Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.65924\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.83940 | −1.26982 | −0.634910 | − | 0.772586i | \(-0.718963\pi\) | ||||
−0.634910 | + | 0.772586i | \(0.718963\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47909 | 0.747472 | 0.373736 | − | 0.927535i | \(-0.378077\pi\) | ||||
0.373736 | + | 0.927535i | \(0.378077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.31849 | −1.47508 | −0.737542 | − | 0.675302i | \(-0.764013\pi\) | ||||
−0.737542 | + | 0.675302i | \(0.764013\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.78284 | 1.40255 | 0.701273 | − | 0.712893i | \(-0.252616\pi\) | ||||
0.701273 | + | 0.712893i | \(0.252616\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.78284 | −1.09726 | −0.548630 | − | 0.836065i | \(-0.684850\pi\) | ||||
−0.548630 | + | 0.836065i | \(0.684850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.90161 | −0.813542 | −0.406771 | − | 0.913530i | \(-0.633345\pi\) | ||||
−0.406771 | + | 0.913530i | \(0.633345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.06221 | 0.612442 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.10133 | −1.31868 | −0.659342 | − | 0.751843i | \(-0.729165\pi\) | ||||
−0.659342 | + | 0.751843i | \(0.729165\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1013 | 1.81425 | 0.907126 | − | 0.420858i | \(-0.138271\pi\) | ||||
0.907126 | + | 0.420858i | \(0.138271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.83940 | −0.479947 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.31849 | −1.03875 | −0.519377 | − | 0.854545i | \(-0.673836\pi\) | ||||
−0.519377 | + | 0.854545i | \(0.673836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41688 | 0.221279 | 0.110640 | − | 0.993861i | \(-0.464710\pi\) | ||||
0.110640 | + | 0.993861i | \(0.464710\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.31849 | 0.506065 | 0.253032 | − | 0.967458i | \(-0.418572\pi\) | ||||
0.253032 | + | 0.967458i | \(0.418572\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.42253 | 0.790957 | 0.395478 | − | 0.918475i | \(-0.370579\pi\) | ||||
0.395478 | + | 0.918475i | \(0.370579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.03912 | −0.949155 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.42253 | 0.705953 | 0.352976 | − | 0.935632i | \(-0.385170\pi\) | ||||
0.352976 | + | 0.935632i | \(0.385170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.72063 | −0.604415 | −0.302208 | − | 0.953242i | \(-0.597724\pi\) | ||||
−0.302208 | + | 0.953242i | \(0.597724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.1013 | 1.87309 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52656 | 0.186499 | 0.0932496 | − | 0.995643i | \(-0.470275\pi\) | ||||
0.0932496 | + | 0.995643i | \(0.470275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7976 | −1.40011 | −0.700057 | − | 0.714087i | \(-0.746842\pi\) | ||||
−0.700057 | + | 0.714087i | \(0.746842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8842 | −1.27390 | −0.636948 | − | 0.770907i | \(-0.719803\pi\) | ||||
−0.636948 | + | 0.770907i | \(0.719803\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.47909 | 0.282518 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.03912 | 0.904472 | 0.452236 | − | 0.891898i | \(-0.350626\pi\) | ||||
0.452236 | + | 0.891898i | \(0.350626\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.8933 | 1.63475 | 0.817374 | − | 0.576108i | \(-0.195429\pi\) | ||||
0.817374 | + | 0.576108i | \(0.195429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4198 | −1.78098 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.41688 | 0.574188 | 0.287094 | − | 0.957902i | \(-0.407311\pi\) | ||||
0.287094 | + | 0.957902i | \(0.407311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.31849 | −0.557529 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.5804 | 1.39332 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.84505 | −0.288871 | −0.144436 | − | 0.989514i | \(-0.546137\pi\) | ||||
−0.144436 | + | 0.989514i | \(0.546137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7828 | 1.37144 | 0.685722 | − | 0.727863i | \(-0.259487\pi\) | ||||
0.685722 | + | 0.727863i | \(0.259487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9464 | −1.47271 | −0.736355 | − | 0.676595i | \(-0.763455\pi\) | ||||
−0.736355 | + | 0.676595i | \(0.763455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.17533 | −0.306971 | −0.153485 | − | 0.988151i | \(-0.549050\pi\) | ||||
−0.153485 | + | 0.988151i | \(0.549050\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.38070 | 0.132247 | 0.0661234 | − | 0.997811i | \(-0.478937\pi\) | ||||
0.0661234 | + | 0.997811i | \(0.478937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.95817 | 0.842714 | 0.421357 | − | 0.906895i | \(-0.361554\pi\) | ||||
0.421357 | + | 0.906895i | \(0.361554\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.0782 | 1.03305 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.78284 | 0.530112 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.85413 | −0.441285 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.50217 | 0.492129 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.6761 | −1.83471 | −0.917354 | − | 0.398073i | \(-0.869679\pi\) | ||||
−0.917354 | + | 0.398073i | \(0.869679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.78014 | −0.767124 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.78284 | −0.414725 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.1726 | 1.55259 | 0.776296 | − | 0.630369i | \(-0.217096\pi\) | ||||
0.776296 | + | 0.630369i | \(0.217096\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4820 | −1.48281 | −0.741403 | − | 0.671060i | \(-0.765839\pi\) | ||||
−0.741403 | + | 0.671060i | \(0.765839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.1850 | −1.10258 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.1635 | 1.67449 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.88688 | 0.809965 | 0.404982 | − | 0.914324i | \(-0.367278\pi\) | ||||
0.404982 | + | 0.914324i | \(0.367278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.72063 | 0.546917 | 0.273459 | − | 0.961884i | \(-0.411832\pi\) | ||||
0.273459 | + | 0.961884i | \(0.411832\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28.6817 | −2.30377 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.5212 | 1.55796 | 0.778979 | − | 0.627050i | \(-0.215738\pi\) | ||||
0.778979 | + | 0.627050i | \(0.215738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.90161 | −0.307490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2472 | 0.802622 | 0.401311 | − | 0.915942i | \(-0.368555\pi\) | ||||
0.401311 | + | 0.915942i | \(0.368555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9582 | 1.00273 | 0.501367 | − | 0.865235i | \(-0.332831\pi\) | ||||
0.501367 | + | 0.865235i | \(0.332831\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.2863 | 1.17587 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9434 | 0.832014 | 0.416007 | − | 0.909361i | \(-0.363429\pi\) | ||||
0.416007 | + | 0.909361i | \(0.363429\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.06221 | 0.231481 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.10404 | −0.605724 | −0.302862 | − | 0.953034i | \(-0.597942\pi\) | ||||
−0.302862 | + | 0.953034i | \(0.597942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.28632 | 0.467258 | 0.233629 | − | 0.972326i | \(-0.424940\pi\) | ||||
0.233629 | + | 0.972326i | \(0.424940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.9407 | 1.31903 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.3362 | 1.04836 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.1461 | −1.24065 | −0.620324 | − | 0.784346i | \(-0.712999\pi\) | ||||
−0.620324 | + | 0.784346i | \(0.712999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.79193 | 0.704838 | 0.352419 | − | 0.935842i | \(-0.385359\pi\) | ||||
0.352419 | + | 0.935842i | \(0.385359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.8338 | 0.771873 | 0.385937 | − | 0.922525i | \(-0.373878\pi\) | ||||
0.385937 | + | 0.922525i | \(0.373878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6761 | 1.25303 | 0.626513 | − | 0.779411i | \(-0.284482\pi\) | ||||
0.626513 | + | 0.779411i | \(0.284482\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.10133 | −0.498416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.02309 | −0.280984 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.8571 | −0.820171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9233 | −1.16505 | −0.582524 | − | 0.812814i | \(-0.697935\pi\) | ||||
−0.582524 | + | 0.812814i | \(0.697935\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.42253 | −0.642611 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1013 | 0.685723 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.7560 | −2.06887 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.31849 | 0.289187 | 0.144594 | − | 0.989491i | \(-0.453812\pi\) | ||||
0.144594 | + | 0.989491i | \(0.453812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2445 | 0.879068 | 0.439534 | − | 0.898226i | \(-0.355144\pi\) | ||||
0.439534 | + | 0.898226i | \(0.355144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.9946 | 1.18912 | 0.594558 | − | 0.804053i | \(-0.297327\pi\) | ||||
0.594558 | + | 0.804053i | \(0.297327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.80322 | −0.249157 | −0.124579 | − | 0.992210i | \(-0.539758\pi\) | ||||
−0.124579 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.3967 | −1.00437 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6643 | 1.66009 | 0.830043 | − | 0.557699i | \(-0.188316\pi\) | ||||
0.830043 | + | 0.557699i | \(0.188316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.1635 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246955\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246955\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.83940 | −0.181403 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.4375 | 1.61855 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.8396 | 1.56786 | 0.783932 | − | 0.620847i | \(-0.213211\pi\) | ||||
0.783932 | + | 0.620847i | \(0.213211\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.67243 | −0.608100 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3660 | 1.02088 | 0.510440 | − | 0.859913i | \(-0.329482\pi\) | ||||
0.510440 | + | 0.859913i | \(0.329482\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.31849 | −0.392612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.6935 | −0.721054 | −0.360527 | − | 0.932749i | \(-0.617403\pi\) | ||||
−0.360527 | + | 0.932749i | \(0.617403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.3576 | −0.697693 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3011 | −0.628066 | −0.314033 | − | 0.949412i | \(-0.601680\pi\) | ||||
−0.314033 | + | 0.949412i | \(0.601680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.07129 | −0.429550 | −0.214775 | − | 0.976664i | \(-0.568902\pi\) | ||||
−0.214775 | + | 0.976664i | \(0.568902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.59148 | 0.457783 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.59785 | −0.336342 | −0.168171 | − | 0.985758i | \(-0.553786\pi\) | ||||
−0.168171 | + | 0.985758i | \(0.553786\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9882 | 0.774812 | 0.387406 | − | 0.921909i | \(-0.373371\pi\) | ||||
0.387406 | + | 0.921909i | \(0.373371\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.35761 | 0.437365 | 0.218682 | − | 0.975796i | \(-0.429824\pi\) | ||||
0.218682 | + | 0.975796i | \(0.429824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.41688 | 0.0836356 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4413 | 0.967133 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.9324 | 1.69025 | 0.845124 | − | 0.534571i | \(-0.179527\pi\) | ||||
0.845124 | + | 0.534571i | \(0.179527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.3967 | −0.896433 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.7507 | 1.20004 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.31849 | 0.191274 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.4038 | 0.767498 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.6155 | 1.74732 | 0.873660 | − | 0.486537i | \(-0.161740\pi\) | ||||
0.873660 | + | 0.486537i | \(0.161740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.41123 | 0.0800235 | 0.0400117 | − | 0.999199i | \(-0.487260\pi\) | ||||
0.0400117 | + | 0.999199i | \(0.487260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7292 | −1.11516 | −0.557581 | − | 0.830123i | \(-0.688270\pi\) | ||||
−0.557581 | + | 0.830123i | \(0.688270\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.70884 | −0.0959783 | −0.0479891 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479891 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.6048 | −0.985680 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.6584 | −1.53896 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.2863 | −0.903402 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.42253 | 0.298954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.51256 | 0.248033 | 0.124016 | − | 0.992280i | \(-0.460422\pi\) | ||||
0.124016 | + | 0.992280i | \(0.460422\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.33453 | −0.236820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9163 | 1.13939 | 0.569693 | − | 0.821858i | \(-0.307062\pi\) | ||||
0.569693 | + | 0.821858i | \(0.307062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.0421 | 1.35610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.10698 | −0.381523 | −0.190761 | − | 0.981636i | \(-0.561096\pi\) | ||||
−0.190761 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.36302 | −0.394134 | −0.197067 | − | 0.980390i | \(-0.563142\pi\) | ||||
−0.197067 | + | 0.980390i | \(0.563142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1016 | −1.12312 | −0.561562 | − | 0.827435i | \(-0.689799\pi\) | ||||
−0.561562 | + | 0.827435i | \(0.689799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.4981 | 1.77789 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7887 | 1.46663 | 0.733316 | − | 0.679887i | \(-0.237971\pi\) | ||||
0.733316 | + | 0.679887i | \(0.237971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.87558 | 0.203978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9046 | 1.61762 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.4680 | 1.74702 | 0.873508 | − | 0.486809i | \(-0.161839\pi\) | ||||
0.873508 | + | 0.486809i | \(0.161839\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.1796 | −1.66620 | −0.833098 | − | 0.553126i | \(-0.813435\pi\) | ||||
−0.833098 | + | 0.553126i | \(0.813435\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.7683 | 1.94517 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.95547 | −0.100446 | −0.0502228 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502228 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.5544 | 1.20357 | 0.601787 | − | 0.798657i | \(-0.294456\pi\) | ||||
0.601787 | + | 0.798657i | \(0.294456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.03912 | −0.358747 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.5603 | 1.49877 | 0.749383 | − | 0.662137i | \(-0.230350\pi\) | ||||
0.749383 | + | 0.662137i | \(0.230350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.5624 | −1.14103 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.8263 | −1.14852 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.3984 | −1.87697 | −0.938485 | − | 0.345319i | \(-0.887771\pi\) | ||||
−0.938485 | + | 0.345319i | \(0.887771\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.1083 | −1.00416 | −0.502080 | − | 0.864821i | \(-0.667432\pi\) | ||||
−0.502080 | + | 0.864821i | \(0.667432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −53.7238 | −2.67617 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.6641 | −0.776439 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.3131 | 1.25165 | 0.625826 | − | 0.779963i | \(-0.284762\pi\) | ||||
0.625826 | + | 0.779963i | \(0.284762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.42253 | 0.266825 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.2880 | −2.07583 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.8338 | 1.11550 | 0.557751 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557751 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2949 | 1.47648 | 0.738242 | − | 0.674536i | \(-0.235656\pi\) | ||||
0.738242 | + | 0.674536i | \(0.235656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.7083 | 0.858977 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.72063 | −0.228448 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.3011 | −1.45955 | −0.729775 | − | 0.683687i | \(-0.760375\pi\) | ||||
−0.729775 | + | 0.683687i | \(0.760375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.8005 | 1.86463 | 0.932317 | − | 0.361642i | \(-0.117784\pi\) | ||||
0.932317 | + | 0.361642i | \(0.117784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.6608 | 0.892667 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.1314 | 1.48582 | 0.742910 | − | 0.669392i | \(-0.233445\pi\) | ||||
0.742910 | + | 0.669392i | \(0.233445\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.15094 | 0.339751 | 0.169876 | − | 0.985466i | \(-0.445663\pi\) | ||||
0.169876 | + | 0.985466i | \(0.445663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.3807 | −0.729115 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.404852 | 0.0191061 | 0.00955307 | − | 0.999954i | \(-0.496959\pi\) | ||||
0.00955307 | + | 0.999954i | \(0.496959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.51256 | 0.165400 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.1013 | 0.707961 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.9946 | 1.26275 | 0.631377 | − | 0.775476i | \(-0.282490\pi\) | ||||
0.631377 | + | 0.775476i | \(0.282490\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.58042 | 0.259906 | 0.129953 | − | 0.991520i | \(-0.458517\pi\) | ||||
0.129953 | + | 0.991520i | \(0.458517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.63698 | −0.401394 | −0.200697 | − | 0.979653i | \(-0.564321\pi\) | ||||
−0.200697 | + | 0.979653i | \(0.564321\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.4295 | −0.852815 | −0.426407 | − | 0.904531i | \(-0.640221\pi\) | ||||
−0.426407 | + | 0.904531i | \(0.640221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52656 | 0.0704901 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.22682 | 0.378269 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.6461 | −0.672007 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.6316 | −1.85650 | −0.928252 | − | 0.371952i | \(-0.878688\pi\) | ||||
−0.928252 | + | 0.371952i | \(0.878688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.6048 | 1.53225 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.07825 | 0.366814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.87722 | 0.0850650 | 0.0425325 | − | 0.999095i | \(-0.486457\pi\) | ||||
0.0425325 | + | 0.999095i | \(0.486457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.9772 | −1.39798 | −0.698990 | − | 0.715132i | \(-0.746367\pi\) | ||||
−0.698990 | + | 0.715132i | \(0.746367\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.0659 | −1.84951 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.7976 | −0.529194 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.5979 | 0.832554 | 0.416277 | − | 0.909238i | \(-0.363335\pi\) | ||||
0.416277 | + | 0.909238i | \(0.363335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.1672 | −1.61262 | −0.806308 | − | 0.591496i | \(-0.798538\pi\) | ||||
−0.806308 | + | 0.591496i | \(0.798538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.1350 | −1.74149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.9018 | −1.32538 | −0.662688 | − | 0.748896i | \(-0.730584\pi\) | ||||
−0.662688 | + | 0.748896i | \(0.730584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.8842 | −0.481487 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.4388 | 1.87008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.4429 | 0.591218 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0866 | −0.923821 | −0.461910 | − | 0.886927i | \(-0.652836\pi\) | ||||
−0.461910 | + | 0.886927i | \(0.652836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9233 | 1.13355 | 0.566773 | − | 0.823874i | \(-0.308192\pi\) | ||||
0.566773 | + | 0.823874i | \(0.308192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 58.4144 | 2.54457 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.77743 | −0.338149 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.53565 | −0.326405 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.01604 | 0.389797 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.47909 | 0.106782 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.836461 | −0.0359623 | −0.0179811 | − | 0.999838i | \(-0.505724\pi\) | ||||
−0.0179811 | + | 0.999838i | \(0.505724\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.92035 | −0.167930 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.94688 | −0.211513 | −0.105757 | − | 0.994392i | \(-0.533726\pi\) | ||||
−0.105757 | + | 0.994392i | \(0.533726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.9645 | 1.44694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.03912 | 0.341858 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.4777 | 1.46087 | 0.730433 | − | 0.682984i | \(-0.239318\pi\) | ||||
0.730433 | + | 0.682984i | \(0.239318\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.6493 | −0.746488 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.22575 | 0.388819 | 0.194409 | − | 0.980920i | \(-0.437721\pi\) | ||||
0.194409 | + | 0.980920i | \(0.437721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.4359 | −1.07009 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.0895 | 1.17757 | 0.588787 | − | 0.808288i | \(-0.299606\pi\) | ||||
0.588787 | + | 0.808288i | \(0.299606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.35066 | −0.182069 | −0.0910347 | − | 0.995848i | \(-0.529017\pi\) | ||||
−0.0910347 | + | 0.995848i | \(0.529017\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.9475 | −0.498247 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9287 | 0.454968 | 0.227484 | − | 0.973782i | \(-0.426950\pi\) | ||||
0.227484 | + | 0.973782i | \(0.426950\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8933 | 0.617876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.91634 | 0.410693 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.87451 | −0.118644 | −0.0593219 | − | 0.998239i | \(-0.518894\pi\) | ||||
−0.0593219 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.3131 | −1.99071 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.8018 | −1.63446 | −0.817232 | − | 0.576308i | \(-0.804493\pi\) | ||||
−0.817232 | + | 0.576308i | \(0.804493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.4198 | −0.673147 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.09298 | −0.248952 | −0.124476 | − | 0.992223i | \(-0.539725\pi\) | ||||
−0.124476 | + | 0.992223i | \(0.539725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.31849 | 0.380109 | 0.190055 | − | 0.981774i | \(-0.439134\pi\) | ||||
0.190055 | + | 0.981774i | \(0.439134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.7828 | 0.560352 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.20807 | 0.170800 | 0.0854002 | − | 0.996347i | \(-0.472783\pi\) | ||||
0.0854002 | + | 0.996347i | \(0.472783\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.8396 | −1.16673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.1013 | −0.407989 | −0.203994 | − | 0.978972i | \(-0.565392\pi\) | ||||
−0.203994 | + | 0.978972i | \(0.565392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9046 | −0.600035 | −0.300017 | − | 0.953934i | \(-0.596992\pi\) | ||||
−0.300017 | + | 0.953934i | \(0.596992\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.5126 | −1.10582 | −0.552912 | − | 0.833240i | \(-0.686483\pi\) | ||||
−0.552912 | + | 0.833240i | \(0.686483\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.41688 | 0.217023 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9339 | −1.23736 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.5388 | −1.45690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.24024 | −0.288230 | −0.144115 | − | 0.989561i | \(-0.546033\pi\) | ||||
−0.144115 | + | 0.989561i | \(0.546033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.7078 | 2.32975 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.31849 | −0.210726 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.7625 | −0.622580 | −0.311290 | − | 0.950315i | \(-0.600761\pi\) | ||||
−0.311290 | + | 0.950315i | \(0.600761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0622 | 0.712304 | 0.356152 | − | 0.934428i | \(-0.384089\pi\) | ||||
0.356152 | + | 0.934428i | \(0.384089\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.0900 | −1.22228 | −0.611138 | − | 0.791524i | \(-0.709288\pi\) | ||||
−0.611138 | + | 0.791524i | \(0.709288\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4429 | 0.527680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.7088 | 0.536469 | 0.268234 | − | 0.963354i | \(-0.413560\pi\) | ||||
0.268234 | + | 0.963354i | \(0.413560\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.9303 | 0.974109 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0394 | 0.624805 | 0.312402 | − | 0.949950i | \(-0.398866\pi\) | ||||
0.312402 | + | 0.949950i | \(0.398866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.4906 | −1.41932 | −0.709660 | − | 0.704544i | \(-0.751152\pi\) | ||||
−0.709660 | + | 0.704544i | \(0.751152\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.5804 | 0.526626 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.7066 | 1.07281 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7029 | −0.451784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.7919 | 0.531640 | 0.265820 | − | 0.964023i | \(-0.414357\pi\) | ||||
0.265820 | + | 0.964023i | \(0.414357\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6313 | 0.408595 | 0.204298 | − | 0.978909i | \(-0.434509\pi\) | ||||
0.204298 | + | 0.978909i | \(0.434509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.84505 | −0.109183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.6340 | −1.05739 | −0.528693 | − | 0.848813i | \(-0.677318\pi\) | ||||
−0.528693 | + | 0.848813i | \(0.677318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −51.5994 | −1.97151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.2740 | −0.810473 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.1190 | −1.67837 | −0.839183 | − | 0.543849i | \(-0.816966\pi\) | ||||
−0.839183 | + | 0.543849i | \(0.816966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 49.6385 | 1.88290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.19358 | 0.310354 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.43382 | 0.205233 | 0.102616 | − | 0.994721i | \(-0.467279\pi\) | ||||
0.102616 | + | 0.994721i | \(0.467279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.2203 | 1.13978 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7828 | 0.518357 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.4771 | 0.956813 | 0.478406 | − | 0.878139i | \(-0.341215\pi\) | ||||
0.478406 | + | 0.878139i | \(0.341215\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.4115 | −1.47597 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.4375 | 1.40008 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.07187 | 0.263736 | 0.131868 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131868 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.9464 | −0.556632 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.7458 | −0.807617 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.7629 | −1.47473 | −0.737363 | − | 0.675497i | \(-0.763929\pi\) | ||||
−0.737363 | + | 0.675497i | \(0.763929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.1903 | 0.709779 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.9609 | −0.441785 | −0.220893 | − | 0.975298i | \(-0.570897\pi\) | ||||
−0.220893 | + | 0.975298i | \(0.570897\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.78448 | 0.139403 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9415 | 0.623202 | 0.311601 | − | 0.950213i | \(-0.399135\pi\) | ||||
0.311601 | + | 0.950213i | \(0.399135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.2920 | −1.18468 | −0.592339 | − | 0.805689i | \(-0.701795\pi\) | ||||
−0.592339 | + | 0.805689i | \(0.701795\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.0728 | −1.02851 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.17533 | −0.116024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1635 | −0.954721 | −0.477361 | − | 0.878708i | \(-0.658406\pi\) | ||||
−0.477361 | + | 0.878708i | \(0.658406\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.0826 | −0.694486 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9109 | 1.52328 | 0.761639 | − | 0.648001i | \(-0.224395\pi\) | ||||
0.761639 | + | 0.648001i | \(0.224395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.1335 | −0.584839 | −0.292419 | − | 0.956290i | \(-0.594460\pi\) | ||||
−0.292419 | + | 0.956290i | \(0.594460\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.38070 | 0.0499846 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.8396 | −1.04134 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.7951 | −1.32687 | −0.663433 | − | 0.748236i | \(-0.730901\pi\) | ||||
−0.663433 | + | 0.748236i | \(0.730901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3155 | −0.514894 | −0.257447 | − | 0.966292i | \(-0.582881\pi\) | ||||
−0.257447 | + | 0.966292i | \(0.582881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.9324 | 1.11112 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.77670 | −0.242801 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.2472 | −1.04655 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −55.4284 | −1.97832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.42890 | 0.0865810 | 0.0432905 | − | 0.999063i | \(-0.486216\pi\) | ||||
0.0432905 | + | 0.999063i | \(0.486216\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.95817 | 0.318516 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.1066 | 0.891563 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.8035 | 1.48075 | 0.740377 | − | 0.672192i | \(-0.234647\pi\) | ||||
0.740377 | + | 0.672192i | \(0.234647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.3576 | 1.10935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.9828 | −0.952202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0782 | 0.390457 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.6670 | −0.515665 | −0.257832 | − | 0.966190i | \(-0.583008\pi\) | ||||
−0.257832 | + | 0.966190i | \(0.583008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.3630 | 0.504354 | 0.252177 | − | 0.967681i | \(-0.418853\pi\) | ||||
0.252177 | + | 0.967681i | \(0.418853\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29.0959 | −1.01919 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.8718 | −0.555284 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.7496 | −1.17787 | −0.588935 | − | 0.808181i | \(-0.700452\pi\) | ||||
−0.588935 | + | 0.808181i | \(0.700452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.4053 | −1.33873 | −0.669363 | − | 0.742936i | \(-0.733433\pi\) | ||||
−0.669363 | + | 0.742936i | \(0.733433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.6137 | −0.890674 | −0.445337 | − | 0.895363i | \(-0.646916\pi\) | ||||
−0.445337 | + | 0.895363i | \(0.646916\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0868 | 0.593450 | 0.296725 | − | 0.954963i | \(-0.404105\pi\) | ||||
0.296725 | + | 0.954963i | \(0.404105\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.78284 | 0.200364 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.7935 | −1.27329 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.8697 | −0.720501 | −0.360251 | − | 0.932856i | \(-0.617309\pi\) | ||||
−0.360251 | + | 0.932856i | \(0.617309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.4289 | 0.738928 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.4040 | −1.49314 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.85413 | −0.166790 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.6523 | 0.845069 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.4289 | 0.357079 | 0.178539 | − | 0.983933i | \(-0.442863\pi\) | ||||
0.178539 | + | 0.983933i | \(0.442863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.8989 | 1.32876 | 0.664381 | − | 0.747394i | \(-0.268695\pi\) | ||||
0.664381 | + | 0.747394i | \(0.268695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.3791 | −0.661205 | −0.330603 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330603 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.1572 | −0.652117 | −0.326059 | − | 0.945350i | \(-0.605721\pi\) | ||||
−0.326059 | + | 0.945350i | \(0.605721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.0728 | −1.05651 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.9297 | 0.676068 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.11900 | −0.275102 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.50217 | 0.186007 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1801 | −0.546362 | −0.273181 | − | 0.961963i | \(-0.588076\pi\) | ||||
−0.273181 | + | 0.961963i | \(0.588076\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.95744 | −0.268093 | −0.134047 | − | 0.990975i | \(-0.542797\pi\) | ||||
−0.134047 | + | 0.990975i | \(0.542797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4107 | 0.484960 | 0.242480 | − | 0.970156i | \(-0.422039\pi\) | ||||
0.242480 | + | 0.970156i | \(0.422039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.8627 | 1.60707 | 0.803537 | − | 0.595255i | \(-0.202949\pi\) | ||||
0.803537 | + | 0.595255i | \(0.202949\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.6761 | −0.693454 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.9351 | −0.867885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.0106 | 0.769160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −71.7329 | −2.39243 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.1314 | 0.770618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.8494 | −0.593334 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.9287 | −0.894153 | −0.447077 | − | 0.894496i | \(-0.647535\pi\) | ||||
−0.447077 | + | 0.894496i | \(0.647535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.7833 | 0.721713 | 0.360857 | − | 0.932621i | \(-0.382484\pi\) | ||||
0.360857 | + | 0.932621i | \(0.382484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.9217 | 1.22193 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.78014 | −0.289946 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.535153 | 0.0176531 | 0.00882653 | − | 0.999961i | \(-0.497190\pi\) | ||||
0.00882653 | + | 0.999961i | \(0.497190\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.7453 | 2.06529 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.3485 | −0.636176 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.4729 | 0.507651 | 0.253825 | − | 0.967250i | \(-0.418311\pi\) | ||||
0.253825 | + | 0.967250i | \(0.418311\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.78284 | −0.156751 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.7061 | −1.33123 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.4359 | 0.896290 | 0.448145 | − | 0.893961i | \(-0.352085\pi\) | ||||
0.448145 | + | 0.893961i | \(0.352085\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.79169 | −0.188804 | −0.0944018 | − | 0.995534i | \(-0.530094\pi\) | ||||
−0.0944018 | + | 0.995534i | \(0.530094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.52810 | −0.180020 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.57771 | −0.148756 | −0.0743778 | − | 0.997230i | \(-0.523697\pi\) | ||||
−0.0743778 | + | 0.997230i | \(0.523697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.8874 | 1.87910 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.1672 | 1.17157 | 0.585785 | − | 0.810466i | \(-0.300786\pi\) | ||||
0.585785 | + | 0.810466i | \(0.300786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.6847 | 1.57540 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.1726 | 0.586825 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.0369 | 2.29151 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.8032 | −0.895017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0885 | 0.613844 | 0.306922 | − | 0.951735i | \(-0.400701\pi\) | ||||
0.306922 | + | 0.951735i | \(0.400701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.6616 | 1.43326 | 0.716630 | − | 0.697454i | \(-0.245684\pi\) | ||||
0.716630 | + | 0.697454i | \(0.245684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.4820 | −0.560448 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.9179 | 1.18111 | 0.590554 | − | 0.806998i | \(-0.298909\pi\) | ||||
0.590554 | + | 0.806998i | \(0.298909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4289 | 0.429190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.0610 | 1.50101 | 0.750507 | − | 0.660862i | \(-0.229809\pi\) | ||||
0.750507 | + | 0.660862i | \(0.229809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.7614 | −0.980139 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9475 | −0.411705 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.6525 | 0.973709 | 0.486855 | − | 0.873483i | \(-0.338144\pi\) | ||||
0.486855 | + | 0.873483i | \(0.338144\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.1896 | −1.59112 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.13137 | −0.162512 | −0.0812561 | − | 0.996693i | \(-0.525893\pi\) | ||||
−0.0812561 | + | 0.996693i | \(0.525893\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6048.2.a.bv.1.1 | yes | 4 | |
3.2 | odd | 2 | 6048.2.a.bo.1.4 | yes | 4 | ||
4.3 | odd | 2 | 6048.2.a.br.1.1 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bm.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bm.1.4 | ✓ | 4 | 12.11 | even | 2 | ||
6048.2.a.bo.1.4 | yes | 4 | 3.2 | odd | 2 | ||
6048.2.a.br.1.1 | yes | 4 | 4.3 | odd | 2 | ||
6048.2.a.bv.1.1 | yes | 4 | 1.1 | even | 1 | trivial |