Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.5 | ||
Root | \(0.500000 + 2.19293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.m.703.6 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 5.13244 | 1.02649 | 0.513244 | − | 0.858242i | \(-0.328443\pi\) | ||||
0.513244 | + | 0.858242i | \(0.328443\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.02516i | − 0.575023i | −0.957777 | − | 0.287511i | \(-0.907172\pi\) | ||||
0.957777 | − | 0.287511i | \(-0.0928279\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.30344i | − 0.391222i | −0.980682 | − | 0.195611i | \(-0.937331\pi\) | ||||
0.980682 | − | 0.195611i | \(-0.0626689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.4862 | 1.42202 | 0.711008 | − | 0.703184i | \(-0.248239\pi\) | ||||
0.711008 | + | 0.703184i | \(0.248239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.5751 | 1.38677 | 0.693384 | − | 0.720568i | \(-0.256119\pi\) | ||||
0.693384 | + | 0.720568i | \(0.256119\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.7259i | 1.14347i | 0.820438 | + | 0.571735i | \(0.193729\pi\) | ||||
−0.820438 | + | 0.571735i | \(0.806271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 30.7461i | 1.33679i | 0.743809 | + | 0.668393i | \(0.233017\pi\) | ||||
−0.743809 | + | 0.668393i | \(0.766983\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.34199 | 0.0536794 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.6840 | −0.437378 | −0.218689 | − | 0.975795i | \(-0.570178\pi\) | ||||
−0.218689 | + | 0.975795i | \(0.570178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.5298i | 0.791283i | 0.918405 | + | 0.395642i | \(0.129478\pi\) | ||||
−0.918405 | + | 0.395642i | \(0.870522\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 20.6589i | − 0.590254i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −18.2314 | −0.492740 | −0.246370 | − | 0.969176i | \(-0.579238\pi\) | ||||
−0.246370 | + | 0.969176i | \(0.579238\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 38.0990 | 0.929244 | 0.464622 | − | 0.885509i | \(-0.346190\pi\) | ||||
0.464622 | + | 0.885509i | \(0.346190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 34.9724i | − 0.813312i | −0.913581 | − | 0.406656i | \(-0.866695\pi\) | ||||
0.913581 | − | 0.406656i | \(-0.133305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 29.6295i | − 0.630415i | −0.949023 | − | 0.315208i | \(-0.897926\pi\) | ||||
0.949023 | − | 0.315208i | \(-0.102074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 32.7981 | 0.669349 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −39.3043 | −0.741591 | −0.370796 | − | 0.928715i | \(-0.620915\pi\) | ||||
−0.370796 | + | 0.928715i | \(0.620915\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 22.0872i | − 0.401585i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 65.3429i | − 1.10751i | −0.832681 | − | 0.553753i | \(-0.813195\pi\) | ||||
0.832681 | − | 0.553753i | \(-0.186805\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29.8541 | 0.489412 | 0.244706 | − | 0.969597i | \(-0.421309\pi\) | ||||
0.244706 | + | 0.969597i | \(0.421309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 94.8794 | 1.45968 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.8634i | − 0.177066i | −0.996073 | − | 0.0885329i | \(-0.971782\pi\) | ||||
0.996073 | − | 0.0885329i | \(-0.0282178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 140.651i | 1.98100i | 0.137529 | + | 0.990498i | \(0.456084\pi\) | ||||
−0.137529 | + | 0.990498i | \(0.543916\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 119.285 | 1.63404 | 0.817022 | − | 0.576607i | \(-0.195624\pi\) | ||||
0.817022 | + | 0.576607i | \(0.195624\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.3220 | −0.224961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 9.18859i | − 0.116311i | −0.998308 | − | 0.0581556i | \(-0.981478\pi\) | ||||
0.998308 | − | 0.0581556i | \(-0.0185220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 113.180i | − 1.36362i | −0.731529 | − | 0.681810i | \(-0.761193\pi\) | ||||
0.731529 | − | 0.681810i | \(-0.238807\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 120.998 | 1.42350 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.88346 | 0.0885782 | 0.0442891 | − | 0.999019i | \(-0.485898\pi\) | ||||
0.0442891 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 74.4099i | − 0.817691i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 111.507i | 1.17376i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 55.5080 | 0.572248 | 0.286124 | − | 0.958193i | \(-0.407633\pi\) | ||||
0.286124 | + | 0.958193i | \(0.407633\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −195.186 | −1.93253 | −0.966265 | − | 0.257550i | \(-0.917085\pi\) | ||||
−0.966265 | + | 0.257550i | \(0.917085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29.3579i | 0.285028i | 0.989793 | + | 0.142514i | \(0.0455186\pi\) | ||||
−0.989793 | + | 0.142514i | \(0.954481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 133.256i | 1.24538i | 0.782468 | + | 0.622691i | \(0.213961\pi\) | ||||
−0.782468 | + | 0.622691i | \(0.786039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 198.485 | 1.82096 | 0.910481 | − | 0.413552i | \(-0.135712\pi\) | ||||
0.910481 | + | 0.413552i | \(0.135712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −178.745 | −1.58182 | −0.790908 | − | 0.611934i | \(-0.790392\pi\) | ||||
−0.790908 | + | 0.611934i | \(0.790392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 157.802i | 1.37220i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 94.8934i | − 0.797424i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 102.480 | 0.846946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −121.423 | −0.971388 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 172.213i | − 1.35601i | −0.735058 | − | 0.678004i | \(-0.762845\pi\) | ||||
0.735058 | − | 0.678004i | \(-0.237155\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 206.300i | − 1.57481i | −0.616435 | − | 0.787406i | \(-0.711424\pi\) | ||||
0.616435 | − | 0.787406i | \(-0.288576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.4503 | 0.657521 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 85.1089 | 0.621233 | 0.310616 | − | 0.950535i | \(-0.399465\pi\) | ||||
0.310616 | + | 0.950535i | \(0.399465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 150.326i | 1.08148i | 0.841189 | + | 0.540742i | \(0.181856\pi\) | ||||
−0.841189 | + | 0.540742i | \(0.818144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 79.5542i | − 0.556323i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −65.0998 | −0.448964 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 111.133 | 0.745861 | 0.372931 | − | 0.927859i | \(-0.378353\pi\) | ||||
0.372931 | + | 0.927859i | \(0.378353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 166.295i | 1.10129i | 0.834739 | + | 0.550646i | \(0.185619\pi\) | ||||
−0.834739 | + | 0.550646i | \(0.814381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 125.898i | 0.812243i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −50.1560 | −0.319465 | −0.159732 | − | 0.987160i | \(-0.551063\pi\) | ||||
−0.159732 | + | 0.987160i | \(0.551063\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 123.758 | 0.768682 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 265.994i | − 1.63187i | −0.578145 | − | 0.815934i | \(-0.696223\pi\) | ||||
0.578145 | − | 0.815934i | \(-0.303777\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 223.651i | 1.33923i | 0.742708 | + | 0.669615i | \(0.233541\pi\) | ||||
−0.742708 | + | 0.669615i | \(0.766459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 172.740 | 1.02213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −55.4735 | −0.320656 | −0.160328 | − | 0.987064i | \(-0.551255\pi\) | ||||
−0.160328 | + | 0.987064i | \(0.551255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 5.40171i | − 0.0308669i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 10.7562i | − 0.0600907i | −0.999549 | − | 0.0300453i | \(-0.990435\pi\) | ||||
0.999549 | − | 0.0300453i | \(-0.00956517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 36.3638 | 0.200905 | 0.100453 | − | 0.994942i | \(-0.467971\pi\) | ||||
0.100453 | + | 0.994942i | \(0.467971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −93.5715 | −0.505792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 101.454i | − 0.542534i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 214.445i | − 1.12275i | −0.827563 | − | 0.561373i | \(-0.810273\pi\) | ||||
0.827563 | − | 0.561373i | \(-0.189727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 280.031 | 1.45094 | 0.725470 | − | 0.688254i | \(-0.241622\pi\) | ||||
0.725470 | + | 0.688254i | \(0.241622\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 254.078 | 1.28974 | 0.644869 | − | 0.764293i | \(-0.276912\pi\) | ||||
0.644869 | + | 0.764293i | \(0.276912\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 150.197i | 0.754757i | 0.926059 | + | 0.377379i | \(0.123174\pi\) | ||||
−0.926059 | + | 0.377379i | \(0.876826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 51.0550i | 0.251503i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 195.541 | 0.953858 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 93.4962 | 0.447350 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 294.457i | 1.39553i | 0.716326 | + | 0.697765i | \(0.245822\pi\) | ||||
−0.716326 | + | 0.697765i | \(0.754178\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 179.494i | − 0.834855i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98.7363 | 0.455006 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 435.813 | 1.97201 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 90.5784i | − 0.406181i | −0.979160 | − | 0.203091i | \(-0.934901\pi\) | ||||
0.979160 | − | 0.203091i | \(-0.0650986\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 401.033i | 1.76667i | 0.468746 | + | 0.883333i | \(0.344706\pi\) | ||||
−0.468746 | + | 0.883333i | \(0.655294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 155.539 | 0.679209 | 0.339605 | − | 0.940568i | \(-0.389707\pi\) | ||||
0.339605 | + | 0.940568i | \(0.389707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −238.595 | −1.02401 | −0.512007 | − | 0.858981i | \(-0.671098\pi\) | ||||
−0.512007 | + | 0.858981i | \(0.671098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 152.072i | − 0.647114i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 61.3314i | − 0.256617i | −0.991734 | − | 0.128308i | \(-0.959045\pi\) | ||||
0.991734 | − | 0.128308i | \(-0.0409547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 270.776 | 1.12355 | 0.561776 | − | 0.827290i | \(-0.310118\pi\) | ||||
0.561776 | + | 0.827290i | \(0.310118\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 168.334 | 0.687079 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 401.630i | 1.62603i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 229.191i | − 0.913110i | −0.889695 | − | 0.456555i | \(-0.849083\pi\) | ||||
0.889695 | − | 0.456555i | \(-0.150917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 132.314 | 0.522979 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −366.617 | −1.42653 | −0.713263 | − | 0.700897i | \(-0.752783\pi\) | ||||
−0.713263 | + | 0.700897i | \(0.752783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 73.3842i | 0.283337i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 159.531i | − 0.606581i | −0.952898 | − | 0.303290i | \(-0.901915\pi\) | ||||
0.952898 | − | 0.303290i | \(-0.0980852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −201.727 | −0.761235 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −91.2480 | −0.339212 | −0.169606 | − | 0.985512i | \(-0.554249\pi\) | ||||
−0.169606 | + | 0.985512i | \(0.554249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 506.145i | − 1.86769i | −0.357675 | − | 0.933846i | \(-0.616430\pi\) | ||||
0.357675 | − | 0.933846i | \(-0.383570\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.77515i | − 0.0210006i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.7143 | 0.103662 | 0.0518308 | − | 0.998656i | \(-0.483494\pi\) | ||||
0.0518308 | + | 0.998656i | \(0.483494\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 194.297 | 0.691447 | 0.345724 | − | 0.938336i | \(-0.387633\pi\) | ||||
0.345724 | + | 0.938336i | \(0.387633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 212.089i | − 0.749432i | −0.927140 | − | 0.374716i | \(-0.877740\pi\) | ||||
0.927140 | − | 0.374716i | \(-0.122260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 153.355i | − 0.534336i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 266.784 | 0.923127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 118.777 | 0.405382 | 0.202691 | − | 0.979243i | \(-0.435031\pi\) | ||||
0.202691 | + | 0.979243i | \(0.435031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 335.369i | − 1.13684i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 568.378i | 1.90093i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −140.769 | −0.467673 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 153.225 | 0.502376 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 118.198i | 0.385011i | 0.981296 | + | 0.192506i | \(0.0616614\pi\) | ||||
−0.981296 | + | 0.192506i | \(0.938339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 57.5386i | 0.185012i | 0.995712 | + | 0.0925059i | \(0.0294877\pi\) | ||||
−0.995712 | + | 0.0925059i | \(0.970512\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −401.012 | −1.28119 | −0.640594 | − | 0.767879i | \(-0.721312\pi\) | ||||
−0.640594 | + | 0.767879i | \(0.721312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.34020 | −0.0263098 | −0.0131549 | − | 0.999913i | \(-0.504187\pi\) | ||||
−0.0131549 | + | 0.999913i | \(0.504187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 54.5847i | 0.171112i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 512.190i | 1.58573i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.8082 | 0.0763330 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −119.264 | −0.362503 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 253.990i | − 0.767340i | −0.923470 | − | 0.383670i | \(-0.874660\pi\) | ||||
0.923470 | − | 0.383670i | \(-0.125340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 60.8883i | − 0.181756i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −620.332 | −1.84075 | −0.920374 | − | 0.391040i | \(-0.872115\pi\) | ||||
−0.920374 | + | 0.391040i | \(0.872115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 105.562 | 0.309567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 329.250i | − 0.959914i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 496.172i | − 1.42989i | −0.699181 | − | 0.714945i | \(-0.746452\pi\) | ||||
0.699181 | − | 0.714945i | \(-0.253548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −63.4267 | −0.181738 | −0.0908692 | − | 0.995863i | \(-0.528965\pi\) | ||||
−0.0908692 | + | 0.995863i | \(0.528965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −439.982 | −1.24641 | −0.623204 | − | 0.782059i | \(-0.714170\pi\) | ||||
−0.623204 | + | 0.782059i | \(0.714170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 721.882i | 2.03347i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 489.550i | − 1.36365i | −0.731516 | − | 0.681824i | \(-0.761187\pi\) | ||||
0.731516 | − | 0.681824i | \(-0.238813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −111.016 | −0.307524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 612.224 | 1.67733 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 393.063i | 1.07102i | 0.844530 | + | 0.535509i | \(0.179880\pi\) | ||||
−0.844530 | + | 0.535509i | \(0.820120\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 158.206i | 0.426432i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4757 | −0.0307658 | −0.0153829 | − | 0.999882i | \(-0.504897\pi\) | ||||
−0.0153829 | + | 0.999882i | \(0.504897\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −234.478 | −0.621959 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 661.804i | − 1.74618i | −0.487556 | − | 0.873092i | \(-0.662112\pi\) | ||||
0.487556 | − | 0.873092i | \(-0.337888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 95.8558i | 0.250276i | 0.992139 | + | 0.125138i | \(0.0399374\pi\) | ||||
−0.992139 | + | 0.125138i | \(0.960063\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −88.9043 | −0.230920 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −471.609 | −1.21236 | −0.606182 | − | 0.795326i | \(-0.707300\pi\) | ||||
−0.606182 | + | 0.795326i | \(0.707300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 724.840i | 1.85381i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 47.1599i | − 0.119392i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −718.221 | −1.80912 | −0.904560 | − | 0.426346i | \(-0.859801\pi\) | ||||
−0.904560 | + | 0.426346i | \(0.859801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −225.675 | −0.562780 | −0.281390 | − | 0.959593i | \(-0.590796\pi\) | ||||
−0.281390 | + | 0.959593i | \(0.590796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 453.462i | 1.12522i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 78.4576i | 0.192770i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 588.917 | 1.43990 | 0.719948 | − | 0.694028i | \(-0.244166\pi\) | ||||
0.719948 | + | 0.694028i | \(0.244166\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −263.015 | −0.636841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 580.892i | − 1.39974i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 121.906i | − 0.290944i | −0.989362 | − | 0.145472i | \(-0.953530\pi\) | ||||
0.989362 | − | 0.145472i | \(-0.0464701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −289.293 | −0.687157 | −0.343578 | − | 0.939124i | \(-0.611639\pi\) | ||||
−0.343578 | + | 0.939124i | \(0.611639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.6374 | 0.0744410 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 120.168i | − 0.281423i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 337.402i | 0.782835i | 0.920213 | + | 0.391418i | \(0.128015\pi\) | ||||
−0.920213 | + | 0.391418i | \(0.871985\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.18171 | −0.0165859 | −0.00829297 | − | 0.999966i | \(-0.502640\pi\) | ||||
−0.00829297 | + | 0.999966i | \(0.502640\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −667.987 | −1.52857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 780.145i | 1.77710i | 0.458783 | + | 0.888548i | \(0.348285\pi\) | ||||
−0.458783 | + | 0.888548i | \(0.651715\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 478.844i | − 1.08091i | −0.841372 | − | 0.540456i | \(-0.818252\pi\) | ||||
0.841372 | − | 0.540456i | \(-0.181748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.4614 | 0.0909245 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 55.5835 | 0.123794 | 0.0618970 | − | 0.998083i | \(-0.480285\pi\) | ||||
0.0618970 | + | 0.998083i | \(0.480285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 163.957i | − 0.363540i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 381.905i | − 0.839351i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.6281 | 0.0692080 | 0.0346040 | − | 0.999401i | \(-0.488983\pi\) | ||||
0.0346040 | + | 0.999401i | \(0.488983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −498.508 | −1.08136 | −0.540681 | − | 0.841228i | \(-0.681833\pi\) | ||||
−0.540681 | + | 0.841228i | \(0.681833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 63.5797i | − 0.137321i | −0.997640 | − | 0.0686606i | \(-0.978127\pi\) | ||||
0.997640 | − | 0.0686606i | \(-0.0218726\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 550.457i | − 1.17871i | −0.807875 | − | 0.589354i | \(-0.799382\pi\) | ||||
0.807875 | − | 0.589354i | \(-0.200618\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −47.7521 | −0.101817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −150.502 | −0.318185 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.1559i | 0.0613808i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 760.357i | 1.58738i | 0.608320 | + | 0.793692i | \(0.291844\pi\) | ||||
−0.608320 | + | 0.793692i | \(0.708156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −337.029 | −0.700683 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 284.892 | 0.587406 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 340.198i | − 0.698558i | −0.937019 | − | 0.349279i | \(-0.886427\pi\) | ||||
0.937019 | − | 0.349279i | \(-0.113573\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 488.166i | 0.994229i | 0.867685 | + | 0.497114i | \(0.165607\pi\) | ||||
−0.867685 | + | 0.497114i | \(0.834393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −299.026 | −0.606543 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 566.141 | 1.13912 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 195.282i | 0.391347i | 0.980669 | + | 0.195674i | \(0.0626893\pi\) | ||||
−0.980669 | + | 0.195674i | \(0.937311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 167.239i | 0.332483i | 0.986085 | + | 0.166241i | \(0.0531631\pi\) | ||||
−0.986085 | + | 0.166241i | \(0.946837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1001.78 | −1.98372 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −374.972 | −0.736683 | −0.368342 | − | 0.929691i | \(-0.620074\pi\) | ||||
−0.368342 | + | 0.929691i | \(0.620074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 480.142i | − 0.939612i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 150.678i | 0.292578i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −127.509 | −0.246632 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −49.7644 | −0.0955170 | −0.0477585 | − | 0.998859i | \(-0.515208\pi\) | ||||
−0.0477585 | + | 0.998859i | \(0.515208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 878.700i | − 1.68012i | −0.542497 | − | 0.840058i | \(-0.682521\pi\) | ||||
0.542497 | − | 0.840058i | \(-0.317479\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 578.291i | 1.09733i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −416.320 | −0.786995 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 704.306 | 1.32140 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 683.928i | 1.27837i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 141.145i | − 0.261864i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −183.963 | −0.340043 | −0.170022 | − | 0.985440i | \(-0.554384\pi\) | ||||
−0.170022 | + | 0.985440i | \(0.554384\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1018.71 | 1.86920 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 642.639i | 1.17484i | 0.809281 | + | 0.587421i | \(0.199857\pi\) | ||||
−0.809281 | + | 0.587421i | \(0.800143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 275.571i | − 0.500129i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.9855 | −0.0668816 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −231.980 | −0.416480 | −0.208240 | − | 0.978078i | \(-0.566774\pi\) | ||||
−0.208240 | + | 0.978078i | \(0.566774\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 646.507i | − 1.15654i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 356.868i | 0.633869i | 0.948447 | + | 0.316935i | \(0.102654\pi\) | ||||
−0.948447 | + | 0.316935i | \(0.897346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −917.400 | −1.62372 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 440.786 | 0.774669 | 0.387334 | − | 0.921939i | \(-0.373396\pi\) | ||||
0.387334 | + | 0.921939i | \(0.373396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 712.649i | 1.24807i | 0.781396 | + | 0.624036i | \(0.214508\pi\) | ||||
−0.781396 | + | 0.624036i | \(0.785492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.2608i | 0.0717579i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −253.401 | −0.439170 | −0.219585 | − | 0.975593i | \(-0.570470\pi\) | ||||
−0.219585 | + | 0.975593i | \(0.570470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −455.569 | −0.784112 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 169.144i | 0.290126i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 800.800i | − 1.36422i | −0.731248 | − | 0.682112i | \(-0.761062\pi\) | ||||
0.731248 | − | 0.682112i | \(-0.238938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −532.932 | −0.904809 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 618.665 | 1.04328 | 0.521640 | − | 0.853166i | \(-0.325321\pi\) | ||||
0.521640 | + | 0.853166i | \(0.325321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 487.035i | − 0.818546i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 249.660i | 0.416795i | 0.978044 | + | 0.208398i | \(0.0668248\pi\) | ||||
−0.978044 | + | 0.208398i | \(0.933175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1137.02 | −1.89188 | −0.945941 | − | 0.324339i | \(-0.894858\pi\) | ||||
−0.945941 | + | 0.324339i | \(0.894858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 525.975 | 0.869380 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 520.853i | − 0.858077i | −0.903286 | − | 0.429038i | \(-0.858852\pi\) | ||||
0.903286 | − | 0.429038i | \(-0.141148\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 547.737i | − 0.896460i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −148.439 | −0.242152 | −0.121076 | − | 0.992643i | \(-0.538635\pi\) | ||||
−0.121076 | + | 0.992643i | \(0.538635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1081.44 | 1.75273 | 0.876366 | − | 0.481646i | \(-0.159961\pi\) | ||||
0.876366 | + | 0.481646i | \(0.159961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 306.359i | − 0.494925i | −0.968897 | − | 0.247463i | \(-0.920403\pi\) | ||||
0.968897 | − | 0.247463i | \(-0.0795967\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 31.7322i | − 0.0509345i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −656.749 | −1.05080 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −429.806 | −0.683316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 807.507i | 1.27973i | 0.768489 | + | 0.639863i | \(0.221009\pi\) | ||||
−0.768489 | + | 0.639863i | \(0.778991\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 883.874i | − 1.39193i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 606.312 | 0.951824 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −387.743 | −0.604904 | −0.302452 | − | 0.953165i | \(-0.597805\pi\) | ||||
−0.302452 | + | 0.953165i | \(0.597805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 978.913i | 1.52242i | 0.648508 | + | 0.761208i | \(0.275393\pi\) | ||||
−0.648508 | + | 0.761208i | \(0.724607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 786.067i | 1.21494i | 0.794342 | + | 0.607470i | \(0.207816\pi\) | ||||
−0.794342 | + | 0.607470i | \(0.792184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −281.199 | −0.433280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −251.026 | −0.384419 | −0.192209 | − | 0.981354i | \(-0.561565\pi\) | ||||
−0.192209 | + | 0.981354i | \(0.561565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1058.82i | − 1.61653i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 933.805i | − 1.41700i | −0.705709 | − | 0.708501i | \(-0.749372\pi\) | ||||
0.705709 | − | 0.708501i | \(-0.250628\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −473.319 | −0.716065 | −0.358033 | − | 0.933709i | \(-0.616552\pi\) | ||||
−0.358033 | + | 0.933709i | \(0.616552\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 448.834 | 0.674938 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 389.982i | − 0.584681i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 128.475i | − 0.191469i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 254.846 | 0.378671 | 0.189336 | − | 0.981912i | \(-0.439367\pi\) | ||||
0.189336 | + | 0.981912i | \(0.439367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −104.575 | −0.154468 | −0.0772338 | − | 0.997013i | \(-0.524609\pi\) | ||||
−0.0772338 | + | 0.997013i | \(0.524609\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 223.429i | − 0.329055i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 623.576i | 0.912995i | 0.889725 | + | 0.456497i | \(0.150896\pi\) | ||||
−0.889725 | + | 0.456497i | \(0.849104\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 436.817 | 0.637689 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −726.588 | −1.05455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 544.623i | − 0.788167i | −0.919075 | − | 0.394083i | \(-0.871062\pi\) | ||||
0.919075 | − | 0.394083i | \(-0.128938\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 771.541i | 1.11013i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 898.186 | 1.28865 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −411.842 | −0.587507 | −0.293753 | − | 0.955881i | \(-0.594904\pi\) | ||||
−0.293753 | + | 0.955881i | \(0.594904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 396.093i | − 0.563433i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 785.653i | 1.11125i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −679.236 | −0.958020 | −0.479010 | − | 0.877809i | \(-0.659004\pi\) | ||||
−0.479010 | + | 0.877809i | \(0.659004\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −754.194 | −1.05778 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 408.308i | − 0.571060i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 619.766i | 0.861983i | 0.902356 | + | 0.430991i | \(0.141836\pi\) | ||||
−0.902356 | + | 0.430991i | \(0.858164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 118.170 | 0.163898 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.0217 | −0.0234782 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1224.73i | 1.68463i | 0.538982 | + | 0.842317i | \(0.318809\pi\) | ||||
−0.538982 | + | 0.842317i | \(0.681191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 824.477i | − 1.12788i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −797.758 | −1.08835 | −0.544173 | − | 0.838973i | \(-0.683156\pi\) | ||||
−0.544173 | + | 0.838973i | \(0.683156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51.0534 | −0.0692719 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 422.067i | 0.571133i | 0.958359 | + | 0.285567i | \(0.0921818\pi\) | ||||
−0.958359 | + | 0.285567i | \(0.907818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 805.671i | − 1.08435i | −0.840266 | − | 0.542174i | \(-0.817601\pi\) | ||||
0.840266 | − | 0.542174i | \(-0.182399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 570.385 | 0.765618 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 536.376 | 0.716123 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1014.96i | 1.35148i | 0.737138 | + | 0.675742i | \(0.236177\pi\) | ||||
−0.737138 | + | 0.675742i | \(0.763823\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 853.501i | 1.13046i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8738 | 0.0196483 | 0.00982416 | − | 0.999952i | \(-0.496873\pi\) | ||||
0.00982416 | + | 0.999952i | \(0.496873\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 884.373 | 1.16212 | 0.581060 | − | 0.813861i | \(-0.302638\pi\) | ||||
0.581060 | + | 0.813861i | \(0.302638\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 798.933i | − 1.04709i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1207.94i | − 1.57489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −775.760 | −1.00879 | −0.504395 | − | 0.863473i | \(-0.668285\pi\) | ||||
−0.504395 | + | 0.863473i | \(0.668285\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 794.115 | 1.02732 | 0.513658 | − | 0.857995i | \(-0.328290\pi\) | ||||
0.513658 | + | 0.857995i | \(0.328290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.9186i | 0.0424756i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 827.736i | 1.06256i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 605.281 | 0.775008 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −257.423 | −0.327927 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 344.287i | − 0.437468i | −0.975785 | − | 0.218734i | \(-0.929807\pi\) | ||||
0.975785 | − | 0.218734i | \(-0.0701927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 719.478i | 0.909581i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 551.890 | 0.695952 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −986.969 | −1.23836 | −0.619178 | − | 0.785251i | \(-0.712534\pi\) | ||||
−0.619178 | + | 0.785251i | \(0.712534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 698.518i | − 0.874240i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 513.336i | − 0.639273i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 635.180 | 0.789043 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.7831 | −0.0417591 | −0.0208795 | − | 0.999782i | \(-0.506647\pi\) | ||||
−0.0208795 | + | 0.999782i | \(0.506647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 174.359i | − 0.214993i | −0.994205 | − | 0.107496i | \(-0.965717\pi\) | ||||
0.994205 | − | 0.107496i | \(-0.0342834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1365.20i | − 1.67509i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 759.808 | 0.929997 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −826.976 | −1.00728 | −0.503640 | − | 0.863914i | \(-0.668006\pi\) | ||||
−0.503640 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 789.862i | 0.959735i | 0.877341 | + | 0.479868i | \(0.159315\pi\) | ||||
−0.877341 | + | 0.479868i | \(0.840685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 94.0797i | − 0.113760i | −0.998381 | − | 0.0568801i | \(-0.981885\pi\) | ||||
0.998381 | − | 0.0568801i | \(-0.0181153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −383.996 | −0.463204 | −0.231602 | − | 0.972811i | \(-0.574397\pi\) | ||||
−0.231602 | + | 0.972811i | \(0.574397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 773.217 | 0.928232 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1147.88i | 1.37470i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1148.75i | 1.36919i | 0.728924 | + | 0.684594i | \(0.240021\pi\) | ||||
−0.728924 | + | 0.684594i | \(0.759979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −680.117 | −0.808700 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 886.576 | 1.04920 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 412.500i | − 0.487013i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 560.543i | − 0.658687i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −165.565 | −0.194097 | −0.0970485 | − | 0.995280i | \(-0.530940\pi\) | ||||
−0.0970485 | + | 0.995280i | \(0.530940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1294.69 | −1.51073 | −0.755363 | − | 0.655307i | \(-0.772539\pi\) | ||||
−0.755363 | + | 0.655307i | \(0.772539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0574i | 0.0163648i | 0.999967 | + | 0.00818241i | \(0.00260457\pi\) | ||||
−0.999967 | + | 0.00818241i | \(0.997395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 409.653i | − 0.474685i | −0.971426 | − | 0.237343i | \(-0.923724\pi\) | ||||
0.971426 | − | 0.237343i | \(-0.0762764\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −284.715 | −0.329150 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.5425 | −0.0455035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 219.309i | − 0.251790i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 488.749i | 0.558570i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0270 | 0.0114333 | 0.00571666 | − | 0.999984i | \(-0.498180\pi\) | ||||
0.00571666 | + | 0.999984i | \(0.498180\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1388.38 | −1.57591 | −0.787956 | − | 0.615731i | \(-0.788861\pi\) | ||||
−0.787956 | + | 0.615731i | \(0.788861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1445.91i | 1.63750i | 0.574153 | + | 0.818748i | \(0.305332\pi\) | ||||
−0.574153 | + | 0.818748i | \(0.694668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 661.924i | − 0.746250i | −0.927781 | − | 0.373125i | \(-0.878286\pi\) | ||||
0.927781 | − | 0.373125i | \(-0.121714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −693.185 | −0.779736 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 643.729 | 0.720861 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 55.2058i | − 0.0616824i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 311.135i | − 0.346090i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −926.602 | −1.02842 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 186.635 | 0.206227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 314.099i | 0.346306i | 0.984895 | + | 0.173153i | \(0.0553955\pi\) | ||||
−0.984895 | + | 0.173153i | \(0.944605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 620.050i | 0.680626i | 0.940312 | + | 0.340313i | \(0.110533\pi\) | ||||
−0.940312 | + | 0.340313i | \(0.889467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −487.065 | −0.533478 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −830.391 | −0.905552 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 259.390i | − 0.282253i | −0.989992 | − | 0.141126i | \(-0.954928\pi\) | ||||
0.989992 | − | 0.141126i | \(-0.0450724\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2600.10i | 2.81701i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4662 | −0.0264500 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −511.871 | −0.550991 | −0.275496 | − | 0.961302i | \(-0.588842\pi\) | ||||
−0.275496 | + | 0.961302i | \(0.588842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 712.569i | 0.765380i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 520.706i | − 0.556905i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 531.153 | 0.566866 | 0.283433 | − | 0.958992i | \(-0.408527\pi\) | ||||
0.283433 | + | 0.958992i | \(0.408527\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1401.22 | −1.48908 | −0.744540 | − | 0.667578i | \(-0.767331\pi\) | ||||
−0.744540 | + | 0.667578i | \(0.767331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1171.39i | 1.24220i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 246.077i | − 0.259849i | −0.991524 | − | 0.129925i | \(-0.958526\pi\) | ||||
0.991524 | − | 0.129925i | \(-0.0414736\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2205.13 | 2.32363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1711.93 | −1.79636 | −0.898178 | − | 0.439631i | \(-0.855109\pi\) | ||||
−0.898178 | + | 0.439631i | \(0.855109\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1100.62i | − 1.15249i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 342.577i | − 0.357223i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 359.290 | 0.373871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1437.25 | 1.48937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 801.048i | − 0.828385i | −0.910189 | − | 0.414192i | \(-0.864064\pi\) | ||||
0.910189 | − | 0.414192i | \(-0.135936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 526.798i | 0.542532i | 0.962504 | + | 0.271266i | \(0.0874423\pi\) | ||||
−0.962504 | + | 0.271266i | \(0.912558\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 605.087 | 0.621877 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −630.886 | −0.645738 | −0.322869 | − | 0.946444i | \(-0.604647\pi\) | ||||
−0.322869 | + | 0.946444i | \(0.604647\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 33.9260i | − 0.0346537i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1553.23i | − 1.58009i | −0.613051 | − | 0.790043i | \(-0.710058\pi\) | ||||
0.613051 | − | 0.790043i | \(-0.289942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1304.04 | 1.32390 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1075.26 | 1.08722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 487.053i | − 0.491476i | −0.969336 | − | 0.245738i | \(-0.920970\pi\) | ||||
0.969336 | − | 0.245738i | \(-0.0790303\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 770.876i | 0.774750i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1665.23 | 1.67024 | 0.835122 | − | 0.550065i | \(-0.185397\pi\) | ||||
0.835122 | + | 0.550065i | \(0.185397\pi\) | |||||||
\(998\) | 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 | 1728.3.g.m.703.5 | 8 | ||
3.2 | odd | 2 | 1728.3.g.j.703.3 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.g.m.703.6 | 8 | ||
8.3 | odd | 2 | 864.3.g.b.703.4 | yes | 8 | ||
8.5 | even | 2 | 864.3.g.b.703.3 | ✓ | 8 | ||
12.11 | even | 2 | 1728.3.g.j.703.4 | 8 | |||
24.5 | odd | 2 | 864.3.g.d.703.5 | yes | 8 | ||
24.11 | even | 2 | 864.3.g.d.703.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.g.b.703.3 | ✓ | 8 | 8.5 | even | 2 | ||
864.3.g.b.703.4 | yes | 8 | 8.3 | odd | 2 | ||
864.3.g.d.703.5 | yes | 8 | 24.5 | odd | 2 | ||
864.3.g.d.703.6 | yes | 8 | 24.11 | even | 2 | ||
1728.3.g.j.703.3 | 8 | 3.2 | odd | 2 | |||
1728.3.g.j.703.4 | 8 | 12.11 | even | 2 | |||
1728.3.g.m.703.5 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.m.703.6 | 8 | 4.3 | odd | 2 | inner |