Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.22700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 28x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-5.03475\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(5\) | 4.31394 | 0.385851 | 0.192925 | − | 0.981213i | \(-0.438203\pi\) | ||||
0.192925 | + | 0.981213i | \(0.438203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 41.9640 | 1.15024 | 0.575120 | − | 0.818069i | \(-0.304955\pi\) | ||||
0.575120 | + | 0.818069i | \(0.304955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.2780 | −0.560631 | −0.280315 | − | 0.959908i | \(-0.590439\pi\) | ||||
−0.280315 | + | 0.959908i | \(0.590439\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.9418 | 0.222771 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 57.8477 | 0.825301 | 0.412651 | − | 0.910889i | \(-0.364603\pi\) | ||||
0.412651 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.16162 | −0.0261006 | −0.0130503 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130503 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 200.960 | 1.82187 | 0.910934 | − | 0.412551i | \(-0.135362\pi\) | ||||
0.910934 | + | 0.412551i | \(0.135362\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −106.390 | −0.851119 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 121.274 | 0.776549 | 0.388275 | − | 0.921544i | \(-0.373071\pi\) | ||||
0.388275 | + | 0.921544i | \(0.373071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −279.830 | −1.62125 | −0.810627 | − | 0.585563i | \(-0.800873\pi\) | ||||
−0.810627 | + | 0.585563i | \(0.800873\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 125.892 | 0.664091 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.1976 | 0.145838 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −124.322 | −0.552391 | −0.276196 | − | 0.961101i | \(-0.589074\pi\) | ||||
−0.276196 | + | 0.961101i | \(0.589074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −78.8340 | −0.323680 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 363.355 | 1.38406 | 0.692030 | − | 0.721868i | \(-0.256716\pi\) | ||||
0.692030 | + | 0.721868i | \(0.256716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 253.488 | 0.898991 | 0.449496 | − | 0.893282i | \(-0.351604\pi\) | ||||
0.449496 | + | 0.893282i | \(0.351604\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 38.8255 | 0.128617 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −84.6279 | −0.262644 | −0.131322 | − | 0.991340i | \(-0.541922\pi\) | ||||
−0.131322 | + | 0.991340i | \(0.541922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 173.543 | 0.476488 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −507.104 | −1.31427 | −0.657133 | − | 0.753775i | \(-0.728231\pi\) | ||||
−0.657133 | + | 0.753775i | \(0.728231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 181.030 | 0.443821 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.48487 | −0.0150692 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 338.027 | 0.745889 | 0.372944 | − | 0.927854i | \(-0.378348\pi\) | ||||
0.372944 | + | 0.927854i | \(0.378348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 529.831 | 1.11210 | 0.556049 | − | 0.831150i | \(-0.312317\pi\) | ||||
0.556049 | + | 0.831150i | \(0.312317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −113.362 | −0.216320 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 429.884 | 0.783860 | 0.391930 | − | 0.919995i | \(-0.371807\pi\) | ||||
0.391930 | + | 0.919995i | \(0.371807\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 602.879 | 1.05186 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1147.54 | −1.91814 | −0.959072 | − | 0.283162i | \(-0.908616\pi\) | ||||
−0.959072 | + | 0.283162i | \(0.908616\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 490.466 | 0.786366 | 0.393183 | − | 0.919460i | \(-0.371374\pi\) | ||||
0.393183 | + | 0.919460i | \(0.371374\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −319.170 | −0.491394 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 293.748 | 0.434750 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −645.131 | −0.918770 | −0.459385 | − | 0.888237i | \(-0.651930\pi\) | ||||
−0.459385 | + | 0.888237i | \(0.651930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 974.314 | 1.28849 | 0.644246 | − | 0.764818i | \(-0.277171\pi\) | ||||
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 249.551 | 0.318443 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 363.821 | 0.448341 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −302.494 | −0.360273 | −0.180137 | − | 0.983642i | \(-0.557654\pi\) | ||||
−0.180137 | + | 0.983642i | \(0.557654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −183.946 | −0.211899 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −839.489 | −0.936031 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.32512 | −0.0100709 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1142.65 | −1.19606 | −0.598032 | − | 0.801472i | \(-0.704051\pi\) | ||||
−0.598032 | + | 0.801472i | \(0.704051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 377.676 | 0.383413 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1022.18 | 1.00703 | 0.503517 | − | 0.863985i | \(-0.332039\pi\) | ||||
0.503517 | + | 0.863985i | \(0.332039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −422.343 | −0.404026 | −0.202013 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202013 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 90.5927 | 0.0841995 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 573.263 | 0.517938 | 0.258969 | − | 0.965886i | \(-0.416617\pi\) | ||||
0.258969 | + | 0.965886i | \(0.416617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1568.49 | 1.37829 | 0.689147 | − | 0.724621i | \(-0.257985\pi\) | ||||
0.689147 | + | 0.724621i | \(0.257985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −372.967 | −0.318923 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 236.274 | 0.196697 | 0.0983486 | − | 0.995152i | \(-0.468644\pi\) | ||||
0.0983486 | + | 0.995152i | \(0.468644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 866.928 | 0.702969 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −236.502 | −0.186877 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 404.934 | 0.311935 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 429.981 | 0.323051 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1090.06 | 0.799088 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −998.202 | −0.714255 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1266.32 | 0.884782 | 0.442391 | − | 0.896822i | \(-0.354130\pi\) | ||||
0.442391 | + | 0.896822i | \(0.354130\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 760.465 | 0.519033 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −591.805 | −0.394704 | −0.197352 | − | 0.980333i | \(-0.563234\pi\) | ||||
−0.197352 | + | 0.980333i | \(0.563234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1314 | −0.00986508 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 116.476 | 0.0742570 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2621.03 | 1.63452 | 0.817262 | − | 0.576266i | \(-0.195491\pi\) | ||||
0.817262 | + | 0.576266i | \(0.195491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1947.48 | 1.18837 | 0.594183 | − | 0.804330i | \(-0.297475\pi\) | ||||
0.594183 | + | 0.804330i | \(0.297475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −253.884 | −0.151637 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1102.73 | −0.644860 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 523.167 | 0.299632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 660.857 | 0.363353 | 0.181676 | − | 0.983358i | \(-0.441848\pi\) | ||||
0.181676 | + | 0.983358i | \(0.441848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2051.46 | −1.10560 | −0.552800 | − | 0.833314i | \(-0.686441\pi\) | ||||
−0.552800 | + | 0.833314i | \(0.686441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 520.629 | 0.275100 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1207.17 | −0.625562 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2673.81 | 1.35919 | 0.679596 | − | 0.733587i | \(-0.262155\pi\) | ||||
0.679596 | + | 0.733587i | \(0.262155\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1521.31 | −0.758792 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1406.72 | 0.688602 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3318.17 | −1.59447 | −0.797236 | − | 0.603667i | \(-0.793705\pi\) | ||||
−0.797236 | + | 0.603667i | \(0.793705\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 543.091 | 0.256240 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2239.35 | −1.03764 | −0.518821 | − | 0.854883i | \(-0.673629\pi\) | ||||
−0.518821 | + | 0.854883i | \(0.673629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1506.47 | −0.685693 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.4546 | −0.00870019 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1656.63 | 0.728040 | 0.364020 | − | 0.931391i | \(-0.381404\pi\) | ||||
0.364020 | + | 0.931391i | \(0.381404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −744.729 | −0.321693 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1014.08 | 0.430639 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −814.515 | −0.340110 | −0.170055 | − | 0.985435i | \(-0.554395\pi\) | ||||
−0.170055 | + | 0.985435i | \(0.554395\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2612.41 | 1.07281 | 0.536406 | − | 0.843960i | \(-0.319781\pi\) | ||||
0.536406 | + | 0.843960i | \(0.319781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1589.49 | 0.642070 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −536.320 | −0.213141 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2427.52 | 0.949294 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −252.729 | −0.0957425 | −0.0478712 | − | 0.998854i | \(-0.515244\pi\) | ||||
−0.0478712 | + | 0.998854i | \(0.515244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4460.67 | 1.66366 | 0.831829 | − | 0.555032i | \(-0.187294\pi\) | ||||
0.831829 | + | 0.555032i | \(0.187294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −340.085 | −0.124892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1499.31 | −0.542242 | −0.271121 | − | 0.962545i | \(-0.587394\pi\) | ||||
−0.271121 | + | 0.962545i | \(0.587394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −454.108 | −0.161763 | −0.0808815 | − | 0.996724i | \(-0.525774\pi\) | ||||
−0.0808815 | + | 0.996724i | \(0.525774\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1289.65 | 0.452562 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 848.915 | 0.293508 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1567.49 | 0.534040 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1808.64 | 0.607290 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −90.7105 | −0.0300219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2278.79 | −0.743501 | −0.371750 | − | 0.928333i | \(-0.621242\pi\) | ||||
−0.371750 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3442.63 | −1.10744 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1093.53 | 0.346876 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1958.81 | −0.612776 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1471.40 | 0.454009 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1520.12 | −0.462689 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1412.43 | 0.424141 | 0.212070 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212070 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −957.509 | −0.283706 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3027.07 | −0.885082 | −0.442541 | − | 0.896748i | \(-0.645923\pi\) | ||||
−0.442541 | + | 0.896748i | \(0.645923\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.14697 | 0.00177381 | 0.000886906 | − | 1.00000i | \(-0.499718\pi\) | ||||
0.000886906 | 1.00000i | \(0.499718\pi\) | ||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 881.245 | 0.251003 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2385.66 | 0.670771 | 0.335386 | − | 0.942081i | \(-0.391133\pi\) | ||||
0.335386 | + | 0.942081i | \(0.391133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −365.080 | −0.101341 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1935.39 | −0.530452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1606.40 | 0.434768 | 0.217384 | − | 0.976086i | \(-0.430248\pi\) | ||||
0.217384 | + | 0.976086i | \(0.430248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 835.200 | 0.223236 | 0.111618 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111618 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 211.383 | 0.0551215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 56.8031 | 0.0146328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2922.94 | 0.743912 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1326.03 | −0.333459 | −0.166730 | − | 0.986003i | \(-0.553321\pi\) | ||||
−0.166730 | + | 0.986003i | \(0.553321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8433.08 | 2.09559 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 748.654 | 0.183853 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5210.12 | 1.26458 | 0.632292 | − | 0.774730i | \(-0.282114\pi\) | ||||
0.632292 | + | 0.774730i | \(0.282114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −870.257 | −0.208784 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1091.46 | 0.258850 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2478.00 | −0.580988 | −0.290494 | − | 0.956877i | \(-0.593820\pi\) | ||||
−0.290494 | + | 0.956877i | \(0.593820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2187.62 | −0.507110 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −907.483 | −0.208004 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4990.25 | 1.13108 | 0.565540 | − | 0.824721i | \(-0.308668\pi\) | ||||
0.565540 | + | 0.824721i | \(0.308668\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6860.80 | 1.53787 | 0.768937 | − | 0.639325i | \(-0.220786\pi\) | ||||
0.768937 | + | 0.639325i | \(0.220786\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −551.838 | −0.122340 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4464.55 | −0.978991 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −781.578 | −0.169532 | −0.0847662 | − | 0.996401i | \(-0.527014\pi\) | ||||
−0.0847662 | + | 0.996401i | \(0.527014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2518.47 | −0.540418 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5447.06 | 1.15638 | 0.578192 | − | 0.815900i | \(-0.303758\pi\) | ||||
0.578192 | + | 0.815900i | \(0.303758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6008.83 | −1.26215 | −0.631074 | − | 0.775723i | \(-0.717385\pi\) | ||||
−0.631074 | + | 0.775723i | \(0.717385\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.9753 | −0.00581444 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2543.48 | 0.523126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1566.65 | −0.318878 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3427.94 | −0.690548 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5840.09 | 1.16444 | 0.582221 | − | 0.813030i | \(-0.302184\pi\) | ||||
0.582221 | + | 0.813030i | \(0.302184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1458.23 | 0.287802 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1133.03 | 0.221364 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5280.81 | −1.02140 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1774.42 | 0.339787 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3066.53 | 0.581411 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2285.66 | 0.429103 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8443.25 | 1.56965 | 0.784824 | − | 0.619719i | \(-0.212753\pi\) | ||||
0.784824 | + | 0.619719i | \(0.212753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1267.03 | −0.233264 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5326.08 | −0.971106 | −0.485553 | − | 0.874207i | \(-0.661382\pi\) | ||||
−0.485553 | + | 0.874207i | \(0.661382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8820.06 | −1.59278 | −0.796388 | − | 0.604786i | \(-0.793259\pi\) | ||||
−0.796388 | + | 0.604786i | \(0.793259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 271.778 | 0.0486126 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.9617 | 0.00566293 | 0.00283147 | − | 0.999996i | \(-0.499099\pi\) | ||||
0.00283147 | + | 0.999996i | \(0.499099\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5089.13 | 0.893218 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1719.79 | 0.299032 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −125.045 | −0.0215408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2795.71 | 0.477164 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4705.47 | 0.795759 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −592.395 | −0.0992699 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 943.305 | 0.156643 | 0.0783214 | − | 0.996928i | \(-0.475044\pi\) | ||||
0.0783214 | + | 0.996928i | \(0.475044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1118.90 | −0.184130 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1854.49 | 0.302453 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2994.01 | −0.483958 | −0.241979 | − | 0.970281i | \(-0.577797\pi\) | ||||
−0.241979 | + | 0.970281i | \(0.577797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 708.822 | 0.113563 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11742.8 | −1.86483 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2600.78 | 0.405859 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −756.781 | −0.117078 | −0.0585391 | − | 0.998285i | \(-0.518644\pi\) | ||||
−0.0585391 | + | 0.998285i | \(0.518644\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6388.02 | 0.979778 | 0.489889 | − | 0.871785i | \(-0.337037\pi\) | ||||
0.489889 | + | 0.871785i | \(0.337037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −709.506 | −0.107893 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 315.429 | 0.0475597 | 0.0237799 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237799 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4950.43 | −0.740117 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1214.80 | 0.180096 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6672.00 | 0.980876 | 0.490438 | − | 0.871476i | \(-0.336837\pi\) | ||||
0.490438 | + | 0.871476i | \(0.336837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6854.33 | −0.999319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1289.94 | 0.186514 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2115.84 | 0.303420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.3540 | −0.00332171 | −0.00166085 | − | 0.999999i | \(-0.500529\pi\) | ||||
−0.00166085 | + | 0.999999i | \(0.500529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3270.19 | 0.461354 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3549.73 | −0.496746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6294.34 | 0.873750 | 0.436875 | − | 0.899522i | \(-0.356085\pi\) | ||||
0.436875 | + | 0.899522i | \(0.356085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2994.61 | −0.412376 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3186.82 | −0.435358 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1311.59 | −0.177762 | −0.0888810 | − | 0.996042i | \(-0.528329\pi\) | ||||
−0.0888810 | + | 0.996042i | \(0.528329\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3798.95 | 0.510829 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3519.66 | −0.469572 | −0.234786 | − | 0.972047i | \(-0.575439\pi\) | ||||
−0.234786 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1267.21 | 0.167748 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2281.40 | 0.299664 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12858.6 | −1.67598 | −0.837988 | − | 0.545689i | \(-0.816268\pi\) | ||||
−0.837988 | + | 0.545689i | \(0.816268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11625.0 | 1.50359 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1775.41 | −0.227882 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2783.05 | −0.354508 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13317.7 | −1.68361 | −0.841807 | − | 0.539779i | \(-0.818508\pi\) | ||||
−0.841807 | + | 0.539779i | \(0.818508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −45.3941 | −0.00569561 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12106.3 | 1.50763 | 0.753817 | − | 0.657085i | \(-0.228211\pi\) | ||||
0.753817 | + | 0.657085i | \(0.228211\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7353.36 | 0.908925 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 349.429 | 0.0428723 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5217.07 | −0.635382 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12778.6 | −1.54489 | −0.772447 | − | 0.635079i | \(-0.780968\pi\) | ||||
−0.772447 | + | 0.635079i | \(0.780968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7863.09 | 0.943693 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2366.19 | 0.281919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4203.13 | 0.497166 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5842.43 | 0.686104 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15045.6 | −1.75423 | −0.877117 | − | 0.480277i | \(-0.840536\pi\) | ||||
−0.877117 | + | 0.480277i | \(0.840536\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2782.26 | −0.322088 | −0.161044 | − | 0.986947i | \(-0.551486\pi\) | ||||
−0.161044 | + | 0.986947i | \(0.551486\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −761.651 | −0.0875478 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6154.41 | −0.702430 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3708.82 | 0.420333 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3308.19 | −0.372310 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5223.64 | −0.583791 | −0.291896 | − | 0.956450i | \(-0.594286\pi\) | ||||
−0.291896 | + | 0.956450i | \(0.594286\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4568.84 | −0.507077 | −0.253539 | − | 0.967325i | \(-0.581594\pi\) | ||||
−0.253539 | + | 0.967325i | \(0.581594\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1569.50 | 0.172993 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −434.399 | −0.0475518 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −380.473 | −0.0413644 | −0.0206822 | − | 0.999786i | \(-0.506584\pi\) | ||||
−0.0206822 | + | 0.999786i | \(0.506584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3397.79 | −0.364411 | −0.182205 | − | 0.983261i | \(-0.558324\pi\) | ||||
−0.182205 | + | 0.983261i | \(0.558324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1304.94 | −0.139012 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1982.57 | 0.209782 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16161.4 | −1.69867 | −0.849336 | − | 0.527853i | \(-0.822997\pi\) | ||||
−0.849336 | + | 0.527853i | \(0.822997\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15247.8 | 1.59200 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6154.39 | −0.638319 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −793.532 | −0.0817612 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8906.44 | 0.911653 | 0.455827 | − | 0.890069i | \(-0.349344\pi\) | ||||
0.455827 | + | 0.890069i | \(0.349344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1561.89 | 0.158829 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3435.99 | 0.347137 | 0.173568 | − | 0.984822i | \(-0.444470\pi\) | ||||
0.173568 | + | 0.984822i | \(0.444470\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7531.44 | −0.755974 | −0.377987 | − | 0.925811i | \(-0.623384\pi\) | ||||
−0.377987 | + | 0.925811i | \(0.623384\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3621.50 | −0.361168 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8808.26 | 0.872800 | 0.436400 | − | 0.899753i | \(-0.356253\pi\) | ||||
0.436400 | + | 0.899753i | \(0.356253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3009.19 | 0.296271 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8021.43 | 0.784730 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10637.4 | 1.03406 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 229.975 | 0.0222147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4563.94 | −0.438089 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −978.352 | −0.0933237 | −0.0466618 | − | 0.998911i | \(-0.514858\pi\) | ||||
−0.0466618 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3266.94 | 0.309688 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4220.15 | 0.397564 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4929.31 | −0.461502 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7188.45 | 0.668870 | 0.334435 | − | 0.942419i | \(-0.391454\pi\) | ||||
0.334435 | + | 0.942419i | \(0.391454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9954.51 | −0.920569 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6156.65 | 0.565877 | 0.282939 | − | 0.959138i | \(-0.408691\pi\) | ||||
0.282939 | + | 0.959138i | \(0.408691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7015.39 | 0.640887 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1629.27 | 0.147940 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8032.80 | −0.724990 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13832.0 | 1.24089 | 0.620445 | − | 0.784250i | \(-0.286952\pi\) | ||||
0.620445 | + | 0.784250i | \(0.286952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6718.05 | −0.599083 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16630.6 | −1.47420 | −0.737100 | − | 0.675783i | \(-0.763805\pi\) | ||||
−0.737100 | + | 0.675783i | \(0.763805\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4409.61 | 0.388564 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4519.40 | −0.395885 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11795.0 | −1.02712 | −0.513562 | − | 0.858053i | \(-0.671674\pi\) | ||||
−0.513562 | + | 0.858053i | \(0.671674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3433.26 | 0.297219 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −58.3638 | −0.00502305 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1821.96 | −0.155894 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3551.33 | −0.302103 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4969.88 | 0.420334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −597.161 | −0.0502151 | −0.0251076 | − | 0.999685i | \(-0.507993\pi\) | ||||
−0.0251076 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6287.96 | −0.525724 | −0.262862 | − | 0.964833i | \(-0.584666\pi\) | ||||
−0.262862 | + | 0.964833i | \(0.584666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2234.19 | −0.185729 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16187.5 | −1.33802 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28217.8 | 2.31921 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3042.25 | 0.248630 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9548.23 | −0.775947 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2473.02 | 0.199847 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2443.55 | −0.196363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2056.24 | 0.164320 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6931.94 | 0.550882 | 0.275441 | − | 0.961318i | \(-0.411176\pi\) | ||||
0.275441 | + | 0.961318i | \(0.411176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7837.24 | 0.619389 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6766.37 | 0.531816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24713.6 | −1.93177 | −0.965884 | − | 0.258976i | \(-0.916615\pi\) | ||||
−0.965884 | + | 0.258976i | \(0.916615\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4768.48 | 0.370699 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −262.148 | −0.0202684 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4515.91 | −0.347263 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1608.96 | −0.123057 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2598.91 | −0.197700 | −0.0988502 | − | 0.995102i | \(-0.531516\pi\) | ||||
−0.0988502 | + | 0.995102i | \(0.531516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6661.17 | −0.504002 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7282.57 | 0.548075 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15673.3 | −1.17327 | −0.586636 | − | 0.809851i | \(-0.699548\pi\) | ||||
−0.586636 | + | 0.809851i | \(0.699548\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1019.27 | 0.0758957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23643.3 | −1.74196 | −0.870981 | − | 0.491316i | \(-0.836516\pi\) | ||||
−0.870981 | + | 0.491316i | \(0.836516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11308.1 | 0.828772 | 0.414386 | − | 0.910101i | \(-0.363996\pi\) | ||||
0.414386 | + | 0.910101i | \(0.363996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −758.186 | −0.0552769 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21380.1 | −1.55063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26768.4 | −1.93134 | −0.965669 | − | 0.259776i | \(-0.916351\pi\) | ||||
−0.965669 | + | 0.259776i | \(0.916351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13382.0 | 0.960513 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6820.20 | 0.487004 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21280.1 | −1.51172 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1020.25 | −0.0721066 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12495.4 | 0.878607 | 0.439304 | − | 0.898339i | \(-0.355225\pi\) | ||||
0.439304 | + | 0.898339i | \(0.355225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 604.886 | 0.0423156 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4497.94 | −0.313063 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1891.59 | 0.130992 | 0.0654959 | − | 0.997853i | \(-0.479137\pi\) | ||||
0.0654959 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1746.86 | 0.120360 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1362.32 | −0.0933939 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6620.09 | −0.451569 | −0.225784 | − | 0.974177i | \(-0.572494\pi\) | ||||
−0.225784 | + | 0.974177i | \(0.572494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28416.4 | −1.92867 | −0.964333 | − | 0.264690i | \(-0.914730\pi\) | ||||
−0.964333 | + | 0.264690i | \(0.914730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3868.95 | 0.261287 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1854.91 | 0.124649 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8543.67 | −0.571297 | −0.285648 | − | 0.958335i | \(-0.592209\pi\) | ||||
−0.285648 | + | 0.958335i | \(0.592209\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2546.74 | 0.169457 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2223.85 | 0.147246 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20334.9 | −1.33984 | −0.669918 | − | 0.742435i | \(-0.733671\pi\) | ||||
−0.669918 | + | 0.742435i | \(0.733671\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4702.47 | 0.308328 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27044.6 | −1.76463 | −0.882315 | − | 0.470660i | \(-0.844016\pi\) | ||||
−0.882315 | + | 0.470660i | \(0.844016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5072.37 | −0.329363 | −0.164682 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164682 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5425.91 | 0.350619 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2117.46 | −0.136170 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8992.56 | 0.575524 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −272.131 | −0.0173331 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7191.76 | −0.455889 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15462.5 | −0.975517 | −0.487759 | − | 0.872979i | \(-0.662185\pi\) | ||||
−0.487759 | + | 0.872979i | \(0.662185\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6836.38 | −0.429260 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5462.81 | 0.341394 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1287.62 | −0.0800901 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10327.9 | −0.639381 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7083.52 | 0.436478 | 0.218239 | − | 0.975895i | \(-0.429969\pi\) | ||||
0.218239 | + | 0.975895i | \(0.429969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22814.3 | 1.39924 | 0.699619 | − | 0.714516i | \(-0.253353\pi\) | ||||
0.699619 | + | 0.714516i | \(0.253353\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3280.60 | 0.200269 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18553.9 | −1.12740 | −0.563700 | − | 0.825980i | \(-0.690623\pi\) | ||||
−0.563700 | + | 0.825980i | \(0.690623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14185.0 | 0.857951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5876.42 | −0.353787 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8293.14 | −0.496992 | −0.248496 | − | 0.968633i | \(-0.579936\pi\) | ||||
−0.248496 | + | 0.968633i | \(0.579936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2553.01 | −0.152297 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4414.20 | 0.262122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22379.6 | −1.32289 | −0.661447 | − | 0.749992i | \(-0.730057\pi\) | ||||
−0.661447 | + | 0.749992i | \(0.730057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13096.5 | −0.770643 | −0.385322 | − | 0.922782i | \(-0.625910\pi\) | ||||
−0.385322 | + | 0.922782i | \(0.625910\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4560.36 | −0.267134 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −65.2758 | −0.00380645 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24371.1 | 1.41477 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4237.30 | 0.244878 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22233.9 | 1.27918 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27876.6 | −1.59668 | −0.798339 | − | 0.602209i | \(-0.794288\pi\) | ||||
−0.798339 | + | 0.602209i | \(0.794288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2872.53 | −0.163798 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2365.28 | −0.134276 | −0.0671381 | − | 0.997744i | \(-0.521387\pi\) | ||||
−0.0671381 | + | 0.997744i | \(0.521387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7998.53 | −0.452070 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9081.20 | −0.511002 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31403.9 | −1.75935 | −0.879675 | − | 0.475576i | \(-0.842240\pi\) | ||||
−0.879675 | + | 0.475576i | \(0.842240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11307.0 | 0.630682 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4409 | 0.00102411 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13325.7 | 0.736818 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14302.5 | 0.787397 | 0.393698 | − | 0.919240i | \(-0.371195\pi\) | ||||
0.393698 | + | 0.919240i | \(0.371195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2643.73 | 0.144917 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8401.30 | 0.458532 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21019.2 | 1.14227 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7156.97 | 0.387270 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32812.2 | 1.76790 | 0.883950 | − | 0.467581i | \(-0.154875\pi\) | ||||
0.883950 | + | 0.467581i | \(0.154875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 268.738 | 0.0144177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1095.24 | −0.0585093 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7155.24 | 0.380623 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34531.4 | −1.82913 | −0.914565 | − | 0.404439i | \(-0.867467\pi\) | ||||
−0.914565 | + | 0.404439i | \(0.867467\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5806.17 | −0.306257 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −56234.4 | −2.95371 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4757.11 | −0.248820 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4819.21 | 0.251013 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1577.27 | −0.0818113 | −0.0409056 | − | 0.999163i | \(-0.513024\pi\) | ||||
−0.0409056 | + | 0.999163i | \(0.513024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2956.40 | −0.152707 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2505.60 | 0.128886 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12902.3 | −0.660936 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35968.9 | 1.83496 | 0.917479 | − | 0.397784i | \(-0.130221\pi\) | ||||
0.917479 | + | 0.397784i | \(0.130221\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14663.7 | 0.741939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19579.7 | −0.986619 | −0.493310 | − | 0.869854i | \(-0.664213\pi\) | ||||
−0.493310 | + | 0.869854i | \(0.664213\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 634.149 | 0.0318244 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18039.7 | 0.901627 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 963.684 | 0.0479698 | 0.0239849 | − | 0.999712i | \(-0.492365\pi\) | ||||
0.0239849 | + | 0.999712i | \(0.492365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 170.409 | 0.00844824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30102.0 | −1.48632 | −0.743158 | − | 0.669115i | \(-0.766673\pi\) | ||||
−0.743158 | + | 0.669115i | \(0.766673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2850.90 | 0.140200 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8768.83 | 0.429498 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4012.84 | 0.195762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19002.8 | 0.923331 | 0.461666 | − | 0.887054i | \(-0.347252\pi\) | ||||
0.461666 | + | 0.887054i | \(0.347252\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3978.09 | −0.192523 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8849.89 | −0.426597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23766.6 | −1.14110 | −0.570550 | − | 0.821263i | \(-0.693270\pi\) | ||||
−0.570550 | + | 0.821263i | \(0.693270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25299.2 | 1.20989 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7390.89 | 0.352063 | 0.176031 | − | 0.984385i | \(-0.443674\pi\) | ||||
0.176031 | + | 0.984385i | \(0.443674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10979.4 | 0.520947 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2245.96 | 0.106148 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8882.68 | −0.418168 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20847.7 | 0.977616 | 0.488808 | − | 0.872391i | \(-0.337432\pi\) | ||||
0.488808 | + | 0.872391i | \(0.337432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15630.4 | 0.730108 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26362.7 | 1.22665 | 0.613325 | − | 0.789831i | \(-0.289832\pi\) | ||||
0.613325 | + | 0.789831i | \(0.289832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29771.0 | 1.37988 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2610.77 | −0.120542 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −785.436 | −0.0361248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48155.5 | −2.20633 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3274.39 | 0.149447 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11534.6 | 0.524445 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9668.13 | −0.437906 | −0.218953 | − | 0.975735i | \(-0.570264\pi\) | ||||
−0.218953 | + | 0.975735i | \(0.570264\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7433.99 | −0.335434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1653.92 | 0.0743445 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13922.9 | −0.623476 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6562.85 | −0.292780 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19201.7 | 0.853398 | 0.426699 | − | 0.904394i | \(-0.359676\pi\) | ||||
0.426699 | + | 0.904394i | \(0.359676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4895.53 | −0.216760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2722.45 | −0.120091 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20582.0 | 0.904510 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6068.49 | 0.265697 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14970.7 | 0.653030 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15965.2 | 0.693829 | 0.346914 | − | 0.937897i | \(-0.387229\pi\) | ||||
0.346914 | + | 0.937897i | \(0.387229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40776.8 | −1.76556 | −0.882778 | − | 0.469791i | \(-0.844329\pi\) | ||||
−0.882778 | + | 0.469791i | \(0.844329\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20582.4 | 0.887892 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14314.4 | −0.615228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −547.947 | −0.0234642 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1655.51 | −0.0706329 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29419.1 | −1.25059 | −0.625296 | − | 0.780388i | \(-0.715022\pi\) | ||||
−0.625296 | + | 0.780388i | \(0.715022\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21955.7 | −0.929925 | −0.464963 | − | 0.885330i | \(-0.653932\pi\) | ||||
−0.464963 | + | 0.885330i | \(0.653932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13393.7 | −0.565221 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31083.4 | −1.30699 | −0.653493 | − | 0.756933i | \(-0.726697\pi\) | ||||
−0.653493 | + | 0.756933i | \(0.726697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20566.2 | 0.861635 | 0.430817 | − | 0.902439i | \(-0.358225\pi\) | ||||
0.430817 | + | 0.902439i | \(0.358225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2344.73 | −0.0978796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2834.54 | 0.117900 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9660.43 | −0.400375 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7555.40 | −0.312010 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12908.4 | 0.531165 | 0.265582 | − | 0.964088i | \(-0.414436\pi\) | ||||
0.265582 | + | 0.964088i | \(0.414436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9681.72 | −0.396971 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16341.2 | 0.667639 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6498.81 | −0.264575 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3009.87 | 0.122102 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18026.5 | −0.728701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24983.8 | −1.00638 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19464.3 | 0.781297 | 0.390648 | − | 0.920540i | \(-0.372251\pi\) | ||||
0.390648 | + | 0.920540i | \(0.372251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −83.9260 | −0.00335697 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17420.5 | −0.694366 | −0.347183 | − | 0.937797i | \(-0.612862\pi\) | ||||
−0.347183 | + | 0.937797i | \(0.612862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17576.1 | −0.698126 | −0.349063 | − | 0.937099i | \(-0.613500\pi\) | ||||
−0.349063 | + | 0.937099i | \(0.613500\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7630.45 | 0.302027 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16781.2 | 0.661920 | 0.330960 | − | 0.943645i | \(-0.392627\pi\) | ||||
0.330960 | + | 0.943645i | \(0.392627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7146.58 | 0.280915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4699.94 | −0.184104 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27072.3 | −1.05681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11296.5 | −0.439456 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10283.8 | −0.398688 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6987.42 | −0.269963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11052.6 | 0.425564 | 0.212782 | − | 0.977100i | \(-0.431748\pi\) | ||||
0.212782 | + | 0.977100i | \(0.431748\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17520.3 | 0.672291 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27155.3 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16920.5 | 0.644869 | 0.322435 | − | 0.946592i | \(-0.395499\pi\) | ||||
0.322435 | + | 0.946592i | \(0.395499\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4374.69 | 0.166162 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12728.0 | 0.481809 | 0.240904 | − | 0.970549i | \(-0.422556\pi\) | ||||
0.240904 | + | 0.970549i | \(0.422556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8864.21 | 0.334416 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3399.09 | 0.127804 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 182.934 | 0.00685514 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3513.77 | −0.131232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15842.4 | −0.589703 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33935.9 | −1.25898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29334.8 | −1.08467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5323.26 | 0.196176 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11269.8 | 0.413945 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7314.94 | −0.267793 | −0.133897 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133897 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9199.59 | 0.335678 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33450.2 | −1.21652 | −0.608262 | − | 0.793736i | \(-0.708133\pi\) | ||||
−0.608262 | + | 0.793736i | \(0.708133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40886.2 | 1.48208 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6856.98 | 0.247743 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4142.63 | −0.149184 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10448.9 | 0.375058 | 0.187529 | − | 0.982259i | \(-0.439952\pi\) | ||||
0.187529 | + | 0.982259i | \(0.439952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25329.8 | 0.906237 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30155.1 | 1.07537 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13226.7 | 0.470151 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3801.08 | −0.134675 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11230.1 | 0.396606 | 0.198303 | − | 0.980141i | \(-0.436457\pi\) | ||||
0.198303 | + | 0.980141i | \(0.436457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −105.920 | −0.00372865 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15978.2 | −0.560669 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10472.2 | 0.366286 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34110.1 | 1.18925 | 0.594625 | − | 0.804003i | \(-0.297300\pi\) | ||||
0.594625 | + | 0.804003i | \(0.297300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26460.2 | −0.919590 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14232.0 | 0.493039 | 0.246520 | − | 0.969138i | \(-0.420713\pi\) | ||||
0.246520 | + | 0.969138i | \(0.420713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 73019.6 | 2.52158 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 815.335 | 0.0280665 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1587.95 | 0.0544893 | 0.0272446 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272446 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12888.5 | −0.440861 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 95.8852 | 0.00326950 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2167.64 | 0.0736796 | 0.0368398 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368398 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1090.26 | −0.0369423 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15267.4 | 0.515700 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18347.2 | 0.617792 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48513.6 | 1.62846 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5159.36 | 0.172646 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19243.1 | 0.641923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36873.9 | 1.22625 | 0.613125 | − | 0.789986i | \(-0.289912\pi\) | ||||
0.613125 | + | 0.789986i | \(0.289912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −375.135 | −0.0124366 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7783.35 | −0.257240 | −0.128620 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128620 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13632.3 | 0.449160 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8387.14 | 0.275491 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32743.7 | 1.07222 | 0.536112 | − | 0.844147i | \(-0.319893\pi\) | ||||
0.536112 | + | 0.844147i | \(0.319893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12693.9 | −0.414401 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14116.4 | 0.459432 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34153.1 | 1.10815 | 0.554076 | − | 0.832466i | \(-0.313072\pi\) | ||||
0.554076 | + | 0.832466i | \(0.313072\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6467.94 | −0.209224 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1777.19 | −0.0573135 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50940.9 | 1.63784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52838.0 | −1.69370 | −0.846849 | − | 0.531833i | \(-0.821503\pi\) | ||||
−0.846849 | + | 0.531833i | \(0.821503\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2829.92 | 0.0904377 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1958.99 | −0.0624163 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24190.0 | −0.768409 | −0.384204 | − | 0.923248i | \(-0.625524\pi\) | ||||
−0.384204 | + | 0.923248i | \(0.625524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3356.71 | −0.106308 |
(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 | 1344.4.a.bv.1.2 | 3 | ||
4.3 | odd | 2 | 1344.4.a.bt.1.2 | 3 | |||
8.3 | odd | 2 | 672.4.a.q.1.2 | yes | 3 | ||
8.5 | even | 2 | 672.4.a.o.1.2 | ✓ | 3 | ||
24.5 | odd | 2 | 2016.4.a.z.1.2 | 3 | |||
24.11 | even | 2 | 2016.4.a.y.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.o.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
672.4.a.q.1.2 | yes | 3 | 8.3 | odd | 2 | ||
1344.4.a.bt.1.2 | 3 | 4.3 | odd | 2 | |||
1344.4.a.bv.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2016.4.a.y.1.2 | 3 | 24.11 | even | 2 | |||
2016.4.a.z.1.2 | 3 | 24.5 | odd | 2 |