Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 264 x^{18} + 28274 x^{16} - 1545308 x^{14} + 45358441 x^{12} - 637328868 x^{10} + \cdots + 194396337216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.11 | ||
Root | \(0.399553 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.q.721.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.399553 | 0.0799105 | 0.0399553 | − | 0.999201i | \(-0.487278\pi\) | ||||
0.0399553 | + | 0.999201i | \(0.487278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.64754 | −1.37822 | −0.689110 | − | 0.724657i | \(-0.741998\pi\) | ||||
−0.689110 | + | 0.724657i | \(0.741998\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.57683 | −0.870621 | −0.435311 | − | 0.900280i | \(-0.643361\pi\) | ||||
−0.435311 | + | 0.900280i | \(0.643361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.40920i | − | 0.723785i | −0.932220 | − | 0.361892i | \(-0.882131\pi\) | ||
0.932220 | − | 0.361892i | \(-0.117869\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.3458 | 1.49093 | 0.745464 | − | 0.666546i | \(-0.232228\pi\) | ||||
0.745464 | + | 0.666546i | \(0.232228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.88030 | − | 18.9067i | 0.0989631 | − | 0.995091i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −14.2995 | −0.621716 | −0.310858 | − | 0.950456i | \(-0.600616\pi\) | ||||
−0.310858 | + | 0.950456i | \(0.600616\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.8404 | −0.993614 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.9418i | 0.377302i | 0.982044 | + | 0.188651i | \(0.0604115\pi\) | ||||
−0.982044 | + | 0.188651i | \(0.939588\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.8914i | 0.415853i | 0.978144 | + | 0.207926i | \(0.0666714\pi\) | ||||
−0.978144 | + | 0.207926i | \(0.933329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.85470 | −0.110134 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.29545i | − | 0.0890663i | −0.999008 | − | 0.0445332i | \(-0.985820\pi\) | ||
0.999008 | − | 0.0445332i | \(-0.0141800\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 63.6191i | − | 1.55168i | −0.630927 | − | 0.775842i | \(-0.717325\pi\) | ||
0.630927 | − | 0.775842i | \(-0.282675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.8821 | 0.625166 | 0.312583 | − | 0.949891i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949891i | \(0.398806\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −18.1542 | −0.386259 | −0.193129 | − | 0.981173i | \(-0.561864\pi\) | ||||
−0.193129 | + | 0.981173i | \(0.561864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.0749 | 0.899489 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36.7558i | 0.693506i | 0.937956 | + | 0.346753i | \(0.112716\pi\) | ||||
−0.937956 | + | 0.346753i | \(0.887284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.82645 | −0.0695718 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.5340i | 0.212440i | 0.994343 | + | 0.106220i | \(0.0338748\pi\) | ||||
−0.994343 | + | 0.106220i | \(0.966125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46.8960 | 0.768787 | 0.384394 | − | 0.923169i | \(-0.374411\pi\) | ||||
0.384394 | + | 0.923169i | \(0.374411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.75947i | − | 0.0578380i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 71.4070i | − | 1.06578i | −0.846186 | − | 0.532888i | \(-0.821107\pi\) | ||
0.846186 | − | 0.532888i | \(-0.178893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 36.3839i | − | 0.512449i | −0.966617 | − | 0.256225i | \(-0.917521\pi\) | ||
0.966617 | − | 0.256225i | \(-0.0824787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.6094 | −0.830266 | −0.415133 | − | 0.909761i | \(-0.636265\pi\) | ||||
−0.415133 | + | 0.909761i | \(0.636265\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 92.3928 | 1.19991 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 101.769i | 1.28821i | 0.764936 | + | 0.644106i | \(0.222770\pi\) | ||||
−0.764936 | + | 0.644106i | \(0.777230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63.1863 | −0.761281 | −0.380640 | − | 0.924723i | \(-0.624296\pi\) | ||||
−0.380640 | + | 0.924723i | \(0.624296\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.1270 | 0.119141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 107.557i | 1.20851i | 0.796792 | + | 0.604254i | \(0.206529\pi\) | ||||
−0.796792 | + | 0.604254i | \(0.793471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 90.7756i | 0.997534i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.751278 | − | 7.55424i | 0.00790819 | − | 0.0795183i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 120.705i | 1.24439i | 0.782864 | + | 0.622193i | \(0.213758\pi\) | ||||
−0.782864 | + | 0.622193i | \(0.786242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 122.849 | 1.21632 | 0.608162 | − | 0.793813i | \(-0.291907\pi\) | ||||
0.608162 | + | 0.793813i | \(0.291907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 43.7202i | 0.424468i | 0.977219 | + | 0.212234i | \(0.0680739\pi\) | ||||
−0.977219 | + | 0.212234i | \(0.931926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 176.900i | 1.65327i | 0.562738 | + | 0.826635i | \(0.309748\pi\) | ||||
−0.562738 | + | 0.826635i | \(0.690252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 141.865i | 1.30151i | 0.759287 | + | 0.650756i | \(0.225548\pi\) | ||||
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 91.8737i | − | 0.813041i | −0.913642 | − | 0.406521i | \(-0.866742\pi\) | ||
0.913642 | − | 0.406521i | \(-0.133258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.71339 | −0.0496816 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −244.524 | −2.05482 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.2843 | −0.242019 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.9139 | −0.159311 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 200.209i | 1.57645i | 0.615388 | + | 0.788225i | \(0.288999\pi\) | ||||
−0.615388 | + | 0.788225i | \(0.711001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −193.983 | −1.48078 | −0.740392 | − | 0.672175i | \(-0.765360\pi\) | ||||
−0.740392 | + | 0.672175i | \(0.765360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.1402 | + | 182.403i | −0.136393 | + | 1.37145i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 239.550 | 1.74854 | 0.874272 | − | 0.485437i | \(-0.161339\pi\) | ||||
0.874272 | + | 0.485437i | \(0.161339\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −62.8976 | −0.452501 | −0.226250 | − | 0.974069i | \(-0.572647\pi\) | ||||
−0.226250 | + | 0.974069i | \(0.572647\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 90.1104i | 0.630142i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.37181i | 0.0301504i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 88.2998 | 0.592616 | 0.296308 | − | 0.955092i | \(-0.404244\pi\) | ||||
0.296308 | + | 0.955092i | \(0.404244\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 206.583i | 1.36810i | 0.729436 | + | 0.684049i | \(0.239783\pi\) | ||||
−0.729436 | + | 0.684049i | \(0.760217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.15081i | 0.0332310i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26.7209 | 0.170197 | 0.0850983 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850983 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 137.955 | 0.856861 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 97.2877 | 0.596857 | 0.298428 | − | 0.954432i | \(-0.403538\pi\) | ||||
0.298428 | + | 0.954432i | \(0.403538\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 223.241i | − | 1.33678i | −0.743813 | − | 0.668388i | \(-0.766985\pi\) | ||
0.743813 | − | 0.668388i | \(-0.233015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 80.4669 | 0.476135 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 204.170i | − | 1.18018i | −0.807339 | − | 0.590088i | \(-0.799093\pi\) | ||
0.807339 | − | 0.590088i | \(-0.200907\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 239.648 | 1.36942 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 232.055i | − | 1.29640i | −0.761471 | − | 0.648199i | \(-0.775522\pi\) | ||
0.761471 | − | 0.648199i | \(-0.224478\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 331.929i | 1.83386i | 0.399046 | + | 0.916931i | \(0.369341\pi\) | ||||
−0.399046 | + | 0.916931i | \(0.630659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.31671i | − | 0.00711734i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −242.732 | −1.29803 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3760 | 0.0909740 | 0.0454870 | − | 0.998965i | \(-0.485516\pi\) | ||||
0.0454870 | + | 0.998965i | \(0.485516\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 76.4470i | − | 0.396098i | −0.980192 | − | 0.198049i | \(-0.936539\pi\) | ||
0.980192 | − | 0.198049i | \(-0.0634606\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −160.689 | −0.815682 | −0.407841 | − | 0.913053i | \(-0.633718\pi\) | ||||
−0.407841 | + | 0.913053i | \(0.633718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 65.4612 | 0.328951 | 0.164475 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164475 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 105.561i | − | 0.520005i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 25.4192i | − | 0.123996i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.0073 | + | 181.067i | −0.0861594 | + | 0.866347i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.14353i | 0.0101589i | 0.999987 | + | 0.00507945i | \(0.00161685\pi\) | ||||
−0.999987 | + | 0.00507945i | \(0.998383\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.7408 | 0.0499573 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 124.371i | − | 0.573136i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 238.483i | − | 1.07911i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 213.813i | 0.958801i | 0.877596 | + | 0.479401i | \(0.159146\pi\) | ||||
−0.877596 | + | 0.479401i | \(0.840854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 255.635i | 1.12615i | 0.826407 | + | 0.563074i | \(0.190381\pi\) | ||||
−0.826407 | + | 0.563074i | \(0.809619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.51136 | −0.0371675 | −0.0185837 | − | 0.999827i | \(-0.505916\pi\) | ||||
−0.0185837 | + | 0.999827i | \(0.505916\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −258.670 | −1.11017 | −0.555087 | − | 0.831793i | \(-0.687315\pi\) | ||||
−0.555087 | + | 0.831793i | \(0.687315\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.25354 | −0.0308661 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −198.289 | −0.829659 | −0.414830 | − | 0.909899i | \(-0.636159\pi\) | ||||
−0.414830 | + | 0.909899i | \(0.636159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 276.361i | 1.14673i | 0.819301 | + | 0.573363i | \(0.194362\pi\) | ||||
−0.819301 | + | 0.573363i | \(0.805638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.6103 | 0.0718786 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −177.897 | − | 17.6921i | −0.720232 | − | 0.0716280i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 36.0391 | 0.143582 | 0.0717910 | − | 0.997420i | \(-0.477129\pi\) | ||||
0.0717910 | + | 0.997420i | \(0.477129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 136.944 | 0.541279 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 54.9763i | 0.213916i | 0.994264 | + | 0.106958i | \(0.0341110\pi\) | ||||
−0.994264 | + | 0.106958i | \(0.965889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.7930i | 0.122753i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 412.873 | 1.56986 | 0.784930 | − | 0.619585i | \(-0.212699\pi\) | ||||
0.784930 | + | 0.619585i | \(0.212699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.6859i | 0.0554185i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 53.5609i | − | 0.199111i | −0.995032 | − | 0.0995556i | \(-0.968258\pi\) | ||
0.995032 | − | 0.0995556i | \(-0.0317421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −144.211 | −0.532144 | −0.266072 | − | 0.963953i | \(-0.585726\pi\) | ||||
−0.266072 | + | 0.963953i | \(0.585726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 237.892 | 0.865062 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −147.518 | −0.532555 | −0.266278 | − | 0.963896i | \(-0.585794\pi\) | ||||
−0.266278 | + | 0.963896i | \(0.585794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 174.862i | 0.622285i | 0.950363 | + | 0.311143i | \(0.100712\pi\) | ||||
−0.950363 | + | 0.311143i | \(0.899288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 369.648 | 1.30618 | 0.653088 | − | 0.757282i | \(-0.273473\pi\) | ||||
0.653088 | + | 0.757282i | \(0.273473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 613.767i | 2.13856i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 353.408 | 1.22286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 412.246i | 1.40698i | 0.710703 | + | 0.703492i | \(0.248377\pi\) | ||||
−0.710703 | + | 0.703492i | \(0.751623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.00798i | 0.0169762i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 134.547i | 0.449988i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −259.346 | −0.861615 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.7374 | 0.0614342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 235.408i | 0.766801i | 0.923582 | + | 0.383401i | \(0.125247\pi\) | ||||
−0.923582 | + | 0.383401i | \(0.874753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −88.0082 | −0.282985 | −0.141492 | − | 0.989939i | \(-0.545190\pi\) | ||||
−0.141492 | + | 0.989939i | \(0.545190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −35.2591 | −0.112649 | −0.0563244 | − | 0.998413i | \(-0.517938\pi\) | ||||
−0.0563244 | + | 0.998413i | \(0.517938\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 158.913i | 0.501304i | 0.968077 | + | 0.250652i | \(0.0806449\pi\) | ||||
−0.968077 | + | 0.250652i | \(0.919355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 104.787i | − | 0.328487i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.6576 | − | 479.206i | 0.147547 | − | 1.48361i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 233.728i | 0.719163i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 175.143 | 0.532349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 137.393i | 0.415083i | 0.978226 | + | 0.207542i | \(0.0665462\pi\) | ||||
−0.978226 | + | 0.207542i | \(0.933454\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 28.5309i | − | 0.0851668i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6995i | 0.0406513i | 0.999793 | + | 0.0203257i | \(0.00647030\pi\) | ||||
−0.999793 | + | 0.0203257i | \(0.993530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 123.459i | − | 0.362050i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47.5147 | 0.138527 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −349.872 | −1.00828 | −0.504138 | − | 0.863623i | \(-0.668190\pi\) | ||||
−0.504138 | + | 0.863623i | \(0.668190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −123.670 | −0.354355 | −0.177178 | − | 0.984179i | \(-0.556697\pi\) | ||||
−0.177178 | + | 0.984179i | \(0.556697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −450.273 | −1.27556 | −0.637781 | − | 0.770218i | \(-0.720147\pi\) | ||||
−0.637781 | + | 0.770218i | \(0.720147\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 14.5373i | − | 0.0409501i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 329.805 | 0.918677 | 0.459339 | − | 0.888261i | \(-0.348086\pi\) | ||||
0.459339 | + | 0.888261i | \(0.348086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −353.929 | − | 71.1006i | −0.980413 | − | 0.196955i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.2167 | −0.0663470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 413.600 | 1.12697 | 0.563487 | − | 0.826125i | \(-0.309459\pi\) | ||||
0.563487 | + | 0.826125i | \(0.309459\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 354.603i | − | 0.955804i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 499.071i | 1.33799i | 0.743266 | + | 0.668996i | \(0.233276\pi\) | ||||
−0.743266 | + | 0.668996i | \(0.766724\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 102.953 | 0.273086 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 288.611i | 0.761506i | 0.924677 | + | 0.380753i | \(0.124335\pi\) | ||||
−0.924677 | + | 0.380753i | \(0.875665\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 208.950i | 0.545561i | 0.962076 | + | 0.272781i | \(0.0879433\pi\) | ||||
−0.962076 | + | 0.272781i | \(0.912057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36.9158 | 0.0958852 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −206.027 | −0.529633 | −0.264816 | − | 0.964299i | \(-0.585311\pi\) | ||||
−0.264816 | + | 0.964299i | \(0.585311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −362.431 | −0.926933 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.6620i | 0.102942i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 565.530 | 1.42451 | 0.712255 | − | 0.701921i | \(-0.247674\pi\) | ||||
0.712255 | + | 0.701921i | \(0.247674\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 590.729i | − | 1.47314i | −0.676362 | − | 0.736569i | \(-0.736444\pi\) | ||
0.676362 | − | 0.736569i | \(-0.263556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 121.298 | 0.300988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.5600i | 0.0775430i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 618.496i | − | 1.51221i | −0.654448 | − | 0.756107i | \(-0.727099\pi\) | ||
0.654448 | − | 0.756107i | \(-0.272901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 120.922i | − | 0.292789i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.2463 | −0.0608344 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 387.207 | 0.924122 | 0.462061 | − | 0.886848i | \(-0.347110\pi\) | ||||
0.462061 | + | 0.886848i | \(0.347110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 624.939i | 1.48442i | 0.670170 | + | 0.742208i | \(0.266221\pi\) | ||||
−0.670170 | + | 0.742208i | \(0.733779\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −629.598 | −1.48141 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −452.431 | −1.05956 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 737.075i | − | 1.71015i | −0.518503 | − | 0.855076i | \(-0.673511\pi\) | ||
0.518503 | − | 0.855076i | \(-0.326489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 75.9481i | 0.175400i | 0.996147 | + | 0.0876999i | \(0.0279517\pi\) | ||||
−0.996147 | + | 0.0876999i | \(0.972048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.8873 | + | 270.356i | −0.0615269 | + | 0.618664i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 230.299i | 0.524599i | 0.964986 | + | 0.262300i | \(0.0844809\pi\) | ||||
−0.964986 | + | 0.262300i | \(0.915519\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 771.602 | 1.74177 | 0.870883 | − | 0.491490i | \(-0.163548\pi\) | ||||
0.870883 | + | 0.491490i | \(0.163548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.9748i | 0.0965725i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 624.898i | − | 1.39175i | −0.718161 | − | 0.695877i | \(-0.755016\pi\) | ||
0.718161 | − | 0.695877i | \(-0.244984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 609.269i | 1.35093i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.2696i | 0.0797135i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 202.318 | 0.442709 | 0.221355 | − | 0.975193i | \(-0.428952\pi\) | ||||
0.221355 | + | 0.975193i | \(0.428952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −760.243 | −1.64912 | −0.824558 | − | 0.565777i | \(-0.808576\pi\) | ||||
−0.824558 | + | 0.565777i | \(0.808576\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −698.217 | −1.50803 | −0.754014 | − | 0.656858i | \(-0.771885\pi\) | ||||
−0.754014 | + | 0.656858i | \(0.771885\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 348.694 | 0.746669 | 0.373334 | − | 0.927697i | \(-0.378214\pi\) | ||||
0.373334 | + | 0.927697i | \(0.378214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 688.902i | 1.46887i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −257.446 | −0.544282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −46.7073 | + | 469.650i | −0.0983311 | + | 0.988737i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 771.639 | 1.61094 | 0.805469 | − | 0.592638i | \(-0.201914\pi\) | ||||
0.805469 | + | 0.592638i | \(0.201914\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.0076 | −0.0644649 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.2282i | 0.0994395i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 388.393i | − | 0.797522i | −0.917055 | − | 0.398761i | \(-0.869440\pi\) | ||
0.917055 | − | 0.398761i | \(-0.130560\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −93.7707 | −0.190979 | −0.0954896 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954896 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 277.327i | 0.562530i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 351.015i | 0.706267i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 805.601 | 1.61443 | 0.807216 | − | 0.590256i | \(-0.200973\pi\) | ||||
0.807216 | + | 0.590256i | \(0.200973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 47.6059 | 0.0946438 | 0.0473219 | − | 0.998880i | \(-0.484931\pi\) | ||||
0.0473219 | + | 0.998880i | \(0.484931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.0845 | 0.0971971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 503.616i | 0.989423i | 0.869057 | + | 0.494712i | \(0.164726\pi\) | ||||
−0.869057 | + | 0.494712i | \(0.835274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 584.731 | 1.14429 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.4685i | 0.0339194i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 173.859 | 0.336285 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 295.180i | 0.566565i | 0.959037 | + | 0.283283i | \(0.0914234\pi\) | ||||
−0.959037 | + | 0.283283i | \(0.908577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 276.982i | 0.529602i | 0.964303 | + | 0.264801i | \(0.0853063\pi\) | ||||
−0.964303 | + | 0.264801i | \(0.914694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 326.743i | 0.620006i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −324.525 | −0.613470 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −598.605 | −1.12309 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 70.6808i | 0.132114i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −422.098 | −0.783114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −290.663 | −0.537270 | −0.268635 | − | 0.963242i | \(-0.586573\pi\) | ||||
−0.268635 | + | 0.963242i | \(0.586573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 56.6825i | 0.104005i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 462.255i | − | 0.845073i | −0.906346 | − | 0.422536i | \(-0.861140\pi\) | ||
0.906346 | − | 0.422536i | \(-0.138860\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 206.873 | + | 20.5738i | 0.375450 | + | 0.0373390i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 981.817i | − | 1.77544i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −262.668 | −0.471576 | −0.235788 | − | 0.971805i | \(-0.575767\pi\) | ||||
−0.235788 | + | 0.971805i | \(0.575767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 252.939i | − | 0.452485i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 778.649i | 1.38303i | 0.722360 | + | 0.691517i | \(0.243057\pi\) | ||||
−0.722360 | + | 0.691517i | \(0.756943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 36.7084i | − | 0.0649706i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 211.390i | 0.371511i | 0.982596 | + | 0.185756i | \(0.0594733\pi\) | ||||
−0.982596 | + | 0.185756i | \(0.940527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 414.687 | 0.726246 | 0.363123 | − | 0.931741i | \(-0.381710\pi\) | ||||
0.363123 | + | 0.931741i | \(0.381710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 355.204 | 0.617746 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −930.861 | −1.61328 | −0.806639 | − | 0.591045i | \(-0.798716\pi\) | ||||
−0.806639 | + | 0.591045i | \(0.798716\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 609.592 | 1.04921 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 352.005i | − | 0.603781i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 423.095 | 0.720776 | 0.360388 | − | 0.932803i | \(-0.382644\pi\) | ||||
0.360388 | + | 0.932803i | \(0.382644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 243.735 | + | 24.2397i | 0.413811 | + | 0.0411541i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −531.055 | −0.895540 | −0.447770 | − | 0.894149i | \(-0.647782\pi\) | ||||
−0.447770 | + | 0.894149i | \(0.647782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −97.7003 | −0.164202 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 97.5458i | − | 0.162848i | −0.996680 | − | 0.0814239i | \(-0.974053\pi\) | ||
0.996680 | − | 0.0814239i | \(-0.0259467\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 660.902i | − | 1.09967i | −0.835273 | − | 0.549835i | \(-0.814690\pi\) | ||
0.835273 | − | 0.549835i | \(-0.185310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.7006 | −0.0193398 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 982.250i | − | 1.61820i | −0.587668 | − | 0.809102i | \(-0.699954\pi\) | ||
0.587668 | − | 0.809102i | \(-0.300046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 170.816i | 0.279568i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 584.604 | 0.953676 | 0.476838 | − | 0.878991i | \(-0.341783\pi\) | ||||
0.476838 | + | 0.878991i | \(0.341783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 517.294 | 0.838402 | 0.419201 | − | 0.907893i | \(-0.362310\pi\) | ||||
0.419201 | + | 0.907893i | \(0.362310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −311.076 | −0.502547 | −0.251273 | − | 0.967916i | \(-0.580849\pi\) | ||||
−0.251273 | + | 0.967916i | \(0.580849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1037.66i | − | 1.66559i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 613.052 | 0.980884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 83.5258i | − | 0.132791i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 316.443 | 0.501494 | 0.250747 | − | 0.968053i | \(-0.419324\pi\) | ||||
0.250747 | + | 0.968053i | \(0.419324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 79.9941i | 0.125975i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 414.710i | − | 0.651036i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 269.856i | − | 0.420992i | −0.977595 | − | 0.210496i | \(-0.932492\pi\) | ||
0.977595 | − | 0.210496i | \(-0.0675078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1088.71 | −1.69317 | −0.846585 | − | 0.532253i | \(-0.821345\pi\) | ||||
−0.846585 | + | 0.532253i | \(0.821345\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1130.62 | −1.74748 | −0.873742 | − | 0.486390i | \(-0.838313\pi\) | ||||
−0.873742 | + | 0.486390i | \(0.838313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 120.036i | − | 0.184955i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 737.823 | 1.12990 | 0.564949 | − | 0.825126i | \(-0.308896\pi\) | ||||
0.564949 | + | 0.825126i | \(0.308896\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −77.5063 | −0.118330 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 837.755i | 1.27125i | 0.771997 | + | 0.635626i | \(0.219258\pi\) | ||||
−0.771997 | + | 0.635626i | \(0.780742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 365.664i | 0.553198i | 0.960985 | + | 0.276599i | \(0.0892074\pi\) | ||||
−0.960985 | + | 0.276599i | \(0.910793\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.24799 | + | 72.8798i | −0.0108992 | + | 0.109594i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 156.461i | − | 0.234575i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −449.115 | −0.669323 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 463.801i | − | 0.689154i | −0.938758 | − | 0.344577i | \(-0.888022\pi\) | ||
0.938758 | − | 0.344577i | \(-0.111978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 174.869i | − | 0.258299i | −0.991625 | − | 0.129150i | \(-0.958775\pi\) | ||
0.991625 | − | 0.129150i | \(-0.0412247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1164.51i | − | 1.71504i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 813.802i | − | 1.19151i | −0.803166 | − | 0.595755i | \(-0.796853\pi\) | ||
0.803166 | − | 0.595755i | \(-0.203147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 95.7130 | 0.139727 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 345.843 | 0.501949 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −132.179 | −0.191286 | −0.0956430 | − | 0.995416i | \(-0.530491\pi\) | ||||
−0.0956430 | + | 0.995416i | \(0.530491\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.1309 | −0.0361596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1612.47i | − | 2.31345i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 567.236 | 0.809182 | 0.404591 | − | 0.914498i | \(-0.367414\pi\) | ||||
0.404591 | + | 0.914498i | \(0.367414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −62.3063 | − | 6.19644i | −0.0886291 | − | 0.00881428i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1185.19 | −1.67636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1074.59 | 1.51564 | 0.757818 | − | 0.652466i | \(-0.226265\pi\) | ||||
0.757818 | + | 0.652466i | \(0.226265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 184.341i | − | 0.258542i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0038i | 0.0503550i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.8511 | −0.0345634 | −0.0172817 | − | 0.999851i | \(-0.505501\pi\) | ||||
−0.0172817 | + | 0.999851i | \(0.505501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 421.792i | − | 0.585010i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 271.797i | − | 0.374893i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9916 | −0.0330008 | −0.0165004 | − | 0.999864i | \(-0.505252\pi\) | ||||
−0.0165004 | + | 0.999864i | \(0.505252\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 681.348 | 0.932076 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1111.45 | −1.51631 | −0.758153 | − | 0.652077i | \(-0.773898\pi\) | ||||
−0.758153 | + | 0.652077i | \(0.773898\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 683.853i | 0.927887i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 125.652 | 0.170030 | 0.0850151 | − | 0.996380i | \(-0.472906\pi\) | ||||
0.0850151 | + | 0.996380i | \(0.472906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 181.459i | − | 0.244225i | −0.992516 | − | 0.122113i | \(-0.961033\pi\) | ||
0.992516 | − | 0.122113i | \(-0.0389669\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.2804 | 0.0473563 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1706.65i | − | 2.27857i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 366.770i | 0.488376i | 0.969728 | + | 0.244188i | \(0.0785214\pi\) | ||||
−0.969728 | + | 0.244188i | \(0.921479\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 82.5407i | 0.109325i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1200.98 | −1.58650 | −0.793249 | − | 0.608897i | \(-0.791612\pi\) | ||||
−0.793249 | + | 0.608897i | \(0.791612\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 75.2919 | 0.0989381 | 0.0494690 | − | 0.998776i | \(-0.484247\pi\) | ||||
0.0494690 | + | 0.998776i | \(0.484247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1368.65i | − | 1.79377i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 117.935 | 0.153761 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1293.99 | −1.68269 | −0.841345 | − | 0.540498i | \(-0.818236\pi\) | ||||
−0.841345 | + | 0.540498i | \(0.818236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 121.722i | 0.157466i | 0.996896 | + | 0.0787332i | \(0.0250875\pi\) | ||||
−0.996896 | + | 0.0787332i | \(0.974912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 320.228i | − | 0.413197i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1202.83 | − | 119.623i | −1.54407 | − | 0.153560i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 348.442i | 0.446149i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.6764 | 0.0136005 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 913.776i | − | 1.16109i | −0.814229 | − | 0.580544i | \(-0.802840\pi\) | ||
0.814229 | − | 0.580544i | \(-0.197160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 886.354i | 1.12055i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 441.254i | − | 0.556437i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 758.213i | 0.951334i | 0.879625 | + | 0.475667i | \(0.157793\pi\) | ||||
−0.879625 | + | 0.475667i | \(0.842207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −460.131 | −0.575884 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 580.446 | 0.722847 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 55.1201 | 0.0684722 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 226.582 | 0.280077 | 0.140039 | − | 0.990146i | \(-0.455277\pi\) | ||||
0.140039 | + | 0.990146i | \(0.455277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 268.988i | 0.331675i | 0.986153 | + | 0.165837i | \(0.0530326\pi\) | ||||
−0.986153 | + | 0.165837i | \(0.946967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.8716 | 0.0476952 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.5464 | − | 508.253i | 0.0618683 | − | 0.622097i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1008.05 | −1.22783 | −0.613915 | − | 0.789372i | \(-0.710406\pi\) | ||||
−0.613915 | + | 0.789372i | \(0.710406\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 747.774 | 0.908595 | 0.454298 | − | 0.890850i | \(-0.349890\pi\) | ||||
0.454298 | + | 0.890850i | \(0.349890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 363.466i | − | 0.439499i | −0.975556 | − | 0.219750i | \(-0.929476\pi\) | ||
0.975556 | − | 0.219750i | \(-0.0705240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.7417i | 0.0515582i | 0.999668 | + | 0.0257791i | \(0.00820665\pi\) | ||||
−0.999668 | + | 0.0257791i | \(0.991793\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1117.11 | 1.34107 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 89.1967i | − | 0.106822i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 769.521i | − | 0.917189i | −0.888646 | − | 0.458594i | \(-0.848353\pi\) | ||
0.888646 | − | 0.458594i | \(-0.151647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 721.278 | 0.857643 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.1508 | 0.0380482 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 282.521 | 0.333555 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.1232i | 0.0553739i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 296.927 | 0.348097 | 0.174049 | − | 0.984737i | \(-0.444315\pi\) | ||||
0.174049 | + | 0.984737i | \(0.444315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 993.109i | 1.15882i | 0.815036 | + | 0.579410i | \(0.196717\pi\) | ||||
−0.815036 | + | 0.579410i | \(0.803283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 761.846 | 0.886899 | 0.443449 | − | 0.896299i | \(-0.353755\pi\) | ||||
0.443449 | + | 0.896299i | \(0.353755\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 886.359i | 1.02707i | 0.858070 | + | 0.513533i | \(0.171664\pi\) | ||||
−0.858070 | + | 0.513533i | \(0.828336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 81.5768i | − | 0.0943085i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 974.622i | − | 1.12154i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −671.883 | −0.771393 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 192.120 | 0.219565 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 775.062i | − | 0.883765i | −0.897073 | − | 0.441883i | \(-0.854311\pi\) | ||
0.897073 | − | 0.441883i | \(-0.145689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 286.737 | 0.325468 | 0.162734 | − | 0.986670i | \(-0.447969\pi\) | ||||
0.162734 | + | 0.986670i | \(0.447969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −771.537 | −0.873768 | −0.436884 | − | 0.899518i | \(-0.643918\pi\) | ||||
−0.436884 | + | 0.899518i | \(0.643918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 361.445i | 0.407492i | 0.979024 | + | 0.203746i | \(0.0653117\pi\) | ||||
−0.979024 | + | 0.203746i | \(0.934688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1931.52i | − | 2.17269i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.1352 | + | 343.236i | −0.0382254 | + | 0.384363i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 92.7183i | − | 0.103596i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −141.055 | −0.156902 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 931.605i | 1.03397i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 132.623i | 0.146545i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 665.325i | − | 0.733544i | −0.930311 | − | 0.366772i | \(-0.880463\pi\) | ||
0.930311 | − | 0.366772i | \(-0.119537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1312.71i | − | 1.44095i | −0.693480 | − | 0.720475i | \(-0.743924\pi\) | ||
0.693480 | − | 0.720475i | \(-0.256076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 605.125 | 0.662787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1871.46 | 2.04085 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −760.325 | −0.827340 | −0.413670 | − | 0.910427i | \(-0.635753\pi\) | ||||
−0.413670 | + | 0.910427i | \(0.635753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −342.343 | −0.370903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 81.8603i | 0.0884976i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −319.967 | −0.344421 | −0.172210 | − | 0.985060i | \(-0.555091\pi\) | ||||
−0.172210 | + | 0.985060i | \(0.555091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.8741 | − | 833.313i | 0.0890162 | − | 0.895073i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −96.9843 | −0.103727 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −85.7418 | −0.0915067 | −0.0457534 | − | 0.998953i | \(-0.514569\pi\) | ||||
−0.0457534 | + | 0.998953i | \(0.514569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1308.42i | 1.39046i | 0.718788 | + | 0.695229i | \(0.244697\pi\) | ||||
−0.718788 | + | 0.695229i | \(0.755303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 909.718i | 0.964707i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1165.13 | −1.23034 | −0.615170 | − | 0.788395i | \(-0.710913\pi\) | ||||
−0.615170 | + | 0.788395i | \(0.710913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 570.286i | 0.600934i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 541.282i | − | 0.567977i | −0.958828 | − | 0.283989i | \(-0.908342\pi\) | ||
0.958828 | − | 0.283989i | \(-0.0916578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.94264 | 0.00726979 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2311.07 | −2.40988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 794.811 | 0.827067 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 30.5446i | − | 0.0316524i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1366.36 | 1.41298 | 0.706492 | − | 0.707721i | \(-0.250276\pi\) | ||||
0.706492 | + | 0.707721i | \(0.250276\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 433.446i | 0.446391i | 0.974774 | + | 0.223195i | \(0.0716488\pi\) | ||||
−0.974774 | + | 0.223195i | \(0.928351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 606.807 | 0.623646 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1597.95i | − | 1.63557i | −0.575523 | − | 0.817786i | \(-0.695201\pi\) | ||
0.575523 | − | 0.817786i | \(-0.304799\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1030.06i | − | 1.05215i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1405.05i | 1.42934i | 0.699459 | + | 0.714672i | \(0.253424\pi\) | ||||
−0.699459 | + | 0.714672i | \(0.746576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −64.2039 | −0.0651816 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −384.400 | −0.388675 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 185.937i | 0.187626i | 0.995590 | + | 0.0938131i | \(0.0299056\pi\) | ||||
−0.995590 | + | 0.0938131i | \(0.970094\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.1552 | 0.0262866 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 644.432 | 0.646371 | 0.323186 | − | 0.946336i | \(-0.395246\pi\) | ||||
0.323186 | + | 0.946336i | \(0.395246\pi\) | |||||||
\(998\) | 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 | 2736.3.o.q.721.11 | 20 | ||
3.2 | odd | 2 | inner | 2736.3.o.q.721.9 | 20 | ||
4.3 | odd | 2 | 1368.3.o.d.721.11 | yes | 20 | ||
12.11 | even | 2 | 1368.3.o.d.721.9 | ✓ | 20 | ||
19.18 | odd | 2 | inner | 2736.3.o.q.721.12 | 20 | ||
57.56 | even | 2 | inner | 2736.3.o.q.721.10 | 20 | ||
76.75 | even | 2 | 1368.3.o.d.721.12 | yes | 20 | ||
228.227 | odd | 2 | 1368.3.o.d.721.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.3.o.d.721.9 | ✓ | 20 | 12.11 | even | 2 | ||
1368.3.o.d.721.10 | yes | 20 | 228.227 | odd | 2 | ||
1368.3.o.d.721.11 | yes | 20 | 4.3 | odd | 2 | ||
1368.3.o.d.721.12 | yes | 20 | 76.75 | even | 2 | ||
2736.3.o.q.721.9 | 20 | 3.2 | odd | 2 | inner | ||
2736.3.o.q.721.10 | 20 | 57.56 | even | 2 | inner | ||
2736.3.o.q.721.11 | 20 | 1.1 | even | 1 | trivial | ||
2736.3.o.q.721.12 | 20 | 19.18 | odd | 2 | inner |