Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
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([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.2 | ||
Root | \(2.82801 + 0.0488466i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.g.895.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 16.6517i | − | 1.48938i | −0.667412 | − | 0.744689i | \(-0.732598\pi\) | ||
0.667412 | − | 0.744689i | \(-0.267402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.0420 | + | 10.8045i | −0.812194 | + | 0.583387i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.0450i | 1.75548i | 0.479136 | + | 0.877741i | \(0.340950\pi\) | ||||
−0.479136 | + | 0.877741i | \(0.659050\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28.6879i | 0.612046i | 0.952024 | + | 0.306023i | \(0.0989985\pi\) | ||||
−0.952024 | + | 0.306023i | \(0.901002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 49.9552i | 0.859892i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 82.9041i | − | 1.18278i | −0.806387 | − | 0.591388i | \(-0.798580\pi\) | ||
0.806387 | − | 0.591388i | \(-0.201420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.1236 | −0.206759 | −0.103379 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103379 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 45.1261 | − | 32.4134i | 0.468921 | − | 0.336819i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 95.0501i | 0.861710i | 0.902421 | + | 0.430855i | \(0.141788\pi\) | ||||
−0.902421 | + | 0.430855i | \(0.858212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −152.281 | −1.21824 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 197.365 | 1.26378 | 0.631892 | − | 0.775056i | \(-0.282278\pi\) | ||||
0.631892 | + | 0.775056i | \(0.282278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 153.515 | 0.889422 | 0.444711 | − | 0.895674i | \(-0.353306\pi\) | ||||
0.444711 | + | 0.895674i | \(0.353306\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 192.135i | − | 1.01353i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 179.913 | + | 250.476i | 0.868883 | + | 1.20966i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.7262 | −0.0476589 | −0.0238294 | − | 0.999716i | \(-0.507586\pi\) | ||||
−0.0238294 | + | 0.999716i | \(0.507586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 86.0638i | − | 0.353365i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 41.1342i | − | 0.156685i | −0.996927 | − | 0.0783425i | \(-0.975037\pi\) | ||
0.996927 | − | 0.0783425i | \(-0.0249628\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 412.497i | − | 1.46291i | −0.681890 | − | 0.731455i | \(-0.738842\pi\) | ||
0.681890 | − | 0.731455i | \(-0.261158\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 149.866i | − | 0.496459i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −477.704 | −1.48256 | −0.741280 | − | 0.671196i | \(-0.765781\pi\) | ||||
−0.741280 | + | 0.671196i | \(0.765781\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 109.526 | − | 325.043i | 0.319319 | − | 0.947647i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 248.712i | 0.682877i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.2304 | 0.0913069 | 0.0456534 | − | 0.998957i | \(-0.485463\pi\) | ||||
0.0456534 | + | 0.998957i | \(0.485463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1066.46 | 2.61457 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 51.3707 | 0.119372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 494.608 | 1.09140 | 0.545699 | − | 0.837981i | \(-0.316264\pi\) | ||||
0.545699 | + | 0.837981i | \(0.316264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 294.084i | − | 0.617273i | −0.951180 | − | 0.308636i | \(-0.900127\pi\) | ||
0.951180 | − | 0.308636i | \(-0.0998727\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −135.378 | + | 97.2403i | −0.270731 | + | 0.194462i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 477.704 | 0.911567 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 207.870i | − | 0.379036i | −0.981877 | − | 0.189518i | \(-0.939307\pi\) | ||
0.981877 | − | 0.189518i | \(-0.0606926\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 285.150i | − | 0.497508i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 534.040i | − | 0.892660i | −0.894869 | − | 0.446330i | \(-0.852731\pi\) | ||
0.894869 | − | 0.446330i | \(-0.147269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 582.270i | 0.933555i | 0.884375 | + | 0.466778i | \(0.154585\pi\) | ||||
−0.884375 | + | 0.466778i | \(0.845415\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 456.842 | 0.703354 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −691.973 | − | 963.368i | −1.02413 | − | 1.42579i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 311.277i | 0.443309i | 0.975125 | + | 0.221654i | \(0.0711457\pi\) | ||||
−0.975125 | + | 0.221654i | \(0.928854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1319.63 | −1.74515 | −0.872577 | − | 0.488477i | \(-0.837553\pi\) | ||||
−0.872577 | + | 0.488477i | \(0.837553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1380.50 | −1.76160 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −592.095 | −0.729646 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 616.091i | 0.733770i | 0.930266 | + | 0.366885i | \(0.119576\pi\) | ||||
−0.930266 | + | 0.366885i | \(0.880424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −309.958 | − | 431.525i | −0.357060 | − | 0.497100i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −460.545 | −0.513508 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 285.137i | 0.307941i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 104.076i | − | 0.108941i | −0.998515 | − | 0.0544706i | \(-0.982653\pi\) | ||
0.998515 | − | 0.0544706i | \(-0.0173471\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 576.405i | 0.585161i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1754.34i | 1.72835i | 0.503196 | + | 0.864173i | \(0.332158\pi\) | ||||
−0.503196 | + | 0.864173i | \(0.667842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −310.370 | −0.296910 | −0.148455 | − | 0.988919i | \(-0.547430\pi\) | ||||
−0.148455 | + | 0.988919i | \(0.547430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −539.740 | − | 751.429i | −0.501650 | − | 0.698400i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 482.444i | 0.435884i | 0.975962 | + | 0.217942i | \(0.0699344\pi\) | ||||
−0.975962 | + | 0.217942i | \(0.930066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 72.5584 | 0.0637600 | 0.0318800 | − | 0.999492i | \(-0.489851\pi\) | ||||
0.0318800 | + | 0.999492i | \(0.489851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 32.1786 | 0.0275159 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1545.99 | −1.28703 | −0.643514 | − | 0.765434i | \(-0.722524\pi\) | ||||
−0.643514 | + | 0.765434i | \(0.722524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1582.75 | 1.28341 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 258.191i | 0.204015i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 895.736 | + | 1247.05i | 0.690017 | + | 0.960645i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2770.76 | −2.08172 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 123.403i | 0.0904621i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 454.269i | 0.325048i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1982.75i | − | 1.38536i | −0.721246 | − | 0.692679i | \(-0.756430\pi\) | ||
0.721246 | − | 0.692679i | \(-0.243570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1237.49i | 0.844612i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 403.984 | 0.269437 | 0.134719 | − | 0.990884i | \(-0.456987\pi\) | ||||
0.134719 | + | 0.990884i | \(0.456987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 257.573 | − | 185.011i | 0.167928 | − | 0.120620i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 449.597i | 0.286631i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1366.78 | −0.852350 | −0.426175 | − | 0.904641i | \(-0.640139\pi\) | ||||
−0.426175 | + | 0.904641i | \(0.640139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1770.10 | −1.08013 | −0.540065 | − | 0.841623i | \(-0.681600\pi\) | ||||
−0.540065 | + | 0.841623i | \(0.681600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1433.11 | 0.855956 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1837.32 | −1.07444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3286.47i | − | 1.88225i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −328.579 | + | 975.129i | −0.184359 | + | 0.547124i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1991.97 | −1.09522 | −0.547612 | − | 0.836732i | \(-0.684463\pi\) | ||||
−0.547612 | + | 0.836732i | \(0.684463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1117.45i | 0.602229i | 0.953588 | + | 0.301115i | \(0.0973586\pi\) | ||||
−0.953588 | + | 0.301115i | \(0.902641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 746.137i | − | 0.394259i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2556.29i | − | 1.32468i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 758.016i | − | 0.385327i | −0.981265 | − | 0.192663i | \(-0.938287\pi\) | ||
0.981265 | − | 0.192663i | \(-0.0617125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −105.691 | −0.0527160 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1026.97 | − | 1429.75i | −0.502710 | − | 0.699876i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 147.846i | − | 0.0710443i | −0.999369 | − | 0.0355222i | \(-0.988691\pi\) | ||
0.999369 | − | 0.0355222i | \(-0.0113094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3199.38 | −1.50953 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1741.92 | 0.807148 | 0.403574 | − | 0.914947i | \(-0.367768\pi\) | ||||
0.403574 | + | 0.914947i | \(0.367768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1374.00 | 0.625400 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −154.112 | −0.0689195 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2686.73i | − | 1.18074i | −0.807131 | − | 0.590372i | \(-0.798981\pi\) | ||
0.807131 | − | 0.590372i | \(-0.201019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2290.61 | − | 1645.31i | 0.989451 | − | 0.710708i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1483.82 | −0.630119 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1032.53i | 0.431146i | 0.976488 | + | 0.215573i | \(0.0691619\pi\) | ||||
−0.976488 | + | 0.215573i | \(0.930838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1608.53i | − | 0.660558i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||
0.943883 | − | 0.330279i | \(-0.107143\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 882.253i | 0.356383i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 178.610i | 0.0709821i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5309.60 | 2.07634 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 406.135 | − | 291.721i | 0.156307 | − | 0.112273i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1970.43i | − | 0.746469i | −0.927737 | − | 0.373235i | \(-0.878249\pi\) | ||
0.927737 | − | 0.373235i | \(-0.121751\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 966.622 | 0.360513 | 0.180256 | − | 0.983620i | \(-0.442307\pi\) | ||||
0.180256 | + | 0.983620i | \(0.442307\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1433.11 | −0.526294 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1068.53 | −0.386443 | −0.193222 | − | 0.981155i | \(-0.561894\pi\) | ||||
−0.193222 | + | 0.981155i | \(0.561894\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −252.660 | −0.0900029 | −0.0450015 | − | 0.998987i | \(-0.514329\pi\) | ||||
−0.0450015 | + | 0.998987i | \(0.514329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 623.611i | 0.218837i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2968.77 | + | 2132.43i | −1.02644 | + | 0.737276i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −684.956 | −0.233363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 855.451i | 0.287237i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1096.68i | − | 0.362961i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4606.20i | − | 1.50286i | −0.659811 | − | 0.751432i | \(-0.729364\pi\) | ||
0.659811 | − | 0.751432i | \(-0.270636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1602.12i | 0.515377i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6868.79 | −2.17883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2309.18 | + | 1658.65i | −0.722383 | + | 0.518877i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1746.81i | − | 0.538988i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2378.35 | 0.723914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1927.65 | −0.578857 | −0.289428 | − | 0.957200i | \(-0.593465\pi\) | ||||
−0.289428 | + | 0.957200i | \(0.593465\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1370.52 | −0.406081 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4063.72 | −1.18819 | −0.594093 | − | 0.804396i | \(-0.702489\pi\) | ||||
−0.594093 | + | 0.804396i | \(0.702489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4096.49i | − | 1.18211i | −0.806631 | − | 0.591056i | \(-0.798711\pi\) | ||
0.806631 | − | 0.591056i | \(-0.201289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2075.92 | + | 2890.10i | 0.591279 | + | 0.823181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1950.08 | 0.548301 | 0.274150 | − | 0.961687i | \(-0.411603\pi\) | ||||
0.274150 | + | 0.961687i | \(0.411603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7954.60i | 2.20809i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 933.831i | − | 0.255944i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2861.53i | − | 0.774465i | −0.921982 | − | 0.387232i | \(-0.873431\pi\) | ||
0.921982 | − | 0.387232i | \(-0.126569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4320.12i | − | 1.15470i | −0.816496 | − | 0.577351i | \(-0.804086\pi\) | ||
0.816496 | − | 0.577351i | \(-0.195914\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5412.53 | − | 1823.81i | −1.41140 | − | 0.475586i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 491.239i | − | 0.126546i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3958.88 | 1.00756 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1366.74 | 0.343698 | 0.171849 | − | 0.985123i | \(-0.445026\pi\) | ||||
0.171849 | + | 0.985123i | \(0.445026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6087.49 | −1.51272 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4141.50 | 1.01706 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5993.21i | − | 1.45465i | −0.686291 | − | 0.727327i | \(-0.740762\pi\) | ||
0.686291 | − | 0.727327i | \(-0.259238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 161.344 | − | 115.891i | 0.0387083 | − | 0.0278036i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1776.28 | 0.421262 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1636.95i | 0.383798i | 0.981415 | + | 0.191899i | \(0.0614646\pi\) | ||||
−0.981415 | + | 0.191899i | \(0.938535\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 586.647i | − | 0.135990i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1848.27i | − | 0.423642i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 7442.41i | − | 1.68688i | −0.537220 | − | 0.843442i | \(-0.680526\pi\) | ||
0.537220 | − | 0.843442i | \(-0.319474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5619.33 | −1.25959 | −0.629797 | − | 0.776760i | \(-0.716862\pi\) | ||||
−0.629797 | + | 0.776760i | \(0.716862\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 929.874 | + | 1294.58i | 0.206149 | + | 0.287001i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 9752.81i | − | 2.13861i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 698.240 | 0.151456 | 0.0757278 | − | 0.997129i | \(-0.475872\pi\) | ||||
0.0757278 | + | 0.997129i | \(0.475872\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1381.63 | 0.296474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5026.99 | −1.06721 | −0.533604 | − | 0.845735i | \(-0.679163\pi\) | ||||
−0.533604 | + | 0.845735i | \(0.679163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3596.17 | −0.755371 | −0.377686 | − | 0.925934i | \(-0.623280\pi\) | ||||
−0.377686 | + | 0.925934i | \(0.623280\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 855.411i | − | 0.177790i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 444.434 | + | 618.743i | 0.0914080 | + | 0.127259i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1960.10 | −0.398961 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 312.227i | 0.0628972i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4095.02i | − | 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8236.09i | − | 1.62550i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1729.22i | − | 0.337843i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2726.79 | −0.527406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4456.81 | + | 6204.79i | 0.853443 | + | 1.18817i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5263.01i | − | 0.997861i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4897.02 | −0.919352 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6214.27 | 1.15527 | 0.577633 | − | 0.816296i | \(-0.303976\pi\) | ||||
0.577633 | + | 0.816296i | \(0.303976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 931.110 | 0.171421 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4044.93 | 0.737514 | 0.368757 | − | 0.929526i | \(-0.379784\pi\) | ||||
0.368757 | + | 0.929526i | \(0.379784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6931.84i | 1.25179i | 0.779907 | + | 0.625896i | \(0.215266\pi\) | ||||
−0.779907 | + | 0.625896i | \(0.784734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1619.22 | + | 2254.29i | 0.289628 | + | 0.403221i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3966.39 | −0.702759 | −0.351379 | − | 0.936233i | \(-0.614287\pi\) | ||||
−0.351379 | + | 0.936233i | \(0.614287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12640.2i | 2.21855i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1447.33i | − | 0.251658i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1419.61i | 0.244549i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4368.61i | − | 0.745622i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −217.675 | −0.0368118 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7185.65 | − | 5161.34i | 1.20413 | − | 0.864906i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9949.84i | 1.65224i | 0.563491 | + | 0.826122i | \(0.309458\pi\) | ||||
−0.563491 | + | 0.826122i | \(0.690542\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −96.5359 | −0.0158863 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3461.41 | −0.564528 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4947.26 | 0.799686 | 0.399843 | − | 0.916584i | \(-0.369065\pi\) | ||||
0.399843 | + | 0.916584i | \(0.369065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4637.96 | 0.743066 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9831.86i | 1.56136i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1864.42 | + | 6072.69i | 0.293496 | + | 0.955960i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4748.25 | −0.740978 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5246.44i | − | 0.811653i | −0.913950 | − | 0.405826i | \(-0.866984\pi\) | ||
0.913950 | − | 0.405826i | \(-0.133016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8703.25i | 1.33488i | 0.744662 | + | 0.667442i | \(0.232611\pi\) | ||||
−0.744662 | + | 0.667442i | \(0.767389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 774.574i | − | 0.117788i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1402.85i | − | 0.211519i | −0.994392 | − | 0.105760i | \(-0.966273\pi\) | ||
0.994392 | − | 0.105760i | \(-0.0337274\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8892.69 | −1.32951 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2687.21 | − | 3741.14i | −0.398381 | − | 0.554628i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9556.07i | − | 1.40487i | −0.711746 | − | 0.702437i | \(-0.752095\pi\) | ||
0.711746 | − | 0.702437i | \(-0.247905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6565.78 | −0.957251 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8312.29 | 1.20188 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9695.81 | 1.39042 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1036.73 | −0.147458 | −0.0737289 | − | 0.997278i | \(-0.523490\pi\) | ||||
−0.0737289 | + | 0.997278i | \(0.523490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 370.208i | − | 0.0522283i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −529.937 | + | 380.646i | −0.0741589 | + | 0.0532672i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10769.4 | −1.49496 | −0.747481 | − | 0.664283i | \(-0.768737\pi\) | ||||
−0.747481 | + | 0.664283i | \(0.768737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1362.81i | − | 0.187667i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5661.99i | 0.773494i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3268.34i | − | 0.442963i | −0.975165 | − | 0.221482i | \(-0.928911\pi\) | ||
0.975165 | − | 0.221482i | \(-0.0710893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5948.25i | 0.799837i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5143.39 | 0.686201 | 0.343101 | − | 0.939299i | \(-0.388523\pi\) | ||||
0.343101 | + | 0.939299i | \(0.388523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16041.8 | + | 11522.6i | −2.12354 | + | 1.52531i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3712.47i | − | 0.487637i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5140.27 | 0.669979 | 0.334990 | − | 0.942222i | \(-0.391267\pi\) | ||||
0.334990 | + | 0.942222i | \(0.391267\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7880.05 | 1.01921 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1211.95 | −0.155560 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5183.30 | 0.660254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6774.24i | 0.856396i | 0.903685 | + | 0.428198i | \(0.140851\pi\) | ||||
−0.903685 | + | 0.428198i | \(0.859149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −772.720 | + | 555.033i | −0.0969533 | + | 0.0696401i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8827.27 | −1.09928 | −0.549642 | − | 0.835401i | \(-0.685236\pi\) | ||||
−0.549642 | + | 0.835401i | \(0.685236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4404.02i | 0.544367i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1348.79i | − | 0.165486i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 686.961i | − | 0.0836643i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 11986.2i | − | 1.44910i | −0.689223 | − | 0.724549i | \(-0.742048\pi\) | ||
0.689223 | − | 0.724549i | \(-0.257952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4100.34 | 0.492105 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7439.92 | + | 5343.98i | −0.886427 | + | 0.636708i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21974.1i | 2.59919i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5310.31 | 0.623614 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4098.42 | −0.477854 | −0.238927 | − | 0.971038i | \(-0.576796\pi\) | ||||
−0.238927 | + | 0.971038i | \(0.576796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −318.996 | −0.0369285 | −0.0184643 | − | 0.999830i | \(-0.505878\pi\) | ||||
−0.0184643 | + | 0.999830i | \(0.505878\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4299.34 | −0.494186 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12624.7i | 1.44091i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3177.43 | + | 4423.63i | 0.360109 | + | 0.501346i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5511.96 | 0.620326 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9939.59i | − | 1.11084i | −0.831569 | − | 0.555422i | \(-0.812557\pi\) | ||
0.831569 | − | 0.555422i | \(-0.187443\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1254.43i | 0.139225i | 0.997574 | + | 0.0696123i | \(0.0221762\pi\) | ||||
−0.997574 | + | 0.0696123i | \(0.977824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9859.41i | 1.08672i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1627.60i | − | 0.178166i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12933.4 | 1.40610 | 0.703049 | − | 0.711141i | \(-0.251821\pi\) | ||||
0.703049 | + | 0.711141i | \(0.251821\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 985.738 | − | 2925.39i | 0.106440 | − | 0.315882i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 596.175i | 0.0639394i | 0.999489 | + | 0.0319697i | \(0.0101780\pi\) | ||||
−0.999489 | + | 0.0319697i | \(0.989822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10259.0 | 1.09286 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5975.91 | 0.632328 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3428.69 | −0.360378 | −0.180189 | − | 0.983632i | \(-0.557671\pi\) | ||||
−0.180189 | + | 0.983632i | \(0.557671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2634.44 | 0.275058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 3352.34i | − | 0.347697i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7185.65 | + | 5161.34i | −0.740370 | + | 0.531797i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19011.5 | 1.94600 | 0.973000 | − | 0.230807i | \(-0.0741367\pi\) | ||||
0.973000 | + | 0.230807i | \(0.0741367\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2238.41i | 0.227626i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13187.0i | 1.33227i | 0.745830 | + | 0.666137i | \(0.232053\pi\) | ||||
−0.745830 | + | 0.666137i | \(0.767947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7425.75i | 0.745364i | 0.927959 | + | 0.372682i | \(0.121562\pi\) | ||||
−0.927959 | + | 0.372682i | \(0.878438\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7668.87i | 0.764807i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11474.1 | −1.13695 | −0.568476 | − | 0.822700i | \(-0.692467\pi\) | ||||
−0.568476 | + | 0.822700i | \(0.692467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2245.93 | + | 3126.80i | 0.221125 | + | 0.307851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2274.05i | 0.222468i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26418.4 | 2.56811 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2607.58 | 0.251882 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 317.073 | 0.0304356 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17924.0 | −1.70975 | −0.854873 | − | 0.518837i | \(-0.826365\pi\) | ||||
−0.854873 | + | 0.518837i | \(0.826365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 307.713i | − | 0.0291694i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3080.90 | + | 4289.25i | 0.290240 | + | 0.404073i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1733.04 | −0.162254 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8161.93i | − | 0.759450i | −0.925099 | − | 0.379725i | \(-0.876019\pi\) | ||
0.925099 | − | 0.379725i | \(-0.123981\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 443.539i | 0.0410174i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17622.4i | − | 1.61973i | −0.586616 | − | 0.809865i | \(-0.699540\pi\) | ||
0.586616 | − | 0.809865i | \(-0.300460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16362.4i | − | 1.49478i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9598.15 | 0.871525 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5770.02 | + | 8033.05i | 0.520766 | + | 0.725013i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6772.04i | 0.607531i | 0.952747 | + | 0.303766i | \(0.0982440\pi\) | ||||
−0.952747 | + | 0.303766i | \(0.901756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5225.75 | −0.466007 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15340.8 | −1.35987 | −0.679935 | − | 0.733273i | \(-0.737992\pi\) | ||||
−0.679935 | + | 0.733273i | \(0.737992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29212.7 | 2.57416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4122.01 | −0.361075 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7729.91i | − | 0.673128i | −0.941661 | − | 0.336564i | \(-0.890735\pi\) | ||
0.941661 | − | 0.336564i | \(-0.109265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6291.12 | − | 8758.53i | −0.544624 | − | 0.758228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 462.336 | 0.0397907 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5168.20i | 0.442210i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 30594.6i | − | 2.60261i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8060.20i | 0.681703i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9454.94i | 0.795064i | 0.917588 | + | 0.397532i | \(0.130133\pi\) | ||||
−0.917588 | + | 0.397532i | \(0.869867\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20468.5 | −1.71133 | −0.855665 | − | 0.517531i | \(-0.826851\pi\) | ||||
−0.855665 | + | 0.517531i | \(0.826851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6871.83 | + | 4935.94i | −0.571260 | + | 0.410327i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12727.0i | − | 1.05199i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3132.47 | 0.257456 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4451.47 | 0.363799 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1180.05 | 0.0958984 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8033.53 | 0.649196 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3097.60i | − | 0.248922i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20817.4 | + | 7014.62i | 1.66358 | + | 0.560559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14593.7 | 1.15976 | 0.579882 | − | 0.814700i | \(-0.303099\pi\) | ||||
0.579882 | + | 0.814700i | \(0.303099\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4825.58i | 0.381373i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1208.22i | − | 0.0949627i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8758.57i | − | 0.684624i | −0.939586 | − | 0.342312i | \(-0.888790\pi\) | ||
0.939586 | − | 0.342312i | \(-0.111210\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2646.76i | − | 0.205758i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3379.59 | −0.261298 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3363.19 | − | 4682.24i | −0.258621 | − | 0.360053i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 535.831i | − | 0.0409815i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3314.26 | 0.252118 | 0.126059 | − | 0.992023i | \(-0.459767\pi\) | ||||
0.126059 | + | 0.992023i | \(0.459767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11833.7 | 0.895369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15928.8 | −1.19878 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21115.0 | −1.58062 | −0.790310 | − | 0.612707i | \(-0.790081\pi\) | ||||
−0.790310 | + | 0.612707i | \(0.790081\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25743.4i | 1.91687i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1218.41 | + | 875.163i | −0.0902438 | + | 0.0648208i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8726.10 | −0.642912 | −0.321456 | − | 0.946924i | \(-0.604172\pi\) | ||||
−0.321456 | + | 0.946924i | \(0.604172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 19948.3i | − | 1.46202i | −0.682369 | − | 0.731008i | \(-0.739050\pi\) | ||
0.682369 | − | 0.731008i | \(-0.260950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5911.30i | 0.430974i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14474.3i | − | 1.04977i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4516.90i | − | 0.325894i | −0.986635 | − | 0.162947i | \(-0.947900\pi\) | ||
0.986635 | − | 0.162947i | \(-0.0521000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2899.87 | −0.208142 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19849.9 | − | 14257.9i | 1.41740 | − | 1.01810i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2256.33i | 0.160288i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4299.34 | 0.303856 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1629.66 | −0.114588 | −0.0572942 | − | 0.998357i | \(-0.518247\pi\) | ||||
−0.0572942 | + | 0.998357i | \(0.518247\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2628.72 | −0.183896 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3205.58 | 0.223113 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6205.32i | − | 0.429717i | −0.976645 | − | 0.214858i | \(-0.931071\pi\) | ||
0.976645 | − | 0.214858i | \(-0.0689290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20765.5 | − | 14915.6i | 1.43076 | − | 1.02770i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 757.980 | 0.0519632 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 752.600i | 0.0513362i | 0.999671 | + | 0.0256681i | \(0.00817131\pi\) | ||||
−0.999671 | + | 0.0256681i | \(0.991829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21945.7i | − | 1.48949i | −0.667348 | − | 0.744746i | \(-0.732570\pi\) | ||
0.667348 | − | 0.744746i | \(-0.267430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1870.83i | − | 0.126345i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 46138.1i | 3.10046i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1770.10 | −0.118363 | −0.0591815 | − | 0.998247i | \(-0.518849\pi\) | ||||
−0.0591815 | + | 0.998247i | \(0.518849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8906.32 | − | 6397.28i | 0.592615 | − | 0.425666i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 13704.3i | − | 0.907395i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22582.9 | 1.48795 | 0.743977 | − | 0.668205i | \(-0.232937\pi\) | ||||
0.743977 | + | 0.668205i | \(0.232937\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2054.87 | 0.134732 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12035.2 | 0.785279 | 0.392639 | − | 0.919692i | \(-0.371562\pi\) | ||||
0.392639 | + | 0.919692i | \(0.371562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 875.313 | 0.0568365 | 0.0284183 | − | 0.999596i | \(-0.490953\pi\) | ||||
0.0284183 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2566.35i | − | 0.165836i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6656.54 | − | 9267.27i | −0.428072 | − | 0.595964i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11470.7 | −0.734125 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3290.03i | 0.209556i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 889.248i | 0.0563698i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18162.8i | − | 1.14588i | −0.819597 | − | 0.572940i | \(-0.805803\pi\) | ||
0.819597 | − | 0.572940i | \(-0.194197\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13818.6i | 0.867679i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33016.2 | −2.06332 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9324.81 | + | 3142.09i | 0.580004 | + | 0.195438i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4806.36i | − | 0.297553i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2528.87 | 0.155826 | 0.0779128 | − | 0.996960i | \(-0.475174\pi\) | ||||
0.0779128 | + | 0.996960i | \(0.475174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22947.8 | 1.40742 | 0.703712 | − | 0.710485i | \(-0.251524\pi\) | ||||
0.703712 | + | 0.710485i | \(0.251524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20606.4 | 1.25795 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8556.53 | −0.519926 | −0.259963 | − | 0.965619i | \(-0.583710\pi\) | ||||
−0.259963 | + | 0.965619i | \(0.583710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31677.2i | 1.91593i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6927.53 | − | 4975.95i | 0.417068 | − | 0.299574i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18532.9 | 1.11064 | 0.555319 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555319 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6727.04i | − | 0.401293i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5240.43i | 0.311185i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20893.8i | 1.23506i | 0.786546 | + | 0.617532i | \(0.211867\pi\) | ||||
−0.786546 | + | 0.617532i | \(0.788133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5459.18i | 0.321237i | 0.987017 | + | 0.160618i | \(0.0513488\pi\) | ||||
−0.987017 | + | 0.160618i | \(0.948651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7135.04 | −0.417952 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3080.76 | − | 4289.04i | −0.179649 | − | 0.250108i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18759.6i | 1.08902i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5782.95 | 0.334203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18834.6 | 1.08361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1716.03 | 0.0982882 | 0.0491441 | − | 0.998792i | \(-0.484351\pi\) | ||||
0.0491441 | + | 0.998792i | \(0.484351\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4111.57 | 0.234451 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 17235.8i | − | 0.978474i | −0.872151 | − | 0.489237i | \(-0.837275\pi\) | ||
0.872151 | − | 0.489237i | \(-0.162725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1124.48 | + | 1565.51i | 0.0635548 | + | 0.0884813i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12191.1 | 0.686000 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19454.4i | − | 1.08990i | −0.838468 | − | 0.544951i | \(-0.816548\pi\) | ||
0.838468 | − | 0.544951i | \(-0.183452\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22759.3i | 1.26947i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12289.5i | 0.682492i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1010.69i | 0.0558840i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17230.7 | 0.948604 | 0.474302 | − | 0.880362i | \(-0.342700\pi\) | ||||
0.474302 | + | 0.880362i | \(0.342700\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6227.76 | − | 8670.31i | −0.341375 | − | 0.475264i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29475.3i | 1.60872i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3410.20 | −0.185323 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5850.25 | −0.316562 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22169.2 | 1.19447 | 0.597233 | − | 0.802068i | \(-0.296267\pi\) | ||||
0.597233 | + | 0.802068i | \(0.296267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 183.671 | 0.00985388 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 23863.8i | − | 1.27484i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18954.7 | − | 26388.8i | −1.00829 | − | 1.40375i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15665.5 | −0.829800 | −0.414900 | − | 0.909867i | \(-0.636183\pi\) | ||||
−0.414900 | + | 0.909867i | \(0.636183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2801.49i | 0.147770i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14591.6i | 0.766424i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30594.6i | 1.60024i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8584.59i | 0.447137i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35225.3 | −1.82709 | −0.913547 | − | 0.406733i | \(-0.866668\pi\) | ||||
−0.913547 | + | 0.406733i | \(0.866668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4668.60 | − | 3353.39i | 0.241148 | − | 0.173213i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12960.3i | 0.666667i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30054.8 | −1.53960 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12778.0 | −0.651872 | −0.325936 | − | 0.945392i | \(-0.605679\pi\) | ||||
−0.325936 | + | 0.945392i | \(0.605679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34197.7 | −1.73030 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9725.54i | 0.490069i | 0.969514 | + | 0.245035i | \(0.0787994\pi\) | ||||
−0.969514 | + | 0.245035i | \(0.921201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16237.6 | + | 5471.42i | 0.814875 | + | 0.274580i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13313.1 | 0.665391 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18977.4i | 0.944648i | 0.881425 | + | 0.472324i | \(0.156585\pi\) | ||||
−0.881425 | + | 0.472324i | \(0.843415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1473.72i | 0.0730612i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18688.2i | 0.922752i | 0.887205 | + | 0.461376i | \(0.152644\pi\) | ||||
−0.887205 | + | 0.461376i | \(0.847356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33169.7i | 1.63120i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11876.6 | −0.581718 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5212.56 | − | 7256.95i | −0.254289 | − | 0.354023i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 19229.5i | − | 0.934345i | −0.884166 | − | 0.467173i | \(-0.845273\pi\) | ||
0.884166 | − | 0.467173i | \(-0.154727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4100.23 | −0.198434 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18607.4 | 0.896946 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35890.6 | −1.72321 | −0.861603 | − | 0.507584i | \(-0.830539\pi\) | ||||
−0.861603 | + | 0.507584i | \(0.830539\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18262.5 | 0.873367 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 16455.3i | − | 0.783843i | −0.919999 | − | 0.391922i | \(-0.871810\pi\) | ||
0.919999 | − | 0.391922i | \(-0.128190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1091.43 | + | 783.956i | −0.0517855 | + | 0.0371968i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12424.5 | −0.587200 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14189.3i | 0.667986i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32125.7i | 1.50648i | 0.657746 | + | 0.753240i | \(0.271510\pi\) | ||||
−0.657746 | + | 0.753240i | \(0.728490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17979.6i | 0.839845i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 302.967i | − | 0.0140970i | −0.999975 | − | 0.00704850i | \(-0.997756\pi\) | ||
0.999975 | − | 0.00704850i | \(-0.00224363\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23377.3 | −1.08353 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −484.033 | + | 347.674i | −0.0223482 | + | 0.0160524i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 704.364i | 0.0323959i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34202.6 | 1.56705 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5328.85 | −0.243215 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12622.3 | −0.573897 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23519.9 | 1.06531 | 0.532653 | − | 0.846334i | \(-0.321195\pi\) | ||||
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 4910.86i | − | 0.221586i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23254.8 | − | 16703.6i | 1.04532 | − | 0.750835i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8436.67 | 0.377800 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1759.94i | 0.0785141i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7210.03i | 0.320442i | 0.987081 | + | 0.160221i | \(0.0512207\pi\) | ||||
−0.987081 | + | 0.160221i | \(0.948779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39603.6i | 1.75354i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5544.82i | 0.244590i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37291.5 | −1.63884 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23807.8 | + | 17100.8i | −1.04238 | + | 0.748725i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22327.2i | 0.973923i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40393.4 | 1.75544 | 0.877722 | − | 0.479170i | \(-0.159062\pi\) | ||||
0.877722 | + | 0.479170i | \(0.159062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29435.6 | 1.27450 | 0.637252 | − | 0.770655i | \(-0.280071\pi\) | ||||
0.637252 | + | 0.770655i | \(0.280071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16858.0 | 0.727227 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2461.90 | −0.105812 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7063.41i | 0.302469i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2789.62 | − | 3883.73i | −0.119020 | − | 0.165700i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12341.4 | −0.524624 | −0.262312 | − | 0.964983i | \(-0.584485\pi\) | ||||
−0.262312 | + | 0.964983i | \(0.584485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22102.8i | − | 0.936153i | −0.883688 | − | 0.468077i | \(-0.844947\pi\) | ||
0.883688 | − | 0.468077i | \(-0.155053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29258.4i | 1.23472i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3867.63i | 0.162625i | 0.996689 | + | 0.0813124i | \(0.0259111\pi\) | ||||
−0.996689 | + | 0.0813124i | \(0.974089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11642.7i | − | 0.487778i | −0.969803 | − | 0.243889i | \(-0.921577\pi\) | ||
0.969803 | − | 0.243889i | \(-0.0784233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2094.72 | −0.0874429 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26947.4 | − | 9080.19i | −1.12086 | − | 0.377683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 29006.0i | − | 1.20215i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4144.90 | −0.171169 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1522.64 | −0.0626546 | −0.0313273 | − | 0.999509i | \(-0.509973\pi\) | ||||
−0.0313273 | + | 0.999509i | \(0.509973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14563.9 | 0.597152 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15081.0 | 0.616152 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 22879.5i | − | 0.931456i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41678.0 | − | 29936.7i | 1.69076 | − | 1.21445i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10788.5 | 0.436114 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1019.53i | − | 0.0410681i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16334.5i | 0.655664i | 0.944736 | + | 0.327832i | \(0.106318\pi\) | ||||
−0.944736 | + | 0.327832i | \(0.893682\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2566.23i | 0.102647i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40489.7i | 1.61389i | 0.590627 | + | 0.806945i | \(0.298880\pi\) | ||||
−0.590627 | + | 0.806945i | \(0.701120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3963.14 | −0.157416 | −0.0787080 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787080 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1333.30 | − | 1856.23i | −0.0527744 | − | 0.0734728i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 38486.3i | − | 1.51806i | −0.651054 | − | 0.759031i | \(-0.725673\pi\) | ||
0.651054 | − | 0.759031i | \(-0.274327\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44738.8 | −1.75857 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5880.29 | 0.230340 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19935.7 | −0.778221 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5963.37 | 0.231988 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 936.681i | − | 0.0363137i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4908.14 | − | 6833.13i | −0.189629 | − | 0.264002i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7715.19 | 0.297062 | 0.148531 | − | 0.988908i | \(-0.452546\pi\) | ||||
0.148531 | + | 0.988908i | \(0.452546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12285.1i | 0.471405i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10746.0i | − | 0.410946i | −0.978663 | − | 0.205473i | \(-0.934127\pi\) | ||
0.978663 | − | 0.205473i | \(-0.0658732\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3332.31i | 0.127000i | 0.997982 | + | 0.0635000i | \(0.0202263\pi\) | ||||
−0.997982 | + | 0.0635000i | \(0.979774\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24708.3i | 0.938485i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29194.6 | −1.10514 | −0.552569 | − | 0.833467i | \(-0.686353\pi\) | ||||
−0.552569 | + | 0.833467i | \(0.686353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21422.6 | + | 29824.6i | 0.808200 | + | 1.12518i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5187.65i | 0.195054i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8179.99 | 0.306532 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17193.5 | 0.642139 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8180.37 | 0.304498 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30298.5 | 1.12404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2920.74i | − | 0.107996i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13370.4 | − | 18614.4i | −0.492736 | − | 0.685989i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26784.8 | −0.983820 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 42775.0i | − | 1.56595i | −0.622051 | − | 0.782976i | \(-0.713701\pi\) | ||
0.622051 | − | 0.782976i | \(-0.286299\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15789.0i | 0.576115i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43757.7i | 1.59139i | 0.605697 | + | 0.795696i | \(0.292895\pi\) | ||||
−0.605697 | + | 0.795696i | \(0.707105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 84515.5i | − | 3.06359i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14691.1 | 0.530788 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6076.75 | + | 4364.84i | −0.218835 | + | 0.157186i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2327.16i | 0.0835322i | 0.999127 | + | 0.0417661i | \(0.0132984\pi\) | ||||
−0.999127 | + | 0.0417661i | \(0.986702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18642.8 | −0.666994 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15320.5 | 0.546349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1633.39 | 0.0580602 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2793.33 | −0.0989698 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 44503.1i | − | 1.57169i | −0.618423 | − | 0.785845i | \(-0.712228\pi\) | ||
0.618423 | − | 0.785845i | \(-0.287772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1875.48 | + | 5565.89i | −0.0660219 | + | 0.195934i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12134.8 | −0.425804 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 88414.0i | − | 3.09246i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19995.0i | − | 0.697128i | −0.937285 | − | 0.348564i | \(-0.886669\pi\) | ||
0.937285 | − | 0.348564i | \(-0.113331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 20795.5i | − | 0.722722i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 5492.38i | − | 0.190272i | −0.995464 | − | 0.0951362i | \(-0.969671\pi\) | ||
0.995464 | − | 0.0951362i | \(-0.0303287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3909.81 | 0.135017 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4857.66 | − | 6762.86i | −0.167217 | − | 0.232800i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25553.9i | 0.876863i | 0.898765 | + | 0.438432i | \(0.144466\pi\) | ||||
−0.898765 | + | 0.438432i | \(0.855534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16704.1 | −0.571379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11899.2 | 0.405738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39066.4 | −1.32790 | −0.663948 | − | 0.747779i | \(-0.731120\pi\) | ||||
−0.663948 | + | 0.747779i | \(0.731120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32811.2 | −1.11177 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 37920.7i | − | 1.28088i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20559.2 | − | 14767.4i | 0.692274 | − | 0.497250i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6224.19 | −0.208928 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4342.00i | 0.145295i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 16095.9i | − | 0.536939i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17718.4i | 0.589229i | 0.955616 | + | 0.294614i | \(0.0951912\pi\) | ||||
−0.955616 | + | 0.294614i | \(0.904809\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 4258.84i | − | 0.141191i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48730.8 | 1.61055 | 0.805276 | − | 0.592900i | \(-0.202017\pi\) | ||||
0.805276 | + | 0.592900i | \(0.202017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26626.0 | − | 19125.0i | 0.877276 | − | 0.630134i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13105.8i | 0.430485i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18189.4 | 0.595629 | 0.297815 | − | 0.954624i | \(-0.403742\pi\) | ||||
0.297815 | + | 0.954624i | \(0.403742\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39457.6 | −1.28812 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 653.026 | 0.0212533 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8921.53 | −0.289474 | −0.144737 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144737 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17792.8i | 0.575560i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21556.9 | + | 15484.0i | −0.695203 | + | 0.499354i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39207.9 | 1.26060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38882.1i | 1.24635i | 0.782083 | + | 0.623174i | \(0.214157\pi\) | ||||
−0.782083 | + | 0.623174i | \(0.785843\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 29849.5i | − | 0.953924i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4207.23i | 0.134048i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 37847.7i | − | 1.20225i | −0.799153 | − | 0.601127i | \(-0.794719\pi\) | ||
0.799153 | − | 0.601127i | \(-0.205281\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 289.608 | 0.00917196 |
(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.b.g.895.2 | 12 | ||
4.3 | odd | 2 | 1344.4.b.h.895.2 | 12 | |||
7.6 | odd | 2 | 1344.4.b.h.895.11 | 12 | |||
8.3 | odd | 2 | 84.4.b.a.55.11 | ✓ | 12 | ||
8.5 | even | 2 | 84.4.b.b.55.12 | yes | 12 | ||
24.5 | odd | 2 | 252.4.b.e.55.1 | 12 | |||
24.11 | even | 2 | 252.4.b.f.55.2 | 12 | |||
28.27 | even | 2 | inner | 1344.4.b.g.895.11 | 12 | ||
56.13 | odd | 2 | 84.4.b.a.55.12 | yes | 12 | ||
56.27 | even | 2 | 84.4.b.b.55.11 | yes | 12 | ||
168.83 | odd | 2 | 252.4.b.e.55.2 | 12 | |||
168.125 | even | 2 | 252.4.b.f.55.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.11 | ✓ | 12 | 8.3 | odd | 2 | ||
84.4.b.a.55.12 | yes | 12 | 56.13 | odd | 2 | ||
84.4.b.b.55.11 | yes | 12 | 56.27 | even | 2 | ||
84.4.b.b.55.12 | yes | 12 | 8.5 | even | 2 | ||
252.4.b.e.55.1 | 12 | 24.5 | odd | 2 | |||
252.4.b.e.55.2 | 12 | 168.83 | odd | 2 | |||
252.4.b.f.55.1 | 12 | 168.125 | even | 2 | |||
252.4.b.f.55.2 | 12 | 24.11 | even | 2 | |||
1344.4.b.g.895.2 | 12 | 1.1 | even | 1 | trivial | ||
1344.4.b.g.895.11 | 12 | 28.27 | even | 2 | inner | ||
1344.4.b.h.895.2 | 12 | 4.3 | odd | 2 | |||
1344.4.b.h.895.11 | 12 | 7.6 | odd | 2 |