Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.902479\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.902479 | −0.638149 | −0.319075 | − | 0.947730i | \(-0.603372\pi\) | ||||
−0.319075 | + | 0.947730i | \(0.603372\pi\) | |||||||
\(3\) | −3.32518 | −1.91980 | −0.959898 | − | 0.280349i | \(-0.909550\pi\) | ||||
−0.959898 | + | 0.280349i | \(0.909550\pi\) | |||||||
\(4\) | −1.18553 | −0.592766 | ||||||||
\(5\) | −0.938362 | −0.419648 | −0.209824 | − | 0.977739i | \(-0.567289\pi\) | ||||
−0.209824 | + | 0.977739i | \(0.567289\pi\) | |||||||
\(6\) | 3.00091 | 1.22512 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.87488 | 1.01642 | ||||||||
\(9\) | 8.05685 | 2.68562 | ||||||||
\(10\) | 0.846852 | 0.267798 | ||||||||
\(11\) | 5.46037 | 1.64636 | 0.823181 | − | 0.567779i | \(-0.192197\pi\) | ||||
0.823181 | + | 0.567779i | \(0.192197\pi\) | |||||||
\(12\) | 3.94211 | 1.13799 | ||||||||
\(13\) | −2.52551 | −0.700449 | −0.350225 | − | 0.936666i | \(-0.613895\pi\) | ||||
−0.350225 | + | 0.936666i | \(0.613895\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.12023 | 0.805639 | ||||||||
\(16\) | −0.223453 | −0.0558632 | ||||||||
\(17\) | 6.71133 | 1.62774 | 0.813868 | − | 0.581049i | \(-0.197358\pi\) | ||||
0.813868 | + | 0.581049i | \(0.197358\pi\) | |||||||
\(18\) | −7.27114 | −1.71382 | ||||||||
\(19\) | 0.857408 | 0.196703 | 0.0983514 | − | 0.995152i | \(-0.468643\pi\) | ||||
0.0983514 | + | 0.995152i | \(0.468643\pi\) | |||||||
\(20\) | 1.11246 | 0.248753 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.92787 | −1.05062 | ||||||||
\(23\) | 4.76683 | 0.993953 | 0.496977 | − | 0.867764i | \(-0.334443\pi\) | ||||
0.496977 | + | 0.867764i | \(0.334443\pi\) | |||||||
\(24\) | −9.55949 | −1.95132 | ||||||||
\(25\) | −4.11948 | −0.823895 | ||||||||
\(26\) | 2.27922 | 0.446991 | ||||||||
\(27\) | −16.8150 | −3.23604 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.28519 | 0.610045 | 0.305023 | − | 0.952345i | \(-0.401336\pi\) | ||||
0.305023 | + | 0.952345i | \(0.401336\pi\) | |||||||
\(30\) | −2.81594 | −0.514118 | ||||||||
\(31\) | 0.119237 | 0.0214157 | 0.0107078 | − | 0.999943i | \(-0.496592\pi\) | ||||
0.0107078 | + | 0.999943i | \(0.496592\pi\) | |||||||
\(32\) | −5.54809 | −0.980773 | ||||||||
\(33\) | −18.1567 | −3.16068 | ||||||||
\(34\) | −6.05684 | −1.03874 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.55165 | −1.59194 | ||||||||
\(37\) | −3.81897 | −0.627835 | −0.313917 | − | 0.949450i | \(-0.601642\pi\) | ||||
−0.313917 | + | 0.949450i | \(0.601642\pi\) | |||||||
\(38\) | −0.773793 | −0.125526 | ||||||||
\(39\) | 8.39777 | 1.34472 | ||||||||
\(40\) | −2.69767 | −0.426540 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.64508 | 0.250873 | 0.125436 | − | 0.992102i | \(-0.459967\pi\) | ||||
0.125436 | + | 0.992102i | \(0.459967\pi\) | |||||||
\(44\) | −6.47344 | −0.975907 | ||||||||
\(45\) | −7.56024 | −1.12701 | ||||||||
\(46\) | −4.30197 | −0.634290 | ||||||||
\(47\) | 4.73681 | 0.690935 | 0.345468 | − | 0.938431i | \(-0.387720\pi\) | ||||
0.345468 | + | 0.938431i | \(0.387720\pi\) | |||||||
\(48\) | 0.743022 | 0.107246 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.71774 | 0.525768 | ||||||||
\(51\) | −22.3164 | −3.12492 | ||||||||
\(52\) | 2.99407 | 0.415202 | ||||||||
\(53\) | 2.24391 | 0.308224 | 0.154112 | − | 0.988053i | \(-0.450748\pi\) | ||||
0.154112 | + | 0.988053i | \(0.450748\pi\) | |||||||
\(54\) | 15.1752 | 2.06508 | ||||||||
\(55\) | −5.12380 | −0.690893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.85104 | −0.377629 | ||||||||
\(58\) | −2.96482 | −0.389300 | ||||||||
\(59\) | 4.44654 | 0.578890 | 0.289445 | − | 0.957195i | \(-0.406529\pi\) | ||||
0.289445 | + | 0.957195i | \(0.406529\pi\) | |||||||
\(60\) | −3.69913 | −0.477555 | ||||||||
\(61\) | 11.9605 | 1.53138 | 0.765690 | − | 0.643210i | \(-0.222398\pi\) | ||||
0.765690 | + | 0.643210i | \(0.222398\pi\) | |||||||
\(62\) | −0.107609 | −0.0136664 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.45394 | 0.681743 | ||||||||
\(65\) | 2.36984 | 0.293942 | ||||||||
\(66\) | 16.3861 | 2.01699 | ||||||||
\(67\) | −11.7311 | −1.43318 | −0.716591 | − | 0.697493i | \(-0.754299\pi\) | ||||
−0.716591 | + | 0.697493i | \(0.754299\pi\) | |||||||
\(68\) | −7.95649 | −0.964867 | ||||||||
\(69\) | −15.8506 | −1.90819 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.78432 | 1.16119 | 0.580593 | − | 0.814194i | \(-0.302821\pi\) | ||||
0.580593 | + | 0.814194i | \(0.302821\pi\) | |||||||
\(72\) | 23.1624 | 2.72972 | ||||||||
\(73\) | −3.71532 | −0.434845 | −0.217422 | − | 0.976078i | \(-0.569765\pi\) | ||||
−0.217422 | + | 0.976078i | \(0.569765\pi\) | |||||||
\(74\) | 3.44654 | 0.400652 | ||||||||
\(75\) | 13.6980 | 1.58171 | ||||||||
\(76\) | −1.01648 | −0.116599 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.57881 | −0.858132 | ||||||||
\(79\) | −2.81292 | −0.316478 | −0.158239 | − | 0.987401i | \(-0.550582\pi\) | ||||
−0.158239 | + | 0.987401i | \(0.550582\pi\) | |||||||
\(80\) | 0.209680 | 0.0234429 | ||||||||
\(81\) | 31.7423 | 3.52692 | ||||||||
\(82\) | −0.902479 | −0.0996622 | ||||||||
\(83\) | 3.41464 | 0.374805 | 0.187403 | − | 0.982283i | \(-0.439993\pi\) | ||||
0.187403 | + | 0.982283i | \(0.439993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.29766 | −0.683077 | ||||||||
\(86\) | −1.48465 | −0.160094 | ||||||||
\(87\) | −10.9239 | −1.17116 | ||||||||
\(88\) | 15.6979 | 1.67340 | ||||||||
\(89\) | −14.2417 | −1.50962 | −0.754808 | − | 0.655946i | \(-0.772270\pi\) | ||||
−0.754808 | + | 0.655946i | \(0.772270\pi\) | |||||||
\(90\) | 6.82296 | 0.719203 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.65123 | −0.589181 | ||||||||
\(93\) | −0.396486 | −0.0411137 | ||||||||
\(94\) | −4.27487 | −0.440920 | ||||||||
\(95\) | −0.804559 | −0.0825460 | ||||||||
\(96\) | 18.4484 | 1.88288 | ||||||||
\(97\) | −8.40546 | −0.853446 | −0.426723 | − | 0.904382i | \(-0.640332\pi\) | ||||
−0.426723 | + | 0.904382i | \(0.640332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43.9934 | 4.42150 | ||||||||
\(100\) | 4.88377 | 0.488377 | ||||||||
\(101\) | −6.27309 | −0.624196 | −0.312098 | − | 0.950050i | \(-0.601032\pi\) | ||||
−0.312098 | + | 0.950050i | \(0.601032\pi\) | |||||||
\(102\) | 20.1401 | 1.99417 | ||||||||
\(103\) | 8.74565 | 0.861735 | 0.430867 | − | 0.902415i | \(-0.358208\pi\) | ||||
0.430867 | + | 0.902415i | \(0.358208\pi\) | |||||||
\(104\) | −7.26051 | −0.711952 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.02508 | −0.196693 | ||||||||
\(107\) | −10.5229 | −1.01729 | −0.508643 | − | 0.860978i | \(-0.669853\pi\) | ||||
−0.508643 | + | 0.860978i | \(0.669853\pi\) | |||||||
\(108\) | 19.9347 | 1.91821 | ||||||||
\(109\) | −3.24852 | −0.311152 | −0.155576 | − | 0.987824i | \(-0.549723\pi\) | ||||
−0.155576 | + | 0.987824i | \(0.549723\pi\) | |||||||
\(110\) | 4.62412 | 0.440893 | ||||||||
\(111\) | 12.6988 | 1.20531 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.20493 | 0.395566 | 0.197783 | − | 0.980246i | \(-0.436626\pi\) | ||||
0.197783 | + | 0.980246i | \(0.436626\pi\) | |||||||
\(114\) | 2.57300 | 0.240984 | ||||||||
\(115\) | −4.47301 | −0.417111 | ||||||||
\(116\) | −3.89470 | −0.361614 | ||||||||
\(117\) | −20.3476 | −1.88114 | ||||||||
\(118\) | −4.01291 | −0.369418 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.97026 | 0.818869 | ||||||||
\(121\) | 18.8156 | 1.71051 | ||||||||
\(122\) | −10.7941 | −0.977248 | ||||||||
\(123\) | −3.32518 | −0.299822 | ||||||||
\(124\) | −0.141360 | −0.0126945 | ||||||||
\(125\) | 8.55737 | 0.765394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.36861 | 0.565123 | 0.282561 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282561 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(128\) | 6.17411 | 0.545720 | ||||||||
\(129\) | −5.47020 | −0.481624 | ||||||||
\(130\) | −2.13873 | −0.187579 | ||||||||
\(131\) | 6.50705 | 0.568524 | 0.284262 | − | 0.958747i | \(-0.408251\pi\) | ||||
0.284262 | + | 0.958747i | \(0.408251\pi\) | |||||||
\(132\) | 21.5254 | 1.87354 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.5871 | 0.914584 | ||||||||
\(135\) | 15.7785 | 1.35800 | ||||||||
\(136\) | 19.2942 | 1.65447 | ||||||||
\(137\) | 13.2635 | 1.13318 | 0.566588 | − | 0.824001i | \(-0.308263\pi\) | ||||
0.566588 | + | 0.824001i | \(0.308263\pi\) | |||||||
\(138\) | 14.3048 | 1.21771 | ||||||||
\(139\) | 5.17790 | 0.439184 | 0.219592 | − | 0.975592i | \(-0.429527\pi\) | ||||
0.219592 | + | 0.975592i | \(0.429527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.7508 | −1.32645 | ||||||||
\(142\) | −8.83015 | −0.741010 | ||||||||
\(143\) | −13.7902 | −1.15319 | ||||||||
\(144\) | −1.80033 | −0.150027 | ||||||||
\(145\) | −3.08270 | −0.256004 | ||||||||
\(146\) | 3.35299 | 0.277496 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.52751 | 0.372159 | ||||||||
\(149\) | 3.67578 | 0.301132 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(150\) | −12.3622 | −1.00937 | ||||||||
\(151\) | 14.2667 | 1.16101 | 0.580505 | − | 0.814257i | \(-0.302855\pi\) | ||||
0.580505 | + | 0.814257i | \(0.302855\pi\) | |||||||
\(152\) | 2.46494 | 0.199933 | ||||||||
\(153\) | 54.0722 | 4.37148 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.111888 | −0.00898705 | ||||||||
\(156\) | −9.95582 | −0.797104 | ||||||||
\(157\) | 9.04941 | 0.722222 | 0.361111 | − | 0.932523i | \(-0.382398\pi\) | ||||
0.361111 | + | 0.932523i | \(0.382398\pi\) | |||||||
\(158\) | 2.53860 | 0.201960 | ||||||||
\(159\) | −7.46140 | −0.591727 | ||||||||
\(160\) | 5.20612 | 0.411580 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −28.6468 | −2.25070 | ||||||||
\(163\) | −8.89264 | −0.696525 | −0.348263 | − | 0.937397i | \(-0.613228\pi\) | ||||
−0.348263 | + | 0.937397i | \(0.613228\pi\) | |||||||
\(164\) | −1.18553 | −0.0925744 | ||||||||
\(165\) | 17.0376 | 1.32637 | ||||||||
\(166\) | −3.08164 | −0.239182 | ||||||||
\(167\) | 7.46298 | 0.577503 | 0.288751 | − | 0.957404i | \(-0.406760\pi\) | ||||
0.288751 | + | 0.957404i | \(0.406760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.62182 | −0.509371 | ||||||||
\(170\) | 5.68350 | 0.435905 | ||||||||
\(171\) | 6.90801 | 0.528269 | ||||||||
\(172\) | −1.95030 | −0.148709 | ||||||||
\(173\) | −15.0207 | −1.14200 | −0.571001 | − | 0.820949i | \(-0.693445\pi\) | ||||
−0.571001 | + | 0.820949i | \(0.693445\pi\) | |||||||
\(174\) | 9.85857 | 0.747377 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.22013 | −0.0919711 | ||||||||
\(177\) | −14.7856 | −1.11135 | ||||||||
\(178\) | 12.8528 | 0.963360 | ||||||||
\(179\) | −17.9193 | −1.33935 | −0.669677 | − | 0.742653i | \(-0.733567\pi\) | ||||
−0.669677 | + | 0.742653i | \(0.733567\pi\) | |||||||
\(180\) | 8.96290 | 0.668055 | ||||||||
\(181\) | −24.9578 | −1.85510 | −0.927548 | − | 0.373705i | \(-0.878087\pi\) | ||||
−0.927548 | + | 0.373705i | \(0.878087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −39.7707 | −2.93994 | ||||||||
\(184\) | 13.7041 | 1.01028 | ||||||||
\(185\) | 3.58358 | 0.263470 | ||||||||
\(186\) | 0.357821 | 0.0262367 | ||||||||
\(187\) | 36.6463 | 2.67984 | ||||||||
\(188\) | −5.61564 | −0.409563 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.726098 | 0.0526767 | ||||||||
\(191\) | 16.3014 | 1.17952 | 0.589762 | − | 0.807577i | \(-0.299221\pi\) | ||||
0.589762 | + | 0.807577i | \(0.299221\pi\) | |||||||
\(192\) | −18.1354 | −1.30881 | ||||||||
\(193\) | −9.74950 | −0.701784 | −0.350892 | − | 0.936416i | \(-0.614122\pi\) | ||||
−0.350892 | + | 0.936416i | \(0.614122\pi\) | |||||||
\(194\) | 7.58576 | 0.544626 | ||||||||
\(195\) | −7.88015 | −0.564309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.4370 | −1.74106 | −0.870531 | − | 0.492114i | \(-0.836224\pi\) | ||||
−0.870531 | + | 0.492114i | \(0.836224\pi\) | |||||||
\(198\) | −39.7031 | −2.82158 | ||||||||
\(199\) | −4.93046 | −0.349511 | −0.174756 | − | 0.984612i | \(-0.555914\pi\) | ||||
−0.174756 | + | 0.984612i | \(0.555914\pi\) | |||||||
\(200\) | −11.8430 | −0.837425 | ||||||||
\(201\) | 39.0081 | 2.75142 | ||||||||
\(202\) | 5.66133 | 0.398330 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 26.4568 | 1.85235 | ||||||||
\(205\) | −0.938362 | −0.0655380 | ||||||||
\(206\) | −7.89277 | −0.549915 | ||||||||
\(207\) | 38.4057 | 2.66938 | ||||||||
\(208\) | 0.564331 | 0.0391293 | ||||||||
\(209\) | 4.68176 | 0.323844 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.1561 | 1.86950 | 0.934751 | − | 0.355303i | \(-0.115622\pi\) | ||||
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(212\) | −2.66022 | −0.182705 | ||||||||
\(213\) | −32.5347 | −2.22924 | ||||||||
\(214\) | 9.49668 | 0.649180 | ||||||||
\(215\) | −1.54368 | −0.105278 | ||||||||
\(216\) | −48.3409 | −3.28918 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.93172 | 0.198561 | ||||||||
\(219\) | 12.3541 | 0.834813 | ||||||||
\(220\) | 6.07442 | 0.409538 | ||||||||
\(221\) | −16.9495 | −1.14015 | ||||||||
\(222\) | −11.4604 | −0.769171 | ||||||||
\(223\) | −8.74237 | −0.585432 | −0.292716 | − | 0.956199i | \(-0.594559\pi\) | ||||
−0.292716 | + | 0.956199i | \(0.594559\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −33.1900 | −2.21267 | ||||||||
\(226\) | −3.79486 | −0.252430 | ||||||||
\(227\) | 14.6898 | 0.975000 | 0.487500 | − | 0.873123i | \(-0.337909\pi\) | ||||
0.487500 | + | 0.873123i | \(0.337909\pi\) | |||||||
\(228\) | 3.38000 | 0.223846 | ||||||||
\(229\) | −5.30412 | −0.350506 | −0.175253 | − | 0.984523i | \(-0.556074\pi\) | ||||
−0.175253 | + | 0.984523i | \(0.556074\pi\) | |||||||
\(230\) | 4.03680 | 0.266179 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.44453 | 0.620064 | ||||||||
\(233\) | −4.42564 | −0.289933 | −0.144967 | − | 0.989437i | \(-0.546307\pi\) | ||||
−0.144967 | + | 0.989437i | \(0.546307\pi\) | |||||||
\(234\) | 18.3633 | 1.20045 | ||||||||
\(235\) | −4.44484 | −0.289950 | ||||||||
\(236\) | −5.27151 | −0.343146 | ||||||||
\(237\) | 9.35347 | 0.607573 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.685835 | −0.0443630 | −0.0221815 | − | 0.999754i | \(-0.507061\pi\) | ||||
−0.0221815 | + | 0.999754i | \(0.507061\pi\) | |||||||
\(240\) | −0.697223 | −0.0450056 | ||||||||
\(241\) | 8.86786 | 0.571229 | 0.285614 | − | 0.958345i | \(-0.407802\pi\) | ||||
0.285614 | + | 0.958345i | \(0.407802\pi\) | |||||||
\(242\) | −16.9807 | −1.09156 | ||||||||
\(243\) | −55.1041 | −3.53493 | ||||||||
\(244\) | −14.1795 | −0.907749 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.00091 | 0.191331 | ||||||||
\(247\) | −2.16539 | −0.137780 | ||||||||
\(248\) | 0.342793 | 0.0217674 | ||||||||
\(249\) | −11.3543 | −0.719550 | ||||||||
\(250\) | −7.72285 | −0.488436 | ||||||||
\(251\) | 3.42941 | 0.216463 | 0.108231 | − | 0.994126i | \(-0.465481\pi\) | ||||
0.108231 | + | 0.994126i | \(0.465481\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.0287 | 1.63641 | ||||||||
\(254\) | −5.74754 | −0.360633 | ||||||||
\(255\) | 20.9409 | 1.31137 | ||||||||
\(256\) | −16.4799 | −1.02999 | ||||||||
\(257\) | 15.2304 | 0.950048 | 0.475024 | − | 0.879973i | \(-0.342439\pi\) | ||||
0.475024 | + | 0.879973i | \(0.342439\pi\) | |||||||
\(258\) | 4.93674 | 0.307348 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.80952 | −0.174239 | ||||||||
\(261\) | 26.4683 | 1.63835 | ||||||||
\(262\) | −5.87248 | −0.362803 | ||||||||
\(263\) | −12.2741 | −0.756852 | −0.378426 | − | 0.925632i | \(-0.623535\pi\) | ||||
−0.378426 | + | 0.925632i | \(0.623535\pi\) | |||||||
\(264\) | −52.1983 | −3.21258 | ||||||||
\(265\) | −2.10560 | −0.129346 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 47.3562 | 2.89815 | ||||||||
\(268\) | 13.9076 | 0.849541 | ||||||||
\(269\) | 12.8300 | 0.782258 | 0.391129 | − | 0.920336i | \(-0.372085\pi\) | ||||
0.391129 | + | 0.920336i | \(0.372085\pi\) | |||||||
\(270\) | −14.2398 | −0.866606 | ||||||||
\(271\) | 17.9718 | 1.09171 | 0.545854 | − | 0.837881i | \(-0.316205\pi\) | ||||
0.545854 | + | 0.837881i | \(0.316205\pi\) | |||||||
\(272\) | −1.49967 | −0.0909306 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.9700 | −0.723135 | ||||||||
\(275\) | −22.4939 | −1.35643 | ||||||||
\(276\) | 18.7914 | 1.13111 | ||||||||
\(277\) | −0.834736 | −0.0501544 | −0.0250772 | − | 0.999686i | \(-0.507983\pi\) | ||||
−0.0250772 | + | 0.999686i | \(0.507983\pi\) | |||||||
\(278\) | −4.67295 | −0.280265 | ||||||||
\(279\) | 0.960678 | 0.0575143 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.96703 | 0.355963 | 0.177982 | − | 0.984034i | \(-0.443043\pi\) | ||||
0.177982 | + | 0.984034i | \(0.443043\pi\) | |||||||
\(282\) | 14.2147 | 0.846476 | ||||||||
\(283\) | 18.4158 | 1.09470 | 0.547352 | − | 0.836902i | \(-0.315636\pi\) | ||||
0.547352 | + | 0.836902i | \(0.315636\pi\) | |||||||
\(284\) | −11.5996 | −0.688311 | ||||||||
\(285\) | 2.67531 | 0.158472 | ||||||||
\(286\) | 12.4454 | 0.735909 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −44.7001 | −2.63398 | ||||||||
\(289\) | 28.0420 | 1.64953 | ||||||||
\(290\) | 2.78207 | 0.163369 | ||||||||
\(291\) | 27.9497 | 1.63844 | ||||||||
\(292\) | 4.40462 | 0.257761 | ||||||||
\(293\) | −18.3646 | −1.07287 | −0.536435 | − | 0.843941i | \(-0.680229\pi\) | ||||
−0.536435 | + | 0.843941i | \(0.680229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.17246 | −0.242930 | ||||||||
\(296\) | −10.9791 | −0.638145 | ||||||||
\(297\) | −91.8158 | −5.32770 | ||||||||
\(298\) | −3.31732 | −0.192167 | ||||||||
\(299\) | −12.0387 | −0.696214 | ||||||||
\(300\) | −16.2394 | −0.937584 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.8754 | −0.740897 | ||||||||
\(303\) | 20.8592 | 1.19833 | ||||||||
\(304\) | −0.191590 | −0.0109885 | ||||||||
\(305\) | −11.2232 | −0.642640 | ||||||||
\(306\) | −48.7990 | −2.78965 | ||||||||
\(307\) | 16.8758 | 0.963153 | 0.481577 | − | 0.876404i | \(-0.340064\pi\) | ||||
0.481577 | + | 0.876404i | \(0.340064\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.0809 | −1.65436 | ||||||||
\(310\) | 0.100976 | 0.00573508 | ||||||||
\(311\) | 10.4537 | 0.592775 | 0.296387 | − | 0.955068i | \(-0.404218\pi\) | ||||
0.296387 | + | 0.955068i | \(0.404218\pi\) | |||||||
\(312\) | 24.1425 | 1.36680 | ||||||||
\(313\) | −6.26929 | −0.354361 | −0.177180 | − | 0.984178i | \(-0.556698\pi\) | ||||
−0.177180 | + | 0.984178i | \(0.556698\pi\) | |||||||
\(314\) | −8.16691 | −0.460885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.33480 | 0.187597 | ||||||||
\(317\) | −26.1750 | −1.47013 | −0.735066 | − | 0.677995i | \(-0.762849\pi\) | ||||
−0.735066 | + | 0.677995i | \(0.762849\pi\) | |||||||
\(318\) | 6.73376 | 0.377610 | ||||||||
\(319\) | 17.9384 | 1.00436 | ||||||||
\(320\) | −5.11777 | −0.286092 | ||||||||
\(321\) | 34.9905 | 1.95298 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.75435 | 0.320181 | ||||||||
\(324\) | −37.6315 | −2.09064 | ||||||||
\(325\) | 10.4038 | 0.577097 | ||||||||
\(326\) | 8.02542 | 0.444487 | ||||||||
\(327\) | 10.8019 | 0.597349 | ||||||||
\(328\) | 2.87488 | 0.158738 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −15.3761 | −0.846424 | ||||||||
\(331\) | 7.35150 | 0.404075 | 0.202037 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202037 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(332\) | −4.04816 | −0.222172 | ||||||||
\(333\) | −30.7689 | −1.68612 | ||||||||
\(334\) | −6.73518 | −0.368533 | ||||||||
\(335\) | 11.0080 | 0.601432 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.58075 | −0.0861092 | −0.0430546 | − | 0.999073i | \(-0.513709\pi\) | ||||
−0.0430546 | + | 0.999073i | \(0.513709\pi\) | |||||||
\(338\) | 5.97606 | 0.325055 | ||||||||
\(339\) | −13.9822 | −0.759407 | ||||||||
\(340\) | 7.46607 | 0.404904 | ||||||||
\(341\) | 0.651080 | 0.0352580 | ||||||||
\(342\) | −6.23433 | −0.337114 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.72940 | 0.254992 | ||||||||
\(345\) | 14.8736 | 0.800767 | ||||||||
\(346\) | 13.5559 | 0.728768 | ||||||||
\(347\) | 21.8834 | 1.17476 | 0.587382 | − | 0.809310i | \(-0.300159\pi\) | ||||
0.587382 | + | 0.809310i | \(0.300159\pi\) | |||||||
\(348\) | 12.9506 | 0.694225 | ||||||||
\(349\) | 5.31231 | 0.284362 | 0.142181 | − | 0.989841i | \(-0.454589\pi\) | ||||
0.142181 | + | 0.989841i | \(0.454589\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 42.4663 | 2.26668 | ||||||||
\(352\) | −30.2946 | −1.61471 | ||||||||
\(353\) | 25.5285 | 1.35874 | 0.679371 | − | 0.733795i | \(-0.262253\pi\) | ||||
0.679371 | + | 0.733795i | \(0.262253\pi\) | |||||||
\(354\) | 13.3437 | 0.709207 | ||||||||
\(355\) | −9.18124 | −0.487289 | ||||||||
\(356\) | 16.8840 | 0.894848 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.1718 | 0.854708 | ||||||||
\(359\) | 20.2278 | 1.06758 | 0.533792 | − | 0.845616i | \(-0.320766\pi\) | ||||
0.533792 | + | 0.845616i | \(0.320766\pi\) | |||||||
\(360\) | −21.7348 | −1.14552 | ||||||||
\(361\) | −18.2649 | −0.961308 | ||||||||
\(362\) | 22.5239 | 1.18383 | ||||||||
\(363\) | −62.5653 | −3.28383 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.48631 | 0.182482 | ||||||||
\(366\) | 35.8922 | 1.87612 | ||||||||
\(367\) | −32.6414 | −1.70387 | −0.851934 | − | 0.523649i | \(-0.824570\pi\) | ||||
−0.851934 | + | 0.523649i | \(0.824570\pi\) | |||||||
\(368\) | −1.06516 | −0.0555254 | ||||||||
\(369\) | 8.05685 | 0.419423 | ||||||||
\(370\) | −3.23410 | −0.168133 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.470047 | 0.0243708 | ||||||||
\(373\) | −8.84603 | −0.458030 | −0.229015 | − | 0.973423i | \(-0.573550\pi\) | ||||
−0.229015 | + | 0.973423i | \(0.573550\pi\) | |||||||
\(374\) | −33.0725 | −1.71014 | ||||||||
\(375\) | −28.4548 | −1.46940 | ||||||||
\(376\) | 13.6177 | 0.702282 | ||||||||
\(377\) | −8.29678 | −0.427306 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5565 | 0.542252 | 0.271126 | − | 0.962544i | \(-0.412604\pi\) | ||||
0.271126 | + | 0.962544i | \(0.412604\pi\) | |||||||
\(380\) | 0.953830 | 0.0489304 | ||||||||
\(381\) | −21.1768 | −1.08492 | ||||||||
\(382\) | −14.7116 | −0.752713 | ||||||||
\(383\) | 24.8543 | 1.27000 | 0.634998 | − | 0.772514i | \(-0.281001\pi\) | ||||
0.634998 | + | 0.772514i | \(0.281001\pi\) | |||||||
\(384\) | −20.5301 | −1.04767 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.79872 | 0.447843 | ||||||||
\(387\) | 13.2542 | 0.673747 | ||||||||
\(388\) | 9.96494 | 0.505893 | ||||||||
\(389\) | 7.24246 | 0.367207 | 0.183604 | − | 0.983000i | \(-0.441224\pi\) | ||||
0.183604 | + | 0.983000i | \(0.441224\pi\) | |||||||
\(390\) | 7.11167 | 0.360113 | ||||||||
\(391\) | 31.9918 | 1.61789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.6372 | −1.09145 | ||||||||
\(394\) | 22.0538 | 1.11106 | ||||||||
\(395\) | 2.63953 | 0.132809 | ||||||||
\(396\) | −52.1555 | −2.62091 | ||||||||
\(397\) | −34.7019 | −1.74164 | −0.870819 | − | 0.491603i | \(-0.836411\pi\) | ||||
−0.870819 | + | 0.491603i | \(0.836411\pi\) | |||||||
\(398\) | 4.44964 | 0.223040 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.920509 | 0.0460254 | ||||||||
\(401\) | 18.7650 | 0.937080 | 0.468540 | − | 0.883442i | \(-0.344780\pi\) | ||||
0.468540 | + | 0.883442i | \(0.344780\pi\) | |||||||
\(402\) | −35.2040 | −1.75582 | ||||||||
\(403\) | −0.301135 | −0.0150006 | ||||||||
\(404\) | 7.43694 | 0.370002 | ||||||||
\(405\) | −29.7858 | −1.48007 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.8530 | −1.03364 | ||||||||
\(408\) | −64.1569 | −3.17624 | ||||||||
\(409\) | 29.6476 | 1.46598 | 0.732989 | − | 0.680241i | \(-0.238125\pi\) | ||||
0.732989 | + | 0.680241i | \(0.238125\pi\) | |||||||
\(410\) | 0.846852 | 0.0418230 | ||||||||
\(411\) | −44.1035 | −2.17547 | ||||||||
\(412\) | −10.3682 | −0.510807 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −34.6603 | −1.70346 | ||||||||
\(415\) | −3.20417 | −0.157286 | ||||||||
\(416\) | 14.0117 | 0.686982 | ||||||||
\(417\) | −17.2175 | −0.843144 | ||||||||
\(418\) | −4.22519 | −0.206661 | ||||||||
\(419\) | −8.62323 | −0.421273 | −0.210636 | − | 0.977564i | \(-0.567554\pi\) | ||||
−0.210636 | + | 0.977564i | \(0.567554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6599 | 0.568267 | 0.284134 | − | 0.958785i | \(-0.408294\pi\) | ||||
0.284134 | + | 0.958785i | \(0.408294\pi\) | |||||||
\(422\) | −24.5078 | −1.19302 | ||||||||
\(423\) | 38.1638 | 1.85559 | ||||||||
\(424\) | 6.45095 | 0.313286 | ||||||||
\(425\) | −27.6472 | −1.34108 | ||||||||
\(426\) | 29.3619 | 1.42259 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.4752 | 0.603012 | ||||||||
\(429\) | 45.8549 | 2.21390 | ||||||||
\(430\) | 1.39314 | 0.0671832 | ||||||||
\(431\) | −28.5212 | −1.37382 | −0.686910 | − | 0.726743i | \(-0.741033\pi\) | ||||
−0.686910 | + | 0.726743i | \(0.741033\pi\) | |||||||
\(432\) | 3.75735 | 0.180776 | ||||||||
\(433\) | −6.13071 | −0.294623 | −0.147312 | − | 0.989090i | \(-0.547062\pi\) | ||||
−0.147312 | + | 0.989090i | \(0.547062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.2506 | 0.491476 | ||||||||
\(436\) | 3.85123 | 0.184440 | ||||||||
\(437\) | 4.08712 | 0.195514 | ||||||||
\(438\) | −11.1493 | −0.532735 | ||||||||
\(439\) | 23.3280 | 1.11338 | 0.556692 | − | 0.830719i | \(-0.312070\pi\) | ||||
0.556692 | + | 0.830719i | \(0.312070\pi\) | |||||||
\(440\) | −14.7303 | −0.702239 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.2966 | 0.727584 | ||||||||
\(443\) | −22.2285 | −1.05611 | −0.528053 | − | 0.849211i | \(-0.677078\pi\) | ||||
−0.528053 | + | 0.849211i | \(0.677078\pi\) | |||||||
\(444\) | −15.0548 | −0.714469 | ||||||||
\(445\) | 13.3639 | 0.633507 | ||||||||
\(446\) | 7.88981 | 0.373593 | ||||||||
\(447\) | −12.2227 | −0.578112 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.6146 | −0.548126 | −0.274063 | − | 0.961712i | \(-0.588368\pi\) | ||||
−0.274063 | + | 0.961712i | \(0.588368\pi\) | |||||||
\(450\) | 29.9533 | 1.41201 | ||||||||
\(451\) | 5.46037 | 0.257119 | ||||||||
\(452\) | −4.98507 | −0.234478 | ||||||||
\(453\) | −47.4395 | −2.22890 | ||||||||
\(454\) | −13.2573 | −0.622195 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.19639 | −0.383831 | ||||||||
\(457\) | −3.42393 | −0.160165 | −0.0800823 | − | 0.996788i | \(-0.525518\pi\) | ||||
−0.0800823 | + | 0.996788i | \(0.525518\pi\) | |||||||
\(458\) | 4.78685 | 0.223675 | ||||||||
\(459\) | −112.851 | −5.26742 | ||||||||
\(460\) | 5.30290 | 0.247249 | ||||||||
\(461\) | 9.15435 | 0.426360 | 0.213180 | − | 0.977013i | \(-0.431618\pi\) | ||||
0.213180 | + | 0.977013i | \(0.431618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.14841 | 0.192793 | 0.0963965 | − | 0.995343i | \(-0.469268\pi\) | ||||
0.0963965 | + | 0.995343i | \(0.469268\pi\) | |||||||
\(464\) | −0.734086 | −0.0340791 | ||||||||
\(465\) | 0.372048 | 0.0172533 | ||||||||
\(466\) | 3.99405 | 0.185021 | ||||||||
\(467\) | −3.34964 | −0.155003 | −0.0775014 | − | 0.996992i | \(-0.524694\pi\) | ||||
−0.0775014 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(468\) | 24.1227 | 1.11507 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.01138 | 0.185031 | ||||||||
\(471\) | −30.0910 | −1.38652 | ||||||||
\(472\) | 12.7832 | 0.588396 | ||||||||
\(473\) | 8.98275 | 0.413027 | ||||||||
\(474\) | −8.44131 | −0.387722 | ||||||||
\(475\) | −3.53207 | −0.162063 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0788 | 0.827772 | ||||||||
\(478\) | 0.618952 | 0.0283102 | ||||||||
\(479\) | −2.03920 | −0.0931733 | −0.0465866 | − | 0.998914i | \(-0.514834\pi\) | ||||
−0.0465866 | + | 0.998914i | \(0.514834\pi\) | |||||||
\(480\) | −17.3113 | −0.790149 | ||||||||
\(481\) | 9.64483 | 0.439766 | ||||||||
\(482\) | −8.00306 | −0.364529 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.3065 | −1.01393 | ||||||||
\(485\) | 7.88737 | 0.358147 | ||||||||
\(486\) | 49.7303 | 2.25581 | ||||||||
\(487\) | 26.9204 | 1.21988 | 0.609941 | − | 0.792447i | \(-0.291193\pi\) | ||||
0.609941 | + | 0.792447i | \(0.291193\pi\) | |||||||
\(488\) | 34.3848 | 1.55653 | ||||||||
\(489\) | 29.5697 | 1.33719 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.1260 | −1.31444 | −0.657218 | − | 0.753700i | \(-0.728267\pi\) | ||||
−0.657218 | + | 0.753700i | \(0.728267\pi\) | |||||||
\(492\) | 3.94211 | 0.177724 | ||||||||
\(493\) | 22.0480 | 0.992993 | ||||||||
\(494\) | 1.95422 | 0.0879244 | ||||||||
\(495\) | −41.2817 | −1.85547 | ||||||||
\(496\) | −0.0266439 | −0.00119635 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.2470 | 0.459180 | ||||||||
\(499\) | −19.9991 | −0.895283 | −0.447642 | − | 0.894213i | \(-0.647736\pi\) | ||||
−0.447642 | + | 0.894213i | \(0.647736\pi\) | |||||||
\(500\) | −10.1450 | −0.453700 | ||||||||
\(501\) | −24.8158 | −1.10869 | ||||||||
\(502\) | −3.09497 | −0.138135 | ||||||||
\(503\) | 41.5151 | 1.85107 | 0.925534 | − | 0.378663i | \(-0.123616\pi\) | ||||
0.925534 | + | 0.378663i | \(0.123616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.88643 | 0.261943 | ||||||||
\(506\) | −23.4903 | −1.04427 | ||||||||
\(507\) | 22.0188 | 0.977888 | ||||||||
\(508\) | −7.55019 | −0.334985 | ||||||||
\(509\) | 29.0128 | 1.28597 | 0.642985 | − | 0.765879i | \(-0.277696\pi\) | ||||
0.642985 | + | 0.765879i | \(0.277696\pi\) | |||||||
\(510\) | −18.8987 | −0.836848 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.52453 | 0.111570 | ||||||||
\(513\) | −14.4173 | −0.636539 | ||||||||
\(514\) | −13.7451 | −0.606272 | ||||||||
\(515\) | −8.20659 | −0.361625 | ||||||||
\(516\) | 6.48509 | 0.285490 | ||||||||
\(517\) | 25.8647 | 1.13753 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.9466 | 2.19241 | ||||||||
\(520\) | 6.81299 | 0.298769 | ||||||||
\(521\) | 11.3478 | 0.497155 | 0.248578 | − | 0.968612i | \(-0.420037\pi\) | ||||
0.248578 | + | 0.968612i | \(0.420037\pi\) | |||||||
\(522\) | −23.8871 | −1.04551 | ||||||||
\(523\) | −25.2211 | −1.10284 | −0.551420 | − | 0.834227i | \(-0.685914\pi\) | ||||
−0.551420 | + | 0.834227i | \(0.685914\pi\) | |||||||
\(524\) | −7.71432 | −0.337002 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.0771 | 0.482984 | ||||||||
\(527\) | 0.800242 | 0.0348591 | ||||||||
\(528\) | 4.05717 | 0.176566 | ||||||||
\(529\) | −0.277306 | −0.0120568 | ||||||||
\(530\) | 1.90026 | 0.0825418 | ||||||||
\(531\) | 35.8251 | 1.55468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.52551 | −0.109392 | ||||||||
\(534\) | −42.7380 | −1.84945 | ||||||||
\(535\) | 9.87427 | 0.426902 | ||||||||
\(536\) | −33.7255 | −1.45672 | ||||||||
\(537\) | 59.5851 | 2.57129 | ||||||||
\(538\) | −11.5788 | −0.499197 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.7059 | −0.804975 | ||||||||
\(541\) | −35.2542 | −1.51570 | −0.757848 | − | 0.652431i | \(-0.773749\pi\) | ||||
−0.757848 | + | 0.652431i | \(0.773749\pi\) | |||||||
\(542\) | −16.2191 | −0.696672 | ||||||||
\(543\) | 82.9891 | 3.56140 | ||||||||
\(544\) | −37.2351 | −1.59644 | ||||||||
\(545\) | 3.04829 | 0.130574 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.7557 | 1.35778 | 0.678889 | − | 0.734241i | \(-0.262462\pi\) | ||||
0.678889 | + | 0.734241i | \(0.262462\pi\) | |||||||
\(548\) | −15.7243 | −0.671708 | ||||||||
\(549\) | 96.3636 | 4.11270 | ||||||||
\(550\) | 20.3002 | 0.865605 | ||||||||
\(551\) | 2.81675 | 0.119998 | ||||||||
\(552\) | −45.5685 | −1.93952 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.753332 | 0.0320060 | ||||||||
\(555\) | −11.9161 | −0.505808 | ||||||||
\(556\) | −6.13857 | −0.260333 | ||||||||
\(557\) | 34.4676 | 1.46044 | 0.730219 | − | 0.683213i | \(-0.239418\pi\) | ||||
0.730219 | + | 0.683213i | \(0.239418\pi\) | |||||||
\(558\) | −0.866992 | −0.0367027 | ||||||||
\(559\) | −4.15466 | −0.175723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −121.856 | −5.14476 | ||||||||
\(562\) | −5.38512 | −0.227158 | ||||||||
\(563\) | 12.2696 | 0.517103 | 0.258552 | − | 0.965997i | \(-0.416755\pi\) | ||||
0.258552 | + | 0.965997i | \(0.416755\pi\) | |||||||
\(564\) | 18.6730 | 0.786277 | ||||||||
\(565\) | −3.94574 | −0.165999 | ||||||||
\(566\) | −16.6199 | −0.698584 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.1287 | 1.18025 | ||||||||
\(569\) | −13.4078 | −0.562083 | −0.281041 | − | 0.959696i | \(-0.590680\pi\) | ||||
−0.281041 | + | 0.959696i | \(0.590680\pi\) | |||||||
\(570\) | −2.41441 | −0.101128 | ||||||||
\(571\) | 10.4275 | 0.436376 | 0.218188 | − | 0.975907i | \(-0.429985\pi\) | ||||
0.218188 | + | 0.975907i | \(0.429985\pi\) | |||||||
\(572\) | 16.3487 | 0.683573 | ||||||||
\(573\) | −54.2050 | −2.26445 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.6369 | −0.818914 | ||||||||
\(576\) | 43.9416 | 1.83090 | ||||||||
\(577\) | 1.40263 | 0.0583921 | 0.0291960 | − | 0.999574i | \(-0.490705\pi\) | ||||
0.0291960 | + | 0.999574i | \(0.490705\pi\) | |||||||
\(578\) | −25.3073 | −1.05264 | ||||||||
\(579\) | 32.4189 | 1.34728 | ||||||||
\(580\) | 3.65464 | 0.151751 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −25.2240 | −1.04557 | ||||||||
\(583\) | 12.2525 | 0.507449 | ||||||||
\(584\) | −10.6811 | −0.441986 | ||||||||
\(585\) | 19.0934 | 0.789416 | ||||||||
\(586\) | 16.5737 | 0.684651 | ||||||||
\(587\) | 40.2338 | 1.66063 | 0.830313 | − | 0.557298i | \(-0.188162\pi\) | ||||
0.830313 | + | 0.557298i | \(0.188162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.102235 | 0.00421253 | ||||||||
\(590\) | 3.76556 | 0.155026 | ||||||||
\(591\) | 81.2574 | 3.34248 | ||||||||
\(592\) | 0.853360 | 0.0350729 | ||||||||
\(593\) | 15.2417 | 0.625903 | 0.312952 | − | 0.949769i | \(-0.398682\pi\) | ||||
0.312952 | + | 0.949769i | \(0.398682\pi\) | |||||||
\(594\) | 82.8619 | 3.39986 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.35776 | −0.178501 | ||||||||
\(597\) | 16.3947 | 0.670990 | ||||||||
\(598\) | 10.8646 | 0.444288 | ||||||||
\(599\) | −2.71702 | −0.111014 | −0.0555071 | − | 0.998458i | \(-0.517678\pi\) | ||||
−0.0555071 | + | 0.998458i | \(0.517678\pi\) | |||||||
\(600\) | 39.3801 | 1.60769 | ||||||||
\(601\) | 22.9588 | 0.936511 | 0.468255 | − | 0.883593i | \(-0.344883\pi\) | ||||
0.468255 | + | 0.883593i | \(0.344883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −94.5158 | −3.84898 | ||||||||
\(604\) | −16.9136 | −0.688206 | ||||||||
\(605\) | −17.6558 | −0.717812 | ||||||||
\(606\) | −18.8250 | −0.764712 | ||||||||
\(607\) | −44.2606 | −1.79648 | −0.898241 | − | 0.439502i | \(-0.855155\pi\) | ||||
−0.898241 | + | 0.439502i | \(0.855155\pi\) | |||||||
\(608\) | −4.75698 | −0.192921 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.1287 | 0.410100 | ||||||||
\(611\) | −11.9628 | −0.483965 | ||||||||
\(612\) | −64.1043 | −2.59126 | ||||||||
\(613\) | 21.0919 | 0.851894 | 0.425947 | − | 0.904748i | \(-0.359941\pi\) | ||||
0.425947 | + | 0.904748i | \(0.359941\pi\) | |||||||
\(614\) | −15.2301 | −0.614635 | ||||||||
\(615\) | 3.12023 | 0.125820 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.5480 | −0.907750 | −0.453875 | − | 0.891065i | \(-0.649959\pi\) | ||||
−0.453875 | + | 0.891065i | \(0.649959\pi\) | |||||||
\(618\) | 26.2449 | 1.05573 | ||||||||
\(619\) | −33.7969 | −1.35841 | −0.679205 | − | 0.733948i | \(-0.737675\pi\) | ||||
−0.679205 | + | 0.733948i | \(0.737675\pi\) | |||||||
\(620\) | 0.132647 | 0.00532721 | ||||||||
\(621\) | −80.1541 | −3.21647 | ||||||||
\(622\) | −9.43424 | −0.378279 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.87651 | −0.0751203 | ||||||||
\(625\) | 12.5675 | 0.502699 | ||||||||
\(626\) | 5.65790 | 0.226135 | ||||||||
\(627\) | −15.5677 | −0.621715 | ||||||||
\(628\) | −10.7284 | −0.428108 | ||||||||
\(629\) | −25.6304 | −1.02195 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.1027 | 1.35761 | 0.678803 | − | 0.734321i | \(-0.262499\pi\) | ||||
0.678803 | + | 0.734321i | \(0.262499\pi\) | |||||||
\(632\) | −8.08679 | −0.321675 | ||||||||
\(633\) | −90.2990 | −3.58906 | ||||||||
\(634\) | 23.6224 | 0.938164 | ||||||||
\(635\) | −5.97606 | −0.237153 | ||||||||
\(636\) | 8.84572 | 0.350756 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.1890 | −0.640929 | ||||||||
\(639\) | 78.8308 | 3.11850 | ||||||||
\(640\) | −5.79355 | −0.229010 | ||||||||
\(641\) | 11.0824 | 0.437728 | 0.218864 | − | 0.975755i | \(-0.429765\pi\) | ||||
0.218864 | + | 0.975755i | \(0.429765\pi\) | |||||||
\(642\) | −31.5782 | −1.24629 | ||||||||
\(643\) | 33.9767 | 1.33991 | 0.669954 | − | 0.742402i | \(-0.266314\pi\) | ||||
0.669954 | + | 0.742402i | \(0.266314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.13302 | 0.202113 | ||||||||
\(646\) | −5.19318 | −0.204323 | ||||||||
\(647\) | 7.89261 | 0.310291 | 0.155145 | − | 0.987892i | \(-0.450415\pi\) | ||||
0.155145 | + | 0.987892i | \(0.450415\pi\) | |||||||
\(648\) | 91.2551 | 3.58484 | ||||||||
\(649\) | 24.2797 | 0.953062 | ||||||||
\(650\) | −9.38918 | −0.368274 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.5425 | 0.412876 | ||||||||
\(653\) | 34.3369 | 1.34370 | 0.671852 | − | 0.740685i | \(-0.265499\pi\) | ||||
0.671852 | + | 0.740685i | \(0.265499\pi\) | |||||||
\(654\) | −9.74853 | −0.381198 | ||||||||
\(655\) | −6.10597 | −0.238580 | ||||||||
\(656\) | −0.223453 | −0.00872437 | ||||||||
\(657\) | −29.9337 | −1.16783 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.9977 | −0.934819 | −0.467409 | − | 0.884041i | \(-0.654813\pi\) | ||||
−0.467409 | + | 0.884041i | \(0.654813\pi\) | |||||||
\(660\) | −20.1986 | −0.786229 | ||||||||
\(661\) | −9.55555 | −0.371668 | −0.185834 | − | 0.982581i | \(-0.559499\pi\) | ||||
−0.185834 | + | 0.982581i | \(0.559499\pi\) | |||||||
\(662\) | −6.63457 | −0.257860 | ||||||||
\(663\) | 56.3602 | 2.18885 | ||||||||
\(664\) | 9.81667 | 0.380961 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.7683 | 1.07600 | ||||||||
\(667\) | 15.6600 | 0.606357 | ||||||||
\(668\) | −8.84759 | −0.342324 | ||||||||
\(669\) | 29.0700 | 1.12391 | ||||||||
\(670\) | −9.93451 | −0.383804 | ||||||||
\(671\) | 65.3085 | 2.52120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.20764 | 0.123645 | 0.0618227 | − | 0.998087i | \(-0.480309\pi\) | ||||
0.0618227 | + | 0.998087i | \(0.480309\pi\) | |||||||
\(674\) | 1.42660 | 0.0549505 | ||||||||
\(675\) | 69.2688 | 2.66616 | ||||||||
\(676\) | 7.85038 | 0.301938 | ||||||||
\(677\) | 1.62436 | 0.0624293 | 0.0312147 | − | 0.999513i | \(-0.490062\pi\) | ||||
0.0312147 | + | 0.999513i | \(0.490062\pi\) | |||||||
\(678\) | 12.6186 | 0.484615 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −18.1050 | −0.694294 | ||||||||
\(681\) | −48.8465 | −1.87180 | ||||||||
\(682\) | −0.587586 | −0.0224998 | ||||||||
\(683\) | 37.7267 | 1.44357 | 0.721786 | − | 0.692117i | \(-0.243322\pi\) | ||||
0.721786 | + | 0.692117i | \(0.243322\pi\) | |||||||
\(684\) | −8.18966 | −0.313140 | ||||||||
\(685\) | −12.4459 | −0.475535 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.6372 | 0.672900 | ||||||||
\(688\) | −0.367598 | −0.0140145 | ||||||||
\(689\) | −5.66699 | −0.215895 | ||||||||
\(690\) | −13.4231 | −0.511009 | ||||||||
\(691\) | 38.9512 | 1.48177 | 0.740886 | − | 0.671631i | \(-0.234406\pi\) | ||||
0.740886 | + | 0.671631i | \(0.234406\pi\) | |||||||
\(692\) | 17.8075 | 0.676940 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.7493 | −0.749674 | ||||||||
\(695\) | −4.85875 | −0.184303 | ||||||||
\(696\) | −31.4048 | −1.19040 | ||||||||
\(697\) | 6.71133 | 0.254210 | ||||||||
\(698\) | −4.79425 | −0.181465 | ||||||||
\(699\) | 14.7161 | 0.556613 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.29770 | −0.313400 | −0.156700 | − | 0.987646i | \(-0.550086\pi\) | ||||
−0.156700 | + | 0.987646i | \(0.550086\pi\) | |||||||
\(702\) | −38.3249 | −1.44648 | ||||||||
\(703\) | −3.27442 | −0.123497 | ||||||||
\(704\) | 29.7805 | 1.12240 | ||||||||
\(705\) | 14.7799 | 0.556644 | ||||||||
\(706\) | −23.0389 | −0.867081 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.5287 | 0.658770 | ||||||||
\(709\) | 21.9274 | 0.823502 | 0.411751 | − | 0.911296i | \(-0.364917\pi\) | ||||
0.411751 | + | 0.911296i | \(0.364917\pi\) | |||||||
\(710\) | 8.28588 | 0.310963 | ||||||||
\(711\) | −22.6633 | −0.849939 | ||||||||
\(712\) | −40.9431 | −1.53441 | ||||||||
\(713\) | 0.568385 | 0.0212862 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.9402 | 0.483935 | ||||||||
\(716\) | 21.2439 | 0.793923 | ||||||||
\(717\) | 2.28053 | 0.0851679 | ||||||||
\(718\) | −18.2552 | −0.681278 | ||||||||
\(719\) | −12.1598 | −0.453485 | −0.226742 | − | 0.973955i | \(-0.572808\pi\) | ||||
−0.226742 | + | 0.973955i | \(0.572808\pi\) | |||||||
\(720\) | 1.68936 | 0.0629586 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.4836 | 0.613458 | ||||||||
\(723\) | −29.4873 | −1.09664 | ||||||||
\(724\) | 29.5882 | 1.09964 | ||||||||
\(725\) | −13.5333 | −0.502614 | ||||||||
\(726\) | 56.4639 | 2.09557 | ||||||||
\(727\) | 5.65386 | 0.209690 | 0.104845 | − | 0.994489i | \(-0.466565\pi\) | ||||
0.104845 | + | 0.994489i | \(0.466565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 88.0044 | 3.25942 | ||||||||
\(730\) | −3.14632 | −0.116451 | ||||||||
\(731\) | 11.0407 | 0.408354 | ||||||||
\(732\) | 47.1494 | 1.74269 | ||||||||
\(733\) | −24.3253 | −0.898475 | −0.449238 | − | 0.893412i | \(-0.648304\pi\) | ||||
−0.449238 | + | 0.893412i | \(0.648304\pi\) | |||||||
\(734\) | 29.4582 | 1.08732 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.4468 | −0.974843 | ||||||||
\(737\) | −64.0561 | −2.35954 | ||||||||
\(738\) | −7.27114 | −0.267654 | ||||||||
\(739\) | −38.7324 | −1.42480 | −0.712398 | − | 0.701776i | \(-0.752391\pi\) | ||||
−0.712398 | + | 0.701776i | \(0.752391\pi\) | |||||||
\(740\) | −4.24844 | −0.156176 | ||||||||
\(741\) | 7.20032 | 0.264510 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.26170 | −0.193033 | −0.0965165 | − | 0.995331i | \(-0.530770\pi\) | ||||
−0.0965165 | + | 0.995331i | \(0.530770\pi\) | |||||||
\(744\) | −1.13985 | −0.0417889 | ||||||||
\(745\) | −3.44921 | −0.126369 | ||||||||
\(746\) | 7.98336 | 0.292291 | ||||||||
\(747\) | 27.5112 | 1.00658 | ||||||||
\(748\) | −43.4454 | −1.58852 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 25.6799 | 0.937697 | ||||||||
\(751\) | 52.3230 | 1.90929 | 0.954646 | − | 0.297743i | \(-0.0962340\pi\) | ||||
0.954646 | + | 0.297743i | \(0.0962340\pi\) | |||||||
\(752\) | −1.05845 | −0.0385978 | ||||||||
\(753\) | −11.4034 | −0.415564 | ||||||||
\(754\) | 7.48767 | 0.272685 | ||||||||
\(755\) | −13.3873 | −0.487215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.9399 | 0.797421 | 0.398710 | − | 0.917077i | \(-0.369458\pi\) | ||||
0.398710 | + | 0.917077i | \(0.369458\pi\) | |||||||
\(758\) | −9.52704 | −0.346038 | ||||||||
\(759\) | −86.5501 | −3.14157 | ||||||||
\(760\) | −2.31301 | −0.0839016 | ||||||||
\(761\) | −9.81830 | −0.355913 | −0.177957 | − | 0.984038i | \(-0.556949\pi\) | ||||
−0.177957 | + | 0.984038i | \(0.556949\pi\) | |||||||
\(762\) | 19.1116 | 0.692341 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.3258 | −0.699182 | ||||||||
\(765\) | −50.7393 | −1.83448 | ||||||||
\(766\) | −22.4305 | −0.810447 | ||||||||
\(767\) | −11.2297 | −0.405483 | ||||||||
\(768\) | 54.7987 | 1.97738 | ||||||||
\(769\) | 3.37717 | 0.121784 | 0.0608920 | − | 0.998144i | \(-0.480605\pi\) | ||||
0.0608920 | + | 0.998144i | \(0.480605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −50.6440 | −1.82390 | ||||||||
\(772\) | 11.5583 | 0.415994 | ||||||||
\(773\) | −38.3502 | −1.37936 | −0.689681 | − | 0.724114i | \(-0.742249\pi\) | ||||
−0.689681 | + | 0.724114i | \(0.742249\pi\) | |||||||
\(774\) | −11.9616 | −0.429951 | ||||||||
\(775\) | −0.491196 | −0.0176443 | ||||||||
\(776\) | −24.1647 | −0.867461 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.53617 | −0.234333 | ||||||||
\(779\) | 0.857408 | 0.0307198 | ||||||||
\(780\) | 9.34216 | 0.334503 | ||||||||
\(781\) | 53.4260 | 1.91173 | ||||||||
\(782\) | −28.8719 | −1.03246 | ||||||||
\(783\) | −55.2404 | −1.97413 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.49162 | −0.303079 | ||||||||
\(786\) | 19.5271 | 0.696508 | ||||||||
\(787\) | −17.2611 | −0.615291 | −0.307645 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307645 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(788\) | 28.9708 | 1.03204 | ||||||||
\(789\) | 40.8136 | 1.45300 | ||||||||
\(790\) | −2.38213 | −0.0847522 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 126.475 | 4.49411 | ||||||||
\(793\) | −30.2062 | −1.07265 | ||||||||
\(794\) | 31.3177 | 1.11143 | ||||||||
\(795\) | 7.00149 | 0.248317 | ||||||||
\(796\) | 5.84521 | 0.207178 | ||||||||
\(797\) | 19.8669 | 0.703722 | 0.351861 | − | 0.936052i | \(-0.385549\pi\) | ||||
0.351861 | + | 0.936052i | \(0.385549\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.7903 | 1.12466 | ||||||||
\(800\) | 22.8552 | 0.808054 | ||||||||
\(801\) | −114.743 | −4.05425 | ||||||||
\(802\) | −16.9350 | −0.597997 | ||||||||
\(803\) | −20.2870 | −0.715912 | ||||||||
\(804\) | −46.2453 | −1.63095 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.271768 | 0.00957262 | ||||||||
\(807\) | −42.6621 | −1.50178 | ||||||||
\(808\) | −18.0344 | −0.634446 | ||||||||
\(809\) | −30.8800 | −1.08568 | −0.542842 | − | 0.839835i | \(-0.682652\pi\) | ||||
−0.542842 | + | 0.839835i | \(0.682652\pi\) | |||||||
\(810\) | 26.8810 | 0.944503 | ||||||||
\(811\) | 22.6923 | 0.796834 | 0.398417 | − | 0.917204i | \(-0.369560\pi\) | ||||
0.398417 | + | 0.917204i | \(0.369560\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −59.7594 | −2.09586 | ||||||||
\(814\) | 18.8194 | 0.659619 | ||||||||
\(815\) | 8.34452 | 0.292296 | ||||||||
\(816\) | 4.98666 | 0.174568 | ||||||||
\(817\) | 1.41051 | 0.0493474 | ||||||||
\(818\) | −26.7563 | −0.935512 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.11246 | 0.0388487 | ||||||||
\(821\) | 30.3921 | 1.06069 | 0.530345 | − | 0.847782i | \(-0.322062\pi\) | ||||
0.530345 | + | 0.847782i | \(0.322062\pi\) | |||||||
\(822\) | 39.8025 | 1.38827 | ||||||||
\(823\) | −51.0855 | −1.78073 | −0.890364 | − | 0.455249i | \(-0.849550\pi\) | ||||
−0.890364 | + | 0.455249i | \(0.849550\pi\) | |||||||
\(824\) | 25.1427 | 0.875886 | ||||||||
\(825\) | 74.7962 | 2.60407 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.5924 | −1.86359 | −0.931794 | − | 0.362987i | \(-0.881757\pi\) | ||||
−0.931794 | + | 0.362987i | \(0.881757\pi\) | |||||||
\(828\) | −45.5311 | −1.58232 | ||||||||
\(829\) | −4.38093 | −0.152156 | −0.0760780 | − | 0.997102i | \(-0.524240\pi\) | ||||
−0.0760780 | + | 0.997102i | \(0.524240\pi\) | |||||||
\(830\) | 2.89169 | 0.100372 | ||||||||
\(831\) | 2.77565 | 0.0962863 | ||||||||
\(832\) | −13.7740 | −0.477526 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.5384 | 0.538051 | ||||||||
\(835\) | −7.00297 | −0.242348 | ||||||||
\(836\) | −5.55038 | −0.191964 | ||||||||
\(837\) | −2.00497 | −0.0693020 | ||||||||
\(838\) | 7.78229 | 0.268835 | ||||||||
\(839\) | −5.15856 | −0.178093 | −0.0890466 | − | 0.996027i | \(-0.528382\pi\) | ||||
−0.0890466 | + | 0.996027i | \(0.528382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2075 | −0.627845 | ||||||||
\(842\) | −10.5228 | −0.362639 | ||||||||
\(843\) | −19.8415 | −0.683376 | ||||||||
\(844\) | −32.1944 | −1.10818 | ||||||||
\(845\) | 6.21367 | 0.213757 | ||||||||
\(846\) | −34.4420 | −1.18414 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.501407 | −0.0172184 | ||||||||
\(849\) | −61.2358 | −2.10161 | ||||||||
\(850\) | 24.9510 | 0.855812 | ||||||||
\(851\) | −18.2044 | −0.624039 | ||||||||
\(852\) | 38.5709 | 1.32142 | ||||||||
\(853\) | 16.7568 | 0.573744 | 0.286872 | − | 0.957969i | \(-0.407385\pi\) | ||||
0.286872 | + | 0.957969i | \(0.407385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.48221 | −0.221687 | ||||||||
\(856\) | −30.2520 | −1.03399 | ||||||||
\(857\) | −32.2109 | −1.10030 | −0.550152 | − | 0.835064i | \(-0.685430\pi\) | ||||
−0.550152 | + | 0.835064i | \(0.685430\pi\) | |||||||
\(858\) | −41.3831 | −1.41280 | ||||||||
\(859\) | −25.0365 | −0.854234 | −0.427117 | − | 0.904196i | \(-0.640471\pi\) | ||||
−0.427117 | + | 0.904196i | \(0.640471\pi\) | |||||||
\(860\) | 1.83008 | 0.0624053 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.7398 | 0.876702 | ||||||||
\(863\) | 5.24286 | 0.178469 | 0.0892346 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892346 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(864\) | 93.2909 | 3.17382 | ||||||||
\(865\) | 14.0948 | 0.479239 | ||||||||
\(866\) | 5.53284 | 0.188013 | ||||||||
\(867\) | −93.2447 | −3.16676 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.3596 | −0.521037 | ||||||||
\(870\) | −9.25091 | −0.313635 | ||||||||
\(871\) | 29.6270 | 1.00387 | ||||||||
\(872\) | −9.33910 | −0.316262 | ||||||||
\(873\) | −67.7216 | −2.29203 | ||||||||
\(874\) | −3.68854 | −0.124767 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.6462 | −0.494849 | ||||||||
\(877\) | 49.7732 | 1.68072 | 0.840361 | − | 0.542028i | \(-0.182343\pi\) | ||||
0.840361 | + | 0.542028i | \(0.182343\pi\) | |||||||
\(878\) | −21.0530 | −0.710505 | ||||||||
\(879\) | 61.0656 | 2.05969 | ||||||||
\(880\) | 1.14493 | 0.0385955 | ||||||||
\(881\) | 4.99315 | 0.168223 | 0.0841117 | − | 0.996456i | \(-0.473195\pi\) | ||||
0.0841117 | + | 0.996456i | \(0.473195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.6535 | −1.50271 | −0.751354 | − | 0.659899i | \(-0.770599\pi\) | ||||
−0.751354 | + | 0.659899i | \(0.770599\pi\) | |||||||
\(884\) | 20.0942 | 0.675840 | ||||||||
\(885\) | 13.8742 | 0.466376 | ||||||||
\(886\) | 20.0607 | 0.673954 | ||||||||
\(887\) | 36.4120 | 1.22259 | 0.611297 | − | 0.791401i | \(-0.290648\pi\) | ||||
0.611297 | + | 0.791401i | \(0.290648\pi\) | |||||||
\(888\) | 36.5074 | 1.22511 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.0606 | −0.404272 | ||||||||
\(891\) | 173.325 | 5.80659 | ||||||||
\(892\) | 10.3644 | 0.347024 | ||||||||
\(893\) | 4.06138 | 0.135909 | ||||||||
\(894\) | 11.0307 | 0.368922 | ||||||||
\(895\) | 16.8148 | 0.562057 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.0308 | 1.33659 | ||||||||
\(898\) | 10.4819 | 0.349786 | ||||||||
\(899\) | 0.391718 | 0.0130645 | ||||||||
\(900\) | 39.3478 | 1.31159 | ||||||||
\(901\) | 15.0596 | 0.501708 | ||||||||
\(902\) | −4.92787 | −0.164080 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.0886 | 0.402062 | ||||||||
\(905\) | 23.4194 | 0.778487 | ||||||||
\(906\) | 42.8131 | 1.42237 | ||||||||
\(907\) | −2.20992 | −0.0733791 | −0.0366896 | − | 0.999327i | \(-0.511681\pi\) | ||||
−0.0366896 | + | 0.999327i | \(0.511681\pi\) | |||||||
\(908\) | −17.4153 | −0.577946 | ||||||||
\(909\) | −50.5413 | −1.67635 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.7251 | 1.54807 | 0.774035 | − | 0.633142i | \(-0.218235\pi\) | ||||
0.774035 | + | 0.633142i | \(0.218235\pi\) | |||||||
\(912\) | 0.637073 | 0.0210956 | ||||||||
\(913\) | 18.6452 | 0.617066 | ||||||||
\(914\) | 3.09002 | 0.102209 | ||||||||
\(915\) | 37.3193 | 1.23374 | ||||||||
\(916\) | 6.28820 | 0.207768 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 101.845 | 3.36140 | ||||||||
\(919\) | 24.9123 | 0.821780 | 0.410890 | − | 0.911685i | \(-0.365218\pi\) | ||||
0.410890 | + | 0.911685i | \(0.365218\pi\) | |||||||
\(920\) | −12.8594 | −0.423961 | ||||||||
\(921\) | −56.1152 | −1.84906 | ||||||||
\(922\) | −8.26161 | −0.272082 | ||||||||
\(923\) | −24.7104 | −0.813352 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.7322 | 0.517270 | ||||||||
\(926\) | −3.74385 | −0.123031 | ||||||||
\(927\) | 70.4624 | 2.31429 | ||||||||
\(928\) | −18.2266 | −0.598316 | ||||||||
\(929\) | −1.10615 | −0.0362915 | −0.0181458 | − | 0.999835i | \(-0.505776\pi\) | ||||
−0.0181458 | + | 0.999835i | \(0.505776\pi\) | |||||||
\(930\) | −0.335765 | −0.0110102 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.24673 | 0.171862 | ||||||||
\(933\) | −34.7605 | −1.13801 | ||||||||
\(934\) | 3.02298 | 0.0989149 | ||||||||
\(935\) | −34.3875 | −1.12459 | ||||||||
\(936\) | −58.4969 | −1.91203 | ||||||||
\(937\) | −4.28847 | −0.140098 | −0.0700491 | − | 0.997544i | \(-0.522316\pi\) | ||||
−0.0700491 | + | 0.997544i | \(0.522316\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.8465 | 0.680301 | ||||||||
\(940\) | 5.26950 | 0.171872 | ||||||||
\(941\) | −20.9465 | −0.682836 | −0.341418 | − | 0.939912i | \(-0.610907\pi\) | ||||
−0.341418 | + | 0.939912i | \(0.610907\pi\) | |||||||
\(942\) | 27.1565 | 0.884806 | ||||||||
\(943\) | 4.76683 | 0.155229 | ||||||||
\(944\) | −0.993591 | −0.0323386 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.10674 | −0.263573 | ||||||||
\(947\) | 7.51231 | 0.244117 | 0.122059 | − | 0.992523i | \(-0.461050\pi\) | ||||
0.122059 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(948\) | −11.0888 | −0.360149 | ||||||||
\(949\) | 9.38305 | 0.304587 | ||||||||
\(950\) | 3.18762 | 0.103420 | ||||||||
\(951\) | 87.0366 | 2.82236 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.4377 | −0.985974 | −0.492987 | − | 0.870037i | \(-0.664095\pi\) | ||||
−0.492987 | + | 0.870037i | \(0.664095\pi\) | |||||||
\(954\) | −16.3157 | −0.528242 | ||||||||
\(955\) | −15.2966 | −0.494985 | ||||||||
\(956\) | 0.813079 | 0.0262969 | ||||||||
\(957\) | −59.6484 | −1.92816 | ||||||||
\(958\) | 1.84033 | 0.0594585 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 17.0175 | 0.549238 | ||||||||
\(961\) | −30.9858 | −0.999541 | ||||||||
\(962\) | −8.70426 | −0.280637 | ||||||||
\(963\) | −84.7813 | −2.73204 | ||||||||
\(964\) | −10.5131 | −0.338605 | ||||||||
\(965\) | 9.14856 | 0.294503 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.8093 | 1.40881 | 0.704405 | − | 0.709798i | \(-0.251214\pi\) | ||||
0.704405 | + | 0.709798i | \(0.251214\pi\) | |||||||
\(968\) | 54.0925 | 1.73860 | ||||||||
\(969\) | −19.1343 | −0.614681 | ||||||||
\(970\) | −7.11818 | −0.228551 | ||||||||
\(971\) | 7.16246 | 0.229854 | 0.114927 | − | 0.993374i | \(-0.463337\pi\) | ||||
0.114927 | + | 0.993374i | \(0.463337\pi\) | |||||||
\(972\) | 65.3276 | 2.09538 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.2951 | −0.778467 | ||||||||
\(975\) | −34.5944 | −1.10791 | ||||||||
\(976\) | −2.67260 | −0.0855477 | ||||||||
\(977\) | 42.0266 | 1.34455 | 0.672276 | − | 0.740301i | \(-0.265317\pi\) | ||||
0.672276 | + | 0.740301i | \(0.265317\pi\) | |||||||
\(978\) | −26.6860 | −0.853325 | ||||||||
\(979\) | −77.7648 | −2.48537 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.1729 | −0.835635 | ||||||||
\(982\) | 26.2856 | 0.838806 | ||||||||
\(983\) | 13.2127 | 0.421421 | 0.210710 | − | 0.977549i | \(-0.432422\pi\) | ||||
0.210710 | + | 0.977549i | \(0.432422\pi\) | |||||||
\(984\) | −9.55949 | −0.304745 | ||||||||
\(985\) | 22.9307 | 0.730633 | ||||||||
\(986\) | −19.8979 | −0.633678 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.56714 | 0.0816715 | ||||||||
\(989\) | 7.84183 | 0.249356 | ||||||||
\(990\) | 37.2559 | 1.18407 | ||||||||
\(991\) | 26.6369 | 0.846150 | 0.423075 | − | 0.906095i | \(-0.360951\pi\) | ||||
0.423075 | + | 0.906095i | \(0.360951\pi\) | |||||||
\(992\) | −0.661540 | −0.0210039 | ||||||||
\(993\) | −24.4451 | −0.775741 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.62656 | 0.146672 | ||||||||
\(996\) | 13.4609 | 0.426525 | ||||||||
\(997\) | 55.5759 | 1.76011 | 0.880054 | − | 0.474874i | \(-0.157506\pi\) | ||||
0.880054 | + | 0.474874i | \(0.157506\pi\) | |||||||
\(998\) | 18.0488 | 0.571324 | ||||||||
\(999\) | 64.2158 | 2.03170 |
(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 | 2009.2.a.s.1.7 | 17 | ||
7.2 | even | 3 | 287.2.e.d.165.11 | ✓ | 34 | ||
7.4 | even | 3 | 287.2.e.d.247.11 | yes | 34 | ||
7.6 | odd | 2 | 2009.2.a.r.1.7 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.11 | ✓ | 34 | 7.2 | even | 3 | ||
287.2.e.d.247.11 | yes | 34 | 7.4 | even | 3 | ||
2009.2.a.r.1.7 | 17 | 7.6 | odd | 2 | |||
2009.2.a.s.1.7 | 17 | 1.1 | even | 1 | trivial |