Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.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: | \(54.6176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.52444 | −0.954148 | −0.477074 | − | 0.878863i | \(-0.658303\pi\) | ||||
−0.477074 | + | 0.878863i | \(0.658303\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.10278 | 0.935522 | 0.467761 | − | 0.883855i | \(-0.345061\pi\) | ||||
0.467761 | + | 0.883855i | \(0.345061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.72999 | 1.86656 | 0.933281 | − | 0.359146i | \(-0.116932\pi\) | ||||
0.933281 | + | 0.359146i | \(0.116932\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.57834 | 0.625339 | 0.312669 | − | 0.949862i | \(-0.398777\pi\) | ||||
0.312669 | + | 0.949862i | \(0.398777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.57834 | 0.954649 | 0.477325 | − | 0.878727i | \(-0.341607\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.10278 | 0.204780 | 0.102390 | − | 0.994744i | \(-0.467351\pi\) | ||||
0.102390 | + | 0.994744i | \(0.467351\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.83276 | 1.40681 | 0.703403 | − | 0.710791i | \(-0.251663\pi\) | ||||
0.703403 | + | 0.710791i | \(0.251663\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.52444 | 0.426708 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.52444 | −0.743813 | −0.371907 | − | 0.928270i | \(-0.621296\pi\) | ||||
−0.371907 | + | 0.928270i | \(0.621296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.15165 | −0.960726 | −0.480363 | − | 0.877070i | \(-0.659495\pi\) | ||||
−0.480363 | + | 0.877070i | \(0.659495\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.68111 | −1.17136 | −0.585679 | − | 0.810543i | \(-0.699172\pi\) | ||||
−0.585679 | + | 0.810543i | \(0.699172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.42166 | 0.499101 | 0.249550 | − | 0.968362i | \(-0.419717\pi\) | ||||
0.249550 | + | 0.968362i | \(0.419717\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.627213 | −0.0896019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.57834 | −0.354162 | −0.177081 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177081 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.10278 | −0.418378 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2056 | 1.32865 | 0.664325 | − | 0.747444i | \(-0.268719\pi\) | ||||
0.664325 | + | 0.747444i | \(0.268719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.8816 | −1.90540 | −0.952699 | − | 0.303914i | \(-0.901706\pi\) | ||||
−0.952699 | + | 0.303914i | \(0.901706\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.72999 | −0.834752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.41110 | 1.02758 | 0.513790 | − | 0.857916i | \(-0.328241\pi\) | ||||
0.513790 | + | 0.857916i | \(0.328241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.45998 | −1.12269 | −0.561346 | − | 0.827581i | \(-0.689716\pi\) | ||||
−0.561346 | + | 0.827581i | \(0.689716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.25443 | −1.08315 | −0.541574 | − | 0.840653i | \(-0.682172\pi\) | ||||
−0.541574 | + | 0.840653i | \(0.682172\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.83276 | −0.892626 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.47054 | 0.490705 | 0.245353 | − | 0.969434i | \(-0.421096\pi\) | ||||
0.245353 | + | 0.969434i | \(0.421096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.57834 | −0.279660 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5628 | 1.54365 | 0.771824 | − | 0.635836i | \(-0.219344\pi\) | ||||
0.771824 | + | 0.635836i | \(0.219344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.9894 | −1.78098 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9355 | −1.31340 | −0.656702 | − | 0.754150i | \(-0.728049\pi\) | ||||
−0.656702 | + | 0.754150i | \(0.728049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4600 | 1.14031 | 0.570155 | − | 0.821537i | \(-0.306883\pi\) | ||||
0.570155 | + | 0.821537i | \(0.306883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5089 | 1.42960 | 0.714800 | − | 0.699329i | \(-0.246518\pi\) | ||||
0.714800 | + | 0.699329i | \(0.246518\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2544 | 1.47470 | 0.737351 | − | 0.675510i | \(-0.236077\pi\) | ||||
0.737351 | + | 0.675510i | \(0.236077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.6167 | 1.59159 | 0.795793 | − | 0.605568i | \(-0.207054\pi\) | ||||
0.795793 | + | 0.605568i | \(0.207054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.37279 | 0.411357 | 0.205679 | − | 0.978620i | \(-0.434060\pi\) | ||||
0.205679 | + | 0.978620i | \(0.434060\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.57834 | −0.426932 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.50885 | −0.596665 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.37279 | −0.124799 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.2544 | −1.70855 | −0.854277 | − | 0.519818i | \(-0.826000\pi\) | ||||
−0.854277 | + | 0.519818i | \(0.826000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4061 | −0.996554 | −0.498277 | − | 0.867018i | \(-0.666034\pi\) | ||||
−0.498277 | + | 0.867018i | \(0.666034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.52444 | 0.218897 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.74557 | 0.234570 | 0.117285 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117285 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.79445 | 0.491479 | 0.245739 | − | 0.969336i | \(-0.420969\pi\) | ||||
0.245739 | + | 0.969336i | \(0.420969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.8816 | 1.74621 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.10278 | −0.0915805 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.09775 | 0.335701 | 0.167850 | − | 0.985812i | \(-0.446317\pi\) | ||||
0.167850 | + | 0.985812i | \(0.446317\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.67609 | −0.543292 | −0.271646 | − | 0.962397i | \(-0.587568\pi\) | ||||
−0.271646 | + | 0.962397i | \(0.587568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.83276 | −0.629143 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.4600 | −1.55308 | −0.776538 | − | 0.630071i | \(-0.783026\pi\) | ||||
−0.776538 | + | 0.630071i | \(0.783026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.5577 | −0.910877 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7300 | 0.997090 | 0.498545 | − | 0.866864i | \(-0.333868\pi\) | ||||
0.498545 | + | 0.866864i | \(0.333868\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.8816 | 1.61587 | 0.807935 | − | 0.589272i | \(-0.200585\pi\) | ||||
0.807935 | + | 0.589272i | \(0.200585\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.2927 | 2.48406 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.372787 | 0.0283425 | 0.0141712 | − | 0.999900i | \(-0.495489\pi\) | ||||
0.0141712 | + | 0.999900i | \(0.495489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.52444 | −0.190830 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.04888 | −0.0783967 | −0.0391983 | − | 0.999231i | \(-0.512480\pi\) | ||||
−0.0391983 | + | 0.999231i | \(0.512480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.36222 | 0.398571 | 0.199285 | − | 0.979941i | \(-0.436138\pi\) | ||||
0.199285 | + | 0.979941i | \(0.436138\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.52444 | 0.332643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.7194 | 1.86099 | 0.930496 | − | 0.366302i | \(-0.119376\pi\) | ||||
0.930496 | + | 0.366302i | \(0.119376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.77886 | 0.559935 | 0.279967 | − | 0.960009i | \(-0.409676\pi\) | ||||
0.279967 | + | 0.960009i | \(0.409676\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.42166 | 0.386277 | 0.193139 | − | 0.981171i | \(-0.438133\pi\) | ||||
0.193139 | + | 0.981171i | \(0.438133\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2056 | 1.00700 | 0.503502 | − | 0.863994i | \(-0.332045\pi\) | ||||
0.503502 | + | 0.863994i | \(0.332045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.78389 | −0.195391 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.15165 | 0.429650 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.10278 | −0.214623 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.09775 | 0.419787 | 0.209893 | − | 0.977724i | \(-0.432688\pi\) | ||||
0.209893 | + | 0.977724i | \(0.432688\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.68111 | 0.523848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.7733 | −1.34230 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3522 | 1.16723 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.8222 | −1.66222 | −0.831109 | − | 0.556110i | \(-0.812293\pi\) | ||||
−0.831109 | + | 0.556110i | \(0.812293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.7839 | 1.51222 | 0.756110 | − | 0.654445i | \(-0.227098\pi\) | ||||
0.756110 | + | 0.654445i | \(0.227098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.47054 | 0.427585 | 0.213793 | − | 0.976879i | \(-0.431418\pi\) | ||||
0.213793 | + | 0.976879i | \(0.431418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.3522 | 1.26780 | 0.633902 | − | 0.773414i | \(-0.281452\pi\) | ||||
0.633902 | + | 0.773414i | \(0.281452\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.42166 | −0.223205 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.9250 | −1.54758 | −0.773789 | − | 0.633443i | \(-0.781641\pi\) | ||||
−0.773789 | + | 0.633443i | \(0.781641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.09775 | −0.521622 | −0.260811 | − | 0.965390i | \(-0.583990\pi\) | ||||
−0.260811 | + | 0.965390i | \(0.583990\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.627213 | 0.0400712 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.72999 | −0.428219 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00502 | −0.0634365 | −0.0317183 | − | 0.999497i | \(-0.510098\pi\) | ||||
−0.0317183 | + | 0.999497i | \(0.510098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2056 | 0.893095 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.7839 | 1.04695 | 0.523475 | − | 0.852041i | \(-0.324635\pi\) | ||||
0.523475 | + | 0.852041i | \(0.324635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4217 | 0.709708 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0383 | 1.35894 | 0.679470 | − | 0.733703i | \(-0.262210\pi\) | ||||
0.679470 | + | 0.733703i | \(0.262210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.57834 | 0.158386 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.3572 | −1.97285 | −0.986427 | − | 0.164202i | \(-0.947495\pi\) | ||||
−0.986427 | + | 0.164202i | \(0.947495\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.1466 | −1.40606 | −0.703029 | − | 0.711161i | \(-0.748169\pi\) | ||||
−0.703029 | + | 0.711161i | \(0.748169\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.10278 | 0.187104 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.8222 | 1.85193 | 0.925963 | − | 0.377614i | \(-0.123255\pi\) | ||||
0.925963 | + | 0.377614i | \(0.123255\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.94610 | 0.235405 | 0.117702 | − | 0.993049i | \(-0.462447\pi\) | ||||
0.117702 | + | 0.993049i | \(0.462447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4756 | 1.03881 | 0.519407 | − | 0.854527i | \(-0.326153\pi\) | ||||
0.519407 | + | 0.854527i | \(0.326153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5295 | 0.916675 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3522 | −0.608952 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.05944 | −0.120314 | −0.0601568 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601568 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2056 | −0.594190 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.8122 | 1.78191 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.3905 | 1.11765 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.8816 | 0.852120 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.2056 | 0.582462 | 0.291231 | − | 0.956653i | \(-0.405935\pi\) | ||||
0.291231 | + | 0.956653i | \(0.405935\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.20053 | 0.0680756 | 0.0340378 | − | 0.999421i | \(-0.489163\pi\) | ||||
0.0340378 | + | 0.999421i | \(0.489163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.45998 | −0.421663 | −0.210831 | − | 0.977522i | \(-0.567617\pi\) | ||||
−0.210831 | + | 0.977522i | \(0.567617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.48059 | 0.251655 | 0.125827 | − | 0.992052i | \(-0.459841\pi\) | ||||
0.125827 | + | 0.992052i | \(0.459841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.42166 | 0.191576 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.57834 | −0.143463 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.72999 | 0.373313 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.63778 | −0.476216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2439 | 1.33256 | 0.666282 | − | 0.745700i | \(-0.267885\pi\) | ||||
0.666282 | + | 0.745700i | \(0.267885\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.41110 | −0.459547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.4444 | 1.27710 | 0.638549 | − | 0.769581i | \(-0.279535\pi\) | ||||
0.638549 | + | 0.769581i | \(0.279535\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.3033 | 1.31610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2544 | 1.03964 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.881639 | −0.0473289 | −0.0236644 | − | 0.999720i | \(-0.507533\pi\) | ||||
−0.0236644 | + | 0.999720i | \(0.507533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.66553 | −0.0891536 | −0.0445768 | − | 0.999006i | \(-0.514194\pi\) | ||||
−0.0445768 | + | 0.999006i | \(0.514194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.00000 | −0.106449 | −0.0532246 | − | 0.998583i | \(-0.516950\pi\) | ||||
−0.0532246 | + | 0.998583i | \(0.516950\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.45998 | 0.502083 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.7194 | 0.935196 | 0.467598 | − | 0.883941i | \(-0.345120\pi\) | ||||
0.467598 | + | 0.883941i | \(0.345120\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.25443 | 0.484399 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.93554 | −0.362032 | −0.181016 | − | 0.983480i | \(-0.557939\pi\) | ||||
−0.181016 | + | 0.983480i | \(0.557939\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.50885 | 0.337923 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.25997 | 0.168795 | 0.0843973 | − | 0.996432i | \(-0.473104\pi\) | ||||
0.0843973 | + | 0.996432i | \(0.473104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.42166 | 0.382235 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1461 | 0.726637 | 0.363318 | − | 0.931665i | \(-0.381644\pi\) | ||||
0.363318 | + | 0.931665i | \(0.381644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.0766 | −1.43465 | −0.717324 | − | 0.696739i | \(-0.754633\pi\) | ||||
−0.717324 | + | 0.696739i | \(0.754633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.83276 | 0.399195 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.3522 | −1.79243 | −0.896213 | − | 0.443623i | \(-0.853693\pi\) | ||||
−0.896213 | + | 0.443623i | \(0.853693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8045 | 0.596979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.2544 | −1.06673 | −0.533365 | − | 0.845885i | \(-0.679073\pi\) | ||||
−0.533365 | + | 0.845885i | \(0.679073\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.8272 | −1.18987 | −0.594937 | − | 0.803772i | \(-0.702823\pi\) | ||||
−0.594937 | + | 0.803772i | \(0.702823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 52.7144 | 2.62589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0383 | −0.695853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.9900 | 0.790652 | 0.395326 | − | 0.918541i | \(-0.370632\pi\) | ||||
0.395326 | + | 0.918541i | \(0.370632\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.7633 | −1.26773 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.47054 | −0.219450 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.30833 | −0.0639159 | −0.0319579 | − | 0.999489i | \(-0.510174\pi\) | ||||
−0.0319579 | + | 0.999489i | \(0.510174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.2333 | −1.91211 | −0.956057 | − | 0.293181i | \(-0.905286\pi\) | ||||
−0.956057 | + | 0.293181i | \(0.905286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.57834 | 0.125068 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.5678 | 1.81803 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.5577 | −1.32741 | −0.663705 | − | 0.747995i | \(-0.731017\pi\) | ||||
−0.663705 | + | 0.747995i | \(0.731017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.58336 | 0.172205 | 0.0861027 | − | 0.996286i | \(-0.472559\pi\) | ||||
0.0861027 | + | 0.996286i | \(0.472559\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.57834 | −0.219012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.68665 | 0.271409 | 0.135705 | − | 0.990749i | \(-0.456670\pi\) | ||||
0.135705 | + | 0.990749i | \(0.456670\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.362741 | −0.0172343 | −0.00861716 | − | 0.999963i | \(-0.502743\pi\) | ||||
−0.00861716 | + | 0.999963i | \(0.502743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5628 | −0.690341 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.799473 | −0.0377295 | −0.0188647 | − | 0.999822i | \(-0.506005\pi\) | ||||
−0.0188647 | + | 0.999822i | \(0.506005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.0872 | −0.898781 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.9894 | 0.796477 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2056 | 1.13229 | 0.566144 | − | 0.824306i | \(-0.308435\pi\) | ||||
0.566144 | + | 0.824306i | \(0.308435\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7633 | −1.10677 | −0.553383 | − | 0.832927i | \(-0.686663\pi\) | ||||
−0.553383 | + | 0.832927i | \(0.686663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.62219 | −0.214811 | −0.107406 | − | 0.994215i | \(-0.534254\pi\) | ||||
−0.107406 | + | 0.994215i | \(0.534254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.98944 | 0.230884 | 0.115442 | − | 0.993314i | \(-0.463172\pi\) | ||||
0.115442 | + | 0.993314i | \(0.463172\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.2333 | −0.980463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.8328 | −1.09583 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.9739 | −0.592790 | −0.296395 | − | 0.955065i | \(-0.595785\pi\) | ||||
−0.296395 | + | 0.955065i | \(0.595785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.4494 | −1.38837 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.9355 | 0.587373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.14663 | 0.323845 | 0.161922 | − | 0.986804i | \(-0.448231\pi\) | ||||
0.161922 | + | 0.986804i | \(0.448231\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1416 | −0.999237 | −0.499618 | − | 0.866246i | \(-0.666526\pi\) | ||||
−0.499618 | + | 0.866246i | \(0.666526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.84333 | 0.128057 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.8811 | 1.07121 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.51890 | −0.202294 | −0.101147 | − | 0.994872i | \(-0.532251\pi\) | ||||
−0.101147 | + | 0.994872i | \(0.532251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.35166 | 0.372382 | 0.186191 | − | 0.982514i | \(-0.440386\pi\) | ||||
0.186191 | + | 0.982514i | \(0.440386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4600 | −0.509962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.28057 | −0.189733 | −0.0948666 | − | 0.995490i | \(-0.530242\pi\) | ||||
−0.0948666 | + | 0.995490i | \(0.530242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.3622 | 1.03348 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.5089 | −0.639336 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.6167 | 0.466920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.1305 | −1.75815 | −0.879075 | − | 0.476683i | \(-0.841839\pi\) | ||||
−0.879075 | + | 0.476683i | \(0.841839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.5189 | 0.897229 | 0.448614 | − | 0.893725i | \(-0.351918\pi\) | ||||
0.448614 | + | 0.893725i | \(0.351918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1955 | 0.879730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.03883 | −0.0886448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.4005 | −1.79326 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.2544 | −0.659506 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.94610 | −0.0838245 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.6867 | −0.674422 | −0.337211 | − | 0.941429i | \(-0.609484\pi\) | ||||
−0.337211 | + | 0.941429i | \(0.609484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.6167 | −0.711779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.8922 | 1.02156 | 0.510778 | − | 0.859712i | \(-0.329357\pi\) | ||||
0.510778 | + | 0.859712i | \(0.329357\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10278 | −0.0469798 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.8222 | −0.967008 | −0.483504 | − | 0.875342i | \(-0.660636\pi\) | ||||
−0.483504 | + | 0.875342i | \(0.660636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −51.6938 | −2.18641 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6061 | 0.657718 | 0.328859 | − | 0.944379i | \(-0.393336\pi\) | ||||
0.328859 | + | 0.944379i | \(0.393336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.37279 | −0.183965 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.691675 | 0.0289965 | 0.0144983 | − | 0.999895i | \(-0.495385\pi\) | ||||
0.0144983 | + | 0.999895i | \(0.495385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.7910 | −1.87445 | −0.937223 | − | 0.348730i | \(-0.886613\pi\) | ||||
−0.937223 | + | 0.348730i | \(0.886613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.57834 | 0.190930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.45998 | 0.144041 | 0.0720203 | − | 0.997403i | \(-0.477055\pi\) | ||||
0.0720203 | + | 0.997403i | \(0.477055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.2856 | −0.468205 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.8328 | −1.14878 | −0.574391 | − | 0.818581i | \(-0.694761\pi\) | ||||
−0.574391 | + | 0.818581i | \(0.694761\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.83276 | −0.322743 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.5889 | 0.722290 | 0.361145 | − | 0.932510i | \(-0.382386\pi\) | ||||
0.361145 | + | 0.932510i | \(0.382386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.50885 | 0.266837 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4700 | 0.795524 | 0.397762 | − | 0.917489i | \(-0.369787\pi\) | ||||
0.397762 | + | 0.917489i | \(0.369787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4777 | 1.65112 | 0.825560 | − | 0.564315i | \(-0.190860\pi\) | ||||
0.825560 | + | 0.564315i | \(0.190860\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.37279 | 0.0558117 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.71440 | 0.191352 | 0.0956758 | − | 0.995413i | \(-0.469499\pi\) | ||||
0.0956758 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.0278 | 0.931603 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.48110 | −0.382938 | −0.191469 | − | 0.981499i | \(-0.561325\pi\) | ||||
−0.191469 | + | 0.981499i | \(0.561325\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.73501 | −0.311400 | −0.155700 | − | 0.987804i | \(-0.549763\pi\) | ||||
−0.155700 | + | 0.987804i | \(0.549763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.12892 | 0.246342 | 0.123171 | − | 0.992385i | \(-0.460694\pi\) | ||||
0.123171 | + | 0.992385i | \(0.460694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.7628 | −1.47287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.6655 | −0.465135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.19550 | 0.167020 | 0.0835102 | − | 0.996507i | \(-0.473387\pi\) | ||||
0.0835102 | + | 0.996507i | \(0.473387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.2544 | 0.764089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.22114 | −0.167247 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.3850 | 1.87159 | 0.935797 | − | 0.352541i | \(-0.114682\pi\) | ||||
0.935797 | + | 0.352541i | \(0.114682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3678 | 0.842662 | 0.421331 | − | 0.906907i | \(-0.361563\pi\) | ||||
0.421331 | + | 0.906907i | \(0.361563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.29274 | −0.365335 | −0.182668 | − | 0.983175i | \(-0.558473\pi\) | ||||
−0.182668 | + | 0.983175i | \(0.558473\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.6655 | 1.24298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9094 | 0.857381 | 0.428690 | − | 0.903451i | \(-0.358975\pi\) | ||||
0.428690 | + | 0.903451i | \(0.358975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.4061 | 0.445672 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.52998 | 0.332281 | 0.166140 | − | 0.986102i | \(-0.446870\pi\) | ||||
0.166140 | + | 0.986102i | \(0.446870\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.36222 | 0.208566 | 0.104283 | − | 0.994548i | \(-0.466745\pi\) | ||||
0.104283 | + | 0.994548i | \(0.466745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.52444 | −0.0978935 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.04888 | 0.195493 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −46.1744 | −1.78254 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.31889 | −0.0893866 | −0.0446933 | − | 0.999001i | \(-0.514231\pi\) | ||||
−0.0446933 | + | 0.999001i | \(0.514231\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.9305 | 1.38092 | 0.690461 | − | 0.723370i | \(-0.257408\pi\) | ||||
0.690461 | + | 0.723370i | \(0.257408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.6550 | 1.25318 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.15667 | 0.197315 | 0.0986573 | − | 0.995121i | \(-0.468545\pi\) | ||||
0.0986573 | + | 0.995121i | \(0.468545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.74557 | −0.104903 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.3522 | −0.661065 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9688 | 0.759650 | 0.379825 | − | 0.925058i | \(-0.375984\pi\) | ||||
0.379825 | + | 0.925058i | \(0.375984\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.79445 | −0.219796 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.8610 | −0.600779 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.2333 | 1.48182 | 0.740911 | − | 0.671604i | \(-0.234394\pi\) | ||||
0.740911 | + | 0.671604i | \(0.234394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.52444 | 0.170642 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.9300 | −1.08802 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8605 | 1.38433 | 0.692163 | − | 0.721741i | \(-0.256658\pi\) | ||||
0.692163 | + | 0.721741i | \(0.256658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.8610 | 1.34301 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.8816 | −0.780929 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.8383 | 0.665256 | 0.332628 | − | 0.943058i | \(-0.392065\pi\) | ||||
0.332628 | + | 0.943058i | \(0.392065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.6267 | −1.36405 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.10278 | 0.0409560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.00554 | −0.0743813 | −0.0371907 | − | 0.999308i | \(-0.511841\pi\) | ||||
−0.0371907 | + | 0.999308i | \(0.511841\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.8045 | −0.732496 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.4288 | −1.60408 | −0.802040 | − | 0.597271i | \(-0.796252\pi\) | ||||
−0.802040 | + | 0.597271i | \(0.796252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.0978 | 0.961323 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6066 | −0.758026 | −0.379013 | − | 0.925391i | \(-0.623736\pi\) | ||||
−0.379013 | + | 0.925391i | \(0.623736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.4499 | 1.74077 | 0.870385 | − | 0.492373i | \(-0.163870\pi\) | ||||
0.870385 | + | 0.492373i | \(0.163870\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.09775 | −0.150130 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −38.5089 | −1.40708 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.83276 | −0.285822 | −0.142911 | − | 0.989736i | \(-0.545646\pi\) | ||||
−0.142911 | + | 0.989736i | \(0.545646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.67609 | 0.242968 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.4600 | −1.57958 | −0.789790 | − | 0.613378i | \(-0.789810\pi\) | ||||
−0.789790 | + | 0.613378i | \(0.789810\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.41110 | 0.0874023 | 0.0437012 | − | 0.999045i | \(-0.486085\pi\) | ||||
0.0437012 | + | 0.999045i | \(0.486085\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.9477 | −1.51861 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 68.6832 | 2.48001 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.09775 | −0.292012 | −0.146006 | − | 0.989284i | \(-0.546642\pi\) | ||||
−0.146006 | + | 0.989284i | \(0.546642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.6172 | −0.489775 | −0.244888 | − | 0.969551i | \(-0.578751\pi\) | ||||
−0.244888 | + | 0.969551i | \(0.578751\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.83276 | 0.281361 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.15165 | 0.220406 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.3522 | −1.05030 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.4600 | 0.694556 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.9099 | 1.31570 | 0.657848 | − | 0.753151i | \(-0.271467\pi\) | ||||
0.657848 | + | 0.753151i | \(0.271467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0388 | −0.392496 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −100.153 | −3.55655 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.4705 | 0.937635 | 0.468817 | − | 0.883295i | \(-0.344680\pi\) | ||||
0.468817 | + | 0.883295i | \(0.344680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.82220 | 0.312107 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.7144 | −1.01331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.5577 | 0.407356 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.2544 | −1.02853 | −0.514265 | − | 0.857631i | \(-0.671935\pi\) | ||||
−0.514265 | + | 0.857631i | \(0.671935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.9200 | 1.36666 | 0.683332 | − | 0.730108i | \(-0.260530\pi\) | ||||
0.683332 | + | 0.730108i | \(0.260530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.7300 | −0.445912 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.68111 | 0.268728 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.6167 | 1.27793 | 0.638965 | − | 0.769236i | \(-0.279363\pi\) | ||||
0.638965 | + | 0.769236i | \(0.279363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5522 | 1.44842 | 0.724209 | − | 0.689580i | \(-0.242205\pi\) | ||||
0.724209 | + | 0.689580i | \(0.242205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.0972 | −0.872716 | −0.436358 | − | 0.899773i | \(-0.643732\pi\) | ||||
−0.436358 | + | 0.899773i | \(0.643732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.9511 | 0.588737 | 0.294368 | − | 0.955692i | \(-0.404891\pi\) | ||||
0.294368 | + | 0.955692i | \(0.404891\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.61717 | −0.0560315 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.8816 | −0.722639 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6555 | 1.02382 | 0.511910 | − | 0.859039i | \(-0.328938\pi\) | ||||
0.511910 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7839 | −0.958065 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.2927 | −1.11090 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.46552 | 0.119077 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.7144 | −0.710081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.4777 | 1.24897 | 0.624486 | − | 0.781036i | \(-0.285308\pi\) | ||||
0.624486 | + | 0.781036i | \(0.285308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.8716 | 0.849597 | 0.424799 | − | 0.905288i | \(-0.360345\pi\) | ||||
0.424799 | + | 0.905288i | \(0.360345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0388 | 0.513118 | 0.256559 | − | 0.966529i | \(-0.417411\pi\) | ||||
0.256559 | + | 0.966529i | \(0.417411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.4877 | 1.37822 | 0.689109 | − | 0.724658i | \(-0.258002\pi\) | ||||
0.689109 | + | 0.724658i | \(0.258002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.372787 | −0.0126751 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.6066 | 1.91804 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.52444 | 0.0853416 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.0822 | −1.35348 | −0.676739 | − | 0.736223i | \(-0.736608\pi\) | ||||
−0.676739 | + | 0.736223i | \(0.736608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0278 | 0.708443 | 0.354221 | − | 0.935162i | \(-0.384746\pi\) | ||||
0.354221 | + | 0.935162i | \(0.384746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.287716 | −0.00968241 | −0.00484121 | − | 0.999988i | \(-0.501541\pi\) | ||||
−0.00484121 | + | 0.999988i | \(0.501541\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.4111 | 0.685338 | 0.342669 | − | 0.939456i | \(-0.388669\pi\) | ||||
0.342669 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.6066 | 1.63021 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.42166 | −0.114502 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.04888 | 0.0350601 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.63778 | 0.288086 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.64782 | −0.221471 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.36222 | −0.178246 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.3799 | −0.543887 | −0.271943 | − | 0.962313i | \(-0.587666\pi\) | ||||
−0.271943 | + | 0.962313i | \(0.587666\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.5855 | 1.67597 | 0.837986 | − | 0.545692i | \(-0.183733\pi\) | ||||
0.837986 | + | 0.545692i | \(0.183733\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8711 | 0.459066 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.7939 | 0.950859 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.7456 | −0.948229 | −0.474114 | − | 0.880463i | \(-0.657232\pi\) | ||||
−0.474114 | + | 0.880463i | \(0.657232\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −63.6655 | −2.09558 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.52444 | −0.148763 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.7733 | 1.63301 | 0.816505 | − | 0.577339i | \(-0.195909\pi\) | ||||
0.816505 | + | 0.577339i | \(0.195909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.627213 | 0.0205561 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.3033 | 1.12064 | 0.560320 | − | 0.828276i | \(-0.310678\pi\) | ||||
0.560320 | + | 0.828276i | \(0.310678\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.6705 | −1.13023 | −0.565114 | − | 0.825013i | \(-0.691168\pi\) | ||||
−0.565114 | + | 0.825013i | \(0.691168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.1643 | −0.917157 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.96169 | −0.193729 | −0.0968644 | − | 0.995298i | \(-0.530881\pi\) | ||||
−0.0968644 | + | 0.995298i | \(0.530881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62.2822 | −2.02177 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.52946 | −0.308690 | −0.154345 | − | 0.988017i | \(-0.549327\pi\) | ||||
−0.154345 | + | 0.988017i | \(0.549327\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7194 | −0.832261 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.93103 | −0.223815 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3522 | 0.979103 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.77886 | −0.250410 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.9844 | −0.642655 | −0.321328 | − | 0.946968i | \(-0.604129\pi\) | ||||
−0.321328 | + | 0.946968i | \(0.604129\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.3900 | −0.590162 | −0.295081 | − | 0.955472i | \(-0.595347\pi\) | ||||
−0.295081 | + | 0.955472i | \(0.595347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.6277 | −0.468943 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.4394 | 1.22978 | 0.614892 | − | 0.788611i | \(-0.289200\pi\) | ||||
0.614892 | + | 0.788611i | \(0.289200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.1849 | 1.44412 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.5260 | −1.73911 | −0.869555 | − | 0.493836i | \(-0.835594\pi\) | ||||
−0.869555 | + | 0.493836i | \(0.835594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.42166 | −0.172749 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1667 | −1.11824 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91995 | 0.0927553 | 0.0463777 | − | 0.998924i | \(-0.485232\pi\) | ||||
0.0463777 | + | 0.998924i | \(0.485232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.2056 | −0.450346 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.2822 | −1.14907 | −0.574534 | − | 0.818481i | \(-0.694817\pi\) | ||||
−0.574534 | + | 0.818481i | \(0.694817\pi\) | |||||||
\(998\) | 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 | 6840.2.a.bf.1.2 | 3 | ||
3.2 | odd | 2 | 2280.2.a.s.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 4560.2.a.bv.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.s.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
4560.2.a.bv.1.2 | 3 | 12.11 | even | 2 | |||
6840.2.a.bf.1.2 | 3 | 1.1 | even | 1 | trivial |