Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64575 | −0.935414 | −0.467707 | − | 0.883883i | \(-0.654920\pi\) | ||||
−0.467707 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.125000 | ||||||||
\(5\) | 10.5830 | 0.946573 | 0.473286 | − | 0.880909i | \(-0.343068\pi\) | ||||
0.473286 | + | 0.880909i | \(0.343068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000 | 1.18789 | 0.593944 | − | 0.804506i | \(-0.297570\pi\) | ||||
0.593944 | + | 0.804506i | \(0.297570\pi\) | |||||||
\(8\) | 23.8118 | 1.05234 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −28.0000 | −0.885438 | ||||||||
\(11\) | 5.29150 | 0.145041 | 0.0725204 | − | 0.997367i | \(-0.476896\pi\) | ||||
0.0725204 | + | 0.997367i | \(0.476896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −58.2065 | −1.11117 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −55.0000 | −0.859375 | ||||||||
\(17\) | 116.413 | 1.66084 | 0.830421 | − | 0.557136i | \(-0.188100\pi\) | ||||
0.830421 | + | 0.557136i | \(0.188100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 126.000 | 1.52139 | 0.760694 | − | 0.649110i | \(-0.224859\pi\) | ||||
0.760694 | + | 0.649110i | \(0.224859\pi\) | |||||||
\(20\) | −10.5830 | −0.118322 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.0000 | −0.135673 | ||||||||
\(23\) | 31.7490 | 0.287832 | 0.143916 | − | 0.989590i | \(-0.454031\pi\) | ||||
0.143916 | + | 0.989590i | \(0.454031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.0000 | −0.104000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −22.0000 | −0.148486 | ||||||||
\(29\) | 52.9150 | 0.338830 | 0.169415 | − | 0.985545i | \(-0.445812\pi\) | ||||
0.169415 | + | 0.985545i | \(0.445812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 182.000 | 1.05446 | 0.527228 | − | 0.849724i | \(-0.323231\pi\) | ||||
0.527228 | + | 0.849724i | \(0.323231\pi\) | |||||||
\(32\) | −44.9778 | −0.248469 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −308.000 | −1.55358 | ||||||||
\(35\) | 232.826 | 1.12442 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 86.0000 | 0.382117 | 0.191058 | − | 0.981579i | \(-0.438808\pi\) | ||||
0.191058 | + | 0.981579i | \(0.438808\pi\) | |||||||
\(38\) | −333.365 | −1.42313 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 252.000 | 0.996117 | ||||||||
\(41\) | 444.486 | 1.69310 | 0.846550 | − | 0.532310i | \(-0.178676\pi\) | ||||
0.846550 | + | 0.532310i | \(0.178676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 96.0000 | 0.340462 | 0.170231 | − | 0.985404i | \(-0.445549\pi\) | ||||
0.170231 | + | 0.985404i | \(0.445549\pi\) | |||||||
\(44\) | −5.29150 | −0.0181301 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −84.0000 | −0.269242 | ||||||||
\(47\) | −365.114 | −1.13313 | −0.566567 | − | 0.824016i | \(-0.691729\pi\) | ||||
−0.566567 | + | 0.824016i | \(0.691729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 141.000 | 0.411079 | ||||||||
\(50\) | 34.3948 | 0.0972831 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −190.494 | −0.493705 | −0.246853 | − | 0.969053i | \(-0.579396\pi\) | ||||
−0.246853 | + | 0.969053i | \(0.579396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.0000 | 0.137292 | ||||||||
\(56\) | 523.859 | 1.25006 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −140.000 | −0.316947 | ||||||||
\(59\) | 587.357 | 1.29606 | 0.648028 | − | 0.761616i | \(-0.275594\pi\) | ||||
0.648028 | + | 0.761616i | \(0.275594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 574.000 | 1.20481 | 0.602403 | − | 0.798192i | \(-0.294210\pi\) | ||||
0.602403 | + | 0.798192i | \(0.294210\pi\) | |||||||
\(62\) | −481.527 | −0.986354 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 559.000 | 1.09180 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 530.000 | 0.966415 | 0.483208 | − | 0.875506i | \(-0.339472\pi\) | ||||
0.483208 | + | 0.875506i | \(0.339472\pi\) | |||||||
\(68\) | −116.413 | −0.207605 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −616.000 | −1.05180 | ||||||||
\(71\) | −809.600 | −1.35327 | −0.676633 | − | 0.736321i | \(-0.736561\pi\) | ||||
−0.676633 | + | 0.736321i | \(0.736561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 154.000 | 0.246909 | 0.123454 | − | 0.992350i | \(-0.460603\pi\) | ||||
0.123454 | + | 0.992350i | \(0.460603\pi\) | |||||||
\(74\) | −227.535 | −0.357437 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −126.000 | −0.190174 | ||||||||
\(77\) | 116.413 | 0.172292 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −460.000 | −0.655114 | −0.327557 | − | 0.944831i | \(-0.606225\pi\) | ||||
−0.327557 | + | 0.944831i | \(0.606225\pi\) | |||||||
\(80\) | −582.065 | −0.813461 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1176.00 | −1.58375 | ||||||||
\(83\) | 322.782 | 0.426866 | 0.213433 | − | 0.976958i | \(-0.431535\pi\) | ||||
0.213433 | + | 0.976958i | \(0.431535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1232.00 | 1.57211 | ||||||||
\(86\) | −253.992 | −0.318473 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 126.000 | 0.152632 | ||||||||
\(89\) | −1439.29 | −1.71421 | −0.857103 | − | 0.515145i | \(-0.827738\pi\) | ||||
−0.857103 | + | 0.515145i | \(0.827738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −31.7490 | −0.0359790 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 966.000 | 1.05995 | ||||||||
\(95\) | 1333.46 | 1.44010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −70.0000 | −0.0732724 | −0.0366362 | − | 0.999329i | \(-0.511664\pi\) | ||||
−0.0366362 | + | 0.999329i | \(0.511664\pi\) | |||||||
\(98\) | −373.051 | −0.384529 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.0000 | 0.0130000 | ||||||||
\(101\) | −1460.45 | −1.43882 | −0.719409 | − | 0.694586i | \(-0.755587\pi\) | ||||
−0.719409 | + | 0.694586i | \(0.755587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1428.00 | −1.36607 | −0.683034 | − | 0.730387i | \(-0.739340\pi\) | ||||
−0.683034 | + | 0.730387i | \(0.739340\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 504.000 | 0.461819 | ||||||||
\(107\) | −1619.20 | −1.46293 | −0.731467 | − | 0.681877i | \(-0.761164\pi\) | ||||
−0.731467 | + | 0.681877i | \(0.761164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 338.000 | 0.297014 | 0.148507 | − | 0.988911i | \(-0.452553\pi\) | ||||
0.148507 | + | 0.988911i | \(0.452553\pi\) | |||||||
\(110\) | −148.162 | −0.128425 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1210.00 | −1.02084 | ||||||||
\(113\) | −1682.70 | −1.40084 | −0.700420 | − | 0.713731i | \(-0.747004\pi\) | ||||
−0.700420 | + | 0.713731i | \(0.747004\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 336.000 | 0.272454 | ||||||||
\(116\) | −52.9150 | −0.0423538 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1554.00 | −1.21235 | ||||||||
\(119\) | 2561.09 | 1.97289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1303.00 | −0.978963 | ||||||||
\(122\) | −1518.66 | −1.12699 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −182.000 | −0.131807 | ||||||||
\(125\) | −1460.45 | −1.04502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −376.000 | −0.262713 | −0.131357 | − | 0.991335i | \(-0.541933\pi\) | ||||
−0.131357 | + | 0.991335i | \(0.541933\pi\) | |||||||
\(128\) | −1119.15 | −0.772813 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −687.895 | −0.458792 | −0.229396 | − | 0.973333i | \(-0.573675\pi\) | ||||
−0.229396 | + | 0.973333i | \(0.573675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2772.00 | 1.80724 | ||||||||
\(134\) | −1402.25 | −0.903998 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2772.00 | 1.74777 | ||||||||
\(137\) | −1396.96 | −0.871168 | −0.435584 | − | 0.900148i | \(-0.643458\pi\) | ||||
−0.435584 | + | 0.900148i | \(0.643458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2100.00 | 1.28144 | 0.640718 | − | 0.767776i | \(-0.278637\pi\) | ||||
0.640718 | + | 0.767776i | \(0.278637\pi\) | |||||||
\(140\) | −232.826 | −0.140553 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2142.00 | 1.26586 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 560.000 | 0.320727 | ||||||||
\(146\) | −407.446 | −0.230962 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −86.0000 | −0.0477646 | ||||||||
\(149\) | 2000.19 | 1.09974 | 0.549872 | − | 0.835249i | \(-0.314677\pi\) | ||||
0.549872 | + | 0.835249i | \(0.314677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3526.00 | −1.90028 | −0.950138 | − | 0.311828i | \(-0.899059\pi\) | ||||
−0.950138 | + | 0.311828i | \(0.899059\pi\) | |||||||
\(152\) | 3000.28 | 1.60102 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −308.000 | −0.161165 | ||||||||
\(155\) | 1926.11 | 0.998120 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3066.00 | 1.55856 | 0.779278 | − | 0.626678i | \(-0.215586\pi\) | ||||
0.779278 | + | 0.626678i | \(0.215586\pi\) | |||||||
\(158\) | 1217.05 | 0.612803 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −476.000 | −0.235194 | ||||||||
\(161\) | 698.478 | 0.341912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3442.00 | 1.65398 | 0.826988 | − | 0.562219i | \(-0.190052\pi\) | ||||
0.826988 | + | 0.562219i | \(0.190052\pi\) | |||||||
\(164\) | −444.486 | −0.211637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −854.000 | −0.399297 | ||||||||
\(167\) | −2693.37 | −1.24802 | −0.624011 | − | 0.781416i | \(-0.714498\pi\) | ||||
−0.624011 | + | 0.781416i | \(0.714498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3259.57 | −1.47057 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −96.0000 | −0.0425577 | ||||||||
\(173\) | 3492.39 | 1.53481 | 0.767404 | − | 0.641164i | \(-0.221548\pi\) | ||||
0.767404 | + | 0.641164i | \(0.221548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −286.000 | −0.123540 | ||||||||
\(176\) | −291.033 | −0.124644 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3808.00 | 1.60349 | ||||||||
\(179\) | 169.328 | 0.0707049 | 0.0353524 | − | 0.999375i | \(-0.488745\pi\) | ||||
0.0353524 | + | 0.999375i | \(0.488745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3374.00 | 1.38557 | 0.692783 | − | 0.721146i | \(-0.256384\pi\) | ||||
0.692783 | + | 0.721146i | \(0.256384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 756.000 | 0.302897 | ||||||||
\(185\) | 910.138 | 0.361701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 616.000 | 0.240890 | ||||||||
\(188\) | 365.114 | 0.141642 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3528.00 | −1.34709 | ||||||||
\(191\) | −1185.30 | −0.449032 | −0.224516 | − | 0.974470i | \(-0.572080\pi\) | ||||
−0.224516 | + | 0.974470i | \(0.572080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1542.00 | 0.575107 | 0.287553 | − | 0.957765i | \(-0.407158\pi\) | ||||
0.287553 | + | 0.957765i | \(0.407158\pi\) | |||||||
\(194\) | 185.203 | 0.0685401 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −141.000 | −0.0513848 | ||||||||
\(197\) | −2127.18 | −0.769318 | −0.384659 | − | 0.923059i | \(-0.625681\pi\) | ||||
−0.384659 | + | 0.923059i | \(0.625681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −952.000 | −0.339123 | −0.169562 | − | 0.985520i | \(-0.554235\pi\) | ||||
−0.169562 | + | 0.985520i | \(0.554235\pi\) | |||||||
\(200\) | −309.553 | −0.109443 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3864.00 | 1.34589 | ||||||||
\(203\) | 1164.13 | 0.402492 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4704.00 | 1.60264 | ||||||||
\(206\) | 3778.13 | 1.27784 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 666.729 | 0.220663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1640.00 | −0.535082 | −0.267541 | − | 0.963547i | \(-0.586211\pi\) | ||||
−0.267541 | + | 0.963547i | \(0.586211\pi\) | |||||||
\(212\) | 190.494 | 0.0617132 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4284.00 | 1.36845 | ||||||||
\(215\) | 1015.97 | 0.322272 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4004.00 | 1.25258 | ||||||||
\(218\) | −894.264 | −0.277831 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −56.0000 | −0.0171615 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4886.00 | 1.46722 | 0.733612 | − | 0.679569i | \(-0.237833\pi\) | ||||
0.733612 | + | 0.679569i | \(0.237833\pi\) | |||||||
\(224\) | −989.511 | −0.295154 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4452.00 | 1.31037 | ||||||||
\(227\) | −1867.90 | −0.546154 | −0.273077 | − | 0.961992i | \(-0.588041\pi\) | ||||
−0.273077 | + | 0.961992i | \(0.588041\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5558.00 | −1.60386 | −0.801928 | − | 0.597421i | \(-0.796192\pi\) | ||||
−0.801928 | + | 0.597421i | \(0.796192\pi\) | |||||||
\(230\) | −888.972 | −0.254857 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1260.00 | 0.356565 | ||||||||
\(233\) | −3577.06 | −1.00575 | −0.502877 | − | 0.864358i | \(-0.667725\pi\) | ||||
−0.502877 | + | 0.864358i | \(0.667725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3864.00 | −1.07259 | ||||||||
\(236\) | −587.357 | −0.162007 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6776.00 | −1.84547 | ||||||||
\(239\) | 2936.78 | 0.794832 | 0.397416 | − | 0.917639i | \(-0.369907\pi\) | ||||
0.397416 | + | 0.917639i | \(0.369907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 602.000 | 0.160906 | 0.0804528 | − | 0.996758i | \(-0.474363\pi\) | ||||
0.0804528 | + | 0.996758i | \(0.474363\pi\) | |||||||
\(242\) | 3447.41 | 0.915736 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −574.000 | −0.150601 | ||||||||
\(245\) | 1492.20 | 0.389116 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4333.74 | 1.10965 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3864.00 | 0.977523 | ||||||||
\(251\) | −3524.14 | −0.886222 | −0.443111 | − | 0.896467i | \(-0.646125\pi\) | ||||
−0.443111 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 168.000 | 0.0417473 | ||||||||
\(254\) | 994.802 | 0.245746 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1511.00 | −0.368896 | ||||||||
\(257\) | 2942.08 | 0.714092 | 0.357046 | − | 0.934087i | \(-0.383784\pi\) | ||||
0.357046 | + | 0.934087i | \(0.383784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1892.00 | 0.453912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1820.00 | 0.429160 | ||||||||
\(263\) | 857.223 | 0.200984 | 0.100492 | − | 0.994938i | \(-0.467958\pi\) | ||||
0.100492 | + | 0.994938i | \(0.467958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2016.00 | −0.467328 | ||||||||
\(266\) | −7334.02 | −1.69052 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −530.000 | −0.120802 | ||||||||
\(269\) | 328.073 | 0.0743605 | 0.0371802 | − | 0.999309i | \(-0.488162\pi\) | ||||
0.0371802 | + | 0.999309i | \(0.488162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2814.00 | 0.630769 | 0.315384 | − | 0.948964i | \(-0.397867\pi\) | ||||
0.315384 | + | 0.948964i | \(0.397867\pi\) | |||||||
\(272\) | −6402.72 | −1.42729 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3696.00 | 0.814903 | ||||||||
\(275\) | −68.7895 | −0.0150842 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3190.00 | −0.691944 | −0.345972 | − | 0.938245i | \(-0.612451\pi\) | ||||
−0.345972 | + | 0.938245i | \(0.612451\pi\) | |||||||
\(278\) | −5556.08 | −1.19867 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5544.00 | 1.18328 | ||||||||
\(281\) | −6116.98 | −1.29861 | −0.649303 | − | 0.760530i | \(-0.724939\pi\) | ||||
−0.649303 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4788.00 | −1.00571 | −0.502857 | − | 0.864370i | \(-0.667718\pi\) | ||||
−0.502857 | + | 0.864370i | \(0.667718\pi\) | |||||||
\(284\) | 809.600 | 0.169158 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9778.70 | 2.01121 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8639.00 | 1.75840 | ||||||||
\(290\) | −1481.62 | −0.300013 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −154.000 | −0.0308636 | ||||||||
\(293\) | 6699.04 | 1.33571 | 0.667854 | − | 0.744293i | \(-0.267213\pi\) | ||||
0.667854 | + | 0.744293i | \(0.267213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6216.00 | 1.22681 | ||||||||
\(296\) | 2047.81 | 0.402117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5292.00 | −1.02872 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2112.00 | 0.404431 | ||||||||
\(302\) | 9328.92 | 1.77755 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6930.00 | −1.30744 | ||||||||
\(305\) | 6074.65 | 1.14044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 406.000 | 0.0754777 | 0.0377388 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377388 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(308\) | −116.413 | −0.0215365 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5096.00 | −0.933656 | ||||||||
\(311\) | 8286.49 | 1.51088 | 0.755440 | − | 0.655217i | \(-0.227423\pi\) | ||||
0.755440 | + | 0.655217i | \(0.227423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5586.00 | −1.00875 | −0.504376 | − | 0.863484i | \(-0.668277\pi\) | ||||
−0.504376 | + | 0.863484i | \(0.668277\pi\) | |||||||
\(314\) | −8111.87 | −1.45790 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 460.000 | 0.0818893 | ||||||||
\(317\) | 8392.32 | 1.48694 | 0.743470 | − | 0.668770i | \(-0.233179\pi\) | ||||
0.743470 | + | 0.668770i | \(0.233179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 280.000 | 0.0491442 | ||||||||
\(320\) | 5915.90 | 1.03347 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1848.00 | −0.319829 | ||||||||
\(323\) | 14668.0 | 2.52679 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9106.68 | −1.54715 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10584.0 | 1.78172 | ||||||||
\(329\) | −8032.50 | −1.34604 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4426.00 | 0.734970 | 0.367485 | − | 0.930030i | \(-0.380219\pi\) | ||||
0.367485 | + | 0.930030i | \(0.380219\pi\) | |||||||
\(332\) | −322.782 | −0.0533583 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7126.00 | 1.16742 | ||||||||
\(335\) | 5608.99 | 0.914782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8370.00 | 1.35295 | 0.676473 | − | 0.736467i | \(-0.263507\pi\) | ||||
0.676473 | + | 0.736467i | \(0.263507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1232.00 | −0.196513 | ||||||||
\(341\) | 963.053 | 0.152939 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4444.00 | −0.699573 | ||||||||
\(344\) | 2285.93 | 0.358282 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9240.00 | −1.43568 | ||||||||
\(347\) | 6095.81 | 0.943056 | 0.471528 | − | 0.881851i | \(-0.343703\pi\) | ||||
0.471528 | + | 0.881851i | \(0.343703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4354.00 | −0.667806 | −0.333903 | − | 0.942607i | \(-0.608366\pi\) | ||||
−0.333903 | + | 0.942607i | \(0.608366\pi\) | |||||||
\(350\) | 756.685 | 0.115561 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −238.000 | −0.0360382 | ||||||||
\(353\) | −3407.73 | −0.513810 | −0.256905 | − | 0.966437i | \(-0.582703\pi\) | ||||
−0.256905 | + | 0.966437i | \(0.582703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8568.00 | −1.28096 | ||||||||
\(356\) | 1439.29 | 0.214276 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −448.000 | −0.0661384 | ||||||||
\(359\) | 7762.63 | 1.14121 | 0.570607 | − | 0.821223i | \(-0.306708\pi\) | ||||
0.570607 | + | 0.821223i | \(0.306708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9017.00 | 1.31462 | ||||||||
\(362\) | −8926.76 | −1.29608 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1629.78 | 0.233717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7784.00 | −1.10714 | −0.553572 | − | 0.832802i | \(-0.686735\pi\) | ||||
−0.553572 | + | 0.832802i | \(0.686735\pi\) | |||||||
\(368\) | −1746.20 | −0.247355 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2408.00 | −0.338340 | ||||||||
\(371\) | −4190.87 | −0.586467 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8510.00 | −1.18132 | −0.590658 | − | 0.806922i | \(-0.701132\pi\) | ||||
−0.590658 | + | 0.806922i | \(0.701132\pi\) | |||||||
\(374\) | −1629.78 | −0.225332 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8694.00 | −1.19244 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1650.00 | −0.223627 | −0.111814 | − | 0.993729i | \(-0.535666\pi\) | ||||
−0.111814 | + | 0.993729i | \(0.535666\pi\) | |||||||
\(380\) | −1333.46 | −0.180013 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3136.00 | 0.420031 | ||||||||
\(383\) | 8662.19 | 1.15566 | 0.577829 | − | 0.816158i | \(-0.303900\pi\) | ||||
0.577829 | + | 0.816158i | \(0.303900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1232.00 | 0.163087 | ||||||||
\(386\) | −4079.75 | −0.537963 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 70.0000 | 0.00915905 | ||||||||
\(389\) | 2423.51 | 0.315879 | 0.157939 | − | 0.987449i | \(-0.449515\pi\) | ||||
0.157939 | + | 0.987449i | \(0.449515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3696.00 | 0.478043 | ||||||||
\(392\) | 3357.46 | 0.432595 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5628.00 | 0.719631 | ||||||||
\(395\) | −4868.18 | −0.620114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1414.00 | 0.178757 | 0.0893786 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893786 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(398\) | 2518.76 | 0.317221 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 715.000 | 0.0893750 | ||||||||
\(401\) | 5228.00 | 0.651058 | 0.325529 | − | 0.945532i | \(-0.394458\pi\) | ||||
0.325529 | + | 0.945532i | \(0.394458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1460.45 | 0.179852 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3080.00 | −0.376497 | ||||||||
\(407\) | 455.069 | 0.0554225 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5782.00 | −0.699026 | −0.349513 | − | 0.936932i | \(-0.613653\pi\) | ||||
−0.349513 | + | 0.936932i | \(0.613653\pi\) | |||||||
\(410\) | −12445.6 | −1.49913 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1428.00 | 0.170759 | ||||||||
\(413\) | 12921.8 | 1.53957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3416.00 | 0.404060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1764.00 | −0.206412 | ||||||||
\(419\) | −11482.6 | −1.33881 | −0.669403 | − | 0.742899i | \(-0.733450\pi\) | ||||
−0.669403 | + | 0.742899i | \(0.733450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14194.0 | 1.64317 | 0.821583 | − | 0.570088i | \(-0.193091\pi\) | ||||
0.821583 | + | 0.570088i | \(0.193091\pi\) | |||||||
\(422\) | 4339.03 | 0.500523 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4536.00 | −0.519546 | ||||||||
\(425\) | −1513.37 | −0.172728 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12628.0 | 1.43118 | ||||||||
\(428\) | 1619.20 | 0.182867 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2688.00 | −0.301458 | ||||||||
\(431\) | −5222.71 | −0.583687 | −0.291844 | − | 0.956466i | \(-0.594269\pi\) | ||||
−0.291844 | + | 0.956466i | \(0.594269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −686.000 | −0.0761364 | −0.0380682 | − | 0.999275i | \(-0.512120\pi\) | ||||
−0.0380682 | + | 0.999275i | \(0.512120\pi\) | |||||||
\(434\) | −10593.6 | −1.17168 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −338.000 | −0.0371268 | ||||||||
\(437\) | 4000.38 | 0.437904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1372.00 | −0.149162 | −0.0745809 | − | 0.997215i | \(-0.523762\pi\) | ||||
−0.0745809 | + | 0.997215i | \(0.523762\pi\) | |||||||
\(440\) | 1333.46 | 0.144478 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2338.84 | 0.250839 | 0.125420 | − | 0.992104i | \(-0.459972\pi\) | ||||
0.125420 | + | 0.992104i | \(0.459972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15232.0 | −1.62262 | ||||||||
\(446\) | −12927.1 | −1.37246 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12298.0 | 1.29693 | ||||||||
\(449\) | −17250.3 | −1.81312 | −0.906561 | − | 0.422074i | \(-0.861302\pi\) | ||||
−0.906561 | + | 0.422074i | \(0.861302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2352.00 | 0.245568 | ||||||||
\(452\) | 1682.70 | 0.175105 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4942.00 | 0.510880 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17866.0 | 1.82874 | 0.914372 | − | 0.404875i | \(-0.132685\pi\) | ||||
0.914372 | + | 0.404875i | \(0.132685\pi\) | |||||||
\(458\) | 14705.1 | 1.50027 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −336.000 | −0.0340567 | ||||||||
\(461\) | −2106.02 | −0.212770 | −0.106385 | − | 0.994325i | \(-0.533928\pi\) | ||||
−0.106385 | + | 0.994325i | \(0.533928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13718.0 | 1.37695 | 0.688477 | − | 0.725258i | \(-0.258280\pi\) | ||||
0.688477 | + | 0.725258i | \(0.258280\pi\) | |||||||
\(464\) | −2910.33 | −0.291182 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9464.00 | 0.940797 | ||||||||
\(467\) | 4095.62 | 0.405830 | 0.202915 | − | 0.979196i | \(-0.434958\pi\) | ||||
0.202915 | + | 0.979196i | \(0.434958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11660.0 | 1.14799 | ||||||||
\(470\) | 10223.2 | 1.00332 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13986.0 | 1.36389 | ||||||||
\(473\) | 507.984 | 0.0493808 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1638.00 | −0.158224 | ||||||||
\(476\) | −2561.09 | −0.246612 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7770.00 | −0.743497 | ||||||||
\(479\) | −8715.10 | −0.831322 | −0.415661 | − | 0.909520i | \(-0.636450\pi\) | ||||
−0.415661 | + | 0.909520i | \(0.636450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1592.74 | −0.150513 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1303.00 | 0.122370 | ||||||||
\(485\) | −740.810 | −0.0693577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4506.00 | −0.419274 | −0.209637 | − | 0.977779i | \(-0.567228\pi\) | ||||
−0.209637 | + | 0.977779i | \(0.567228\pi\) | |||||||
\(488\) | 13668.0 | 1.26787 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3948.00 | −0.363985 | ||||||||
\(491\) | −21621.1 | −1.98726 | −0.993631 | − | 0.112683i | \(-0.964056\pi\) | ||||
−0.993631 | + | 0.112683i | \(0.964056\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6160.00 | 0.562743 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10010.0 | −0.906174 | ||||||||
\(497\) | −17811.2 | −1.60753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 786.000 | 0.0705134 | 0.0352567 | − | 0.999378i | \(-0.488775\pi\) | ||||
0.0352567 | + | 0.999378i | \(0.488775\pi\) | |||||||
\(500\) | 1460.45 | 0.130627 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9324.00 | 0.828985 | ||||||||
\(503\) | 2106.02 | 0.186685 | 0.0933426 | − | 0.995634i | \(-0.470245\pi\) | ||||
0.0933426 | + | 0.995634i | \(0.470245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15456.0 | −1.36195 | ||||||||
\(506\) | −444.486 | −0.0390510 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 376.000 | 0.0328392 | ||||||||
\(509\) | −8392.32 | −0.730812 | −0.365406 | − | 0.930848i | \(-0.619070\pi\) | ||||
−0.365406 | + | 0.930848i | \(0.619070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3388.00 | 0.293300 | ||||||||
\(512\) | 12951.0 | 1.11788 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7784.00 | −0.667972 | ||||||||
\(515\) | −15112.5 | −1.29308 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1932.00 | −0.164351 | ||||||||
\(518\) | −5005.76 | −0.424596 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3905.13 | 0.328382 | 0.164191 | − | 0.986429i | \(-0.447499\pi\) | ||||
0.164191 | + | 0.986429i | \(0.447499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17668.0 | −1.47718 | −0.738592 | − | 0.674152i | \(-0.764509\pi\) | ||||
−0.738592 | + | 0.674152i | \(0.764509\pi\) | |||||||
\(524\) | 687.895 | 0.0573489 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2268.00 | −0.188003 | ||||||||
\(527\) | 21187.2 | 1.75129 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11159.0 | −0.917153 | ||||||||
\(530\) | 5333.83 | 0.437145 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2772.00 | −0.225905 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17136.0 | −1.38477 | ||||||||
\(536\) | 12620.2 | 1.01700 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −868.000 | −0.0695579 | ||||||||
\(539\) | 746.102 | 0.0596232 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1650.00 | 0.131126 | 0.0655629 | − | 0.997848i | \(-0.479116\pi\) | ||||
0.0655629 | + | 0.997848i | \(0.479116\pi\) | |||||||
\(542\) | −7445.14 | −0.590030 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5236.00 | −0.412668 | ||||||||
\(545\) | 3577.06 | 0.281145 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3796.00 | 0.296719 | 0.148359 | − | 0.988934i | \(-0.452601\pi\) | ||||
0.148359 | + | 0.988934i | \(0.452601\pi\) | |||||||
\(548\) | 1396.96 | 0.108896 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 182.000 | 0.0141100 | ||||||||
\(551\) | 6667.29 | 0.515492 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10120.0 | −0.778203 | ||||||||
\(554\) | 8439.95 | 0.647254 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2100.00 | −0.160180 | ||||||||
\(557\) | 2063.69 | 0.156986 | 0.0784930 | − | 0.996915i | \(-0.474989\pi\) | ||||
0.0784930 | + | 0.996915i | \(0.474989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12805.4 | −0.966301 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16184.0 | 1.21473 | ||||||||
\(563\) | 26034.2 | 1.94886 | 0.974432 | − | 0.224683i | \(-0.0721346\pi\) | ||||
0.974432 | + | 0.224683i | \(0.0721346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17808.0 | −1.32600 | ||||||||
\(566\) | 12667.9 | 0.940759 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19278.0 | −1.42410 | ||||||||
\(569\) | −3640.55 | −0.268225 | −0.134112 | − | 0.990966i | \(-0.542818\pi\) | ||||
−0.134112 | + | 0.990966i | \(0.542818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19612.0 | −1.43737 | −0.718684 | − | 0.695337i | \(-0.755255\pi\) | ||||
−0.718684 | + | 0.695337i | \(0.755255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25872.0 | −1.88132 | ||||||||
\(575\) | −412.737 | −0.0299345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15722.0 | −1.13434 | −0.567171 | − | 0.823600i | \(-0.691962\pi\) | ||||
−0.567171 | + | 0.823600i | \(0.691962\pi\) | |||||||
\(578\) | −22856.6 | −1.64483 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −560.000 | −0.0400909 | ||||||||
\(581\) | 7101.20 | 0.507069 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1008.00 | −0.0716074 | ||||||||
\(584\) | 3667.01 | 0.259832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17724.0 | −1.24944 | ||||||||
\(587\) | −2725.12 | −0.191615 | −0.0958074 | − | 0.995400i | \(-0.530543\pi\) | ||||
−0.0958074 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22932.0 | 1.60424 | ||||||||
\(590\) | −16446.0 | −1.14758 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4730.00 | −0.328381 | ||||||||
\(593\) | −18012.3 | −1.24734 | −0.623672 | − | 0.781686i | \(-0.714360\pi\) | ||||
−0.623672 | + | 0.781686i | \(0.714360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27104.0 | 1.86749 | ||||||||
\(596\) | −2000.19 | −0.137468 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12181.0 | 0.830891 | 0.415446 | − | 0.909618i | \(-0.363626\pi\) | ||||
0.415446 | + | 0.909618i | \(0.363626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5950.00 | 0.403836 | 0.201918 | − | 0.979402i | \(-0.435283\pi\) | ||||
0.201918 | + | 0.979402i | \(0.435283\pi\) | |||||||
\(602\) | −5587.83 | −0.378310 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3526.00 | 0.237535 | ||||||||
\(605\) | −13789.7 | −0.926660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14168.0 | 0.947383 | 0.473691 | − | 0.880691i | \(-0.342921\pi\) | ||||
0.473691 | + | 0.880691i | \(0.342921\pi\) | |||||||
\(608\) | −5667.20 | −0.378019 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16072.0 | −1.06678 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6326.00 | 0.416810 | 0.208405 | − | 0.978043i | \(-0.433173\pi\) | ||||
0.208405 | + | 0.978043i | \(0.433173\pi\) | |||||||
\(614\) | −1074.18 | −0.0706029 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2772.00 | 0.181310 | ||||||||
\(617\) | −8805.06 | −0.574519 | −0.287260 | − | 0.957853i | \(-0.592744\pi\) | ||||
−0.287260 | + | 0.957853i | \(0.592744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24486.0 | 1.58994 | 0.794972 | − | 0.606646i | \(-0.207485\pi\) | ||||
0.794972 | + | 0.606646i | \(0.207485\pi\) | |||||||
\(620\) | −1926.11 | −0.124765 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21924.0 | −1.41330 | ||||||||
\(623\) | −31664.4 | −2.03628 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13831.0 | −0.885184 | ||||||||
\(626\) | 14779.2 | 0.943601 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3066.00 | −0.194820 | ||||||||
\(629\) | 10011.5 | 0.634635 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22430.0 | −1.41509 | −0.707547 | − | 0.706666i | \(-0.750198\pi\) | ||||
−0.707547 | + | 0.706666i | \(0.750198\pi\) | |||||||
\(632\) | −10953.4 | −0.689404 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22204.0 | −1.39090 | ||||||||
\(635\) | −3979.21 | −0.248677 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −740.810 | −0.0459702 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11844.0 | −0.731524 | ||||||||
\(641\) | 27484.1 | 1.69353 | 0.846767 | − | 0.531964i | \(-0.178546\pi\) | ||||
0.846767 | + | 0.531964i | \(0.178546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16478.0 | −1.01062 | −0.505310 | − | 0.862938i | \(-0.668622\pi\) | ||||
−0.505310 | + | 0.862938i | \(0.668622\pi\) | |||||||
\(644\) | −698.478 | −0.0427390 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38808.0 | −2.36359 | ||||||||
\(647\) | −26563.3 | −1.61408 | −0.807042 | − | 0.590494i | \(-0.798933\pi\) | ||||
−0.807042 | + | 0.590494i | \(0.798933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3108.00 | 0.187981 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3442.00 | −0.206747 | ||||||||
\(653\) | −20287.6 | −1.21580 | −0.607899 | − | 0.794014i | \(-0.707987\pi\) | ||||
−0.607899 | + | 0.794014i | \(0.707987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7280.00 | −0.434280 | ||||||||
\(656\) | −24446.7 | −1.45501 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21252.0 | 1.25910 | ||||||||
\(659\) | −656.146 | −0.0387858 | −0.0193929 | − | 0.999812i | \(-0.506173\pi\) | ||||
−0.0193929 | + | 0.999812i | \(0.506173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14238.0 | 0.837812 | 0.418906 | − | 0.908030i | \(-0.362414\pi\) | ||||
0.418906 | + | 0.908030i | \(0.362414\pi\) | |||||||
\(662\) | −11710.1 | −0.687501 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7686.00 | 0.449209 | ||||||||
\(665\) | 29336.1 | 1.71068 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1680.00 | 0.0975260 | ||||||||
\(668\) | 2693.37 | 0.156003 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14840.0 | −0.855700 | ||||||||
\(671\) | 3037.32 | 0.174746 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4874.00 | −0.279166 | −0.139583 | − | 0.990210i | \(-0.544576\pi\) | ||||
−0.139583 | + | 0.990210i | \(0.544576\pi\) | |||||||
\(674\) | −22144.9 | −1.26557 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21801.0 | −1.23764 | −0.618818 | − | 0.785534i | \(-0.712388\pi\) | ||||
−0.618818 | + | 0.785534i | \(0.712388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1540.00 | −0.0870394 | ||||||||
\(680\) | 29336.1 | 1.65439 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2548.00 | −0.143062 | ||||||||
\(683\) | 8746.85 | 0.490028 | 0.245014 | − | 0.969520i | \(-0.421207\pi\) | ||||
0.245014 | + | 0.969520i | \(0.421207\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14784.0 | −0.824624 | ||||||||
\(686\) | 11757.7 | 0.654390 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5280.00 | −0.292584 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −294.000 | −0.0161857 | −0.00809283 | − | 0.999967i | \(-0.502576\pi\) | ||||
−0.00809283 | + | 0.999967i | \(0.502576\pi\) | |||||||
\(692\) | −3492.39 | −0.191851 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16128.0 | −0.882148 | ||||||||
\(695\) | 22224.3 | 1.21297 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51744.0 | 2.81197 | ||||||||
\(698\) | 11519.6 | 0.624675 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 286.000 | 0.0154425 | ||||||||
\(701\) | −15758.1 | −0.849037 | −0.424519 | − | 0.905419i | \(-0.639557\pi\) | ||||
−0.424519 | + | 0.905419i | \(0.639557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10836.0 | 0.581348 | ||||||||
\(704\) | 2957.95 | 0.158355 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9016.00 | 0.480626 | ||||||||
\(707\) | −32130.0 | −1.70916 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6722.00 | 0.356065 | 0.178032 | − | 0.984025i | \(-0.443027\pi\) | ||||
0.178032 | + | 0.984025i | \(0.443027\pi\) | |||||||
\(710\) | 22668.8 | 1.19823 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34272.0 | −1.80393 | ||||||||
\(713\) | 5778.32 | 0.303506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −169.328 | −0.00883811 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20538.0 | −1.06751 | ||||||||
\(719\) | 31.7490 | 0.00164679 | 0.000823393 | − | 1.00000i | \(-0.499738\pi\) | ||||
0.000823393 | 1.00000i | \(0.499738\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31416.0 | −1.62274 | ||||||||
\(722\) | −23856.7 | −1.22972 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3374.00 | −0.173196 | ||||||||
\(725\) | −687.895 | −0.0352383 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12824.0 | 0.654217 | 0.327109 | − | 0.944987i | \(-0.393926\pi\) | ||||
0.327109 | + | 0.944987i | \(0.393926\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4312.00 | −0.218622 | ||||||||
\(731\) | 11175.7 | 0.565453 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29610.0 | 1.49205 | 0.746023 | − | 0.665920i | \(-0.231961\pi\) | ||||
0.746023 | + | 0.665920i | \(0.231961\pi\) | |||||||
\(734\) | 20594.5 | 1.03564 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1428.00 | −0.0715174 | ||||||||
\(737\) | 2804.50 | 0.140170 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15622.0 | 0.777625 | 0.388812 | − | 0.921317i | \(-0.372885\pi\) | ||||
0.388812 | + | 0.921317i | \(0.372885\pi\) | |||||||
\(740\) | −910.138 | −0.0452126 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11088.0 | 0.548589 | ||||||||
\(743\) | 8588.11 | 0.424047 | 0.212024 | − | 0.977265i | \(-0.431995\pi\) | ||||
0.212024 | + | 0.977265i | \(0.431995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21168.0 | 1.04099 | ||||||||
\(746\) | 22515.3 | 1.10502 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −616.000 | −0.0301112 | ||||||||
\(749\) | −35622.4 | −1.73780 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29468.0 | 1.43183 | 0.715914 | − | 0.698189i | \(-0.246010\pi\) | ||||
0.715914 | + | 0.698189i | \(0.246010\pi\) | |||||||
\(752\) | 20081.3 | 0.973787 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37315.7 | −1.79875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35030.0 | −1.68189 | −0.840943 | − | 0.541124i | \(-0.817999\pi\) | ||||
−0.840943 | + | 0.541124i | \(0.817999\pi\) | |||||||
\(758\) | 4365.49 | 0.209184 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 31752.0 | 1.51548 | ||||||||
\(761\) | 22330.1 | 1.06369 | 0.531844 | − | 0.846842i | \(-0.321499\pi\) | ||||
0.531844 | + | 0.846842i | \(0.321499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7436.00 | 0.352819 | ||||||||
\(764\) | 1185.30 | 0.0561290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22918.0 | −1.08102 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27342.0 | 1.28216 | 0.641078 | − | 0.767476i | \(-0.278488\pi\) | ||||
0.641078 | + | 0.767476i | \(0.278488\pi\) | |||||||
\(770\) | −3259.57 | −0.152554 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1542.00 | −0.0718883 | ||||||||
\(773\) | −11884.7 | −0.552993 | −0.276496 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276496 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2366.00 | −0.109664 | ||||||||
\(776\) | −1666.82 | −0.0771076 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6412.00 | −0.295477 | ||||||||
\(779\) | 56005.3 | 2.57586 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4284.00 | −0.196279 | ||||||||
\(782\) | −9778.70 | −0.447168 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7755.00 | −0.353271 | ||||||||
\(785\) | 32447.5 | 1.47529 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22666.0 | −1.02663 | −0.513314 | − | 0.858201i | \(-0.671582\pi\) | ||||
−0.513314 | + | 0.858201i | \(0.671582\pi\) | |||||||
\(788\) | 2127.18 | 0.0961647 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12880.0 | 0.580063 | ||||||||
\(791\) | −37019.4 | −1.66404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3741.09 | −0.167212 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 952.000 | 0.0423904 | ||||||||
\(797\) | 582.065 | 0.0258693 | 0.0129346 | − | 0.999916i | \(-0.495883\pi\) | ||||
0.0129346 | + | 0.999916i | \(0.495883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42504.0 | −1.88196 | ||||||||
\(800\) | 584.711 | 0.0258408 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13832.0 | −0.609009 | ||||||||
\(803\) | 814.891 | 0.0358118 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7392.00 | 0.323644 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −34776.0 | −1.51413 | ||||||||
\(809\) | 793.725 | 0.0344943 | 0.0172472 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172472 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9478.00 | 0.410379 | 0.205190 | − | 0.978722i | \(-0.434219\pi\) | ||||
0.205190 | + | 0.978722i | \(0.434219\pi\) | |||||||
\(812\) | −1164.13 | −0.0503115 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1204.00 | −0.0518430 | ||||||||
\(815\) | 36426.7 | 1.56561 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12096.0 | 0.517975 | ||||||||
\(818\) | 15297.7 | 0.653879 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4704.00 | −0.200330 | ||||||||
\(821\) | −3227.82 | −0.137213 | −0.0686063 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686063 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40476.0 | 1.71434 | 0.857172 | − | 0.515031i | \(-0.172219\pi\) | ||||
0.857172 | + | 0.515031i | \(0.172219\pi\) | |||||||
\(824\) | −34003.2 | −1.43757 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34188.0 | −1.44014 | ||||||||
\(827\) | −7169.99 | −0.301481 | −0.150741 | − | 0.988573i | \(-0.548166\pi\) | ||||
−0.150741 | + | 0.988573i | \(0.548166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27482.0 | 1.15137 | 0.575687 | − | 0.817670i | \(-0.304735\pi\) | ||||
0.575687 | + | 0.817670i | \(0.304735\pi\) | |||||||
\(830\) | −9037.89 | −0.377963 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16414.2 | 0.682737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28504.0 | −1.18134 | ||||||||
\(836\) | −666.729 | −0.0275829 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30380.0 | 1.25234 | ||||||||
\(839\) | −19128.8 | −0.787126 | −0.393563 | − | 0.919298i | \(-0.628758\pi\) | ||||
−0.393563 | + | 0.919298i | \(0.628758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21589.0 | −0.885194 | ||||||||
\(842\) | −37553.8 | −1.53704 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1640.00 | 0.0668852 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28666.0 | −1.16290 | ||||||||
\(848\) | 10477.2 | 0.424278 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4004.00 | 0.161572 | ||||||||
\(851\) | 2730.42 | 0.109985 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31962.0 | −1.28295 | −0.641476 | − | 0.767143i | \(-0.721678\pi\) | ||||
−0.641476 | + | 0.767143i | \(0.721678\pi\) | |||||||
\(854\) | −33410.5 | −1.33874 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −38556.0 | −1.53951 | ||||||||
\(857\) | −4931.68 | −0.196573 | −0.0982865 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982865 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11704.0 | 0.464884 | 0.232442 | − | 0.972610i | \(-0.425328\pi\) | ||||
0.232442 | + | 0.972610i | \(0.425328\pi\) | |||||||
\(860\) | −1015.97 | −0.0402840 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13818.0 | 0.545989 | ||||||||
\(863\) | −2280.64 | −0.0899581 | −0.0449790 | − | 0.998988i | \(-0.514322\pi\) | ||||
−0.0449790 | + | 0.998988i | \(0.514322\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36960.0 | 1.45281 | ||||||||
\(866\) | 1814.99 | 0.0712191 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4004.00 | −0.156572 | ||||||||
\(869\) | −2434.09 | −0.0950183 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8048.38 | 0.312560 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10584.0 | −0.409621 | ||||||||
\(875\) | −32130.0 | −1.24136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1006.00 | 0.0387346 | 0.0193673 | − | 0.999812i | \(-0.493835\pi\) | ||||
0.0193673 | + | 0.999812i | \(0.493835\pi\) | |||||||
\(878\) | 3629.97 | 0.139528 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3080.00 | −0.117985 | ||||||||
\(881\) | 40681.1 | 1.55571 | 0.777855 | − | 0.628444i | \(-0.216308\pi\) | ||||
0.777855 | + | 0.628444i | \(0.216308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 124.000 | 0.00472586 | 0.00236293 | − | 0.999997i | \(-0.499248\pi\) | ||||
0.00236293 | + | 0.999997i | \(0.499248\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6188.00 | −0.234639 | ||||||||
\(887\) | −16573.0 | −0.627358 | −0.313679 | − | 0.949529i | \(-0.601562\pi\) | ||||
−0.313679 | + | 0.949529i | \(0.601562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8272.00 | −0.312074 | ||||||||
\(890\) | 40300.1 | 1.51782 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4886.00 | −0.183403 | ||||||||
\(893\) | −46004.3 | −1.72394 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1792.00 | 0.0669273 | ||||||||
\(896\) | −24621.4 | −0.918016 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45640.0 | 1.69602 | ||||||||
\(899\) | 9630.53 | 0.357282 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22176.0 | −0.819966 | ||||||||
\(902\) | −6222.81 | −0.229708 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −40068.0 | −1.47416 | ||||||||
\(905\) | 35707.1 | 1.31154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42996.0 | −1.57404 | −0.787022 | − | 0.616924i | \(-0.788378\pi\) | ||||
−0.787022 | + | 0.616924i | \(0.788378\pi\) | |||||||
\(908\) | 1867.90 | 0.0682692 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53169.0 | 1.93366 | 0.966832 | − | 0.255413i | \(-0.0822113\pi\) | ||||
0.966832 | + | 0.255413i | \(0.0822113\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1708.00 | 0.0619130 | ||||||||
\(914\) | −47269.0 | −1.71063 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5558.00 | 0.200482 | ||||||||
\(917\) | −15133.7 | −0.544993 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8244.00 | 0.295913 | 0.147957 | − | 0.988994i | \(-0.452730\pi\) | ||||
0.147957 | + | 0.988994i | \(0.452730\pi\) | |||||||
\(920\) | 8000.75 | 0.286714 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5572.00 | 0.199028 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1118.00 | −0.0397401 | ||||||||
\(926\) | −36294.4 | −1.28802 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2380.00 | −0.0841889 | ||||||||
\(929\) | −16192.0 | −0.571843 | −0.285922 | − | 0.958253i | \(-0.592300\pi\) | ||||
−0.285922 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17766.0 | 0.625410 | ||||||||
\(932\) | 3577.06 | 0.125719 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10836.0 | −0.379620 | ||||||||
\(935\) | 6519.13 | 0.228020 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18214.0 | −0.635032 | −0.317516 | − | 0.948253i | \(-0.602849\pi\) | ||||
−0.317516 | + | 0.948253i | \(0.602849\pi\) | |||||||
\(938\) | −30849.5 | −1.07385 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3864.00 | 0.134074 | ||||||||
\(941\) | −13916.7 | −0.482115 | −0.241057 | − | 0.970511i | \(-0.577494\pi\) | ||||
−0.241057 | + | 0.970511i | \(0.577494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14112.0 | 0.487328 | ||||||||
\(944\) | −32304.6 | −1.11380 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1344.00 | −0.0461916 | ||||||||
\(947\) | 40400.6 | 1.38632 | 0.693159 | − | 0.720784i | \(-0.256218\pi\) | ||||
0.693159 | + | 0.720784i | \(0.256218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4333.74 | 0.148005 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 60984.0 | 2.07616 | ||||||||
\(953\) | −21271.8 | −0.723046 | −0.361523 | − | 0.932363i | \(-0.617743\pi\) | ||||
−0.361523 | + | 0.932363i | \(0.617743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12544.0 | −0.425041 | ||||||||
\(956\) | −2936.78 | −0.0993540 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23058.0 | 0.777631 | ||||||||
\(959\) | −30733.0 | −1.03485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3333.00 | 0.111879 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −602.000 | −0.0201132 | ||||||||
\(965\) | 16319.0 | 0.544380 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9578.00 | −0.318519 | −0.159259 | − | 0.987237i | \(-0.550911\pi\) | ||||
−0.159259 | + | 0.987237i | \(0.550911\pi\) | |||||||
\(968\) | −31026.7 | −1.03020 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1960.00 | 0.0648782 | ||||||||
\(971\) | −44956.6 | −1.48581 | −0.742907 | − | 0.669394i | \(-0.766554\pi\) | ||||
−0.742907 | + | 0.669394i | \(0.766554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46200.0 | 1.52220 | ||||||||
\(974\) | 11921.8 | 0.392195 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31570.0 | −1.03538 | ||||||||
\(977\) | −32765.0 | −1.07292 | −0.536461 | − | 0.843925i | \(-0.680239\pi\) | ||||
−0.536461 | + | 0.843925i | \(0.680239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7616.00 | −0.248630 | ||||||||
\(980\) | −1492.20 | −0.0486395 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 57204.0 | 1.85891 | ||||||||
\(983\) | 47438.3 | 1.53921 | 0.769607 | − | 0.638518i | \(-0.220452\pi\) | ||||
0.769607 | + | 0.638518i | \(0.220452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22512.0 | −0.728215 | ||||||||
\(986\) | −16297.8 | −0.526398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3047.91 | 0.0979957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6848.00 | −0.219509 | −0.109755 | − | 0.993959i | \(-0.535007\pi\) | ||||
−0.109755 | + | 0.993959i | \(0.535007\pi\) | |||||||
\(992\) | −8185.95 | −0.262000 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 47124.0 | 1.50370 | ||||||||
\(995\) | −10075.0 | −0.321005 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5810.00 | −0.184558 | −0.0922791 | − | 0.995733i | \(-0.529415\pi\) | ||||
−0.0922791 | + | 0.995733i | \(0.529415\pi\) | |||||||
\(998\) | −2079.56 | −0.0659593 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.p.1.1 | 2 | ||
3.2 | odd | 2 | inner | 1521.4.a.p.1.2 | 2 | ||
13.12 | even | 2 | 117.4.a.e.1.2 | yes | 2 | ||
39.38 | odd | 2 | 117.4.a.e.1.1 | ✓ | 2 | ||
52.51 | odd | 2 | 1872.4.a.ba.1.1 | 2 | |||
156.155 | even | 2 | 1872.4.a.ba.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.a.e.1.1 | ✓ | 2 | 39.38 | odd | 2 | ||
117.4.a.e.1.2 | yes | 2 | 13.12 | even | 2 | ||
1521.4.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.p.1.2 | 2 | 3.2 | odd | 2 | inner | ||
1872.4.a.ba.1.1 | 2 | 52.51 | odd | 2 | |||
1872.4.a.ba.1.2 | 2 | 156.155 | even | 2 |