Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(47,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ch (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 575.1 | ||
Root | \(0.939693 - 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.575 |
Dual form | 912.2.ch.d.479.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.70574 | + | 0.300767i | 0.984808 | + | 0.173648i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.93242 | + | 2.27038i | −1.48631 | + | 0.858124i | −0.999878 | − | 0.0155920i | \(-0.995037\pi\) |
−0.486436 | + | 0.873716i | \(0.661703\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.81908 | + | 1.02606i | 0.939693 | + | 0.342020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.507274 | + | 2.87689i | 0.140692 | + | 0.797907i | 0.970725 | + | 0.240192i | \(0.0772105\pi\) |
−0.830033 | + | 0.557714i | \(0.811678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 2.59808i | 0.802955 | + | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.39053 | + | 2.68993i | −1.61275 | + | 0.586991i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.868241 | + | 4.92404i | 0.173648 | + | 0.984808i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.50000 | + | 2.59808i | 0.866025 | + | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.27244 | + | 4.19875i | −1.30617 | + | 0.754117i | −0.981455 | − | 0.191695i | \(-0.938602\pi\) |
−0.324714 | + | 0.945812i | \(0.605268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.02734 | 1.15529 | 0.577644 | − | 0.816289i | \(-0.303972\pi\) | ||||
0.577644 | + | 0.816289i | \(0.303972\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.05980i | 0.810216i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.03596 | + | 9.57688i | −1.22547 | + | 1.46046i | −0.381246 | + | 0.924473i | \(0.624505\pi\) |
−0.844226 | + | 0.535988i | \(0.819939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.80928 | − | 11.7940i | 0.972754 | − | 1.68486i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.18866 | + | 5.48432i | 0.687255 | + | 0.726416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.80406 | − | 4.03109i | 0.615097 | − | 0.516128i | −0.281161 | − | 0.959661i | \(-0.590719\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.4153 | + | 2.36549i | −1.69017 | + | 0.298023i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.59492 | − | 15.3719i | 0.683529 | − | 1.87798i | 0.305424 | − | 0.952217i | \(-0.401202\pi\) |
0.378105 | − | 0.925763i | \(-0.376576\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.87686 | − | 16.3155i | 0.336711 | − | 1.90958i | −0.0729331 | − | 0.997337i | \(-0.523236\pi\) |
0.409644 | − | 0.912245i | \(-0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.66025i | 1.00000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.84137 | − | 1.20632i | −0.769714 | − | 0.135721i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
−0.544696 | + | 0.838633i | \(0.683355\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.89440 | + | 5.78509i | 0.766044 | + | 0.642788i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.52646 | − | 10.1614i | −0.893816 | − | 1.06521i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.6677 | + | 4.97464i | −1.41728 | + | 0.515846i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.69846 | − | 1.71010i | 0.477057 | − | 0.173634i | −0.0922897 | − | 0.995732i | \(-0.529419\pi\) |
0.569346 | + | 0.822098i | \(0.307196\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4315 | + | 7.75470i | 1.32345 | + | 0.764094i | 0.984277 | − | 0.176631i | \(-0.0565198\pi\) |
0.339172 | + | 0.940724i | \(0.389853\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0228 | − | 10.9274i | −1.24735 | − | 1.04665i | −0.996912 | − | 0.0785223i | \(-0.974980\pi\) |
−0.250441 | − | 0.968132i | \(-0.580576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.9868 | + | 2.11360i | 1.13774 | + | 0.200614i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.52182 | + | 8.63068i | −0.140692 | + | 0.797907i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.1746 | − | 3.90998i | 1.96768 | − | 0.346954i | 0.976134 | − | 0.217171i | \(-0.0696829\pi\) |
0.991542 | − | 0.129783i | \(-0.0414282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.5876 | + | 13.9187i | −1.46046 | + | 1.22547i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.6621 | − | 2.27038i | −1.70492 | − | 0.196867i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.1951 | + | 4.08991i | −1.96738 | + | 0.346902i | −0.975417 | + | 0.220366i | \(0.929275\pi\) |
−0.991962 | + | 0.126536i | \(0.959614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.1621 | − | 18.0695i | 1.25055 | − | 1.49035i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.66025i | − | 0.704761i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) | ||
0.935857 | − | 0.352381i | \(-0.114628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5424 | + | 14.7198i | 1.40003 | + | 1.17477i | 0.961085 | + | 0.276254i | \(0.0890931\pi\) |
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6336 | + | 6.71664i | 0.911212 | + | 0.526088i | 0.880821 | − | 0.473450i | \(-0.156991\pi\) |
0.0303908 | + | 0.999538i | \(0.490325\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.19681 | − | 1.52752i | 0.322832 | − | 0.117501i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.20099 | + | 10.9154i | 0.550673 | + | 0.834721i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.5937 | − | 17.3921i | −1.10318 | − | 1.31472i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.57785 | − | 2.39414i | −0.488928 | − | 0.177955i | 0.0857797 | − | 0.996314i | \(-0.472662\pi\) |
−0.574707 | + | 0.818359i | \(0.694884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.40689 | − | 5.43107i | 0.695377 | − | 0.401476i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.5945 | −1.71625 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.31954 | − | 7.48351i | 0.0949829 | − | 0.538675i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.994753 | − | 0.102310i | \(-0.0326233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.38872 | − | 12.0579i | 0.311108 | − | 0.854762i | −0.681326 | − | 0.731980i | \(-0.738596\pi\) |
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.1668 | − | 24.5377i | 0.999252 | − | 1.73076i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.66503 | − | 26.5545i | −0.665368 | − | 1.82808i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
−0.114625 | − | 0.993409i | \(-0.536567\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.0655 | − | 33.0225i | 1.29425 | − | 2.24171i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.81433 | − | 26.9647i | 0.663191 | − | 1.82210i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.5646 | − | 19.7410i | 1.10925 | − | 1.32195i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
0.941838 | − | 0.336066i | \(-0.109097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.60472 | + | 14.7721i | −0.173648 | + | 0.984808i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.7820 | −1.83589 | −0.917943 | − | 0.396713i | \(-0.870151\pi\) | ||||
−0.917943 | + | 0.396713i | \(0.870151\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.3068 | − | 4.11532i | −0.734452 | − | 0.267319i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.31702 | + | 24.4830i | 0.278084 | + | 1.57709i | 0.728993 | + | 0.684521i | \(0.239989\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0201 | + | 11.9415i | 0.642788 | + | 0.766044i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.69893 | + | 11.3871i | −0.362614 | + | 0.724542i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.6344 | + | 15.9548i | −1.71712 | + | 0.991380i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0201 | − | 11.9415i | 0.608676 | − | 0.725391i | −0.370403 | − | 0.928871i | \(-0.620781\pi\) |
0.979079 | + | 0.203479i | \(0.0652250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.4877 | − | 19.8972i | −0.695266 | − | 1.20424i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5000 | + | 26.8468i | −0.931305 | + | 1.61307i | −0.150210 | + | 0.988654i | \(0.547995\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.8097 | + | 4.37463i | −1.48532 | + | 0.261902i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.70115 | + | 21.1587i | 0.457786 | + | 1.25776i | 0.927130 | + | 0.374741i | \(0.122268\pi\) |
−0.469344 | + | 0.883016i | \(0.655509\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0228 | − | 10.9274i | 0.766044 | − | 0.642788i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.52869 | − | 1.50384i | 0.499960 | − | 0.0881565i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.85756 | − | 55.9050i | 0.568181 | − | 3.22231i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.70574 | − | 0.300767i | −0.0973516 | − | 0.0171657i | 0.124760 | − | 0.992187i | \(-0.460184\pi\) |
−0.222112 | + | 0.975021i | \(0.571295\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.5783 | + | 17.2673i | 1.17066 | + | 0.982300i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.8892 | − | 11.9707i | −1.85901 | − | 0.676624i | −0.979731 | − | 0.200316i | \(-0.935803\pi\) |
−0.879279 | − | 0.476308i | \(-0.841975\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.7255 | + | 4.99567i | −0.761354 | + | 0.277110i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.9268 | − | 22.5561i | −1.04665 | − | 1.24735i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.61705 | + | 2.66565i | 0.253776 | + | 0.146518i | 0.621492 | − | 0.783420i | \(-0.286527\pi\) |
−0.367716 | + | 0.929938i | \(0.619860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.8106 | + | 7.21048i | 1.08562 | + | 0.395132i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.7750 | + | 22.4669i | 1.45853 | + | 1.22385i | 0.926049 | + | 0.377403i | \(0.123183\pi\) |
0.532476 | + | 0.846445i | \(0.321262\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30.0533i | 1.62273i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.653886 | + | 1.13256i | 0.0350017 | + | 0.0606247i | 0.882996 | − | 0.469381i | \(-0.155523\pi\) |
−0.847994 | + | 0.530006i | \(0.822190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.19166 | + | 14.2640i | −0.277110 | + | 0.761354i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.51636 | + | 17.9035i | 0.342020 | + | 0.939693i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.6104 | − | 6.45540i | 1.91105 | − | 0.336969i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
0.997555 | + | 0.0698862i | \(0.0222636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | − | 32.9090i | −0.983783 | − | 1.70396i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
−0.336557 | − | 0.941663i | \(-0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.0479i | − | 1.23526i | −0.786469 | − | 0.617629i | \(-0.788093\pi\) | ||
0.786469 | − | 0.617629i | \(-0.211907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.0000 | 1.99803 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.4805 | + | 18.7526i | −1.65107 | + | 0.953248i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.0292 | − | 13.4775i | 1.85844 | − | 0.676417i | 0.878300 | − | 0.478110i | \(-0.158678\pi\) |
0.980140 | − | 0.198307i | \(-0.0635442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.8555 | − | 9.78639i | −1.64483 | − | 0.489933i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.7685 | − | 18.7921i | −0.785483 | − | 0.936102i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.7083 | + | 12.9968i | 1.76566 | + | 0.642649i | 1.00000 | 0.000593299i | \(-0.000188853\pi\) | |
0.765663 | + | 0.643242i | \(0.222411\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.7948 | −1.99773 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.11958 | + | 40.3771i | −0.346987 | + | 1.96786i | −0.131927 | + | 0.991259i | \(0.542117\pi\) |
−0.215060 | + | 0.976601i | \(0.568995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.73947 | + | 26.7590i | −0.471326 | + | 1.29496i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.0940 | + | 26.0910i | −1.49428 | + | 1.25385i | −0.605231 | + | 0.796050i | \(0.706919\pi\) |
−0.889053 | + | 0.457804i | \(0.848636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3241 | + | 39.3552i | 0.683653 | + | 1.87832i | 0.373425 | + | 0.927660i | \(0.378183\pi\) |
0.310228 | + | 0.950662i | \(0.399595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.2973 | − | 26.2615i | 1.49035 | − | 1.25055i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.60472 | − | 14.7721i | 0.122381 | − | 0.694055i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.2012 | −1.83376 | −0.916878 | − | 0.399169i | \(-0.869299\pi\) | ||||
−0.916878 | + | 0.399169i | \(0.869299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.4129 | − | 21.0230i | 1.69225 | − | 0.977021i | 0.739553 | − | 0.673098i | \(-0.235037\pi\) |
0.952697 | − | 0.303923i | \(-0.0982964\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8986 | + | 73.1515i | 0.595601 | + | 3.37782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.4954 | + | 30.3843i | 1.17477 | + | 1.40003i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.75418 | + | 19.4899i | −0.447553 | + | 0.894258i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.56479 | + | 20.2169i | 0.162540 | + | 0.921812i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.5000 | + | 18.1865i | −1.42740 | + | 0.824110i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
−0.430486 | + | 0.902597i | \(0.641658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.8237 | + | 14.9558i | 0.806014 | + | 0.676326i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.13000 | + | 2.53844i | −0.0953521 | + | 0.113636i | −0.811610 | − | 0.584199i | \(-0.801409\pi\) |
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.61809 | − | 1.34327i | 0.338331 | − | 0.0596569i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.7294 | + | 70.6909i | 1.13820 | + | 3.12718i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.00000 | + | 20.7846i | 0.397360 | + | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.4093 | + | 42.3366i | −0.673800 | + | 1.85125i | −0.174908 | + | 0.984585i | \(0.555963\pi\) |
−0.498892 | + | 0.866664i | \(0.666259\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.6621 | − | 34.0557i | −0.858124 | − | 1.48631i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.99391 | + | 22.6506i | −0.173648 | + | 0.984808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.09462 | − | 0.398408i | −0.0470613 | − | 0.0171289i | 0.318382 | − | 0.947962i | \(-0.396860\pi\) |
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.5000 | − | 6.06218i | −0.450598 | − | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6143 | + | 26.9506i | 0.966917 | + | 1.15233i | 0.988295 | + | 0.152555i | \(0.0487501\pi\) |
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.6792 | − | 6.43469i | 0.754528 | − | 0.274626i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.6419 | − | 10.7888i | 1.26050 | − | 0.458785i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.6281 | − | 18.2605i | −1.33773 | − | 0.772337i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −40.2460 | − | 7.09646i | −1.69017 | − | 0.298023i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 36.8452i | − | 1.54192i | −0.636882 | − | 0.770961i | \(-0.719776\pi\) | ||
0.636882 | − | 0.770961i | \(-0.280224\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.50000 | − | 9.52628i | −0.228968 | − | 0.396584i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.50159 | − | 12.3680i | 0.187080 | − | 0.513998i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.3622 | − | 4.19875i | −1.49828 | − | 0.173006i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.1126 | − | 19.2476i | 0.454809 | − | 0.787753i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.3187 | − | 40.3891i | −0.951188 | − | 1.64751i | −0.742859 | − | 0.669448i | \(-0.766531\pi\) |
−0.208329 | − | 0.978059i | \(-0.566802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.5450 | − | 37.5939i | 1.28461 | − | 1.53094i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.8762i | 0.482040i | 0.970520 | + | 0.241020i | \(0.0774820\pi\) | ||||
−0.970520 | + | 0.241020i | \(0.922518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.0041 | + | 30.2110i | 1.45419 | + | 1.22021i | 0.929449 | + | 0.368950i | \(0.120283\pi\) |
0.524742 | + | 0.851261i | \(0.324162\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5614 | − | 12.4485i | −0.866626 | − | 0.500347i | −0.000400419 | − | 1.00000i | \(-0.500127\pi\) |
−0.866226 | + | 0.499653i | \(0.833461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.4923 | + | 8.55050i | −0.939693 | + | 0.342020i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3200 | − | 28.9835i | −0.968164 | − | 1.15381i | −0.988069 | − | 0.154011i | \(-0.950781\pi\) |
0.0199047 | − | 0.999802i | \(-0.493664\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.49928 | − | 48.2018i | −0.337816 | − | 1.91585i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.3843 | + | 13.6068i | 1.48122 | + | 0.539120i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.4623 | − | 5.90030i | −1.31962 | − | 0.232685i | −0.530901 | − | 0.847434i | \(-0.678146\pi\) |
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 42.4528 | − | 50.5933i | 1.66386 | − | 1.98291i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.8508 | − | 43.0428i | 0.969520 | − | 1.67926i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.1097 | − | 24.4259i | 1.13224 | − | 0.950059i | 0.133078 | − | 0.991106i | \(-0.457514\pi\) |
0.999157 | + | 0.0410470i | \(0.0130693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.1924 | − | 28.6908i | 1.32195 | − | 1.10925i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.1642 | + | 19.3369i | −0.430346 | + | 0.745382i | −0.996903 | − | 0.0786409i | \(-0.974942\pi\) |
0.566557 | + | 0.824023i | \(0.308275\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.88594 | + | 24.4139i | −0.342020 | + | 0.939693i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.5937 | + | 17.3921i | −0.560056 | + | 0.667449i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.3888 | − | 8.35592i | −1.80799 | − | 0.318798i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.5000 | − | 9.52628i | 0.627690 | − | 0.362397i | −0.152167 | − | 0.988355i | \(-0.548625\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.5957 | + | 18.2576i | 0.927644 | + | 0.688597i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.48674 | − | 14.1030i | −0.0933915 | − | 0.529649i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
0.901837 | − | 0.432077i | \(-0.142219\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.0486 | − | 10.4204i | −0.676875 | − | 0.390794i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −70.4246 | −2.62275 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.0600i | 1.60142i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.5314 | − | 39.9611i | 1.24361 | − | 1.48208i | 0.427675 | − | 0.903933i | \(-0.359333\pi\) |
0.815935 | − | 0.578144i | \(-0.196223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.50000 | + | 6.06218i | −0.129275 | + | 0.223912i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) |
0.794121 | + | 0.607760i | \(0.207932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.30313 | − | 6.32780i | −0.0847220 | − | 0.232772i | 0.890096 | − | 0.455773i | \(-0.150637\pi\) |
−0.974818 | + | 0.223001i | \(0.928415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.1457 | + | 17.7093i | −0.482921 | + | 0.650567i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.89399 | − | 18.9411i | 0.251565 | − | 0.691170i | −0.748056 | − | 0.663636i | \(-0.769012\pi\) |
0.999621 | − | 0.0275338i | \(-0.00876539\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.12289 | − | 40.3959i | 0.258886 | − | 1.46822i | −0.527011 | − | 0.849858i | \(-0.676688\pi\) |
0.785897 | − | 0.618357i | \(-0.212201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 76.0203 | + | 13.4044i | 2.75212 | + | 0.485273i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.9180 | − | 12.7091i | −1.25918 | − | 0.458303i | −0.375684 | − | 0.926748i | \(-0.622592\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.9890 | − | 32.1643i | −0.969474 | − | 1.15537i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −51.9358 | + | 18.9031i | −1.86319 | + | 0.678144i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.8754 | + | 16.6712i | 1.02930 | + | 0.594265i | 0.916783 | − | 0.399385i | \(-0.130776\pi\) |
0.112514 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0340 | + | 11.7759i | 0.498361 | + | 0.418175i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.6434 | − | 7.51919i | 1.49741 | − | 0.264034i | 0.635901 | − | 0.771771i | \(-0.280629\pi\) |
0.861512 | + | 0.507736i | \(0.169518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.6832 | − | 17.3553i | 0.725391 | − | 0.608676i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −53.0073 | + | 12.6411i | −1.85449 | + | 0.442255i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.6105 | − | 37.3946i | −0.475590 | − | 1.30667i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56.2893 | − | 9.92533i | 1.96212 | − | 0.345975i | 0.965929 | − | 0.258808i | \(-0.0833297\pi\) |
0.996194 | − | 0.0871670i | \(-0.0277814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0635 | + | 22.6266i | 0.453713 | + | 0.785854i | 0.998613 | − | 0.0526472i | \(-0.0167659\pi\) |
−0.544900 | + | 0.838501i | \(0.683433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.5136 | + | 41.1317i | −1.19726 | + | 1.42684i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.6346 | −1.50823 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2153 | + | 18.6408i | 0.766044 | + | 0.642788i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.2566 | − | 24.9742i | −1.48631 | − | 0.858124i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.77228 | + | 38.4075i | 0.232424 | + | 1.31814i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.4420 | + | 19.4513i | −1.82982 | + | 0.665999i | −0.836877 | + | 0.547391i | \(0.815621\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.5159 | − | 39.9428i | −1.14355 | − | 1.36283i | −0.921772 | − | 0.387732i | \(-0.873259\pi\) |
−0.221777 | − | 0.975097i | \(-0.571186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.5000 | − | 14.7224i | 0.866025 | − | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.0615 | + | 8.29822i | 1.59462 | + | 0.281174i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0000 | 0.507673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.26832 | − | 41.2207i | 0.245434 | − | 1.39192i | −0.574049 | − | 0.818821i | \(-0.694628\pi\) |
0.819483 | − | 0.573103i | \(-0.194261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.802937 | − | 2.20605i | 0.0270210 | − | 0.0742396i | −0.925449 | − | 0.378873i | \(-0.876312\pi\) |
0.952470 | + | 0.304633i | \(0.0985339\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −78.3226 | + | 65.7205i | −2.62686 | + | 2.20419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.6288 | − | 92.3944i | 1.11910 | − | 3.07469i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.79339 | + | 9.28780i | −0.258775 | + | 0.308396i | −0.879752 | − | 0.475433i | \(-0.842292\pi\) |
0.620977 | + | 0.783829i | \(0.286736\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.96940 | − | 5.75583i | 0.328860 | − | 0.189867i | −0.326475 | − | 0.945206i | \(-0.605861\pi\) |
0.655335 | + | 0.755338i | \(0.272528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.81908 | − | 1.02606i | −0.0928918 | − | 0.0338098i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.10142 | + | 34.6029i | 0.200614 | + | 1.13774i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.9078 | + | 35.6427i | 0.982300 | + | 1.17066i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.4742 | − | 23.5880i | 1.78532 | − | 0.773066i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.69434 | − | 49.3081i | −0.284032 | − | 1.61082i | −0.708723 | − | 0.705487i | \(-0.750729\pi\) |
0.424691 | − | 0.905338i | \(-0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.5000 | − | 30.3109i | −1.71327 | − | 0.989158i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.3973 | 1.57104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7589 | − | 34.2235i | 0.637385 | − | 1.10398i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.2663 | − | 58.4288i | −0.683880 | − | 1.87894i | −0.362301 | − | 0.932061i | \(-0.618009\pi\) |
−0.321578 | − | 0.946883i | \(-0.604213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 81.9270 | − | 68.7449i | 2.62646 | − | 2.20386i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.9146 | + | 4.39312i | −0.797907 | + | 0.140692i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5000 | − | 44.1673i | −0.814152 | − | 1.41015i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.12045 | − | 1.07920i | −0.194423 | − | 0.0342819i | 0.0755888 | − | 0.997139i | \(-0.475916\pi\) |
−0.270011 | + | 0.962857i | \(0.587027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.07373 | + | 5.93556i | 0.224478 | + | 0.188359i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2099 | + | 4.08007i | 0.355021 | + | 0.129217i | 0.513373 | − | 0.858166i | \(-0.328396\pi\) |
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.6230 | + | 18.2576i | 1.00051 | + | 0.577644i |
(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 | 912.2.ch.d.575.1 | yes | 6 | |
3.2 | odd | 2 | CM | 912.2.ch.d.575.1 | yes | 6 | |
4.3 | odd | 2 | 912.2.ch.c.575.1 | yes | 6 | ||
12.11 | even | 2 | 912.2.ch.c.575.1 | yes | 6 | ||
19.4 | even | 9 | 912.2.ch.c.479.1 | ✓ | 6 | ||
57.23 | odd | 18 | 912.2.ch.c.479.1 | ✓ | 6 | ||
76.23 | odd | 18 | inner | 912.2.ch.d.479.1 | yes | 6 | |
228.23 | even | 18 | inner | 912.2.ch.d.479.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ch.c.479.1 | ✓ | 6 | 19.4 | even | 9 | ||
912.2.ch.c.479.1 | ✓ | 6 | 57.23 | odd | 18 | ||
912.2.ch.c.575.1 | yes | 6 | 4.3 | odd | 2 | ||
912.2.ch.c.575.1 | yes | 6 | 12.11 | even | 2 | ||
912.2.ch.d.479.1 | yes | 6 | 76.23 | odd | 18 | inner | |
912.2.ch.d.479.1 | yes | 6 | 228.23 | even | 18 | inner | |
912.2.ch.d.575.1 | yes | 6 | 1.1 | even | 1 | trivial | |
912.2.ch.d.575.1 | yes | 6 | 3.2 | odd | 2 | CM |