Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(1,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.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: | \(39.1266969904\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 11x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.31342\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.1 |
$q$-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 | ||||||||
\(3\) | 1.73205 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.27492 | 0.685913 | 0.342957 | − | 0.939351i | \(-0.388572\pi\) | ||||
0.342957 | + | 0.939351i | \(0.388572\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.09095 | −1.68933 | −0.844663 | − | 0.535299i | \(-0.820199\pi\) | ||||
−0.844663 | + | 0.535299i | \(0.820199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.77753 | 1.15872 | 0.579360 | − | 0.815072i | \(-0.303303\pi\) | ||||
0.579360 | + | 0.815072i | \(0.303303\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27492 | −0.980733 | −0.490367 | − | 0.871516i | \(-0.663137\pi\) | ||||
−0.490367 | + | 0.871516i | \(0.663137\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.894797 | 0.186578 | 0.0932891 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932891 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.27492 | −0.608137 | −0.304068 | − | 0.952650i | \(-0.598345\pi\) | ||||
−0.304068 | + | 0.952650i | \(0.598345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.27492 | −0.767798 | −0.383899 | − | 0.923375i | \(-0.625419\pi\) | ||||
−0.383899 | + | 0.923375i | \(0.625419\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.94027 | 0.685913 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.61478 | −0.923064 | −0.461532 | − | 0.887124i | \(-0.652700\pi\) | ||||
−0.461532 | + | 0.887124i | \(0.652700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.5498 | −1.68933 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2749 | −1.76085 | −0.880423 | − | 0.474189i | \(-0.842741\pi\) | ||||
−0.880423 | + | 0.474189i | \(0.842741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.50958 | −0.992701 | −0.496351 | − | 0.868122i | \(-0.665327\pi\) | ||||
−0.496351 | + | 0.868122i | \(0.665327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.15068 | 0.313709 | 0.156854 | − | 0.987622i | \(-0.449865\pi\) | ||||
0.156854 | + | 0.987622i | \(0.449865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.27492 | 1.15872 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.40437 | 1.01707 | 0.508534 | − | 0.861042i | \(-0.330187\pi\) | ||||
0.508534 | + | 0.861042i | \(0.330187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.40437 | −0.980733 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.27492 | 0.556547 | 0.278273 | − | 0.960502i | \(-0.410238\pi\) | ||||
0.278273 | + | 0.960502i | \(0.410238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.54983 | 0.198436 | 0.0992180 | − | 0.995066i | \(-0.468366\pi\) | ||||
0.0992180 | + | 0.995066i | \(0.468366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9140 | −1.69986 | −0.849930 | − | 0.526896i | \(-0.823356\pi\) | ||||
−0.849930 | + | 0.526896i | \(0.823356\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.54983 | 0.186578 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5498 | 1.25204 | 0.626018 | − | 0.779809i | \(-0.284684\pi\) | ||||
0.626018 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.15068 | 0.251718 | 0.125859 | − | 0.992048i | \(-0.459831\pi\) | ||||
0.125859 | + | 0.992048i | \(0.459831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.274917 | −0.0309306 | −0.0154653 | − | 0.999880i | \(-0.504923\pi\) | ||||
−0.0154653 | + | 0.999880i | \(0.504923\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.67232 | 0.622618 | 0.311309 | − | 0.950309i | \(-0.399233\pi\) | ||||
0.311309 | + | 0.950309i | \(0.399233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.67232 | −0.608137 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.00000 | −0.741999 | −0.370999 | − | 0.928633i | \(-0.620985\pi\) | ||||
−0.370999 | + | 0.928633i | \(0.620985\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.40437 | −0.767798 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.92820 | −0.703452 | −0.351726 | − | 0.936103i | \(-0.614405\pi\) | ||||
−0.351726 | + | 0.936103i | \(0.614405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.54983 | 0.154214 | 0.0771071 | − | 0.997023i | \(-0.475432\pi\) | ||||
0.0771071 | + | 0.997023i | \(0.475432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.56930 | 0.253161 | 0.126581 | − | 0.991956i | \(-0.459600\pi\) | ||||
0.126581 | + | 0.991956i | \(0.459600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.9140 | −1.34511 | −0.672556 | − | 0.740046i | \(-0.734804\pi\) | ||||
−0.672556 | + | 0.740046i | \(0.734804\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.54983 | 0.340012 | 0.170006 | − | 0.985443i | \(-0.445621\pi\) | ||||
0.170006 | + | 0.985443i | \(0.445621\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.72508 | −0.923064 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0192 | 1.22474 | 0.612369 | − | 0.790572i | \(-0.290217\pi\) | ||||
0.612369 | + | 0.790572i | \(0.290217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.82475 | −0.529523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.5287 | −1.76085 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.78959 | 0.158801 | 0.0794004 | − | 0.996843i | \(-0.474699\pi\) | ||||
0.0794004 | + | 0.996843i | \(0.474699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.2749 | −0.992701 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.2749 | −1.59669 | −0.798343 | − | 0.602202i | \(-0.794290\pi\) | ||||
−0.798343 | + | 0.602202i | \(0.794290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.19397 | 0.785494 | 0.392747 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392747 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0997 | −1.45037 | −0.725187 | − | 0.688551i | \(-0.758247\pi\) | ||||
−0.725187 | + | 0.688551i | \(0.758247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.72508 | 0.313709 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8564 | −1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.54983 | 0.618507 | 0.309253 | − | 0.950980i | \(-0.399921\pi\) | ||||
0.309253 | + | 0.950980i | \(0.399921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2749 | −1.64995 | −0.824975 | − | 0.565170i | \(-0.808811\pi\) | ||||
−0.824975 | + | 0.565170i | \(0.808811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8685 | 0.867399 | 0.433699 | − | 0.901058i | \(-0.357208\pi\) | ||||
0.433699 | + | 0.901058i | \(0.357208\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.8248 | 1.01707 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.40437 | −0.579955 | −0.289978 | − | 0.957033i | \(-0.593648\pi\) | ||||
−0.289978 | + | 0.957033i | \(0.593648\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.6005 | 0.975058 | 0.487529 | − | 0.873107i | \(-0.337898\pi\) | ||||
0.487529 | + | 0.873107i | \(0.337898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0997 | 1.85382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.7490 | −1.42546 | −0.712731 | − | 0.701438i | \(-0.752542\pi\) | ||||
−0.712731 | + | 0.701438i | \(0.752542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.40437 | 0.556547 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.274917 | 0.0205483 | 0.0102741 | − | 0.999947i | \(-0.496730\pi\) | ||||
0.0102741 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7251 | −1.24317 | −0.621583 | − | 0.783348i | \(-0.713510\pi\) | ||||
−0.621583 | + | 0.783348i | \(0.713510\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.68439 | 0.198436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8685 | 0.794782 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.8248 | 1.65154 | 0.825771 | − | 0.564006i | \(-0.190741\pi\) | ||||
0.825771 | + | 0.564006i | \(0.190741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.19397 | −0.661796 | −0.330898 | − | 0.943666i | \(-0.607352\pi\) | ||||
−0.330898 | + | 0.943666i | \(0.607352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0383 | 1.85515 | 0.927576 | − | 0.373634i | \(-0.121888\pi\) | ||||
0.927576 | + | 0.373634i | \(0.121888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.72508 | 0.689393 | 0.344696 | − | 0.938714i | \(-0.387982\pi\) | ||||
0.344696 | + | 0.938714i | \(0.387982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.0997 | −1.69986 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.72508 | −0.672698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6495 | −1.35273 | −0.676364 | − | 0.736568i | \(-0.736445\pi\) | ||||
−0.676364 | + | 0.736568i | \(0.736445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.2728 | 1.25204 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.72508 | 0.251718 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.0997 | −1.95746 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.71780 | 0.583787 | 0.291893 | − | 0.956451i | \(-0.405715\pi\) | ||||
0.291893 | + | 0.956451i | \(0.405715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.45203 | −0.428236 | −0.214118 | − | 0.976808i | \(-0.568688\pi\) | ||||
−0.214118 | + | 0.976808i | \(0.568688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.27492 | −0.282494 | −0.141247 | − | 0.989974i | \(-0.545111\pi\) | ||||
−0.141247 | + | 0.989974i | \(0.545111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6339 | 1.22075 | 0.610375 | − | 0.792113i | \(-0.291019\pi\) | ||||
0.610375 | + | 0.792113i | \(0.291019\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.476171 | −0.0309306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.5498 | −0.941151 | −0.470575 | − | 0.882360i | \(-0.655954\pi\) | ||||
−0.470575 | + | 0.882360i | \(0.655954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8248 | −0.826115 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0383 | 1.65678 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.82475 | 0.622618 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.45017 | −0.344011 | −0.172006 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172006 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.03559 | 0.127976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.7249 | −1.54230 | −0.771148 | − | 0.636656i | \(-0.780317\pi\) | ||||
−0.771148 | + | 0.636656i | \(0.780317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.9331 | 1.66077 | 0.830383 | − | 0.557193i | \(-0.188122\pi\) | ||||
0.830383 | + | 0.557193i | \(0.188122\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1244 | −0.741999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.5498 | −1.80169 | −0.900843 | − | 0.434146i | \(-0.857050\pi\) | ||||
−0.900843 | + | 0.434146i | \(0.857050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8248 | −0.779048 | −0.389524 | − | 0.921016i | \(-0.627361\pi\) | ||||
−0.389524 | + | 0.921016i | \(0.627361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6339 | 1.11960 | 0.559802 | − | 0.828626i | \(-0.310877\pi\) | ||||
0.559802 | + | 0.828626i | \(0.310877\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.5863 | −1.16428 | −0.582142 | − | 0.813087i | \(-0.697785\pi\) | ||||
−0.582142 | + | 0.813087i | \(0.697785\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.82475 | 0.342632 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92820 | 0.404750 | 0.202375 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202375 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.8208 | −0.685913 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.45017 | −0.315191 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.68439 | 0.154214 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.99782 | −0.228167 | −0.114084 | − | 0.993471i | \(-0.536393\pi\) | ||||
−0.114084 | + | 0.993471i | \(0.536393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.45017 | 0.253161 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8248 | 0.727225 | 0.363612 | − | 0.931550i | \(-0.381543\pi\) | ||||
0.363612 | + | 0.931550i | \(0.381543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4477 | 0.816630 | 0.408315 | − | 0.912841i | \(-0.366116\pi\) | ||||
0.408315 | + | 0.912841i | \(0.366116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.82518 | 0.214844 | 0.107422 | − | 0.994214i | \(-0.465740\pi\) | ||||
0.107422 | + | 0.994214i | \(0.465740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.45017 | −0.417129 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0997 | −1.34511 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.4235 | −1.13640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.14849 | 0.340012 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.82475 | −0.265192 | −0.132596 | − | 0.991170i | \(-0.542331\pi\) | ||||
−0.132596 | + | 0.991170i | \(0.542331\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0192 | −0.709198 | −0.354599 | − | 0.935018i | \(-0.615383\pi\) | ||||
−0.354599 | + | 0.935018i | \(0.615383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.5498 | 1.22474 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.72508 | −0.526643 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.1244 | 0.650870 | 0.325435 | − | 0.945564i | \(-0.394489\pi\) | ||||
0.325435 | + | 0.945564i | \(0.394489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2749 | −0.603532 | −0.301766 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301766 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.6495 | 1.68933 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.2608 | 1.13160 | 0.565799 | − | 0.824543i | \(-0.308568\pi\) | ||||
0.565799 | + | 0.824543i | \(0.308568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.37459 | −0.0725479 | −0.0362739 | − | 0.999342i | \(-0.511549\pi\) | ||||
−0.0362739 | + | 0.999342i | \(0.511549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.725083 | −0.0381623 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0888 | −0.529523 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7512 | −0.770007 | −0.385003 | − | 0.922915i | \(-0.625800\pi\) | ||||
−0.385003 | + | 0.922915i | \(0.625800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.61478 | 0.290722 | 0.145361 | − | 0.989379i | \(-0.453566\pi\) | ||||
0.145361 | + | 0.989379i | \(0.453566\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.9474 | 1.02734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6495 | 1.21479 | 0.607397 | − | 0.794399i | \(-0.292214\pi\) | ||||
0.607397 | + | 0.794399i | \(0.292214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.09967 | 0.158801 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.0049 | 1.02220 | 0.511101 | − | 0.859520i | \(-0.329238\pi\) | ||||
0.511101 | + | 0.859520i | \(0.329238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.37459 | −0.272502 | −0.136251 | − | 0.990674i | \(-0.543505\pi\) | ||||
−0.136251 | + | 0.990674i | \(0.543505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.27492 | 0.216192 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.6531 | −1.59669 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.1698 | 0.761352 | 0.380676 | − | 0.924708i | \(-0.375691\pi\) | ||||
0.380676 | + | 0.924708i | \(0.375691\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | 0.149813 | 0.0749064 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749064 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.0383 | 1.29706 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7732 | −0.633142 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0997 | 0.499396 | 0.249698 | − | 0.968324i | \(-0.419669\pi\) | ||||
0.249698 | + | 0.968324i | \(0.419669\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9244 | 0.785494 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.6175 | −1.45037 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0997 | 0.835373 | 0.417687 | − | 0.908591i | \(-0.362841\pi\) | ||||
0.417687 | + | 0.908591i | \(0.362841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.27492 | 0.159610 | 0.0798048 | − | 0.996811i | \(-0.474570\pi\) | ||||
0.0798048 | + | 0.996811i | \(0.474570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.0000 | −1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.3746 | 0.933241 | 0.466620 | − | 0.884458i | \(-0.345471\pi\) | ||||
0.466620 | + | 0.884458i | \(0.345471\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8756 | −1.29156 | −0.645778 | − | 0.763525i | \(-0.723467\pi\) | ||||
−0.645778 | + | 0.763525i | \(0.723467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.82518 | −0.182983 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.17525 | 0.0560915 | 0.0280458 | − | 0.999607i | \(-0.491072\pi\) | ||||
0.0280458 | + | 0.999607i | \(0.491072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.1244 | −0.576046 | −0.288023 | − | 0.957624i | \(-0.592998\pi\) | ||||
−0.288023 | + | 0.957624i | \(0.592998\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.0767 | 0.618507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.8248 | −1.21875 | −0.609373 | − | 0.792884i | \(-0.708579\pi\) | ||||
−0.609373 | + | 0.792884i | \(0.708579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.6495 | −1.20779 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.1172 | −1.64995 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4235 | 0.955372 | 0.477686 | − | 0.878531i | \(-0.341476\pi\) | ||||
0.477686 | + | 0.878531i | \(0.341476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.8248 | −1.15872 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.50958 | 0.302526 | 0.151263 | − | 0.988494i | \(-0.451666\pi\) | ||||
0.151263 | + | 0.988494i | \(0.451666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.1676 | −0.886973 | −0.443486 | − | 0.896281i | \(-0.646259\pi\) | ||||
−0.443486 | + | 0.896281i | \(0.646259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.8248 | 0.867399 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.8087 | −0.680907 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8248 | −0.585978 | −0.292989 | − | 0.956116i | \(-0.594650\pi\) | ||||
−0.292989 | + | 0.956116i | \(0.594650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.1993 | 1.55936 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.4427 | 1.51543 | 0.757716 | − | 0.652584i | \(-0.226315\pi\) | ||||
0.757716 | + | 0.652584i | \(0.226315\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.8248 | −0.579955 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4502 | −0.606997 | −0.303499 | − | 0.952832i | \(-0.598155\pi\) | ||||
−0.303499 | + | 0.952832i | \(0.598155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.6460 | −0.704660 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.3746 | 1.76265 | 0.881324 | − | 0.472512i | \(-0.156653\pi\) | ||||
0.881324 | + | 0.472512i | \(0.156653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.8248 | 0.975058 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.1797 | −0.721418 | −0.360709 | − | 0.932678i | \(-0.617465\pi\) | ||||
−0.360709 | + | 0.932678i | \(0.617465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 41.7419 | 1.85382 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.5498 | −1.30977 | −0.654887 | − | 0.755727i | \(-0.727284\pi\) | ||||
−0.654887 | + | 0.755727i | \(0.727284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.2131 | 0.980733 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.89261 | 0.215177 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.4743 | −1.42546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.8248 | −0.561863 | −0.280931 | − | 0.959728i | \(-0.590643\pi\) | ||||
−0.280931 | + | 0.959728i | \(0.590643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7057 | 0.511856 | 0.255928 | − | 0.966696i | \(-0.417619\pi\) | ||||
0.255928 | + | 0.966696i | \(0.417619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.4235 | −0.889663 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1993 | −0.965189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 68.6750 | 2.97464 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.476171 | 0.0205483 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.45017 | −0.105341 | −0.0526704 | − | 0.998612i | \(-0.516773\pi\) | ||||
−0.0526704 | + | 0.998612i | \(0.516773\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.9687 | −1.24317 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.1271 | 1.54468 | 0.772341 | − | 0.635208i | \(-0.219086\pi\) | ||||
0.772341 | + | 0.635208i | \(0.219086\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0000 | 0.596420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.61478 | 0.237906 | 0.118953 | − | 0.992900i | \(-0.462046\pi\) | ||||
0.118953 | + | 0.992900i | \(0.462046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.6495 | 1.67700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.8248 | 0.794782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.2394 | 0.515831 | 0.257916 | − | 0.966167i | \(-0.416964\pi\) | ||||
0.257916 | + | 0.966167i | \(0.416964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.3746 | −1.23145 | −0.615723 | − | 0.787962i | \(-0.711136\pi\) | ||||
−0.615723 | + | 0.787962i | \(0.711136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.274917 | −0.0115049 | −0.00575246 | − | 0.999983i | \(-0.501831\pi\) | ||||
−0.00575246 | + | 0.999983i | \(0.501831\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.5336 | 1.65154 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.24163 | −0.343103 | −0.171552 | − | 0.985175i | \(-0.554878\pi\) | ||||
−0.171552 | + | 0.985175i | \(0.554878\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.9244 | −0.661796 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.8443 | 0.697621 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.9715 | −0.576665 | −0.288333 | − | 0.957530i | \(-0.593101\pi\) | ||||
−0.288333 | + | 0.957530i | \(0.593101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.2749 | 0.753005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.0997 | 1.85515 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.3084 | 0.833968 | 0.416984 | − | 0.908914i | \(-0.363087\pi\) | ||||
0.416984 | + | 0.908914i | \(0.363087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.8443 | 0.689393 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.27492 | −0.0929506 | −0.0464753 | − | 0.998919i | \(-0.514799\pi\) | ||||
−0.0464753 | + | 0.998919i | \(0.514799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.1868 | −1.30642 | −0.653211 | − | 0.757176i | \(-0.726579\pi\) | ||||
−0.653211 | + | 0.757176i | \(0.726579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0997 | −0.529956 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.0219 | 1.49530 | 0.747650 | − | 0.664093i | \(-0.231182\pi\) | ||||
0.747650 | + | 0.664093i | \(0.231182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.57919 | 0.144093 | 0.0720464 | − | 0.997401i | \(-0.477047\pi\) | ||||
0.0720464 | + | 0.997401i | \(0.477047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.9244 | 1.76547 | 0.882736 | − | 0.469870i | \(-0.155699\pi\) | ||||
0.882736 | + | 0.469870i | \(0.155699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.64950 | −0.186578 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.8443 | −0.672698 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.8248 | −1.06957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.90033 | 0.115460 | 0.0577302 | − | 0.998332i | \(-0.481614\pi\) | ||||
0.0577302 | + | 0.998332i | \(0.481614\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −34.0339 | −1.35273 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.0997 | 1.10987 | 0.554935 | − | 0.831894i | \(-0.312743\pi\) | ||||
0.554935 | + | 0.831894i | \(0.312743\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.3353 | 1.51180 | 0.755898 | − | 0.654689i | \(-0.227200\pi\) | ||||
0.755898 | + | 0.654689i | \(0.227200\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.779710 | 0.0306535 | 0.0153268 | − | 0.999883i | \(-0.495121\pi\) | ||||
0.0153268 | + | 0.999883i | \(0.495121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.72508 | 0.381743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.0219 | −1.44878 | −0.724389 | − | 0.689392i | \(-0.757878\pi\) | ||||
−0.724389 | + | 0.689392i | \(0.757878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.4502 | −0.991398 | −0.495699 | − | 0.868494i | \(-0.665088\pi\) | ||||
−0.495699 | + | 0.868494i | \(0.665088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5498 | −0.604818 | −0.302409 | − | 0.953178i | \(-0.597791\pi\) | ||||
−0.302409 | + | 0.953178i | \(0.597791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −50.4021 | −1.95746 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.93039 | −0.113465 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.0997 | 0.583787 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.52575 | 0.136110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.57919 | 0.137968 | 0.0689838 | − | 0.997618i | \(-0.478024\pi\) | ||||
0.0689838 | + | 0.997618i | \(0.478024\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.6098 | 0.945831 | 0.472916 | − | 0.881108i | \(-0.343202\pi\) | ||||
0.472916 | + | 0.881108i | \(0.343202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.1752 | −0.428236 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7035 | −0.600879 | −0.300440 | − | 0.953801i | \(-0.597133\pi\) | ||||
−0.300440 | + | 0.953801i | \(0.597133\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.40437 | −0.282494 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.0997 | −1.71816 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.37459 | −0.280542 | −0.140271 | − | 0.990113i | \(-0.544797\pi\) | ||||
−0.140271 | + | 0.990113i | \(0.544797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.8662 | −2.04033 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.2749 | 1.22075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.8248 | −0.522154 | −0.261077 | − | 0.965318i | \(-0.584078\pi\) | ||||
−0.261077 | + | 0.965318i | \(0.584078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0027 | 0.905280 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.5498 | −0.959544 | −0.479772 | − | 0.877393i | \(-0.659281\pi\) | ||||
−0.479772 | + | 0.877393i | \(0.659281\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.82518 | −0.143254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.2011 | −0.941151 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.37459 | 0.275026 | 0.137513 | − | 0.990500i | \(-0.456089\pi\) | ||||
0.137513 | + | 0.990500i | \(0.456089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.2131 | −0.826115 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6915 | −0.693228 | −0.346614 | − | 0.938008i | \(-0.612669\pi\) | ||||
−0.346614 | + | 0.938008i | \(0.612669\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.0997 | −1.15026 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.3276 | 1.23098 | 0.615491 | − | 0.788144i | \(-0.288958\pi\) | ||||
0.615491 | + | 0.788144i | \(0.288958\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.6531 | −1.16596 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.9244 | 1.17436 | 0.587179 | − | 0.809457i | \(-0.300238\pi\) | ||||
0.587179 | + | 0.809457i | \(0.300238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.0997 | 1.65678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.5287 | −0.716440 | −0.358220 | − | 0.933637i | \(-0.616616\pi\) | ||||
−0.358220 | + | 0.933637i | \(0.616616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2749 | −0.812823 | −0.406412 | − | 0.913690i | \(-0.633220\pi\) | ||||
−0.406412 | + | 0.913690i | \(0.633220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.43996 | −0.344011 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.43996 | 0.343101 | 0.171551 | − | 0.985175i | \(-0.445122\pi\) | ||||
0.171551 | + | 0.985175i | \(0.445122\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.52575 | 0.127976 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.9244 | −1.08476 | −0.542380 | − | 0.840133i | \(-0.682477\pi\) | ||||
−0.542380 | + | 0.840133i | \(0.682477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.0383 | −0.940189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.8248 | −1.54230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.2366 | −0.979634 | −0.489817 | − | 0.871825i | \(-0.662936\pi\) | ||||
−0.489817 | + | 0.871825i | \(0.662936\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.1993 | 1.72692 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.0170 | 0.608137 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.73205 | −0.0617409 | −0.0308705 | − | 0.999523i | \(-0.509828\pi\) | ||||
−0.0308705 | + | 0.999523i | \(0.509828\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 46.6495 | 1.66077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.43996 | −0.335223 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.3873 | −1.04095 | −0.520476 | − | 0.853876i | \(-0.674246\pi\) | ||||
−0.520476 | + | 0.853876i | \(0.674246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2749 | 0.363500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.89261 | 0.172657 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −51.1818 | −1.80169 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.1993 | 1.51881 | 0.759404 | − | 0.650619i | \(-0.225491\pi\) | ||||
0.759404 | + | 0.650619i | \(0.225491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.5498 | 0.791832 | 0.395916 | − | 0.918287i | \(-0.370427\pi\) | ||||
0.395916 | + | 0.918287i | \(0.370427\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.2131 | −0.779048 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.8279 | 0.973575 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.3746 | 0.606377 | 0.303189 | − | 0.952931i | \(-0.401949\pi\) | ||||
0.303189 | + | 0.952931i | \(0.401949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.3019 | −1.12597 | −0.562987 | − | 0.826466i | \(-0.690348\pi\) | ||||
−0.562987 | + | 0.826466i | \(0.690348\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.5670 | −1.58452 | −0.792261 | − | 0.610183i | \(-0.791096\pi\) | ||||
−0.792261 | + | 0.610183i | \(0.791096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.92442 | 0.0668379 | 0.0334189 | − | 0.999441i | \(-0.489360\pi\) | ||||
0.0334189 | + | 0.999441i | \(0.489360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.2749 | 1.11960 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.2131 | 0.767798 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9003 | 0.376321 | 0.188161 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188161 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2749 | −0.630170 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3923 | 0.357930 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33.9244 | −1.16428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.02409 | −0.172224 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.4547 | −1.04275 | −0.521375 | − | 0.853327i | \(-0.674581\pi\) | ||||
−0.521375 | + | 0.853327i | \(0.674581\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.3276 | 1.13845 | 0.569224 | − | 0.822182i | \(-0.307244\pi\) | ||||
0.569224 | + | 0.822182i | \(0.307244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3746 | 1.20697 | 0.603483 | − | 0.797376i | \(-0.293779\pi\) | ||||
0.603483 | + | 0.797376i | \(0.293779\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.1435 | −0.855895 | −0.427947 | − | 0.903804i | \(-0.640763\pi\) | ||||
−0.427947 | + | 0.903804i | \(0.640763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0888 | 0.342632 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.625414 | −0.0212157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 84.7492 | 2.87162 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.6722 | −1.50847 | −0.754237 | − | 0.656602i | \(-0.771993\pi\) | ||||
−0.754237 | + | 0.656602i | \(0.771993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000 | 0.404750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0241 | 1.34845 | 0.674223 | − | 0.738528i | \(-0.264479\pi\) | ||||
0.674223 | + | 0.738528i | \(0.264479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.6695 | 0.695585 | 0.347792 | − | 0.937572i | \(-0.386931\pi\) | ||||
0.347792 | + | 0.937572i | \(0.386931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.2301 | 1.31722 | 0.658609 | − | 0.752486i | \(-0.271145\pi\) | ||||
0.658609 | + | 0.752486i | \(0.271145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.4743 | −0.685913 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.19397 | −0.307664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.43996 | −0.315191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.0000 | 0.466926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.3746 | 1.17850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.3210 | 1.50486 | 0.752430 | − | 0.658672i | \(-0.228881\pi\) | ||||
0.752430 | + | 0.658672i | \(0.228881\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.09967 | 0.168960 | 0.0844798 | − | 0.996425i | \(-0.473077\pi\) | ||||
0.0844798 | + | 0.996425i | \(0.473077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9041 | 0.427062 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.92442 | 0.195429 | 0.0977143 | − | 0.995215i | \(-0.468847\pi\) | ||||
0.0977143 | + | 0.995215i | \(0.468847\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.92442 | −0.228167 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −64.2585 | −2.11509 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.9003 | −0.587291 | −0.293645 | − | 0.955914i | \(-0.594868\pi\) | ||||
−0.293645 | + | 0.955914i | \(0.594868\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.2131 | 0.727225 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5074 | −0.343262 | −0.171631 | − | 0.985161i | \(-0.554904\pi\) | ||||
−0.171631 | + | 0.985161i | \(0.554904\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.0241 | 0.816630 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.27492 | 0.139358 | 0.0696792 | − | 0.997569i | \(-0.477802\pi\) | ||||
0.0696792 | + | 0.997569i | \(0.477802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0888 | −0.328535 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.7419 | 1.35643 | 0.678214 | − | 0.734865i | \(-0.262754\pi\) | ||||
0.678214 | + | 0.734865i | \(0.262754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.0997 | −0.425233 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.62541 | 0.214844 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.6175 | −0.959405 | −0.479702 | − | 0.877431i | \(-0.659255\pi\) | ||||
−0.479702 | + | 0.877431i | \(0.659255\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.9041 | −0.417129 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.7251 | −0.410487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.50958 | −0.209334 | −0.104667 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104667 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.3746 | −1.13640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.9244 | 0.511039 | 0.255519 | − | 0.966804i | \(-0.417754\pi\) | ||||
0.255519 | + | 0.966804i | \(0.417754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.8443 | −0.538898 | −0.269449 | − | 0.963015i | \(-0.586842\pi\) | ||||
−0.269449 | + | 0.963015i | \(0.586842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.9244 | −0.508947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.2103 | 1.18682 | 0.593412 | − | 0.804899i | \(-0.297780\pi\) | ||||
0.593412 | + | 0.804899i | \(0.297780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.82475 | −0.185216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.4743 | −1.09511 | −0.547555 | − | 0.836769i | \(-0.684441\pi\) | ||||
−0.547555 | + | 0.836769i | \(0.684441\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.35671 | −0.265192 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.77753 | 0.151306 | 0.0756529 | − | 0.997134i | \(-0.475896\pi\) | ||||
0.0756529 | + | 0.997134i | \(0.475896\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.1752 | 0.923064 |
(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 | 4900.2.a.be.1.4 | 4 | ||
5.2 | odd | 4 | 980.2.e.f.589.2 | 4 | |||
5.3 | odd | 4 | 980.2.e.f.589.4 | 4 | |||
5.4 | even | 2 | inner | 4900.2.a.be.1.2 | 4 | ||
7.2 | even | 3 | 700.2.i.f.501.1 | 8 | |||
7.4 | even | 3 | 700.2.i.f.401.1 | 8 | |||
7.6 | odd | 2 | 4900.2.a.bf.1.2 | 4 | |||
35.2 | odd | 12 | 140.2.q.b.109.1 | yes | 4 | ||
35.3 | even | 12 | 980.2.q.b.569.1 | 4 | |||
35.4 | even | 6 | 700.2.i.f.401.4 | 8 | |||
35.9 | even | 6 | 700.2.i.f.501.4 | 8 | |||
35.12 | even | 12 | 980.2.q.b.949.2 | 4 | |||
35.13 | even | 4 | 980.2.e.c.589.1 | 4 | |||
35.17 | even | 12 | 980.2.q.g.569.2 | 4 | |||
35.18 | odd | 12 | 140.2.q.b.9.2 | yes | 4 | ||
35.23 | odd | 12 | 140.2.q.a.109.1 | yes | 4 | ||
35.27 | even | 4 | 980.2.e.c.589.3 | 4 | |||
35.32 | odd | 12 | 140.2.q.a.9.1 | ✓ | 4 | ||
35.33 | even | 12 | 980.2.q.g.949.2 | 4 | |||
35.34 | odd | 2 | 4900.2.a.bf.1.4 | 4 | |||
105.2 | even | 12 | 1260.2.bm.b.109.2 | 4 | |||
105.23 | even | 12 | 1260.2.bm.a.109.2 | 4 | |||
105.32 | even | 12 | 1260.2.bm.a.289.2 | 4 | |||
105.53 | even | 12 | 1260.2.bm.b.289.1 | 4 | |||
140.23 | even | 12 | 560.2.bw.e.529.1 | 4 | |||
140.67 | even | 12 | 560.2.bw.e.289.1 | 4 | |||
140.107 | even | 12 | 560.2.bw.a.529.1 | 4 | |||
140.123 | even | 12 | 560.2.bw.a.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.q.a.9.1 | ✓ | 4 | 35.32 | odd | 12 | ||
140.2.q.a.109.1 | yes | 4 | 35.23 | odd | 12 | ||
140.2.q.b.9.2 | yes | 4 | 35.18 | odd | 12 | ||
140.2.q.b.109.1 | yes | 4 | 35.2 | odd | 12 | ||
560.2.bw.a.289.2 | 4 | 140.123 | even | 12 | |||
560.2.bw.a.529.1 | 4 | 140.107 | even | 12 | |||
560.2.bw.e.289.1 | 4 | 140.67 | even | 12 | |||
560.2.bw.e.529.1 | 4 | 140.23 | even | 12 | |||
700.2.i.f.401.1 | 8 | 7.4 | even | 3 | |||
700.2.i.f.401.4 | 8 | 35.4 | even | 6 | |||
700.2.i.f.501.1 | 8 | 7.2 | even | 3 | |||
700.2.i.f.501.4 | 8 | 35.9 | even | 6 | |||
980.2.e.c.589.1 | 4 | 35.13 | even | 4 | |||
980.2.e.c.589.3 | 4 | 35.27 | even | 4 | |||
980.2.e.f.589.2 | 4 | 5.2 | odd | 4 | |||
980.2.e.f.589.4 | 4 | 5.3 | odd | 4 | |||
980.2.q.b.569.1 | 4 | 35.3 | even | 12 | |||
980.2.q.b.949.2 | 4 | 35.12 | even | 12 | |||
980.2.q.g.569.2 | 4 | 35.17 | even | 12 | |||
980.2.q.g.949.2 | 4 | 35.33 | even | 12 | |||
1260.2.bm.a.109.2 | 4 | 105.23 | even | 12 | |||
1260.2.bm.a.289.2 | 4 | 105.32 | even | 12 | |||
1260.2.bm.b.109.2 | 4 | 105.2 | even | 12 | |||
1260.2.bm.b.289.1 | 4 | 105.53 | even | 12 | |||
4900.2.a.be.1.2 | 4 | 5.4 | even | 2 | inner | ||
4900.2.a.be.1.4 | 4 | 1.1 | even | 1 | trivial | ||
4900.2.a.bf.1.2 | 4 | 7.6 | odd | 2 | |||
4900.2.a.bf.1.4 | 4 | 35.34 | odd | 2 |