Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{137}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.35235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.70470 | −0.241916 | −0.120958 | − | 0.992658i | \(-0.538597\pi\) | ||||
−0.120958 | + | 0.992658i | \(0.538597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.1141 | 1.75738 | 0.878688 | − | 0.477397i | \(-0.158420\pi\) | ||||
0.878688 | + | 0.477397i | \(0.158420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 70.8188 | 1.51089 | 0.755446 | − | 0.655211i | \(-0.227420\pi\) | ||||
0.755446 | + | 0.655211i | \(0.227420\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.11410 | 0.139670 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.7047 | −0.209789 | −0.104895 | − | 0.994483i | \(-0.533450\pi\) | ||||
−0.104895 | + | 0.994483i | \(0.533450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 159.047 | 1.92041 | 0.960207 | − | 0.279288i | \(-0.0900983\pi\) | ||||
0.960207 | + | 0.279288i | \(0.0900983\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −172.570 | −1.56450 | −0.782249 | − | 0.622966i | \(-0.785927\pi\) | ||||
−0.782249 | + | 0.622966i | \(0.785927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −117.685 | −0.941477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18.2282 | 0.116720 | 0.0583602 | − | 0.998296i | \(-0.481413\pi\) | ||||
0.0583602 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 149.409 | 0.865636 | 0.432818 | − | 0.901481i | \(-0.357519\pi\) | ||||
0.432818 | + | 0.901481i | \(0.357519\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −192.342 | −1.01462 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.7718 | 0.185601 | 0.0928006 | − | 0.995685i | \(-0.470418\pi\) | ||||
0.0928006 | + | 0.995685i | \(0.470418\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −212.456 | −0.872314 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −50.2081 | −0.191248 | −0.0956242 | − | 0.995418i | \(-0.530485\pi\) | ||||
−0.0956242 | + | 0.995418i | \(0.530485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −388.000 | −1.37603 | −0.688017 | − | 0.725695i | \(-0.741518\pi\) | ||||
−0.688017 | + | 0.725695i | \(0.741518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −24.3423 | −0.0806386 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −494.550 | −1.53484 | −0.767421 | − | 0.641143i | \(-0.778460\pi\) | ||||
−0.767421 | + | 0.641143i | \(0.778460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 44.1141 | 0.121122 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 469.772 | 1.21751 | 0.608756 | − | 0.793358i | \(-0.291669\pi\) | ||||
0.608756 | + | 0.793358i | \(0.291669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −173.409 | −0.425137 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −477.141 | −1.10875 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 343.275 | 0.757468 | 0.378734 | − | 0.925506i | \(-0.376359\pi\) | ||||
0.378734 | + | 0.925506i | \(0.376359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.4966 | −0.152168 | −0.0760839 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760839 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −191.544 | −0.365509 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 293.597 | 0.535353 | 0.267676 | − | 0.963509i | \(-0.413744\pi\) | ||||
0.267676 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 517.711 | 0.903263 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 629.940 | 1.05296 | 0.526479 | − | 0.850188i | \(-0.323512\pi\) | ||||
0.526479 | + | 0.850188i | \(0.323512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 696.685 | 1.11700 | 0.558498 | − | 0.829506i | \(-0.311378\pi\) | ||||
0.558498 | + | 0.829506i | \(0.311378\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 353.054 | 0.543562 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −640.685 | −0.912439 | −0.456219 | − | 0.889867i | \(-0.650797\pi\) | ||||
−0.456219 | + | 0.889867i | \(0.650797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1072.72 | 1.41864 | 0.709318 | − | 0.704888i | \(-0.249003\pi\) | ||||
0.709318 | + | 0.704888i | \(0.249003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 39.7718 | 0.0507513 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.6846 | −0.0673886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 667.430 | 0.794914 | 0.397457 | − | 0.917621i | \(-0.369893\pi\) | ||||
0.397457 | + | 0.917621i | \(0.369893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −448.228 | −0.499775 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −430.174 | −0.464579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1307.50 | 1.36863 | 0.684314 | − | 0.729188i | \(-0.260102\pi\) | ||||
0.684314 | + | 0.729188i | \(0.260102\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 577.027 | 0.585792 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 720.342 | 0.709671 | 0.354835 | − | 0.934929i | \(-0.384537\pi\) | ||||
0.354835 | + | 0.934929i | \(0.384537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1762.51 | −1.68607 | −0.843035 | − | 0.537858i | \(-0.819234\pi\) | ||||
−0.843035 | + | 0.537858i | \(0.819234\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 139.309 | 0.125864 | 0.0629322 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629322 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 569.544 | 0.500481 | 0.250240 | − | 0.968184i | \(-0.419490\pi\) | ||||
0.250240 | + | 0.968184i | \(0.419490\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −125.315 | −0.107157 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1843.48 | −1.53469 | −0.767344 | − | 0.641236i | \(-0.778422\pi\) | ||||
−0.767344 | + | 0.641236i | \(0.778422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 466.751 | 0.378476 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 637.369 | 0.503631 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2779.62 | 2.08837 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 150.624 | 0.110417 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 656.389 | 0.469674 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −506.510 | −0.353902 | −0.176951 | − | 0.984220i | \(-0.556623\pi\) | ||||
−0.176951 | + | 0.984220i | \(0.556623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1164.00 | 0.794453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1054.82 | −0.703511 | −0.351756 | − | 0.936092i | \(-0.614415\pi\) | ||||
−0.351756 | + | 0.936092i | \(0.614415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 73.0269 | 0.0465567 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1690.00 | −1.05392 | −0.526958 | − | 0.849891i | \(-0.676667\pi\) | ||||
−0.526958 | + | 0.849891i | \(0.676667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1732.30 | 1.05706 | 0.528530 | − | 0.848915i | \(-0.322743\pi\) | ||||
0.528530 | + | 0.848915i | \(0.322743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1483.65 | 0.886142 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4540.48 | 2.65520 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −49.3018 | −0.0282365 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 338.121 | 0.185906 | 0.0929528 | − | 0.995671i | \(-0.470369\pi\) | ||||
0.0929528 | + | 0.995671i | \(0.470369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.17440 | 0.00332759 | 0.00166379 | − | 0.999999i | \(-0.499470\pi\) | ||||
0.00166379 | + | 0.999999i | \(0.499470\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −132.342 | −0.0699297 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −404.108 | −0.209411 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 731.691 | 0.371945 | 0.185972 | − | 0.982555i | \(-0.440456\pi\) | ||||
0.185972 | + | 0.982555i | \(0.440456\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1409.32 | −0.702931 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −761.249 | −0.365801 | −0.182901 | − | 0.983131i | \(-0.558549\pi\) | ||||
−0.182901 | + | 0.983131i | \(0.558549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 520.228 | 0.245453 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2731.03 | −1.26547 | −0.632736 | − | 0.774368i | \(-0.718068\pi\) | ||||
−0.632736 | + | 0.774368i | \(0.718068\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2818.30 | 1.28280 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1431.42 | 0.640138 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3721.16 | −1.63534 | −0.817672 | − | 0.575684i | \(-0.804736\pi\) | ||||
−0.817672 | + | 0.575684i | \(0.804736\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1029.83 | −0.437324 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2386.15 | −0.996366 | −0.498183 | − | 0.867072i | \(-0.665999\pi\) | ||||
−0.498183 | + | 0.867072i | \(0.665999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3819.54 | 1.56853 | 0.784266 | − | 0.620424i | \(-0.213040\pi\) | ||||
0.784266 | + | 0.620424i | \(0.213040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 217.490 | 0.0878541 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −112.980 | −0.0448998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −942.779 | −0.368678 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −214.168 | −0.0811343 | −0.0405671 | − | 0.999177i | \(-0.512916\pi\) | ||||
−0.0405671 | + | 0.999177i | \(0.512916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3778.44 | 1.40921 | 0.704607 | − | 0.709598i | \(-0.251123\pi\) | ||||
0.704607 | + | 0.709598i | \(0.251123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 574.631 | 0.211026 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3395.01 | 1.22784 | 0.613919 | − | 0.789369i | \(-0.289592\pi\) | ||||
0.613919 | + | 0.789369i | \(0.289592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3926.17 | 1.39859 | 0.699294 | − | 0.714834i | \(-0.253498\pi\) | ||||
0.699294 | + | 0.714834i | \(0.253498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −880.792 | −0.309086 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 135.798 | 0.0462660 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1553.13 | −0.521499 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10197.2 | 3.37489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 816.108 | 0.266271 | 0.133135 | − | 0.991098i | \(-0.457495\pi\) | ||||
0.133135 | + | 0.991098i | \(0.457495\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1889.82 | −0.607926 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1049.42 | 0.332884 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2090.05 | −0.644898 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1041.37 | −0.316969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −630.094 | −0.189212 | −0.0946059 | − | 0.995515i | \(-0.530159\pi\) | ||||
−0.0946059 | + | 0.995515i | \(0.530159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1059.16 | −0.313826 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −827.759 | −0.242028 | −0.121014 | − | 0.992651i | \(-0.538615\pi\) | ||||
−0.121014 | + | 0.992651i | \(0.538615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4280.78 | 1.23529 | 0.617646 | − | 0.786456i | \(-0.288086\pi\) | ||||
0.617646 | + | 0.786456i | \(0.288086\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 764.846 | 0.215050 | 0.107525 | − | 0.994202i | \(-0.465707\pi\) | ||||
0.107525 | + | 0.994202i | \(0.465707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1337.61 | 0.371302 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1922.05 | 0.526797 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3467.43 | 0.938449 | 0.469225 | − | 0.883079i | \(-0.344533\pi\) | ||||
0.469225 | + | 0.883079i | \(0.344533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4350.54 | 1.16283 | 0.581416 | − | 0.813606i | \(-0.302499\pi\) | ||||
0.581416 | + | 0.813606i | \(0.302499\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11263.5 | 2.90154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3218.17 | −0.819050 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −522.335 | −0.131353 | −0.0656763 | − | 0.997841i | \(-0.520920\pi\) | ||||
−0.0656763 | + | 0.997841i | \(0.520920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11064.2 | −2.74941 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −119.315 | −0.0293013 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4629.93 | 1.12376 | 0.561881 | − | 0.827218i | \(-0.310078\pi\) | ||||
0.561881 | + | 0.827218i | \(0.310078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 164.054 | 0.0389068 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4357.01 | 1.02154 | 0.510770 | − | 0.859717i | \(-0.329360\pi\) | ||||
0.510770 | + | 0.859717i | \(0.329360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1270.59 | −0.294535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2002.29 | −0.458944 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4187.23 | 0.949070 | 0.474535 | − | 0.880237i | \(-0.342616\pi\) | ||||
0.474535 | + | 0.880237i | \(0.342616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6508.31 | −1.45886 | −0.729431 | − | 0.684054i | \(-0.760215\pi\) | ||||
−0.729431 | + | 0.684054i | \(0.760215\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7545.24 | −1.65453 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3212.03 | −0.696722 | −0.348361 | − | 0.937360i | \(-0.613262\pi\) | ||||
−0.348361 | + | 0.937360i | \(0.613262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1344.68 | 0.288545 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1047.83 | 0.222449 | 0.111224 | − | 0.993795i | \(-0.464523\pi\) | ||||
0.111224 | + | 0.993795i | \(0.464523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6936.63 | 1.45703 | 0.728516 | − | 0.685029i | \(-0.240210\pi\) | ||||
0.728516 | + | 0.685029i | \(0.240210\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1290.52 | 0.268225 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4696.77 | −0.955989 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3922.51 | −0.790177 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −823.738 | −0.164243 | −0.0821217 | − | 0.996622i | \(-0.526170\pi\) | ||||
−0.0821217 | + | 0.996622i | \(0.526170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −928.456 | −0.183243 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1731.08 | −0.338207 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12221.2 | −2.36379 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2161.03 | −0.409729 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 196.082 | 0.0368118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8658.16 | −1.60960 | −0.804800 | − | 0.593546i | \(-0.797728\pi\) | ||||
−0.804800 | + | 0.593546i | \(0.797728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5287.53 | 0.973453 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2648.97 | −0.482988 | −0.241494 | − | 0.970402i | \(-0.577637\pi\) | ||||
−0.241494 | + | 0.970402i | \(0.577637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.2208 | 0.00491569 | 0.00245785 | − | 0.999997i | \(-0.499218\pi\) | ||||
0.00245785 | + | 0.999997i | \(0.499218\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6919.25 | −1.22594 | −0.612971 | − | 0.790105i | \(-0.710026\pi\) | ||||
−0.612971 | + | 0.790105i | \(0.710026\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1168.68 | 0.205122 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −417.927 | −0.0726679 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2338.74 | −0.402882 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8334.28 | −1.42247 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1708.63 | −0.288953 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8973.80 | 1.49017 | 0.745083 | − | 0.666972i | \(-0.232410\pi\) | ||||
0.745083 | + | 0.666972i | \(0.232410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 375.946 | 0.0618670 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −794.093 | −0.129510 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3825.65 | 0.618387 | 0.309194 | − | 0.950999i | \(-0.399941\pi\) | ||||
0.309194 | + | 0.950999i | \(0.399941\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5530.43 | 0.886052 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9579.25 | 1.52125 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1400.25 | −0.218513 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8795.51 | 1.36071 | 0.680357 | − | 0.732881i | \(-0.261825\pi\) | ||||
0.680357 | + | 0.732881i | \(0.261825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7841.92 | 1.20277 | 0.601387 | − | 0.798958i | \(-0.294615\pi\) | ||||
0.601387 | + | 0.798958i | \(0.294615\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1912.11 | −0.290771 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1885.40 | 0.284277 | 0.142139 | − | 0.989847i | \(-0.454602\pi\) | ||||
0.142139 | + | 0.989847i | \(0.454602\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1703.80 | −0.254727 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4189.95 | −0.615981 | −0.307991 | − | 0.951389i | \(-0.599657\pi\) | ||||
−0.307991 | + | 0.951389i | \(0.599657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18436.9 | 2.68799 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8338.85 | −1.20572 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1884.32 | −0.270219 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9444.08 | −1.34326 | −0.671631 | − | 0.740886i | \(-0.734406\pi\) | ||||
−0.671631 | + | 0.740886i | \(0.734406\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −451.873 | −0.0637495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11745.2 | 1.63041 | 0.815203 | − | 0.579175i | \(-0.196625\pi\) | ||||
0.815203 | + | 0.579175i | \(0.196625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1969.17 | −0.271166 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1290.90 | 0.176352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13493.4 | −1.82878 | −0.914390 | − | 0.404834i | \(-0.867329\pi\) | ||||
−0.914390 | + | 0.404834i | \(0.867329\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1519.53 | 0.204325 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6921.48 | 0.923423 | 0.461711 | − | 0.887030i | \(-0.347236\pi\) | ||||
0.461711 | + | 0.887030i | \(0.347236\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3492.00 | −0.458678 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14049.2 | −1.83116 | −0.915579 | − | 0.402138i | \(-0.868267\pi\) | ||||
−0.915579 | + | 0.402138i | \(0.868267\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2537.60 | 0.328214 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3164.46 | 0.406172 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1732.86 | 0.220733 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5403.10 | 0.683057 | 0.341529 | − | 0.939871i | \(-0.389055\pi\) | ||||
0.341529 | + | 0.939871i | \(0.389055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 322.994 | 0.0402234 | 0.0201117 | − | 0.999798i | \(-0.493598\pi\) | ||||
0.0201117 | + | 0.999798i | \(0.493598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10581.0 | 1.30788 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −219.081 | −0.0268795 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2678.16 | 0.326171 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10375.5 | −1.25437 | −0.627185 | − | 0.778871i | \(-0.715793\pi\) | ||||
−0.627185 | + | 0.778871i | \(0.715793\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5070.00 | 0.608478 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2901.40 | −0.343191 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5196.89 | −0.610294 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13078.3 | −1.52487 | −0.762433 | − | 0.647068i | \(-0.775995\pi\) | ||||
−0.762433 | + | 0.647068i | \(0.775995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2406.12 | −0.278544 | −0.139272 | − | 0.990254i | \(-0.544476\pi\) | ||||
−0.139272 | + | 0.990254i | \(0.544476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4450.95 | −0.511614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1730.52 | 0.197512 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13621.5 | −1.53298 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14524.3 | −1.62323 | −0.811613 | − | 0.584195i | \(-0.801410\pi\) | ||||
−0.811613 | + | 0.584195i | \(0.801410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13632.0 | 1.51296 | 0.756482 | − | 0.654014i | \(-0.226916\pi\) | ||||
0.756482 | + | 0.654014i | \(0.226916\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 147.905 | 0.0163024 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27446.8 | −3.00448 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 544.026 | 0.0591457 | 0.0295728 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295728 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5856.32 | 0.628086 | 0.314043 | − | 0.949409i | \(-0.398316\pi\) | ||||
0.314043 | + | 0.949409i | \(0.398316\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1805.20 | −0.192302 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1014.36 | −0.107333 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8548.36 | −0.898490 | −0.449245 | − | 0.893408i | \(-0.648307\pi\) | ||||
−0.449245 | + | 0.893408i | \(0.648307\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3219.05 | −0.336095 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.5232 | −0.00192118 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7222.35 | 0.739272 | 0.369636 | − | 0.929177i | \(-0.379482\pi\) | ||||
0.369636 | + | 0.929177i | \(0.379482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 397.027 | 0.0403739 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3618.93 | −0.365619 | −0.182810 | − | 0.983148i | \(-0.558519\pi\) | ||||
−0.182810 | + | 0.983148i | \(0.558519\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7517.89 | 0.754614 | 0.377307 | − | 0.926088i | \(-0.376850\pi\) | ||||
0.377307 | + | 0.926088i | \(0.376850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1212.32 | 0.120903 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3677.56 | −0.364405 | −0.182202 | − | 0.983261i | \(-0.558323\pi\) | ||||
−0.182202 | + | 0.983261i | \(0.558323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2195.07 | −0.214742 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24876.3 | −2.41821 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18717.4 | −1.80803 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4227.95 | 0.405837 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13044.6 | 1.24431 | 0.622153 | − | 0.782896i | \(-0.286258\pi\) | ||||
0.622153 | + | 0.782896i | \(0.286258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2958.23 | 0.280423 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3536.40 | −0.331092 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9080.46 | 0.844917 | 0.422459 | − | 0.906382i | \(-0.361167\pi\) | ||||
0.422459 | + | 0.906382i | \(0.361167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2283.75 | 0.211195 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11300.9 | 1.03870 | 0.519349 | − | 0.854562i | \(-0.326175\pi\) | ||||
0.519349 | + | 0.854562i | \(0.326175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −268.040 | −0.0244867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1560.68 | −0.141712 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5993.29 | 0.537668 | 0.268834 | − | 0.963187i | \(-0.413362\pi\) | ||||
0.268834 | + | 0.963187i | \(0.413362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8193.10 | 0.730620 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9330.15 | −0.827059 | −0.413530 | − | 0.910491i | \(-0.635704\pi\) | ||||
−0.413530 | + | 0.910491i | \(0.635704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1948.31 | −0.171680 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8454.91 | −0.740623 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8438.69 | 0.734849 | 0.367425 | − | 0.930053i | \(-0.380240\pi\) | ||||
0.367425 | + | 0.930053i | \(0.380240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4294.27 | −0.369584 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4767.06 | 0.407887 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31707.7 | −2.69729 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11163.5 | 0.944167 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11099.5 | −0.933354 | −0.466677 | − | 0.884428i | \(-0.654549\pi\) | ||||
−0.466677 | + | 0.884428i | \(0.654549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2079.76 | 0.173884 | 0.0869422 | − | 0.996213i | \(-0.472290\pi\) | ||||
0.0869422 | + | 0.996213i | \(0.472290\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2197.02 | −0.181601 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17613.6 | 1.44765 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3089.48 | 0.252489 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3555.68 | −0.288956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −376.789 | −0.0304486 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7158.46 | 0.575252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18154.1 | 1.44271 | 0.721354 | − | 0.692566i | \(-0.243520\pi\) | ||||
0.721354 | + | 0.692566i | \(0.243520\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11458.6 | −0.905593 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1540.44 | −0.121074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12923.0 | −1.01015 | −0.505073 | − | 0.863077i | \(-0.668534\pi\) | ||||
−0.505073 | + | 0.863077i | \(0.668534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −652.469 | −0.0507226 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2899.14 | 0.224152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 338.941 | 0.0259229 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17153.3 | 1.30486 | 0.652432 | − | 0.757847i | \(-0.273749\pi\) | ||||
0.652432 | + | 0.757847i | \(0.273749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27477.7 | −2.07904 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2828.34 | 0.212856 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15580.4 | −1.16632 | −0.583159 | − | 0.812358i | \(-0.698183\pi\) | ||||
−0.583159 | + | 0.812358i | \(0.698183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4986.05 | 0.371265 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5886.08 | −0.433668 | −0.216834 | − | 0.976208i | \(-0.569573\pi\) | ||||
−0.216834 | + | 0.976208i | \(0.569573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7028.85 | −0.515146 | −0.257573 | − | 0.966259i | \(-0.582923\pi\) | ||||
−0.257573 | + | 0.966259i | \(0.582923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 642.504 | 0.0468429 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20308.9 | 1.47294 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5400.24 | 0.389627 | 0.194814 | − | 0.980840i | \(-0.437590\pi\) | ||||
0.194814 | + | 0.980840i | \(0.437590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11335.3 | −0.813610 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30119.0 | 2.13962 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1723.89 | −0.121836 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 49.2876 | 0.00346562 | 0.00173281 | − | 0.999998i | \(-0.499448\pi\) | ||||
0.00173281 | + | 0.999998i | \(0.499448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23763.1 | 1.66238 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10185.0 | −0.708893 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13358.7 | −0.925088 | −0.462544 | − | 0.886596i | \(-0.653063\pi\) | ||||
−0.462544 | + | 0.886596i | \(0.653063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11778.5 | −0.807475 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2507.44 | 0.171037 | 0.0855186 | − | 0.996337i | \(-0.472745\pi\) | ||||
0.0855186 | + | 0.996337i | \(0.472745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8526.26 | 0.578691 | 0.289345 | − | 0.957225i | \(-0.406562\pi\) | ||||
0.289345 | + | 0.957225i | \(0.406562\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2642.38 | 0.178451 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7518.03 | −0.505209 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8403.41 | 0.561918 | 0.280959 | − | 0.959720i | \(-0.409348\pi\) | ||||
0.280959 | + | 0.959720i | \(0.409348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35023.5 | −2.31898 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6519.91 | 0.429587 | 0.214793 | − | 0.976660i | \(-0.431092\pi\) | ||||
0.214793 | + | 0.976660i | \(0.431092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −407.394 | −0.0267117 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3562.51 | −0.232449 | −0.116225 | − | 0.993223i | \(-0.537079\pi\) | ||||
−0.116225 | + | 0.993223i | \(0.537079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19199.6 | −1.24669 | −0.623343 | − | 0.781949i | \(-0.714226\pi\) | ||||
−0.623343 | + | 0.781949i | \(0.714226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4659.40 | 0.301088 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12935.2 | 0.827855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30591.5 | −1.94849 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −614.242 | −0.0389371 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29850.0 | −1.88322 | −0.941608 | − | 0.336712i | \(-0.890685\pi\) | ||||
−0.941608 | + | 0.336712i | \(0.890685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2448.32 | −0.153732 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1369.96 | 0.0856144 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5669.46 | 0.350986 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21452.1 | −1.32185 | −0.660925 | − | 0.750452i | \(-0.729836\pi\) | ||||
−0.660925 | + | 0.750452i | \(0.729836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31670.1 | 1.94238 | 0.971188 | − | 0.238313i | \(-0.0765943\pi\) | ||||
0.971188 | + | 0.238313i | \(0.0765943\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3148.27 | −0.192191 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24750.4 | −1.50392 | −0.751961 | − | 0.659208i | \(-0.770892\pi\) | ||||
−0.751961 | + | 0.659208i | \(0.770892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22008.8 | 1.33116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10186.4 | 0.610449 | 0.305225 | − | 0.952280i | \(-0.401268\pi\) | ||||
0.305225 | + | 0.952280i | \(0.401268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2852.97 | 0.170190 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6270.16 | 0.372332 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7856.84 | 0.464429 | 0.232215 | − | 0.972665i | \(-0.425403\pi\) | ||||
0.232215 | + | 0.972665i | \(0.425403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19490.1 | −1.14686 | −0.573432 | − | 0.819253i | \(-0.694388\pi\) | ||||
−0.573432 | + | 0.819253i | \(0.694388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3124.11 | 0.183002 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3145.65 | −0.182609 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1890.28 | 0.109241 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4648.05 | −0.267416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4872.89 | −0.279102 | −0.139551 | − | 0.990215i | \(-0.544566\pi\) | ||||
−0.139551 | + | 0.990215i | \(0.544566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3177.48 | 0.181187 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24279.8 | 1.37836 | 0.689179 | − | 0.724591i | \(-0.257971\pi\) | ||||
0.689179 | + | 0.724591i | \(0.257971\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2483.28 | 0.139735 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12278.3 | 0.687871 | 0.343936 | − | 0.938993i | \(-0.388240\pi\) | ||||
0.343936 | + | 0.938993i | \(0.388240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4570.94 | 0.254959 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12842.3 | −0.713196 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33268.7 | 1.83953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8367.76 | 0.460672 | 0.230336 | − | 0.973111i | \(-0.426017\pi\) | ||||
0.230336 | + | 0.973111i | \(0.426017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4685.34 | −0.255720 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 738.295 | 0.0401218 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2294.54 | −0.124159 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −510.228 | −0.0274908 | −0.0137454 | − | 0.999906i | \(-0.504375\pi\) | ||||
−0.0137454 | + | 0.999906i | \(0.504375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6643.68 | 0.356431 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4012.83 | −0.214372 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12705.0 | 0.672985 | 0.336493 | − | 0.941686i | \(-0.390759\pi\) | ||||
0.336493 | + | 0.941686i | \(0.390759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5766.16 | −0.304146 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25783.7 | −1.35429 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12280.6 | −0.642336 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10402.3 | −0.541814 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19865.9 | −1.03042 | −0.515210 | − | 0.857064i | \(-0.672286\pi\) | ||||
−0.515210 | + | 0.857064i | \(0.672286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13051.6 | −0.671362 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2145.18 | −0.109890 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3822.62 | 0.195011 | 0.0975055 | − | 0.995235i | \(-0.468914\pi\) | ||||
0.0975055 | + | 0.995235i | \(0.468914\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5705.42 | 0.288677 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12366.8 | −0.623161 | −0.311580 | − | 0.950220i | \(-0.600858\pi\) | ||||
−0.311580 | + | 0.950220i | \(0.600858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18823.7 | 0.940816 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10276.9 | 0.511557 | 0.255779 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255779 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33790.6 | −1.67521 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27250.9 | 1.34554 | 0.672771 | − | 0.739851i | \(-0.265104\pi\) | ||||
0.672771 | + | 0.739851i | \(0.265104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −914.515 | −0.0449735 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9654.52 | 0.472879 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2674.31 | 0.129943 | 0.0649713 | − | 0.997887i | \(-0.479304\pi\) | ||||
0.0649713 | + | 0.997887i | \(0.479304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1567.01 | 0.0758365 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6999 | −0.000804996 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15084.1 | −0.724231 | −0.362115 | − | 0.932133i | \(-0.617945\pi\) | ||||
−0.362115 | + | 0.932133i | \(0.617945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33192.6 | 1.58737 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24803.1 | −1.18149 | −0.590743 | − | 0.806860i | \(-0.701165\pi\) | ||||
−0.590743 | + | 0.806860i | \(0.701165\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 357.946 | 0.0169171 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24310.3 | 1.14445 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1080.40 | −0.0506637 | −0.0253318 | − | 0.999679i | \(-0.508064\pi\) | ||||
−0.0253318 | + | 0.999679i | \(0.508064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13889.8 | −0.648804 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2971.20 | −0.138249 | −0.0691247 | − | 0.997608i | \(-0.522021\pi\) | ||||
−0.0691247 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17583.2 | −0.814976 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7985.45 | −0.367276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40388.0 | 1.85044 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −492.161 | −0.0224629 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1979.01 | −0.0899793 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13716.6 | 0.621274 | 0.310637 | − | 0.950529i | \(-0.399458\pi\) | ||||
0.310637 | + | 0.950529i | \(0.399458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13071.0 | −0.589786 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5134.12 | −0.229909 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3811.78 | 0.170050 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2618.52 | 0.116377 | 0.0581887 | − | 0.998306i | \(-0.481468\pi\) | ||||
0.0581887 | + | 0.998306i | \(0.481468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7272.22 | 0.321993 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6006.87 | 0.264971 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44667.3 | 1.96298 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12561.7 | −0.547946 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 827.878 | 0.0359785 | 0.0179893 | − | 0.999838i | \(-0.494274\pi\) | ||||
0.0179893 | + | 0.999838i | \(0.494274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11981.9 | 0.518795 | 0.259397 | − | 0.965771i | \(-0.416476\pi\) | ||||
0.259397 | + | 0.965771i | \(0.416476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19524.9 | 0.842274 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2058.95 | 0.0884931 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −61710.2 | −2.64256 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25832.3 | −1.09812 | −0.549058 | − | 0.835784i | \(-0.685013\pi\) | ||||
−0.549058 | + | 0.835784i | \(0.685013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13384.1 | −0.566879 | −0.283439 | − | 0.958990i | \(-0.591475\pi\) | ||||
−0.283439 | + | 0.958990i | \(0.591475\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22635.7 | 0.955242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5108.38 | 0.214796 | 0.107398 | − | 0.994216i | \(-0.465748\pi\) | ||||
0.107398 | + | 0.994216i | \(0.465748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34769.2 | −1.45668 | −0.728338 | − | 0.685218i | \(-0.759707\pi\) | ||||
−0.728338 | + | 0.685218i | \(0.759707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9636.08 | 0.402253 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7386.63 | 0.306137 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4034.05 | −0.166592 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4354.20 | 0.179170 | 0.0895851 | − | 0.995979i | \(-0.471446\pi\) | ||||
0.0895851 | + | 0.995979i | \(0.471446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24056.7 | −0.986376 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3143.48 | −0.128431 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7622.66 | −0.310328 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20809.9 | −0.841218 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7208.58 | −0.290372 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25709.6 | −1.03198 | −0.515991 | − | 0.856594i | \(-0.672576\pi\) | ||||
−0.515991 | + | 0.856594i | \(0.672576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3871.57 | −0.154860 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41466.8 | 1.65284 | 0.826418 | − | 0.563057i | \(-0.190375\pi\) | ||||
0.826418 | + | 0.563057i | \(0.190375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27860.3 | 1.10661 | 0.553306 | − | 0.832978i | \(-0.313366\pi\) | ||||
0.553306 | + | 0.832978i | \(0.313366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31885.8 | −1.25771 | −0.628857 | − | 0.777521i | \(-0.716477\pi\) | ||||
−0.628857 | + | 0.777521i | \(0.716477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10064.6 | 0.395616 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14090.3 | 0.551940 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41076.9 | −1.60350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20792.2 | 0.808860 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11767.5 | 0.456209 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25529.7 | −0.982982 | −0.491491 | − | 0.870883i | \(-0.663548\pi\) | ||||
−0.491491 | + | 0.870883i | \(0.663548\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2471.21 | 0.0948259 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34416.4 | 1.31614 | 0.658069 | − | 0.752958i | \(-0.271374\pi\) | ||||
0.658069 | + | 0.752958i | \(0.271374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24910.1 | 0.949369 | 0.474684 | − | 0.880156i | \(-0.342562\pi\) | ||||
0.474684 | + | 0.880156i | \(0.342562\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2785.37 | 0.105796 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14817.5 | −0.560906 | −0.280453 | − | 0.959868i | \(-0.590485\pi\) | ||||
−0.280453 | + | 0.959868i | \(0.590485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5193.24 | 0.195264 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −78656.8 | −2.94753 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6453.83 | 0.241037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36663.7 | 1.36473 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2723.46 | 0.101037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6907.85 | −0.255421 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10330.7 | −0.379453 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37979.4 | −1.39039 | −0.695196 | − | 0.718820i | \(-0.744682\pi\) | ||||
−0.695196 | + | 0.718820i | \(0.744682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6483.08 | 0.236557 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30092.3 | −1.09440 | −0.547202 | − | 0.837001i | \(-0.684307\pi\) | ||||
−0.547202 | + | 0.837001i | \(0.684307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68776.8 | 2.49308 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −588.245 | −0.0212533 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31083.4 | 1.11572 | 0.557859 | − | 0.829936i | \(-0.311623\pi\) | ||||
0.557859 | + | 0.829936i | \(0.311623\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25974.5 | 0.929303 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44611.6 | 1.59091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4915.90 | −0.174739 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15862.6 | −0.562024 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5772.29 | 0.203857 | 0.101928 | − | 0.994792i | \(-0.467499\pi\) | ||||
0.101928 | + | 0.994792i | \(0.467499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7946.90 | 0.278853 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2549.93 | 0.0891890 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21399.5 | 0.746096 | 0.373048 | − | 0.927812i | \(-0.378313\pi\) | ||||
0.373048 | + | 0.927812i | \(0.378313\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −81.6625 | −0.00283808 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11275.1 | 0.390603 | 0.195302 | − | 0.980743i | \(-0.437431\pi\) | ||||
0.195302 | + | 0.980743i | \(0.437431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8664.44 | 0.299208 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45888.3 | 1.57462 | 0.787312 | − | 0.616554i | \(-0.211472\pi\) | ||||
0.787312 | + | 0.616554i | \(0.211472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49338.4 | 1.68766 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20757.7 | 0.707798 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35717.5 | −1.21406 | −0.607032 | − | 0.794677i | \(-0.707640\pi\) | ||||
−0.607032 | + | 0.794677i | \(0.707640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 579.260 | 0.0196277 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3506.05 | −0.118427 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7467.83 | −0.250674 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1253.78 | 0.0419548 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10219.6 | −0.340911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6864.36 | −0.228276 | −0.114138 | − | 0.993465i | \(-0.536411\pi\) | ||||
−0.114138 | + | 0.993465i | \(0.536411\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7016.22 | 0.232604 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13333.7 | 0.440680 | 0.220340 | − | 0.975423i | \(-0.429283\pi\) | ||||
0.220340 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25002.8 | 0.821264 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2222.94 | 0.0727923 | 0.0363962 | − | 0.999337i | \(-0.488412\pi\) | ||||
0.0363962 | + | 0.999337i | \(0.488412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42791.6 | 1.39696 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5125.89 | 0.166827 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30862.1 | −1.00137 | −0.500686 | − | 0.865629i | \(-0.666919\pi\) | ||||
−0.500686 | + | 0.865629i | \(0.666919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9182.48 | −0.297034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 66957.4 | 2.15280 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11593.9 | −0.371637 | −0.185819 | − | 0.982584i | \(-0.559494\pi\) | ||||
−0.185819 | + | 0.982584i | \(0.559494\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26921.4 | −0.860347 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10619.1 | −0.338341 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36631.7 | 1.16363 | 0.581814 | − | 0.813322i | \(-0.302343\pi\) | ||||
0.581814 | + | 0.813322i | \(0.302343\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1127.84 | −0.0357190 |
(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 | 1176.4.a.s.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 2352.4.a.ce.1.1 | 2 | |||
7.6 | odd | 2 | 1176.4.a.t.1.2 | yes | 2 | ||
28.27 | even | 2 | 2352.4.a.bm.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.s.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1176.4.a.t.1.2 | yes | 2 | 7.6 | odd | 2 | ||
2352.4.a.bm.1.2 | 2 | 28.27 | even | 2 | |||
2352.4.a.ce.1.1 | 2 | 4.3 | odd | 2 |