Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.99382\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.99382 | −1.33888 | −0.669439 | − | 0.742867i | \(-0.733466\pi\) | ||||
−0.669439 | + | 0.742867i | \(0.733466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.65862 | −1.76079 | −0.880397 | − | 0.474238i | \(-0.842724\pi\) | ||||
−0.880397 | + | 0.474238i | \(0.842724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.962769 | 0.290286 | 0.145143 | − | 0.989411i | \(-0.453636\pi\) | ||||
0.145143 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.976361 | 0.270794 | 0.135397 | − | 0.990791i | \(-0.456769\pi\) | ||||
0.135397 | + | 0.990791i | \(0.456769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.99382 | −0.773002 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.56202 | 0.621381 | 0.310690 | − | 0.950511i | \(-0.399440\pi\) | ||||
0.310690 | + | 0.950511i | \(0.399440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.42193 | 1.93212 | 0.966062 | − | 0.258311i | \(-0.0831658\pi\) | ||||
0.966062 | + | 0.258311i | \(0.0831658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.65862 | −1.01659 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.29084 | 1.31173 | 0.655865 | − | 0.754878i | \(-0.272304\pi\) | ||||
0.655865 | + | 0.754878i | \(0.272304\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.96298 | 0.792596 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.04318 | −0.565104 | −0.282552 | − | 0.959252i | \(-0.591181\pi\) | ||||
−0.282552 | + | 0.959252i | \(0.591181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1421 | −1.82158 | −0.910788 | − | 0.412875i | \(-0.864525\pi\) | ||||
−0.910788 | + | 0.412875i | \(0.864525\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.962769 | 0.167597 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.9471 | 2.35749 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7136 | 1.76130 | 0.880651 | − | 0.473766i | \(-0.157106\pi\) | ||||
0.880651 | + | 0.473766i | \(0.157106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.976361 | 0.156343 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.413133 | 0.0645205 | 0.0322602 | − | 0.999480i | \(-0.489729\pi\) | ||||
0.0322602 | + | 0.999480i | \(0.489729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.35521 | −0.816662 | −0.408331 | − | 0.912834i | \(-0.633889\pi\) | ||||
−0.408331 | + | 0.912834i | \(0.633889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.99382 | −0.446293 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.47126 | −1.23566 | −0.617830 | − | 0.786312i | \(-0.711988\pi\) | ||||
−0.617830 | + | 0.786312i | \(0.711988\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.7028 | 2.10039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.56202 | 0.358754 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1750 | −1.80973 | −0.904865 | − | 0.425699i | \(-0.860028\pi\) | ||||
−0.904865 | + | 0.425699i | \(0.860028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.88236 | −0.388658 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.42193 | 1.11551 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.101385 | −0.0131992 | −0.00659962 | − | 0.999978i | \(-0.502101\pi\) | ||||
−0.00659962 | + | 0.999978i | \(0.502101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3711 | −1.84003 | −0.920014 | − | 0.391886i | \(-0.871823\pi\) | ||||
−0.920014 | + | 0.391886i | \(0.871823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.65862 | −0.586931 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.92305 | −0.362560 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.7656 | −1.43740 | −0.718698 | − | 0.695323i | \(-0.755261\pi\) | ||||
−0.718698 | + | 0.695323i | \(0.755261\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.29084 | 0.757328 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5261 | 1.48657 | 0.743285 | − | 0.668975i | \(-0.233267\pi\) | ||||
0.743285 | + | 0.668975i | \(0.233267\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0294 | −1.29090 | −0.645449 | − | 0.763803i | \(-0.723330\pi\) | ||||
−0.645449 | + | 0.763803i | \(0.723330\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.96298 | 0.457606 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.48518 | −0.511134 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.47183 | −0.165594 | −0.0827969 | − | 0.996566i | \(-0.526385\pi\) | ||||
−0.0827969 | + | 0.996566i | \(0.526385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.56878 | −0.501489 | −0.250744 | − | 0.968053i | \(-0.580675\pi\) | ||||
−0.250744 | + | 0.968053i | \(0.580675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.67023 | −0.831953 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.04318 | −0.326263 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.20803 | 0.870049 | 0.435025 | − | 0.900419i | \(-0.356740\pi\) | ||||
0.435025 | + | 0.900419i | \(0.356740\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.54850 | −0.476812 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.1421 | −1.05169 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25.2138 | −2.58688 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1603 | 1.13316 | 0.566579 | − | 0.824007i | \(-0.308266\pi\) | ||||
0.566579 | + | 0.824007i | \(0.308266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.962769 | 0.0967620 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.03063 | −0.500566 | −0.250283 | − | 0.968173i | \(-0.580524\pi\) | ||||
−0.250283 | + | 0.968173i | \(0.580524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.19615 | 0.709057 | 0.354529 | − | 0.935045i | \(-0.384641\pi\) | ||||
0.354529 | + | 0.935045i | \(0.384641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.9471 | 1.36110 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.9736 | −1.44755 | −0.723777 | − | 0.690034i | \(-0.757595\pi\) | ||||
−0.723777 | + | 0.690034i | \(0.757595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.32527 | −0.126938 | −0.0634690 | − | 0.997984i | \(-0.520216\pi\) | ||||
−0.0634690 | + | 0.997984i | \(0.520216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.7136 | 1.01689 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.09741 | 0.761740 | 0.380870 | − | 0.924629i | \(-0.375625\pi\) | ||||
0.380870 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.8337 | −1.75625 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.976361 | 0.0902646 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.9355 | −1.09412 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0731 | −0.915734 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.413133 | 0.0372509 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.10465 | 0.277688 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.8311 | −1.40479 | −0.702393 | − | 0.711789i | \(-0.747885\pi\) | ||||
−0.702393 | + | 0.711789i | \(0.747885\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.35521 | −0.471500 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.80759 | −0.507412 | −0.253706 | − | 0.967281i | \(-0.581649\pi\) | ||||
−0.253706 | + | 0.967281i | \(0.581649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39.2346 | −3.40207 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.99382 | −0.257667 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.6048 | −1.76039 | −0.880195 | − | 0.474612i | \(-0.842589\pi\) | ||||
−0.880195 | + | 0.474612i | \(0.842589\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.58360 | −0.643233 | −0.321616 | − | 0.946870i | \(-0.604226\pi\) | ||||
−0.321616 | + | 0.946870i | \(0.604226\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.47126 | −0.713409 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.940010 | 0.0786076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.11074 | 0.756605 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.7028 | 1.21266 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7087 | 1.04114 | 0.520569 | − | 0.853819i | \(-0.325720\pi\) | ||||
0.520569 | + | 0.853819i | \(0.325720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4023 | 1.17204 | 0.586021 | − | 0.810296i | \(-0.300694\pi\) | ||||
0.586021 | + | 0.810296i | \(0.300694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.56202 | 0.207127 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.3637 | 2.43887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.84981 | −0.626483 | −0.313241 | − | 0.949674i | \(-0.601415\pi\) | ||||
−0.313241 | + | 0.949674i | \(0.601415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.1750 | −1.04485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −29.3067 | −2.30969 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.151488 | 0.0118654 | 0.00593272 | − | 0.999982i | \(-0.498112\pi\) | ||||
0.00593272 | + | 0.999982i | \(0.498112\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.88236 | −0.224392 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0467 | −0.926671 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.42193 | 0.644041 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9592 | 0.833212 | 0.416606 | − | 0.909087i | \(-0.363220\pi\) | ||||
0.416606 | + | 0.909087i | \(0.363220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.4620 | −1.39560 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.101385 | −0.00762059 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6334 | 1.09375 | 0.546874 | − | 0.837215i | \(-0.315818\pi\) | ||||
0.546874 | + | 0.837215i | \(0.315818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.60022 | −0.341932 | −0.170966 | − | 0.985277i | \(-0.554689\pi\) | ||||
−0.170966 | + | 0.985277i | \(0.554689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.3711 | −1.06234 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32.0746 | −2.35817 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.46663 | 0.180378 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.65862 | −0.338865 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2571 | −1.24868 | −0.624339 | − | 0.781153i | \(-0.714632\pi\) | ||||
−0.624339 | + | 0.781153i | \(0.714632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.6499 | −0.838580 | −0.419290 | − | 0.907852i | \(-0.637721\pi\) | ||||
−0.419290 | + | 0.907852i | \(0.637721\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.92305 | −0.209324 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.8741 | 0.774747 | 0.387373 | − | 0.921923i | \(-0.373382\pi\) | ||||
0.387373 | + | 0.921923i | \(0.373382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.11256 | 0.645972 | 0.322986 | − | 0.946404i | \(-0.395313\pi\) | ||||
0.322986 | + | 0.946404i | \(0.395313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.7656 | −0.829881 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.1770 | 0.995031 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.23685 | −0.0863851 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.29084 | 0.437244 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.10838 | 0.560868 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1269 | −1.24791 | −0.623953 | − | 0.781462i | \(-0.714474\pi\) | ||||
−0.623953 | + | 0.781462i | \(0.714474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.5261 | 0.858272 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.0326 | 1.09341 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.2482 | 3.20742 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.0294 | −0.745301 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50146 | 0.168266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2420 | −0.953716 | −0.476858 | − | 0.878980i | \(-0.658224\pi\) | ||||
−0.476858 | + | 0.878980i | \(0.658224\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.96298 | 0.264199 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5377 | 0.699410 | 0.349705 | − | 0.936860i | \(-0.386282\pi\) | ||||
0.349705 | + | 0.936860i | \(0.386282\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.2304 | 1.33686 | 0.668431 | − | 0.743774i | \(-0.266966\pi\) | ||||
0.668431 | + | 0.743774i | \(0.266966\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.48518 | −0.295103 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.4478 | 1.53612 | 0.768059 | − | 0.640379i | \(-0.221223\pi\) | ||||
0.768059 | + | 0.640379i | \(0.221223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.3615 | 1.65440 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.47183 | −0.0956056 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.49855 | 0.549726 | 0.274863 | − | 0.961483i | \(-0.411368\pi\) | ||||
0.274863 | + | 0.961483i | \(0.411368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.5989 | −1.19806 | −0.599031 | − | 0.800726i | \(-0.704447\pi\) | ||||
−0.599031 | + | 0.800726i | \(0.704447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −44.0175 | −2.81217 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.22285 | 0.523207 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.56878 | −0.289535 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.98372 | −0.188331 | −0.0941655 | − | 0.995557i | \(-0.530018\pi\) | ||||
−0.0941655 | + | 0.995557i | \(0.530018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.05663 | 0.380777 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.67023 | −0.480329 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.66532 | 0.291014 | 0.145507 | − | 0.989357i | \(-0.453519\pi\) | ||||
0.145507 | + | 0.989357i | \(0.453519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −49.9105 | −3.10129 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.04318 | −0.188368 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.4032 | −0.703151 | −0.351576 | − | 0.936159i | \(-0.614354\pi\) | ||||
−0.351576 | + | 0.936159i | \(0.614354\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.4437 | 2.42301 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.20803 | 0.502323 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.5202 | −1.06823 | −0.534114 | − | 0.845413i | \(-0.679355\pi\) | ||||
−0.534114 | + | 0.845413i | \(0.679355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.07499 | −0.247538 | −0.123769 | − | 0.992311i | \(-0.539498\pi\) | ||||
−0.123769 | + | 0.992311i | \(0.539498\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.54850 | −0.275288 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.81544 | 0.230079 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9380 | 1.37821 | 0.689105 | − | 0.724661i | \(-0.258004\pi\) | ||||
0.689105 | + | 0.724661i | \(0.258004\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.1421 | −0.607192 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4485 | −0.742615 | −0.371308 | − | 0.928510i | \(-0.621091\pi\) | ||||
−0.371308 | + | 0.928510i | \(0.621091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.2448 | −1.26287 | −0.631436 | − | 0.775428i | \(-0.717534\pi\) | ||||
−0.631436 | + | 0.775428i | \(0.717534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.2138 | −1.49354 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.92463 | −0.113607 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4361 | −0.613886 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1603 | 0.654229 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.52870 | 0.206149 | 0.103074 | − | 0.994674i | \(-0.467132\pi\) | ||||
0.103074 | + | 0.994674i | \(0.467132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.303530 | 0.0176722 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.962769 | 0.0558655 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.14213 | 0.355209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.9479 | 1.43797 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.03063 | −0.289002 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.0245 | 2.46357 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5946 | −0.890031 | −0.445016 | − | 0.895523i | \(-0.646802\pi\) | ||||
−0.445016 | + | 0.895523i | \(0.646802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.19615 | 0.409374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.111395 | −0.00631664 | −0.00315832 | − | 0.999995i | \(-0.501005\pi\) | ||||
−0.00315832 | + | 0.999995i | \(0.501005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8427 | −0.895484 | −0.447742 | − | 0.894163i | \(-0.647772\pi\) | ||||
−0.447742 | + | 0.894163i | \(0.647772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.9471 | 0.785830 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3265 | 1.02932 | 0.514658 | − | 0.857395i | \(-0.327919\pi\) | ||||
0.514658 | + | 0.857395i | \(0.327919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.92988 | −0.164042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9736 | −0.835745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.5771 | 1.20058 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.86930 | 0.214630 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.32527 | −0.0732877 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.4644 | 2.17574 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.26802 | −0.344521 | −0.172261 | − | 0.985051i | \(-0.555107\pi\) | ||||
−0.172261 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.7136 | 0.587101 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 35.2241 | 1.92450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.78190 | −0.532854 | −0.266427 | − | 0.963855i | \(-0.585843\pi\) | ||||
−0.266427 | + | 0.963855i | \(0.585843\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.09741 | 0.439791 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.76450 | −0.528778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −35.8843 | −1.93757 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.8337 | −1.01397 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.68557 | 0.144169 | 0.0720845 | − | 0.997399i | \(-0.477035\pi\) | ||||
0.0720845 | + | 0.997399i | \(0.477035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1287 | −0.863351 | −0.431675 | − | 0.902029i | \(-0.642077\pi\) | ||||
−0.431675 | + | 0.902029i | \(0.642077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.976361 | 0.0521143 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.8777 | 1.11121 | 0.555604 | − | 0.831447i | \(-0.312487\pi\) | ||||
0.555604 | + | 0.831447i | \(0.312487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.5008 | −1.99034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.9355 | −0.631692 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.52417 | −0.291555 | −0.145777 | − | 0.989317i | \(-0.546568\pi\) | ||||
−0.145777 | + | 0.989317i | \(0.546568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.9289 | 2.73310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0731 | −0.528699 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.0202 | 1.72836 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.8197 | −1.39998 | −0.699988 | − | 0.714155i | \(-0.746811\pi\) | ||||
−0.699988 | + | 0.714155i | \(0.746811\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.413133 | 0.0215068 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 61.3775 | 3.18656 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.13709 | −0.110655 | −0.0553273 | − | 0.998468i | \(-0.517620\pi\) | ||||
−0.0553273 | + | 0.998468i | \(0.517620\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.10465 | 0.160324 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.97124 | −0.153027 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5192 | −0.797167 | −0.398583 | − | 0.917132i | \(-0.630498\pi\) | ||||
−0.398583 | + | 0.917132i | \(0.630498\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8311 | −0.811054 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.7717 | −1.62346 | −0.811730 | − | 0.584033i | \(-0.801474\pi\) | ||||
−0.811730 | + | 0.584033i | \(0.801474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4278 | 0.684346 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.35521 | −0.272221 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.7661 | 1.40780 | 0.703898 | − | 0.710301i | \(-0.251441\pi\) | ||||
0.703898 | + | 0.710301i | \(0.251441\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.1172 | 0.815084 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.80759 | −0.292954 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.40640 | 0.221710 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2186 | 1.21550 | 0.607748 | − | 0.794130i | \(-0.292073\pi\) | ||||
0.607748 | + | 0.794130i | \(0.292073\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39.2346 | −1.96419 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.8639 | 1.84089 | 0.920447 | − | 0.390867i | \(-0.127825\pi\) | ||||
0.920447 | + | 0.390867i | \(0.127825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.90235 | −0.493271 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.99382 | −0.148764 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3147 | 0.511281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.05203 | −0.348700 | −0.174350 | − | 0.984684i | \(-0.555782\pi\) | ||||
−0.174350 | + | 0.984684i | \(0.555782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.6048 | −1.01636 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.472316 | 0.0232411 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.6781 | 0.671433 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.58360 | −0.371371 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.1446 | 1.32610 | 0.663051 | − | 0.748574i | \(-0.269261\pi\) | ||||
0.663051 | + | 0.748574i | \(0.269261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1971 | 1.08182 | 0.540910 | − | 0.841080i | \(-0.318080\pi\) | ||||
0.540910 | + | 0.841080i | \(0.318080\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.47126 | −0.411887 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.1532 | 0.492504 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 66.9494 | 3.23991 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.940010 | 0.0453841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.0366 | 0.627952 | 0.313976 | − | 0.949431i | \(-0.398339\pi\) | ||||
0.313976 | + | 0.949431i | \(0.398339\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.48494 | 0.359703 | 0.179852 | − | 0.983694i | \(-0.442438\pi\) | ||||
0.179852 | + | 0.983694i | \(0.442438\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.11074 | 0.436826 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 52.9810 | 2.53443 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.8500 | −1.52012 | −0.760059 | − | 0.649854i | \(-0.774830\pi\) | ||||
−0.760059 | + | 0.649854i | \(0.774830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.7028 | 0.700131 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.08246 | 0.384009 | 0.192005 | − | 0.981394i | \(-0.438501\pi\) | ||||
0.192005 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.5734 | −1.16489 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7087 | 0.601102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.0405 | −1.74805 | −0.874024 | − | 0.485884i | \(-0.838498\pi\) | ||||
−0.874024 | + | 0.485884i | \(0.838498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.397751 | 0.0187294 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.4023 | 0.676679 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6174 | 0.638394 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4599 | 0.816739 | 0.408370 | − | 0.912817i | \(-0.366097\pi\) | ||||
0.408370 | + | 0.912817i | \(0.366097\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.56202 | 0.119585 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6672 | −0.589972 | −0.294986 | − | 0.955502i | \(-0.595315\pi\) | ||||
−0.294986 | + | 0.955502i | \(0.595315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.9913 | −0.743177 | −0.371588 | − | 0.928398i | \(-0.621187\pi\) | ||||
−0.371588 | + | 0.928398i | \(0.621187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.3637 | 1.40808 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.8847 | −1.42917 | −0.714587 | − | 0.699547i | \(-0.753385\pi\) | ||||
−0.714587 | + | 0.699547i | \(0.753385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.8114 | 2.53096 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.84981 | −0.361700 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.15583 | −0.237065 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.3760 | 1.53139 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.1750 | −0.603243 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.4760 | −0.844188 | −0.422094 | − | 0.906552i | \(-0.638705\pi\) | ||||
−0.422094 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.4603 | 0.476950 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.3067 | −1.33350 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.4120 | −1.51716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9533 | −0.541656 | −0.270828 | − | 0.962628i | \(-0.587297\pi\) | ||||
−0.270828 | + | 0.962628i | \(0.587297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.151488 | 0.00685051 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.63468 | 0.299419 | 0.149709 | − | 0.988730i | \(-0.452166\pi\) | ||||
0.149709 | + | 0.988730i | \(0.452166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.79668 | −0.351145 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.88236 | −0.129553 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −58.3542 | −2.61754 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.3783 | −1.89711 | −0.948557 | − | 0.316605i | \(-0.897457\pi\) | ||||
−0.948557 | + | 0.316605i | \(0.897457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.3222 | −1.08447 | −0.542237 | − | 0.840226i | \(-0.682422\pi\) | ||||
−0.542237 | + | 0.840226i | \(0.682422\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0608 | 0.670197 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0467 | −0.535014 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.02710 | −0.311471 | −0.155735 | − | 0.987799i | \(-0.549775\pi\) | ||||
−0.155735 | + | 0.987799i | \(0.549775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.3820 | 2.27301 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.42193 | 0.371837 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.5440 | −0.949342 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.15587 | −0.358695 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9592 | 0.481055 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.5312 | 1.03092 | 0.515461 | − | 0.856913i | \(-0.327621\pi\) | ||||
0.515461 | + | 0.856913i | \(0.327621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.3371 | −1.89500 | −0.947500 | − | 0.319755i | \(-0.896399\pi\) | ||||
−0.947500 | + | 0.319755i | \(0.896399\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.4620 | −0.805749 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.9843 | −1.13189 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5747 | 0.720638 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.101385 | −0.00439975 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.403367 | 0.0174717 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 44.8283 | 1.93810 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.6334 | 0.631476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.1554 | 0.609715 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0364 | −1.07640 | −0.538201 | − | 0.842817i | \(-0.680896\pi\) | ||||
−0.538201 | + | 0.842817i | \(0.680896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.60022 | −0.197414 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.96763 | 0.169955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.78599 | 0.204634 | 0.102317 | − | 0.994752i | \(-0.467374\pi\) | ||||
0.102317 | + | 0.994752i | \(0.467374\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.3711 | −0.613342 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.6294 | −1.09185 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.85670 | 0.291576 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.0746 | −1.36149 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.00703 | −0.212155 | −0.106077 | − | 0.994358i | \(-0.533829\pi\) | ||||
−0.106077 | + | 0.994358i | \(0.533829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.22862 | −0.221147 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.46663 | 0.104141 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.9366 | −1.55669 | −0.778346 | − | 0.627836i | \(-0.783941\pi\) | ||||
−0.778346 | + | 0.627836i | \(0.783941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.2422 | −1.01988 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.65862 | −0.195644 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.3118 | −1.18689 | −0.593447 | − | 0.804873i | \(-0.702233\pi\) | ||||
−0.593447 | + | 0.804873i | \(0.702233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.56835 | 0.274877 | 0.137438 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137438 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.2571 | −0.720925 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.9305 | 1.03967 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.2317 | −1.38345 | −0.691727 | − | 0.722160i | \(-0.743150\pi\) | ||||
−0.691727 | + | 0.722160i | \(0.743150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.6499 | −0.484154 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.2842 | 0.883018 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.6845 | −0.525339 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.92305 | −0.120853 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5810 | −0.560546 | −0.280273 | − | 0.959920i | \(-0.590425\pi\) | ||||
−0.280273 | + | 0.959920i | \(0.590425\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −85.4161 | −3.51951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.8741 | 0.447300 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.20329 | 0.213674 | 0.106837 | − | 0.994277i | \(-0.465928\pi\) | ||||
0.106837 | + | 0.994277i | \(0.465928\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.7327 | 1.46490 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.11256 | 0.372952 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.2141 | −0.417337 | −0.208668 | − | 0.977986i | \(-0.566913\pi\) | ||||
−0.208668 | + | 0.977986i | \(0.566913\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.4052 | 0.709971 | 0.354986 | − | 0.934872i | \(-0.384486\pi\) | ||||
0.354986 | + | 0.934872i | \(0.384486\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7656 | −0.479132 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.1570 | 1.22606 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.73864 | 0.354691 | 0.177345 | − | 0.984149i | \(-0.443249\pi\) | ||||
0.177345 | + | 0.984149i | \(0.443249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.1770 | 0.574482 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.27101 | −0.334609 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.9839 | 1.13026 | 0.565130 | − | 0.825002i | \(-0.308826\pi\) | ||||
0.565130 | + | 0.825002i | \(0.308826\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.23685 | −0.0498745 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8615 | −1.44373 | −0.721864 | − | 0.692035i | \(-0.756714\pi\) | ||||
−0.721864 | + | 0.692035i | \(0.756714\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.4287 | 1.02207 | 0.511033 | − | 0.859561i | \(-0.329263\pi\) | ||||
0.511033 | + | 0.859561i | \(0.329263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.29084 | 0.252443 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.2381 | −1.53198 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1097 | −1.16439 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.10838 | 0.323817 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.4484 | 1.09444 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.3659 | −1.36808 | −0.684042 | − | 0.729442i | \(-0.739780\pi\) | ||||
−0.684042 | + | 0.729442i | \(0.739780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.1269 | −0.720479 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 47.3956 | 1.88084 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.3552 | 0.568774 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.5261 | 0.495523 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.6147 | −1.09071 | −0.545357 | − | 0.838204i | \(-0.683606\pi\) | ||||
−0.545357 | + | 0.838204i | \(0.683606\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.24094 | −0.0489379 | −0.0244689 | − | 0.999701i | \(-0.507789\pi\) | ||||
−0.0244689 | + | 0.999701i | \(0.507789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.0326 | 0.631281 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.0085 | −0.983186 | −0.491593 | − | 0.870825i | \(-0.663585\pi\) | ||||
−0.491593 | + | 0.870825i | \(0.663585\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.0976106 | −0.00383155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 47.2482 | 1.85180 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.7223 | 1.08486 | 0.542429 | − | 0.840101i | \(-0.317505\pi\) | ||||
0.542429 | + | 0.840101i | \(0.317505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3869 | 0.679363 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0294 | −0.430300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.4052 | 0.405330 | 0.202665 | − | 0.979248i | \(-0.435040\pi\) | ||||
0.202665 | + | 0.979248i | \(0.435040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.4554 | −0.562251 | −0.281126 | − | 0.959671i | \(-0.590708\pi\) | ||||
−0.281126 | + | 0.959671i | \(0.590708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.50146 | 0.0971485 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 117.461 | 4.55496 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1441 | −0.741264 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.2420 | −0.550628 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8360 | −0.534134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.62407 | 0.370981 | 0.185490 | − | 0.982646i | \(-0.440613\pi\) | ||||
0.185490 | + | 0.982646i | \(0.440613\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.96298 | 0.152535 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.4117 | 1.09195 | 0.545974 | − | 0.837802i | \(-0.316160\pi\) | ||||
0.545974 | + | 0.837802i | \(0.316160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.9917 | −1.99526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5377 | 0.403805 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.05896 | −0.117048 | −0.0585239 | − | 0.998286i | \(-0.518639\pi\) | ||||
−0.0585239 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 61.6873 | 2.35695 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.2304 | 0.771838 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.8636 | −0.490064 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0725 | −0.763594 | −0.381797 | − | 0.924246i | \(-0.624695\pi\) | ||||
−0.381797 | + | 0.924246i | \(0.624695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.48518 | −0.170378 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.7040 | 0.861211 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05845 | 0.0400918 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.4478 | 0.886878 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9984 | −0.981947 | −0.490974 | − | 0.871174i | \(-0.663359\pi\) | ||||
−0.490974 | + | 0.871174i | \(0.663359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 90.2291 | 3.40305 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.3615 | 0.955168 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.4358 | 0.881393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.35327 | 0.351270 | 0.175635 | − | 0.984455i | \(-0.443802\pi\) | ||||
0.175635 | + | 0.984455i | \(0.443802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.47183 | −0.0551979 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −63.8024 | −2.38942 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.81423 | −0.105246 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.49855 | 0.317384 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.5227 | −1.36207 | −0.681034 | − | 0.732252i | \(-0.738469\pi\) | ||||
−0.681034 | + | 0.732252i | \(0.738469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.5241 | −1.24850 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.5989 | −0.691701 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0601 | −0.447899 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.4767 | −0.981966 | −0.490983 | − | 0.871169i | \(-0.663362\pi\) | ||||
−0.490983 | + | 0.871169i | \(0.663362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.7201 | −0.507458 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7117 | −1.02355 | −0.511777 | − | 0.859118i | \(-0.671013\pi\) | ||||
−0.511777 | + | 0.859118i | \(0.671013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −44.0175 | −1.62361 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.3275 | −0.417255 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.5867 | 1.30908 | 0.654538 | − | 0.756029i | \(-0.272863\pi\) | ||||
0.654538 | + | 0.756029i | \(0.272863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.22285 | 0.302074 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.8212 | 1.53427 | 0.767135 | − | 0.641485i | \(-0.221681\pi\) | ||||
0.767135 | + | 0.641485i | \(0.221681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.0477 | −1.39396 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.56878 | −0.167163 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 69.7564 | 2.54884 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.9341 | 1.42073 | 0.710363 | − | 0.703836i | \(-0.248531\pi\) | ||||
0.710363 | + | 0.703836i | \(0.248531\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.98372 | −0.108733 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.1179 | −1.56922 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3933 | −0.486787 | −0.243394 | − | 0.969928i | \(-0.578261\pi\) | ||||
−0.243394 | + | 0.969928i | \(0.578261\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.05663 | 0.219842 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.8875 | 1.95342 | 0.976710 | − | 0.214564i | \(-0.0688332\pi\) | ||||
0.976710 | + | 0.214564i | \(0.0688332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.17394 | 0.223512 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.67023 | −0.277318 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0989887 | −0.00357427 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.2334 | −0.621453 | −0.310727 | − | 0.950499i | \(-0.600572\pi\) | ||||
−0.310727 | + | 0.950499i | \(0.600572\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.66532 | 0.168017 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.4756 | −1.81548 | −0.907741 | − | 0.419532i | \(-0.862194\pi\) | ||||
−0.907741 | + | 0.419532i | \(0.862194\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.1930 | −1.44377 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −49.9105 | −1.79053 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.47937 | 0.124662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0597 | 0.431530 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.04318 | −0.108754 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.5009 | 0.838784 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2874 | 1.04398 | 0.521991 | − | 0.852951i | \(-0.325189\pi\) | ||||
0.521991 | + | 0.852951i | \(0.325189\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.4032 | −0.405965 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.7228 | −1.34127 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0314 | −0.498268 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 39.4437 | 1.39892 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.07432 | −0.0380543 | −0.0190272 | − | 0.999819i | \(-0.506057\pi\) | ||||
−0.0190272 | + | 0.999819i | \(0.506057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7035 | −0.767815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.20803 | 0.290016 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.6188 | −0.374730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 87.7389 | 3.09239 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5202 | −0.616741 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.8689 | 0.804028 | 0.402014 | − | 0.915634i | \(-0.368310\pi\) | ||||
0.402014 | + | 0.915634i | \(0.368310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4412 | 0.717788 | 0.358894 | − | 0.933378i | \(-0.383154\pi\) | ||||
0.358894 | + | 0.933378i | \(0.383154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.07499 | −0.142916 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.453527 | −0.0158864 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.1012 | −1.57789 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.54850 | −0.158937 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.3421 | 1.40795 | 0.703974 | − | 0.710226i | \(-0.251407\pi\) | ||||
0.703974 | + | 0.710226i | \(0.251407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.6160 | −1.69465 | −0.847323 | − | 0.531078i | \(-0.821787\pi\) | ||||
−0.847323 | + | 0.531078i | \(0.821787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.81544 | 0.132836 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.6734 | −1.37958 | −0.689790 | − | 0.724009i | \(-0.742297\pi\) | ||||
−0.689790 | + | 0.724009i | \(0.742297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.4157 | 1.64681 | 0.823407 | − | 0.567451i | \(-0.192071\pi\) | ||||
0.823407 | + | 0.567451i | \(0.192071\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.9380 | 0.795710 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.6687 | 1.30514 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.99382 | 0.103606 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.1421 | −0.350562 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.74261 | −0.301828 | −0.150914 | − | 0.988547i | \(-0.548222\pi\) | ||||
−0.150914 | + | 0.988547i | \(0.548222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7391 | −0.680658 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.4485 | −0.428749 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.0658 | 1.24070 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.9267 | 1.61242 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.2448 | −0.729119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.3974 | 2.31035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.82336 | −0.0966701 | −0.0483350 | − | 0.998831i | \(-0.515392\pi\) | ||||
−0.0483350 | + | 0.998831i | \(0.515392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.2138 | −0.862293 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.6895 | −1.35577 | −0.677883 | − | 0.735170i | \(-0.737103\pi\) | ||||
−0.677883 | + | 0.735170i | \(0.737103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.796057 | −0.0271611 | −0.0135805 | − | 0.999908i | \(-0.504323\pi\) | ||||
−0.0135805 | + | 0.999908i | \(0.504323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.92463 | −0.0655912 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.43568 | 0.253113 | 0.126557 | − | 0.991959i | \(-0.459607\pi\) | ||||
0.126557 | + | 0.991959i | \(0.459607\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.8099 | −1.11557 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.4361 | −0.354427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.41703 | −0.0480695 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4875 | −0.389238 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.1603 | 0.377720 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.4634 | −0.488952 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0468 | −0.440558 | −0.220279 | − | 0.975437i | \(-0.570697\pi\) | ||||
−0.220279 | + | 0.975437i | \(0.570697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.52870 | 0.119020 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.0090 | 1.31425 | 0.657123 | − | 0.753783i | \(-0.271773\pi\) | ||||
0.657123 | + | 0.753783i | \(0.271773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.17514 | −0.106852 | −0.0534261 | − | 0.998572i | \(-0.517014\pi\) | ||||
−0.0534261 | + | 0.998572i | \(0.517014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.303530 | 0.0102030 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.6773 | −0.660698 | −0.330349 | − | 0.943859i | \(-0.607166\pi\) | ||||
−0.330349 | + | 0.943859i | \(0.607166\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 73.7513 | 2.47354 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.962769 | 0.0322540 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −71.3444 | −2.38745 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.8097 | −1.46440 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.14213 | 0.205080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.8642 | 1.02938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.7547 | −1.12453 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.9479 | 0.830214 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.7723 | 0.457805 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3941 | −0.444745 | −0.222372 | − | 0.974962i | \(-0.571380\pi\) | ||||
−0.222372 | + | 0.974962i | \(0.571380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.03063 | −0.166855 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.3696 | 0.476085 | 0.238043 | − | 0.971255i | \(-0.423494\pi\) | ||||
0.238043 | + | 0.971255i | \(0.423494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.39868 | −0.145575 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.0245 | 1.42234 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.0554 | 0.893447 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.6199 | −0.548241 | −0.274121 | − | 0.961695i | \(-0.588387\pi\) | ||||
−0.274121 | + | 0.961695i | \(0.588387\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.5946 | −0.513860 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.2300 | 0.402554 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.4577 | 1.39600 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.19615 | 0.236352 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7181 | −0.581313 | −0.290657 | − | 0.956827i | \(-0.593874\pi\) | ||||
−0.290657 | + | 0.956827i | \(0.593874\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 123.826 | 4.05822 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.111395 | −0.00364691 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.38466 | −0.241504 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.4997 | 1.84576 | 0.922882 | − | 0.385083i | \(-0.125827\pi\) | ||||
0.922882 | + | 0.385083i | \(0.125827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.8427 | −0.517008 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.4198 | 0.926460 | 0.463230 | − | 0.886238i | \(-0.346690\pi\) | ||||
0.463230 | + | 0.886238i | \(0.346690\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.59895 | 0.0846335 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.9471 | 0.453699 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.1922 | 0.883628 | 0.441814 | − | 0.897107i | \(-0.354335\pi\) | ||||
0.441814 | + | 0.897107i | \(0.354335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.7687 | −0.349567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.3265 | 0.594276 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0549 | −1.29751 | −0.648753 | − | 0.760999i | \(-0.724709\pi\) | ||||
−0.648753 | + | 0.760999i | \(0.724709\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.6647 | 1.67183 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.92988 | −0.0947095 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 95.9902 | 3.09968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.8622 | 2.31814 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.9736 | −0.482518 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.8778 | 1.12276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.2604 | 0.908795 | 0.454397 | − | 0.890799i | \(-0.349855\pi\) | ||||
0.454397 | + | 0.890799i | \(0.349855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.5771 | 0.693158 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.3946 | 1.84188 | 0.920940 | − | 0.389704i | \(-0.127423\pi\) | ||||
0.920940 | + | 0.389704i | \(0.127423\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.3291 | 1.13260 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.86930 | 0.123917 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.6415 | 1.04429 | 0.522147 | − | 0.852855i | \(-0.325131\pi\) | ||||
0.522147 | + | 0.852855i | \(0.325131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.90244 | 0.252563 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.32527 | −0.0423127 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.11976 | −0.195190 | −0.0975950 | − | 0.995226i | \(-0.531115\pi\) | ||||
−0.0975950 | + | 0.995226i | \(0.531115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.5551 | −1.03729 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.4644 | 1.25617 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.6888 | −1.07124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.2483 | −0.992636 | −0.496318 | − | 0.868141i | \(-0.665315\pi\) | ||||
−0.496318 | + | 0.868141i | \(0.665315\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.26802 | −0.198910 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.2814 | −0.864878 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.4045 | 0.487866 | 0.243933 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243933 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.7136 | 0.338963 |
(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 | 4008.2.a.i.1.2 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.2 | 9 | 4.3 | odd | 2 |