0.354762i | \(-0.115438\pi\) | ||||
0.934957 | + | 0.354762i | \(0.115438\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.15344 | 0.584059 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.964913 | −0.0907714 | −0.0453857 | − | 0.998970i | \(-0.514452\pi\) | ||||
−0.0453857 | + | 0.998970i | \(0.514452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.84223 | 0.451540 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.3047 | −1.13757 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.01768 | 0.368300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.2587 | 1.75079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.56313 | −0.501610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.35361 | 0.741263 | 0.370632 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370632 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.700922 | 0.0617127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.3261 | −1.77590 | −0.887948 | − | 0.459943i | \(-0.847870\pi\) | ||||
−0.887948 | + | 0.459943i | \(0.847870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.12968 | −0.618221 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.86117 | −0.332317 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.6583 | −1.08147 | −0.540737 | − | 0.841192i | \(-0.681855\pi\) | ||||
−0.540737 | + | 0.841192i | \(0.681855\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.61985 | 0.391851 | 0.195925 | − | 0.980619i | \(-0.437229\pi\) | ||||
0.195925 | + | 0.980619i | \(0.437229\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.09109 | −0.512963 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.9802 | −2.25620 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.850146 | 0.0706008 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.700922 | −0.0578111 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6885 | 1.03948 | 0.519740 | − | 0.854325i | \(-0.326029\pi\) | ||||
0.519740 | + | 0.854325i | \(0.326029\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.65548 | 0.704373 | 0.352186 | − | 0.935930i | \(-0.385438\pi\) | ||||
0.352186 | + | 0.935930i | \(0.385438\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.0792 | 0.814854 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.51909 | 0.764592 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.39864 | 0.351049 | 0.175525 | − | 0.984475i | \(-0.443838\pi\) | ||||
0.175525 | + | 0.984475i | \(0.443838\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.67822 | 0.688227 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.84223 | 0.381621 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8824 | 0.930698 | 0.465349 | − | 0.885127i | \(-0.345929\pi\) | ||||
0.465349 | + | 0.885127i | \(0.345929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.85563 | −0.300160 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.4849 | 1.89470 | 0.947351 | − | 0.320197i | \(-0.103749\pi\) | ||||
0.947351 | + | 0.320197i | \(0.103749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0569 | 0.850532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.8863 | −1.36780 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.2616 | 1.76854 | 0.884272 | − | 0.466972i | \(-0.154655\pi\) | ||||
0.884272 | + | 0.466972i | \(0.154655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.56362 | 0.643681 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.497675 | −0.0371979 | −0.0185990 | − | 0.999827i | \(-0.505921\pi\) | ||||
−0.0185990 | + | 0.999827i | \(0.505921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.06830 | 0.153735 | 0.0768677 | − | 0.997041i | \(-0.475508\pi\) | ||||
0.0768677 | + | 0.997041i | \(0.475508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.66848 | 0.640792 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.77907 | 0.645450 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.1004 | 1.61614 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.86117 | −0.280859 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.6610 | 1.13319 | 0.566597 | − | 0.823995i | \(-0.308260\pi\) | ||||
0.566597 | + | 0.823995i | \(0.308260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3643 | 1.03396 | 0.516981 | − | 0.855997i | \(-0.327056\pi\) | ||||
0.516981 | + | 0.855997i | \(0.327056\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.43787 | 0.246191 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.66662 | −0.474977 | −0.237488 | − | 0.971390i | \(-0.576324\pi\) | ||||
−0.237488 | + | 0.971390i | \(0.576324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3085 | 0.872525 | 0.436263 | − | 0.899819i | \(-0.356302\pi\) | ||||
0.436263 | + | 0.899819i | \(0.356302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.69102 | −0.119275 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.850146 | 0.0596685 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.93687 | −0.554335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.1477 | 0.844326 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −39.2189 | −2.71283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7807 | 1.70597 | 0.852985 | − | 0.521935i | \(-0.174790\pi\) | ||||
0.852985 | + | 0.521935i | \(0.174790\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.52055 | 0.446781 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.51909 | 0.646198 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.11237 | −0.210315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.7059 | −1.32556 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.5342 | −1.50900 | −0.754500 | − | 0.656300i | \(-0.772121\pi\) | ||||
−0.754500 | + | 0.656300i | \(0.772121\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.50871 | −0.167247 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9115 | 0.856967 | 0.428484 | − | 0.903550i | \(-0.359048\pi\) | ||||
0.428484 | + | 0.903550i | \(0.359048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.1759 | 0.738527 | 0.369264 | − | 0.929325i | \(-0.379610\pi\) | ||||
0.369264 | + | 0.929325i | \(0.379610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.85563 | −0.253682 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6628 | 0.764057 | 0.382029 | − | 0.924150i | \(-0.375226\pi\) | ||||
0.382029 | + | 0.924150i | \(0.375226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.69012 | −0.566881 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.95117 | 0.451527 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9495 | −1.41979 | −0.709897 | − | 0.704305i | \(-0.751259\pi\) | ||||
−0.709897 | + | 0.704305i | \(0.751259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.2572 | 1.30488 | 0.652441 | − | 0.757840i | \(-0.273745\pi\) | ||||
0.652441 | + | 0.757840i | \(0.273745\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9618 | −0.959799 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.9695 | 2.22506 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.4879 | −0.664645 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.77732 | 0.617139 | 0.308570 | − | 0.951202i | \(-0.400150\pi\) | ||||
0.308570 | + | 0.951202i | \(0.400150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.6361 | 1.67460 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.81608 | −0.176350 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6053 | 0.911054 | 0.455527 | − | 0.890222i | \(-0.349451\pi\) | ||||
0.455527 | + | 0.890222i | \(0.349451\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.77907 | 0.545505 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.13277 | 0.132015 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.1734 | −1.12062 | −0.560309 | − | 0.828284i | \(-0.689318\pi\) | ||||
−0.560309 | + | 0.828284i | \(0.689318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.3811 | 0.760568 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.68074 | −0.470054 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.4154 | −1.36669 | −0.683345 | − | 0.730096i | \(-0.739476\pi\) | ||||
−0.683345 | + | 0.730096i | \(0.739476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3825 | −1.23815 | −0.619076 | − | 0.785331i | \(-0.712493\pi\) | ||||
−0.619076 | + | 0.785331i | \(0.712493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.43787 | 0.208069 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.50079 | −0.331710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.3170 | −1.28081 | −0.640406 | − | 0.768037i | \(-0.721234\pi\) | ||||
−0.640406 | + | 0.768037i | \(0.721234\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.8806 | 1.42970 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.1995 | −0.727760 | −0.363880 | − | 0.931446i | \(-0.618548\pi\) | ||||
−0.363880 | + | 0.931446i | \(0.618548\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.577862 | 0.0343503 | 0.0171752 | − | 0.999852i | \(-0.494533\pi\) | ||||
0.0171752 | + | 0.999852i | \(0.494533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.99735 | 0.296017 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.93687 | −0.468499 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.858242 | −0.0504848 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.51248 | −0.323148 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.8053 | −1.85809 | −0.929043 | − | 0.369973i | \(-0.879367\pi\) | ||||
−0.929043 | + | 0.369973i | \(0.879367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2176 | 0.711339 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.2395 | −1.23244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.7501 | −1.37350 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | 0.0576390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.33016 | −0.306209 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3673 | 0.708147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.79472 | −0.159503 | −0.0797516 | − | 0.996815i | \(-0.525413\pi\) | ||||
−0.0797516 | + | 0.996815i | \(0.525413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.00628679 | −0.000357643 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2066 | 1.20252 | 0.601258 | − | 0.799055i | \(-0.294666\pi\) | ||||
0.601258 | + | 0.799055i | \(0.294666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4215 | −0.815151 | −0.407575 | − | 0.913172i | \(-0.633626\pi\) | ||||
−0.407575 | + | 0.913172i | \(0.633626\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.50871 | −0.141350 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.2521 | 1.02514 | 0.512571 | − | 0.858645i | \(-0.328693\pi\) | ||||
0.512571 | + | 0.858645i | \(0.328693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.67648 | 0.261832 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.5874 | 0.646746 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.6448 | −1.59384 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.90479 | 0.272069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.6837 | −0.756712 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.69012 | −0.479102 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0934 | −0.664716 | −0.332358 | − | 0.943153i | \(-0.607844\pi\) | ||||
−0.332358 | + | 0.943153i | \(0.607844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.0241 | 1.20691 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.41256 | −0.131812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.1131 | −0.823266 | −0.411633 | − | 0.911350i | \(-0.635041\pi\) | ||||
−0.411633 | + | 0.911350i | \(0.635041\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.676329 | 0.0367331 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 52.3625 | 2.83559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.39402 | −0.182728 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5488 | −0.673657 | −0.336829 | − | 0.941566i | \(-0.609354\pi\) | ||||
−0.336829 | + | 0.941566i | \(0.609354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.90686 | −0.423245 | −0.211622 | − | 0.977352i | \(-0.567875\pi\) | ||||
−0.211622 | + | 0.977352i | \(0.567875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9382 | 1.01085 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.61723 | 0.458649 | 0.229325 | − | 0.973350i | \(-0.426348\pi\) | ||||
0.229325 | + | 0.973350i | \(0.426348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.30283 | 0.493743 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.81608 | −0.149043 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.39810 | 0.179345 | 0.0896724 | − | 0.995971i | \(-0.471418\pi\) | ||||
0.0896724 | + | 0.995971i | \(0.471418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.8323 | 1.67538 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.4988 | −0.708506 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.44040 | −0.232421 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.53561 | 0.497755 | 0.248877 | − | 0.968535i | \(-0.419938\pi\) | ||||
0.248877 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.9113 | −1.03654 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.3811 | 0.642797 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5512 | 0.598101 | 0.299050 | − | 0.954237i | \(-0.403330\pi\) | ||||
0.299050 | + | 0.954237i | \(0.403330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.700922 | 0.0361955 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.16978 | −0.214755 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.0125 | 1.13071 | 0.565353 | − | 0.824849i | \(-0.308740\pi\) | ||||
0.565353 | + | 0.824849i | \(0.308740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.85523 | −0.299973 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.6300 | −1.36073 | −0.680366 | − | 0.732873i | \(-0.738179\pi\) | ||||
−0.680366 | + | 0.732873i | \(0.738179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.50079 | −0.280346 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.50871 | 0.127525 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.09908 | −0.207831 | −0.103916 | − | 0.994586i | \(-0.533137\pi\) | ||||
−0.103916 | + | 0.994586i | \(0.533137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4545 | 0.983858 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.2470 | 0.718665 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.91718 | 0.498987 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.9487 | 1.40271 | 0.701353 | − | 0.712814i | \(-0.252579\pi\) | ||||
0.701353 | + | 0.712814i | \(0.252579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.99735 | 0.250180 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.04308 | 0.201902 | 0.100951 | − | 0.994891i | \(-0.467811\pi\) | ||||
0.100951 | + | 0.994891i | \(0.467811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −46.6891 | −2.32575 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.81974 | −0.239495 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.2918 | 2.39374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.2768 | 1.84322 | 0.921609 | − | 0.388120i | \(-0.126875\pi\) | ||||
0.921609 | + | 0.388120i | \(0.126875\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.87250 | 0.437648 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.2176 | 0.601191 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.9630 | −0.734507 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.23816 | −0.158573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.5634 | −1.00459 | −0.502294 | − | 0.864697i | \(-0.667510\pi\) | ||||
−0.502294 | + | 0.864697i | \(0.667510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8001 | 1.30616 | 0.653078 | − | 0.757290i | \(-0.273477\pi\) | ||||
0.653078 | + | 0.757290i | \(0.273477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.8010 | −1.06000 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.01768 | −0.194886 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3673 | 0.598493 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.9110 | 0.913032 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.7229 | 1.52804 | 0.764018 | − | 0.645195i | \(-0.223224\pi\) | ||||
0.764018 | + | 0.645195i | \(0.223224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.937133 | 0.0450358 | 0.0225179 | − | 0.999746i | \(-0.492832\pi\) | ||||
0.0225179 | + | 0.999746i | \(0.492832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.595886 | −0.0285705 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.5235 | −1.65148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4961 | 0.644133 | 0.322066 | − | 0.946717i | \(-0.395623\pi\) | ||||
0.322066 | + | 0.946717i | \(0.395623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.50871 | −0.119462 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.5597 | −1.26189 | −0.630945 | − | 0.775828i | \(-0.717332\pi\) | ||||
−0.630945 | + | 0.775828i | \(0.717332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9581 | −0.519462 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.89362 | −0.420654 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.941531 | −0.0444336 | −0.0222168 | − | 0.999753i | \(-0.507072\pi\) | ||||
−0.0222168 | + | 0.999753i | \(0.507072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.6591 | −2.05583 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.06682 | −0.285044 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.90479 | 0.229940 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.4449 | 0.582149 | 0.291075 | − | 0.956700i | \(-0.405987\pi\) | ||||
0.291075 | + | 0.956700i | \(0.405987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.5130 | −0.724083 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.2939 | 1.45750 | 0.728752 | − | 0.684778i | \(-0.240101\pi\) | ||||
0.728752 | + | 0.684778i | \(0.240101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5292 | −0.535809 | −0.267904 | − | 0.963445i | \(-0.586331\pi\) | ||||
−0.267904 | + | 0.963445i | \(0.586331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.67214 | −0.309413 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.0190768 | 0.000882768 0 | 0.000441384 | − | 1.00000i | \(-0.499860\pi\) | ||||
0.000441384 | 1.00000i | \(0.499860\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.41256 | −0.111402 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.08310 | −0.142062 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.50079 | 0.252927 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.12968 | 0.327132 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.0607 | 1.42217 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.71186 | 0.0782169 | 0.0391084 | − | 0.999235i | \(-0.487548\pi\) | ||||
0.0391084 | + | 0.999235i | \(0.487548\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.0595 | −1.96334 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.39402 | −0.154433 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.86462 | −0.357114 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7652 | −0.940960 | −0.470480 | − | 0.882411i | \(-0.655919\pi\) | ||||
−0.470480 | + | 0.882411i | \(0.655919\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.32860 | −0.376632 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.9787 | 0.991886 | 0.495943 | − | 0.868355i | \(-0.334823\pi\) | ||||
0.495943 | + | 0.868355i | \(0.334823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.41561 | 0.153832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.7999 | −0.620259 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.30283 | 0.417289 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8772 | 0.486929 | 0.243464 | − | 0.969910i | \(-0.421716\pi\) | ||||
0.243464 | + | 0.969910i | \(0.421716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.1620 | −0.766743 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.75037 | −0.345572 | −0.172786 | − | 0.984959i | \(-0.555277\pi\) | ||||
−0.172786 | + | 0.984959i | \(0.555277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.60449 | −0.338395 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.75004 | −0.344191 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.8415 | 1.27838 | 0.639189 | − | 0.769049i | \(-0.279270\pi\) | ||||
0.639189 | + | 0.769049i | \(0.279270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.44040 | −0.196432 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.5289 | 1.21543 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.00896932 | −0.000395235 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −47.8025 | −2.10235 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.3045 | −0.715690 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.79743 | 0.341612 | 0.170806 | − | 0.985305i | \(-0.445363\pi\) | ||||
0.170806 | + | 0.985305i | \(0.445363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.09397 | −0.310198 | −0.155099 | − | 0.987899i | \(-0.549570\pi\) | ||||
−0.155099 | + | 0.987899i | \(0.549570\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.700922 | 0.0305907 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.2447 | 1.66596 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.447180 | 0.0194426 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.6505 | 1.33012 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.9287 | 1.68619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.5317 | 0.714726 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.348831 | 0.0150532 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.50079 | −0.236936 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0751 | 0.519148 | 0.259574 | − | 0.965723i | \(-0.416418\pi\) | ||||
0.259574 | + | 0.965723i | \(0.416418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.44972 | −0.0622132 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.5225 | −0.836251 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4066 | −0.573226 | −0.286613 | − | 0.958046i | \(-0.592529\pi\) | ||||
−0.286613 | + | 0.958046i | \(0.592529\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.0258 | 1.32415 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.06126 | −0.258219 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.91718 | 0.421721 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.15344 | −0.261199 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.8946 | −0.758219 | −0.379109 | − | 0.925352i | \(-0.623770\pi\) | ||||
−0.379109 | + | 0.925352i | \(0.623770\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.90479 | −0.207450 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.4907 | −0.654017 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.8359 | 0.835983 | 0.417992 | − | 0.908451i | \(-0.362734\pi\) | ||||
0.417992 | + | 0.908451i | \(0.362734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.964913 | 0.0405942 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.81974 | −0.202410 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.40891 | 0.142909 | 0.0714544 | − | 0.997444i | \(-0.477236\pi\) | ||||
0.0714544 | + | 0.997444i | \(0.477236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.8121 | 1.41499 | 0.707497 | − | 0.706717i | \(-0.249824\pi\) | ||||
0.707497 | + | 0.706717i | \(0.249824\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.9772 | −0.458578 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.84223 | −0.201935 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.2352 | 1.67501 | 0.837506 | − | 0.546427i | \(-0.184013\pi\) | ||||
0.837506 | + | 0.546427i | \(0.184013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0682 | −0.418421 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9630 | −0.620771 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 68.1061 | 2.82067 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.3047 | 0.508736 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.95467 | 0.121952 | 0.0609762 | − | 0.998139i | \(-0.480579\pi\) | ||||
0.0609762 | + | 0.998139i | \(0.480579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.8680 | −2.79645 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.67278 | 0.192212 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.9000 | −1.88489 | −0.942444 | − | 0.334364i | \(-0.891478\pi\) | ||||
−0.942444 | + | 0.334364i | \(0.891478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.01768 | −0.164709 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.62729 | −0.353091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.5193 | 0.879257 | 0.439628 | − | 0.898180i | \(-0.355110\pi\) | ||||
0.439628 | + | 0.898180i | \(0.355110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2130 | −0.824505 | −0.412253 | − | 0.911070i | \(-0.635258\pi\) | ||||
−0.412253 | + | 0.911070i | \(0.635258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.05242 | −0.246474 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.2587 | −0.782978 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3892 | 0.462273 | 0.231136 | − | 0.972921i | \(-0.425756\pi\) | ||||
0.231136 | + | 0.972921i | \(0.425756\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.595886 | −0.0241465 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.6232 | 1.72435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.744736 | −0.0300796 | −0.0150398 | − | 0.999887i | \(-0.504787\pi\) | ||||
−0.0150398 | + | 0.999887i | \(0.504787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.56313 | 0.224327 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.2496 | −0.774961 | −0.387481 | − | 0.921878i | \(-0.626655\pi\) | ||||
−0.387481 | + | 0.921878i | \(0.626655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.2763 | −1.45807 | −0.729034 | − | 0.684478i | \(-0.760030\pi\) | ||||
−0.729034 | + | 0.684478i | \(0.760030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.6967 | −0.750272 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.9581 | −0.439025 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.4894 | 1.09782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.2715 | 1.40637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.85163 | 0.193140 | 0.0965702 | − | 0.995326i | \(-0.469213\pi\) | ||||
0.0965702 | + | 0.995326i | \(0.469213\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.3693 | −0.690368 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.35361 | −0.331503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.90479 | 0.194335 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.3381 | 0.923240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.3651 | 0.843871 | 0.421935 | − | 0.906626i | \(-0.361351\pi\) | ||||
0.421935 | + | 0.906626i | \(0.361351\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.44504 | 0.214732 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.700922 | −0.0275988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.5641 | −1.04434 | −0.522171 | − | 0.852841i | \(-0.674878\pi\) | ||||
−0.522171 | + | 0.852841i | \(0.674878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 67.2067 | 2.63809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.67214 | −0.261502 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.8253 | −0.541026 | −0.270513 | − | 0.962716i | \(-0.587193\pi\) | ||||
−0.270513 | + | 0.962716i | \(0.587193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.3261 | 0.794205 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.1397 | −0.434600 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.5177 | −1.38357 | −0.691787 | − | 0.722101i | \(-0.743176\pi\) | ||||
−0.691787 | + | 0.722101i | \(0.743176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.7029 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.8123 | 0.536424 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.12968 | 0.276477 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.11660 | 0.159395 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.7947 | 0.610659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.0297 | 2.62626 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.00976 | 0.347301 | 0.173650 | − | 0.984807i | \(-0.444444\pi\) | ||||
0.173650 | + | 0.984807i | \(0.444444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.86117 | 0.148617 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.4758 | 0.633218 | 0.316609 | − | 0.948556i | \(-0.397456\pi\) | ||||
0.316609 | + | 0.948556i | \(0.397456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.86462 | −0.301816 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.04996 | −0.346795 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.7149 | 0.907426 | 0.453713 | − | 0.891148i | \(-0.350099\pi\) | ||||
0.453713 | + | 0.891148i | \(0.350099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6583 | 0.483650 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.83346 | −0.298865 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −60.7269 | −2.31351 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6835 | 0.672711 | 0.336355 | − | 0.941735i | \(-0.390806\pi\) | ||||
0.336355 | + | 0.941735i | \(0.390806\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.7999 | −0.524214 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.61985 | −0.175241 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.8878 | −1.20784 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.17473 | −0.309197 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9125 | 1.16755 | 0.583774 | − | 0.811916i | \(-0.301575\pi\) | ||||
0.583774 | + | 0.811916i | \(0.301575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −62.5919 | −2.36070 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.09109 | 0.229404 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.60449 | −0.285996 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.07846 | −0.0780584 | −0.0390292 | − | 0.999238i | \(-0.512427\pi\) | ||||
−0.0390292 | + | 0.999238i | \(0.512427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.8793 | 0.933047 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.0936 | 1.72622 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.9802 | 1.00900 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.3849 | 0.574559 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.55907 | −0.356493 | −0.178247 | − | 0.983986i | \(-0.557042\pi\) | ||||
−0.178247 | + | 0.983986i | \(0.557042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.00896932 | −0.000334035 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.1987 | −0.528056 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.850146 | −0.0315736 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.8862 | −1.14551 | −0.572753 | − | 0.819728i | \(-0.694125\pi\) | ||||
−0.572753 | + | 0.819728i | \(0.694125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.97219 | −0.147118 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.01768 | 0.148599 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.4356 | −1.23497 | −0.617485 | − | 0.786582i | \(-0.711849\pi\) | ||||
−0.617485 | + | 0.786582i | \(0.711849\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.700922 | 0.0258539 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.2710 | −0.488844 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.1993 | 1.11090 | 0.555449 | − | 0.831550i | \(-0.312546\pi\) | ||||
0.555449 | + | 0.831550i | \(0.312546\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.5109 | −0.900431 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.9868 | −0.953363 | −0.476681 | − | 0.879076i | \(-0.658160\pi\) | ||||
−0.476681 | + | 0.879076i | \(0.658160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.6885 | −0.464869 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.5379 | −1.37344 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.5317 | 0.604054 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0619 | −0.695580 | −0.347790 | − | 0.937572i | \(-0.613068\pi\) | ||||
−0.347790 | + | 0.937572i | \(0.613068\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.85314 | −0.249742 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.65548 | −0.315005 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.7062 | 1.26142 | 0.630709 | − | 0.776019i | \(-0.282764\pi\) | ||||
0.630709 | + | 0.776019i | \(0.282764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.6698 | −0.677672 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.6874 | 0.423670 | 0.211835 | − | 0.977305i | \(-0.432056\pi\) | ||||
0.211835 | + | 0.977305i | \(0.432056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.5225 | −0.706761 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.0792 | −0.364414 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −59.9249 | −2.16376 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.361368 | −0.0130313 | −0.00651564 | − | 0.999979i | \(-0.502074\pi\) | ||||
−0.00651564 | + | 0.999979i | \(0.502074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.2372 | −0.368683 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.22709 | 0.295908 | 0.147954 | − | 0.988994i | \(-0.452731\pi\) | ||||
0.147954 | + | 0.988994i | \(0.452731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.51909 | −0.341936 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.15344 | −0.220754 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 56.5873 | 2.02745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.1729 | 1.83111 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.28256 | −0.117309 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.39864 | −0.156994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.2262 | −1.22003 | −0.610015 | − | 0.792390i | \(-0.708837\pi\) | ||||
−0.610015 | + | 0.792390i | \(0.708837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.7381 | 0.453489 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.964913 | 0.0343084 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −60.6587 | −2.15405 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.67822 | −0.307785 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5824 | 0.622800 | 0.311400 | − | 0.950279i | \(-0.399202\pi\) | ||||
0.311400 | + | 0.950279i | \(0.399202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.9141 | −1.23517 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.4906 | −0.971332 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.4257 | −0.861964 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.84223 | −0.170666 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.7114 | 0.553069 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.04653 | −0.142269 | −0.0711343 | − | 0.997467i | \(-0.522662\pi\) | ||||
−0.0711343 | + | 0.997467i | \(0.522662\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.0783 | −1.02108 | −0.510538 | − | 0.859855i | \(-0.670554\pi\) | ||||
−0.510538 | + | 0.859855i | \(0.670554\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.2866 | 0.501052 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8824 | −0.416221 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.12968 | −0.249436 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.3047 | 0.429960 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.8888 | 0.798826 | 0.399413 | − | 0.916771i | \(-0.369214\pi\) | ||||
0.399413 | + | 0.916771i | \(0.369214\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.1394 | −1.67803 | −0.839017 | − | 0.544105i | \(-0.816869\pi\) | ||||
−0.839017 | + | 0.544105i | \(0.816869\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.85563 | 0.134236 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.0777 | −0.350436 | −0.175218 | − | 0.984530i | \(-0.556063\pi\) | ||||
−0.175218 | + | 0.984530i | \(0.556063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0579 | −1.32180 | −0.660902 | − | 0.750472i | \(-0.729826\pi\) | ||||
−0.660902 | + | 0.750472i | \(0.729826\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9415 | 0.518316 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.01768 | −0.139204 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.4849 | −0.847336 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.7549 | −1.27043 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.4667 | 0.844686 | 0.422343 | − | 0.906436i | \(-0.361208\pi\) | ||||
0.422343 | + | 0.906436i | \(0.361208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2773 | −0.975078 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.55088 | 0.294508 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0569 | −0.380370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.2587 | −0.661737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.405036 | −0.0139008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.5103 | 1.45723 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.62748 | 0.124203 | 0.0621013 | − | 0.998070i | \(-0.480220\pi\) | ||||
0.0621013 | + | 0.998070i | \(0.480220\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.8863 | 0.611698 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.6691 | 0.979319 | 0.489659 | − | 0.871914i | \(-0.337121\pi\) | ||||
0.489659 | + | 0.871914i | \(0.337121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.3605 | −0.762932 | −0.381466 | − | 0.924383i | \(-0.624581\pi\) | ||||
−0.381466 | + | 0.924383i | \(0.624581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.56313 | 0.189591 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.0247 | 1.66882 | 0.834411 | − | 0.551143i | \(-0.185808\pi\) | ||||
0.834411 | + | 0.551143i | \(0.185808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.2616 | −0.790917 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.601561 | 0.0204301 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.5523 | 1.85056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.8331 | 0.400950 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.7300 | −0.667761 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.4759 | −0.725188 | −0.362594 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362594 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.2930 | 0.751925 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.1537 | −0.544231 | −0.272116 | − | 0.962265i | \(-0.587723\pi\) | ||||
−0.272116 | + | 0.962265i | \(0.587723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8838 | 0.399921 | 0.199960 | − | 0.979804i | \(-0.435919\pi\) | ||||
0.199960 | + | 0.979804i | \(0.435919\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.56362 | −0.287863 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.1485 | −1.21375 | −0.606875 | − | 0.794798i | \(-0.707577\pi\) | ||||
−0.606875 | + | 0.794798i | \(0.707577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.35361 | −0.280171 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.5124 | −0.888199 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.9577 | 2.07334 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.497675 | 0.0166354 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.6470 | 0.555826 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.09262 | 0.269904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.7435 | 1.65720 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.700922 | −0.0233252 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.06830 | −0.0687526 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.0738 | 0.633337 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.0775 | −0.632759 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.51196 | −0.215751 | −0.107875 | − | 0.994164i | \(-0.534405\pi\) | ||||
−0.107875 | + | 0.994164i | \(0.534405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −82.3086 | −2.72402 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.66848 | −0.286571 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.3261 | 0.671226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.8181 | −1.31348 | −0.656740 | − | 0.754117i | \(-0.728065\pi\) | ||||
−0.656740 | + | 0.754117i | \(0.728065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.95888 | 0.0645473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.6284 | −1.50188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.77907 | −0.288654 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0225014 | −0.000739043 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1467 | 1.02189 | 0.510946 | − | 0.859613i | \(-0.329295\pi\) | ||||
0.510946 | + | 0.859613i | \(0.329295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.12968 | 0.233666 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.8642 | −0.486632 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.1004 | −0.722761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.4314 | −0.830809 | −0.415404 | − | 0.909637i | \(-0.636360\pi\) | ||||
−0.415404 | + | 0.909637i | \(0.636360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.1083 | 0.329873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.3306 | 0.336769 | 0.168384 | − | 0.985721i | \(-0.446145\pi\) | ||||
0.168384 | + | 0.985721i | \(0.446145\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.4321 | −1.25152 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.86117 | 0.125604 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.2624 | 0.820916 | 0.410458 | − | 0.911879i | \(-0.365369\pi\) | ||||
0.410458 | + | 0.911879i | \(0.365369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.7792 | 0.706983 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7933 | −0.414851 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.8248 | −1.51680 | −0.758402 | − | 0.651787i | \(-0.774020\pi\) | ||||
−0.758402 | + | 0.651787i | \(0.774020\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.6610 | −0.506780 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.27784 | −0.105958 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.6583 | 0.408759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.6131 | 1.92300 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.4731 | 1.33645 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.3643 | −0.462402 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.76684 | −0.0889756 | −0.0444878 | − | 0.999010i | \(-0.514166\pi\) | ||||
−0.0444878 | + | 0.999010i | \(0.514166\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.0777 | 0.644990 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.43069 | −0.142188 | −0.0710939 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710939 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.61985 | −0.148106 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.43787 | −0.110100 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.0333 | 0.768893 | 0.384447 | − | 0.923147i | \(-0.374392\pi\) | ||||
0.384447 | + | 0.923147i | \(0.374392\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −60.2780 | −1.92649 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48.9762 | −1.56369 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.1819 | −1.47297 | −0.736487 | − | 0.676452i | \(-0.763517\pi\) | ||||
−0.736487 | + | 0.676452i | \(0.763517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.66662 | 0.212416 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.09109 | 0.193882 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.84223 | 0.153974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.3610 | −0.869152 | −0.434576 | − | 0.900635i | \(-0.643102\pi\) | ||||
−0.434576 | + | 0.900635i | \(0.643102\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.47656 | 0.268996 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.3085 | −0.390205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.0922 | 1.36474 | 0.682372 | − | 0.731005i | \(-0.260948\pi\) | ||||
0.682372 | + | 0.731005i | \(0.260948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33.8975 | −1.07247 |
(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 | 6020.2.a.j.1.5 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6020.2.a.j.1.5 | ✓ | 13 | 1.1 | even | 1 | trivial |