Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,4,Mod(1,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.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: | \(82.6026740080\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.00000 | 0.962250 | 0.481125 | − | 0.876652i | \(-0.340228\pi\) | ||||
0.481125 | + | 0.876652i | \(0.340228\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.0000 | −0.981393 | −0.490696 | − | 0.871331i | \(-0.663258\pi\) | ||||
−0.490696 | + | 0.871331i | \(0.663258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 127.000 | 1.81188 | 0.905942 | − | 0.423402i | \(-0.139164\pi\) | ||||
0.905942 | + | 0.423402i | \(0.139164\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 117.000 | 1.41272 | 0.706359 | − | 0.707854i | \(-0.250336\pi\) | ||||
0.706359 | + | 0.707854i | \(0.250336\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.0000 | 0.363696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 80.0000 | 0.725268 | 0.362634 | − | 0.931932i | \(-0.381878\pi\) | ||||
0.362634 | + | 0.931932i | \(0.381878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.0000 | 0.217712 | 0.108856 | − | 0.994058i | \(-0.465281\pi\) | ||||
0.108856 | + | 0.994058i | \(0.465281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −292.000 | −1.69177 | −0.845883 | − | 0.533368i | \(-0.820926\pi\) | ||||
−0.845883 | + | 0.533368i | \(0.820926\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 55.0000 | 0.290129 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −376.000 | −1.67065 | −0.835325 | − | 0.549757i | \(-0.814720\pi\) | ||||
−0.835325 | + | 0.549757i | \(0.814720\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −230.000 | −0.944346 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 507.000 | 1.93122 | 0.965611 | − | 0.259991i | \(-0.0837197\pi\) | ||||
0.965611 | + | 0.259991i | \(0.0837197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.0000 | 0.113487 | 0.0567437 | − | 0.998389i | \(-0.481928\pi\) | ||||
0.0567437 | + | 0.998389i | \(0.481928\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −134.000 | −0.415870 | −0.207935 | − | 0.978143i | \(-0.566674\pi\) | ||||
−0.207935 | + | 0.978143i | \(0.566674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 635.000 | 1.74349 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 612.000 | 1.58613 | 0.793063 | − | 0.609140i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609140i | \(0.208485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 585.000 | 1.35939 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 780.000 | 1.72114 | 0.860571 | − | 0.509331i | \(-0.170107\pi\) | ||||
0.860571 | + | 0.509331i | \(0.170107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −426.000 | −0.894159 | −0.447080 | − | 0.894494i | \(-0.647536\pi\) | ||||
−0.447080 | + | 0.894494i | \(0.647536\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.0000 | −0.0279974 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −207.000 | −0.377449 | −0.188724 | − | 0.982030i | \(-0.560435\pi\) | ||||
−0.188724 | + | 0.982030i | \(0.560435\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 400.000 | 0.697889 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 702.000 | 1.17341 | 0.586705 | − | 0.809801i | \(-0.300425\pi\) | ||||
0.586705 | + | 0.809801i | \(0.300425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1185.00 | 1.89991 | 0.949957 | − | 0.312380i | \(-0.101126\pi\) | ||||
0.949957 | + | 0.312380i | \(0.101126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54.0000 | 0.0769047 | 0.0384524 | − | 0.999260i | \(-0.487757\pi\) | ||||
0.0384524 | + | 0.999260i | \(0.487757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −309.000 | −0.408640 | −0.204320 | − | 0.978904i | \(-0.565498\pi\) | ||||
−0.204320 | + | 0.978904i | \(0.565498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 170.000 | 0.209493 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −339.000 | −0.403752 | −0.201876 | − | 0.979411i | \(-0.564704\pi\) | ||||
−0.201876 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −322.000 | −0.370932 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1460.00 | −1.62790 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 182.000 | 0.190508 | 0.0952541 | − | 0.995453i | \(-0.469634\pi\) | ||||
0.0952541 | + | 0.995453i | \(0.469634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.0000 | −0.0223342 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1152.00 | 1.13493 | 0.567467 | − | 0.823396i | \(-0.307924\pi\) | ||||
0.567467 | + | 0.823396i | \(0.307924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1588.00 | 1.51913 | 0.759565 | − | 0.650432i | \(-0.225412\pi\) | ||||
0.759565 | + | 0.650432i | \(0.225412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1661.00 | −1.50070 | −0.750350 | − | 0.661041i | \(-0.770115\pi\) | ||||
−0.750350 | + | 0.661041i | \(0.770115\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.0000 | 0.0615118 | 0.0307559 | − | 0.999527i | \(-0.490209\pi\) | ||||
0.0307559 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1880.00 | −1.60758 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1839.00 | 1.53096 | 0.765480 | − | 0.643459i | \(-0.222501\pi\) | ||||
0.765480 | + | 0.643459i | \(0.222501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 92.0000 | 0.0726958 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 889.000 | 0.684828 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1210.00 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2535.00 | 1.85832 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.000 | 0.0740628 | 0.0370314 | − | 0.999314i | \(-0.488210\pi\) | ||||
0.0370314 | + | 0.999314i | \(0.488210\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 160.000 | 0.109203 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1152.00 | −0.768326 | −0.384163 | − | 0.923265i | \(-0.625510\pi\) | ||||
−0.384163 | + | 0.923265i | \(0.625510\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 819.000 | 0.533957 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1557.00 | 0.970974 | 0.485487 | − | 0.874244i | \(-0.338642\pi\) | ||||
0.485487 | + | 0.874244i | \(0.338642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 733.000 | 0.447282 | 0.223641 | − | 0.974672i | \(-0.428206\pi\) | ||||
0.223641 | + | 0.974672i | \(0.428206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −670.000 | −0.400171 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −506.000 | −0.295901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 245.000 | 0.137464 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 44.0000 | 0.0241921 | 0.0120960 | − | 0.999927i | \(-0.496150\pi\) | ||||
0.0120960 | + | 0.999927i | \(0.496150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2360.00 | 1.27188 | 0.635941 | − | 0.771738i | \(-0.280612\pi\) | ||||
0.635941 | + | 0.771738i | \(0.280612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −254.000 | −0.134214 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2324.00 | 1.18137 | 0.590686 | − | 0.806902i | \(-0.298857\pi\) | ||||
0.590686 | + | 0.806902i | \(0.298857\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3060.00 | 1.52625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 560.000 | 0.274125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2261.00 | 1.08647 | 0.543237 | − | 0.839580i | \(-0.317199\pi\) | ||||
0.543237 | + | 0.839580i | \(0.317199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −772.000 | −0.357719 | −0.178860 | − | 0.983875i | \(-0.557241\pi\) | ||||
−0.178860 | + | 0.983875i | \(0.557241\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.0000 | −0.0368685 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −234.000 | −0.104646 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 26.0000 | 0.0114263 | 0.00571313 | − | 0.999984i | \(-0.498181\pi\) | ||||
0.00571313 | + | 0.999984i | \(0.498181\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3900.00 | 1.65617 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2339.00 | 0.976676 | 0.488338 | − | 0.872654i | \(-0.337603\pi\) | ||||
0.488338 | + | 0.872654i | \(0.337603\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2270.00 | −0.932198 | −0.466099 | − | 0.884733i | \(-0.654341\pi\) | ||||
−0.466099 | + | 0.884733i | \(0.654341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2130.00 | −0.860405 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1397.00 | 0.546304 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1015.00 | −0.390637 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4206.00 | −1.59338 | −0.796690 | − | 0.604389i | \(-0.793417\pi\) | ||||
−0.796690 | + | 0.604389i | \(0.793417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2683.00 | −1.00066 | −0.500328 | − | 0.865836i | \(-0.666787\pi\) | ||||
−0.500328 | + | 0.865836i | \(0.666787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 978.000 | 0.353704 | 0.176852 | − | 0.984237i | \(-0.443409\pi\) | ||||
0.176852 | + | 0.984237i | \(0.443409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2450.00 | −0.872743 | −0.436372 | − | 0.899767i | \(-0.643737\pi\) | ||||
−0.436372 | + | 0.899767i | \(0.643737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1035.00 | −0.363200 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 238.000 | 0.0822873 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −160.000 | −0.0537235 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1287.00 | 0.425950 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3543.00 | −1.15597 | −0.577986 | − | 0.816047i | \(-0.696161\pi\) | ||||
−0.577986 | + | 0.816047i | \(0.696161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3510.00 | 1.12911 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2044.00 | −0.639427 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5925.00 | 1.82819 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5842.00 | −1.77817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5310.00 | 1.59455 | 0.797273 | − | 0.603618i | \(-0.206275\pi\) | ||||
0.797273 | + | 0.603618i | \(0.206275\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2876.00 | 0.840911 | 0.420456 | − | 0.907313i | \(-0.361870\pi\) | ||||
0.420456 | + | 0.907313i | \(0.361870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2150.00 | −0.620419 | −0.310210 | − | 0.950668i | \(-0.600399\pi\) | ||||
−0.310210 | + | 0.950668i | \(0.600399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 385.000 | 0.109659 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4086.00 | 1.14885 | 0.574427 | − | 0.818556i | \(-0.305225\pi\) | ||||
0.574427 | + | 0.818556i | \(0.305225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 270.000 | 0.0740016 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 52.0000 | 0.0140736 | 0.00703682 | − | 0.999975i | \(-0.497760\pi\) | ||||
0.00703682 | + | 0.999975i | \(0.497760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5285.00 | −1.41260 | −0.706300 | − | 0.707912i | \(-0.749637\pi\) | ||||
−0.706300 | + | 0.707912i | \(0.749637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 560.000 | 0.147835 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5382.00 | −1.38643 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1545.00 | −0.393214 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2661.00 | −0.669167 | −0.334583 | − | 0.942366i | \(-0.608596\pi\) | ||||
−0.334583 | + | 0.942366i | \(0.608596\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 880.000 | 0.218676 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6786.00 | 1.64708 | 0.823539 | − | 0.567260i | \(-0.191996\pi\) | ||||
0.823539 | + | 0.567260i | \(0.191996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2632.00 | −0.631446 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −68.0000 | −0.0161268 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2162.00 | −0.506900 | −0.253450 | − | 0.967349i | \(-0.581565\pi\) | ||||
−0.253450 | + | 0.967349i | \(0.581565\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1695.00 | −0.388511 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4486.00 | −1.01679 | −0.508395 | − | 0.861124i | \(-0.669761\pi\) | ||||
−0.508395 | + | 0.861124i | \(0.669761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7810.00 | 1.75064 | 0.875321 | − | 0.483543i | \(-0.160650\pi\) | ||||
0.875321 | + | 0.483543i | \(0.160650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1610.00 | −0.356929 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8026.00 | 1.74092 | 0.870461 | − | 0.492237i | \(-0.163821\pi\) | ||||
0.870461 | + | 0.492237i | \(0.163821\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 584.000 | 0.125316 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3586.00 | −0.761291 | −0.380646 | − | 0.924721i | \(-0.624298\pi\) | ||||
−0.380646 | + | 0.924721i | \(0.624298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1747.00 | 0.366955 | 0.183478 | − | 0.983024i | \(-0.441264\pi\) | ||||
0.183478 | + | 0.983024i | \(0.441264\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3549.00 | 0.729933 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11216.0 | 2.28292 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 910.000 | 0.183317 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 506.000 | 0.100890 | 0.0504451 | − | 0.998727i | \(-0.483936\pi\) | ||||
0.0504451 | + | 0.998727i | \(0.483936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1595.00 | −0.311620 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3680.00 | −0.711772 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 224.000 | 0.0428942 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5760.00 | 1.09209 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2661.00 | 0.494695 | 0.247347 | − | 0.968927i | \(-0.420441\pi\) | ||||
0.247347 | + | 0.968927i | \(0.420441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7940.00 | 1.46178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5838.00 | 1.06445 | 0.532223 | − | 0.846604i | \(-0.321357\pi\) | ||||
0.532223 | + | 0.846604i | \(0.321357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1818.00 | −0.328305 | −0.164152 | − | 0.986435i | \(-0.552489\pi\) | ||||
−0.164152 | + | 0.986435i | \(0.552489\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6780.00 | −1.20127 | −0.600635 | − | 0.799523i | \(-0.705086\pi\) | ||||
−0.600635 | + | 0.799523i | \(0.705086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 374.000 | 0.0656426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8305.00 | −1.44405 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14859.0 | 2.55968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 350.000 | 0.0591897 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −938.000 | −0.157184 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −929.000 | −0.154267 | −0.0771336 | − | 0.997021i | \(-0.524577\pi\) | ||||
−0.0771336 | + | 0.997021i | \(0.524577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 752.000 | 0.123752 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8829.00 | −1.42714 | −0.713570 | − | 0.700584i | \(-0.752923\pi\) | ||||
−0.713570 | + | 0.700584i | \(0.752923\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9195.00 | 1.47317 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3212.00 | −0.510087 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5469.00 | −0.846084 | −0.423042 | − | 0.906110i | \(-0.639038\pi\) | ||||
−0.423042 | + | 0.906110i | \(0.639038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4840.00 | −0.742347 | −0.371174 | − | 0.928563i | \(-0.621045\pi\) | ||||
−0.371174 | + | 0.928563i | \(0.621045\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6670.00 | 1.01430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7058.00 | −1.06419 | −0.532096 | − | 0.846684i | \(-0.678595\pi\) | ||||
−0.532096 | + | 0.846684i | \(0.678595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4445.00 | 0.658976 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7470.00 | −1.09819 | −0.549097 | − | 0.835759i | \(-0.685028\pi\) | ||||
−0.549097 | + | 0.835759i | \(0.685028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6830.00 | 0.995772 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6050.00 | −0.874773 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 88.0000 | 0.0125165 | 0.00625826 | − | 0.999980i | \(-0.498008\pi\) | ||||
0.00625826 | + | 0.999980i | \(0.498008\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1014.00 | −0.143053 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4284.00 | 0.599499 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7092.00 | −0.984477 | −0.492238 | − | 0.870460i | \(-0.663821\pi\) | ||||
−0.492238 | + | 0.870460i | \(0.663821\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1564.00 | −0.213661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8689.00 | 1.17764 | 0.588818 | − | 0.808266i | \(-0.299594\pi\) | ||||
0.588818 | + | 0.808266i | \(0.299594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 530.000 | 0.0712670 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6162.00 | 0.822098 | 0.411049 | − | 0.911613i | \(-0.365163\pi\) | ||||
0.411049 | + | 0.911613i | \(0.365163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −64.0000 | −0.00840647 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2472.00 | 0.322199 | 0.161099 | − | 0.986938i | \(-0.448496\pi\) | ||||
0.161099 | + | 0.986938i | \(0.448496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10160.0 | 1.31410 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5760.00 | −0.739322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3662.00 | −0.462948 | −0.231474 | − | 0.972841i | \(-0.574355\pi\) | ||||
−0.231474 | + | 0.972841i | \(0.574355\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4095.00 | 0.513801 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7987.00 | −0.994643 | −0.497321 | − | 0.867566i | \(-0.665683\pi\) | ||||
−0.497321 | + | 0.867566i | \(0.665683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13432.0 | 1.66029 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4136.00 | −0.503720 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9301.00 | −1.12446 | −0.562231 | − | 0.826980i | \(-0.690057\pi\) | ||||
−0.562231 | + | 0.826980i | \(0.690057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7785.00 | 0.934321 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5460.00 | 0.650530 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3665.00 | 0.430398 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4721.00 | 0.550444 | 0.275222 | − | 0.961381i | \(-0.411249\pi\) | ||||
0.275222 | + | 0.961381i | \(0.411249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5276.00 | −0.610776 | −0.305388 | − | 0.952228i | \(-0.598786\pi\) | ||||
−0.305388 | + | 0.952228i | \(0.598786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 268.000 | 0.0308052 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2982.00 | −0.337960 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2530.00 | −0.284731 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4868.00 | −0.544045 | −0.272022 | − | 0.962291i | \(-0.587692\pi\) | ||||
−0.272022 | + | 0.962291i | \(0.587692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1825.00 | −0.202549 | −0.101275 | − | 0.994858i | \(-0.532292\pi\) | ||||
−0.101275 | + | 0.994858i | \(0.532292\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9360.00 | 1.02460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6164.00 | −0.670140 | −0.335070 | − | 0.942193i | \(-0.608760\pi\) | ||||
−0.335070 | + | 0.942193i | \(0.608760\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −98.0000 | −0.0105820 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12243.0 | −1.31305 | −0.656527 | − | 0.754303i | \(-0.727975\pi\) | ||||
−0.656527 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 220.000 | 0.0232788 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3959.00 | −0.416118 | −0.208059 | − | 0.978116i | \(-0.566715\pi\) | ||||
−0.208059 | + | 0.978116i | \(0.566715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5577.00 | 0.582285 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11800.0 | 1.22387 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10239.0 | −1.04805 | −0.524026 | − | 0.851702i | \(-0.675571\pi\) | ||||
−0.524026 | + | 0.851702i | \(0.675571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18415.0 | −1.87263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9630.00 | −0.972915 | −0.486457 | − | 0.873704i | \(-0.661711\pi\) | ||||
−0.486457 | + | 0.873704i | \(0.661711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10312.0 | −1.03507 | −0.517537 | − | 0.855661i | \(-0.673151\pi\) | ||||
−0.517537 | + | 0.855661i | \(0.673151\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2604.00 | −0.258027 | −0.129014 | − | 0.991643i | \(-0.541181\pi\) | ||||
−0.129014 | + | 0.991643i | \(0.541181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1449.00 | −0.142662 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11620.0 | 1.13678 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 352.000 | 0.0342177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1224.00 | −0.117491 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4434.00 | 0.422953 | 0.211477 | − | 0.977383i | \(-0.432173\pi\) | ||||
0.211477 | + | 0.977383i | \(0.432173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17296.0 | 1.63956 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2800.00 | 0.263777 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14422.0 | 1.34194 | 0.670968 | − | 0.741486i | \(-0.265879\pi\) | ||||
0.670968 | + | 0.741486i | \(0.265879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11305.0 | 1.04546 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18908.0 | 1.73789 | 0.868947 | − | 0.494905i | \(-0.164797\pi\) | ||||
0.868947 | + | 0.494905i | \(0.164797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4318.00 | 0.394468 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4914.00 | 0.443507 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11164.0 | 1.00154 | 0.500771 | − | 0.865580i | \(-0.333050\pi\) | ||||
0.500771 | + | 0.865580i | \(0.333050\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3860.00 | −0.344216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21190.0 | −1.87836 | −0.939180 | − | 0.343424i | \(-0.888413\pi\) | ||||
−0.939180 | + | 0.343424i | \(0.888413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −405.000 | −0.0354767 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11706.0 | 1.01937 | 0.509685 | − | 0.860361i | \(-0.329762\pi\) | ||||
0.509685 | + | 0.860361i | \(0.329762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8295.00 | 0.718100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16965.0 | −1.46008 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1474.00 | −0.125390 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 130.000 | 0.0109949 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2037.00 | −0.171291 | −0.0856455 | − | 0.996326i | \(-0.527295\pi\) | ||||
−0.0856455 | + | 0.996326i | \(0.527295\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17941.0 | 1.50001 | 0.750005 | − | 0.661432i | \(-0.230051\pi\) | ||||
0.750005 | + | 0.661432i | \(0.230051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37084.0 | −3.06528 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5767.00 | −0.473987 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1560.00 | −0.127492 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23322.0 | −1.89529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11695.0 | 0.939807 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −946.000 | −0.0751788 | −0.0375894 | − | 0.999293i | \(-0.511968\pi\) | ||||
−0.0375894 | + | 0.999293i | \(0.511968\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11350.0 | −0.897008 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1237.00 | −0.0966916 | −0.0483458 | − | 0.998831i | \(-0.515395\pi\) | ||||
−0.0483458 | + | 0.998831i | \(0.515395\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 852.000 | 0.0662340 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3978.00 | 0.307565 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 378.000 | 0.0290673 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24108.0 | −1.83391 | −0.916956 | − | 0.398989i | \(-0.869361\pi\) | ||||
−0.916956 | + | 0.398989i | \(0.869361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1472.00 | −0.111376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6985.00 | 0.525681 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23564.0 | 1.76395 | 0.881975 | − | 0.471296i | \(-0.156214\pi\) | ||||
0.881975 | + | 0.471296i | \(0.156214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4697.00 | −0.347893 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2451.00 | −0.180582 | −0.0902911 | − | 0.995915i | \(-0.528780\pi\) | ||||
−0.0902911 | + | 0.995915i | \(0.528780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9292.00 | −0.681012 | −0.340506 | − | 0.940242i | \(-0.610598\pi\) | ||||
−0.340506 | + | 0.940242i | \(0.610598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21030.0 | −1.53323 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17573.0 | 1.26789 | 0.633946 | − | 0.773377i | \(-0.281434\pi\) | ||||
0.633946 | + | 0.773377i | \(0.281434\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13415.0 | −0.962881 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2163.00 | −0.154452 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6732.00 | 0.478235 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1837.00 | −0.129167 | −0.0645836 | − | 0.997912i | \(-0.520572\pi\) | ||||
−0.0645836 | + | 0.997912i | \(0.520572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34164.0 | −2.38999 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4890.00 | 0.340351 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11887.0 | −0.823171 | −0.411586 | − | 0.911371i | \(-0.635025\pi\) | ||||
−0.411586 | + | 0.911371i | \(0.635025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12250.0 | −0.839798 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14216.0 | −0.969700 | −0.484850 | − | 0.874597i | \(-0.661126\pi\) | ||||
−0.484850 | + | 0.874597i | \(0.661126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25299.0 | −1.71708 | −0.858542 | − | 0.512743i | \(-0.828629\pi\) | ||||
−0.858542 | + | 0.512743i | \(0.828629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 414.000 | 0.0279592 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10556.0 | 0.705856 | 0.352928 | − | 0.935650i | \(-0.385186\pi\) | ||||
0.352928 | + | 0.935650i | \(0.385186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1190.00 | 0.0791810 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6164.00 | 0.408132 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24086.0 | −1.58699 | −0.793495 | − | 0.608577i | \(-0.791741\pi\) | ||||
−0.793495 | + | 0.608577i | \(0.791741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4834.00 | −0.315412 | −0.157706 | − | 0.987486i | \(-0.550410\pi\) | ||||
−0.157706 | + | 0.987486i | \(0.550410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25628.0 | −1.66410 | −0.832049 | − | 0.554703i | \(-0.812832\pi\) | ||||
−0.832049 | + | 0.554703i | \(0.812832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11600.0 | −0.749584 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2373.00 | −0.152604 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6435.00 | 0.409871 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47752.0 | −3.02702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6976.00 | −0.440111 | −0.220056 | − | 0.975487i | \(-0.570624\pi\) | ||||
−0.220056 | + | 0.975487i | \(0.570624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17715.0 | −1.11233 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2254.00 | −0.140199 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1404.00 | −0.0869192 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14690.0 | 0.905180 | 0.452590 | − | 0.891719i | \(-0.350500\pi\) | ||||
0.452590 | + | 0.891719i | \(0.350500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1528.00 | −0.0937145 | −0.0468573 | − | 0.998902i | \(-0.514921\pi\) | ||||
−0.0468573 | + | 0.998902i | \(0.514921\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24984.0 | 1.51812 | 0.759059 | − | 0.651022i | \(-0.225659\pi\) | ||||
0.759059 | + | 0.651022i | \(0.225659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8580.00 | 0.518944 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10220.0 | −0.615289 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11188.0 | 0.670475 | 0.335238 | − | 0.942134i | \(-0.391183\pi\) | ||||
0.335238 | + | 0.942134i | \(0.391183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2370.00 | −0.140734 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21497.0 | 1.27072 | 0.635360 | − | 0.772216i | \(-0.280852\pi\) | ||||
0.635360 | + | 0.772216i | \(0.280852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1258.00 | −0.0740250 | −0.0370125 | − | 0.999315i | \(-0.511784\pi\) | ||||
−0.0370125 | + | 0.999315i | \(0.511784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29210.0 | −1.71104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2720.00 | 0.157899 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26550.0 | 1.53435 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4686.00 | −0.269599 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22562.0 | 1.29228 | 0.646138 | − | 0.763221i | \(-0.276383\pi\) | ||||
0.646138 | + | 0.763221i | \(0.276383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21888.0 | −1.24258 | −0.621288 | − | 0.783582i | \(-0.713390\pi\) | ||||
−0.621288 | + | 0.783582i | \(0.713390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1274.00 | 0.0720054 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14380.0 | 0.809167 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7453.00 | −0.417542 | −0.208771 | − | 0.977965i | \(-0.566946\pi\) | ||||
−0.208771 | + | 0.977965i | \(0.566946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10750.0 | −0.596999 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28152.0 | −1.55661 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4743.00 | −0.261118 | −0.130559 | − | 0.991441i | \(-0.541677\pi\) | ||||
−0.130559 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −154.000 | −0.00844152 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64389.0 | 3.49915 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20430.0 | 1.10548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19488.0 | 1.05000 | 0.525001 | − | 0.851102i | \(-0.324065\pi\) | ||||
0.525001 | + | 0.851102i | \(0.324065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43992.0 | −2.36016 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8064.00 | 0.428965 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 980.000 | 0.0519107 | 0.0259553 | − | 0.999663i | \(-0.491737\pi\) | ||||
0.0259553 | + | 0.999663i | \(0.491737\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −108.000 | −0.00569665 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23360.0 | −1.22698 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 260.000 | 0.0135424 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14448.0 | −0.749401 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11116.0 | 0.574177 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26425.0 | −1.35928 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25922.0 | −1.32241 | −0.661206 | − | 0.750204i | \(-0.729955\pi\) | ||||
−0.661206 | + | 0.750204i | \(0.729955\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4064.00 | 0.205626 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31768.0 | −1.60079 | −0.800394 | − | 0.599474i | \(-0.795376\pi\) | ||||
−0.800394 | + | 0.599474i | \(0.795376\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2277.00 | −0.113805 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19972.0 | −0.994157 | −0.497078 | − | 0.867706i | \(-0.665594\pi\) | ||||
−0.497078 | + | 0.867706i | \(0.665594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26910.0 | −1.33409 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18664.0 | 0.921556 | 0.460778 | − | 0.887516i | \(-0.347571\pi\) | ||||
0.460778 | + | 0.887516i | \(0.347571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 618.000 | 0.0302697 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11627.0 | −0.567211 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −358.000 | −0.0173949 | −0.00869747 | − | 0.999962i | \(-0.502769\pi\) | ||||
−0.00869747 | + | 0.999962i | \(0.502769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13305.0 | −0.643906 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 774.000 | 0.0371618 | 0.0185809 | − | 0.999827i | \(-0.494085\pi\) | ||||
0.0185809 | + | 0.999827i | \(0.494085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4400.00 | 0.210421 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2885.00 | −0.137426 | −0.0687130 | − | 0.997636i | \(-0.521889\pi\) | ||||
−0.0687130 | + | 0.997636i | \(0.521889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 490.000 | 0.0232493 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35880.0 | −1.68912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6173.00 | −0.289472 | −0.144736 | − | 0.989470i | \(-0.546233\pi\) | ||||
−0.144736 | + | 0.989470i | \(0.546233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33930.0 | 1.58490 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17780.0 | 0.827299 | 0.413650 | − | 0.910436i | \(-0.364254\pi\) | ||||
0.413650 | + | 0.910436i | \(0.364254\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13160.0 | −0.607609 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59319.0 | 2.72827 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7722.00 | 0.353796 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4930.00 | −0.225011 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17460.0 | −0.790828 | −0.395414 | − | 0.918503i | \(-0.629399\pi\) | ||||
−0.395414 | + | 0.918503i | \(0.629399\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10810.0 | −0.487765 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12873.0 | 0.578649 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19596.0 | 0.877521 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26530.0 | 1.17910 | 0.589549 | − | 0.807733i | \(-0.299306\pi\) | ||||
0.589549 | + | 0.807733i | \(0.299306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17018.0 | −0.753509 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 678.000 | 0.0299076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13035.0 | 0.572846 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22430.0 | −0.978406 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12854.0 | 0.558619 | 0.279309 | − | 0.960201i | \(-0.409894\pi\) | ||||
0.279309 | + | 0.960201i | \(0.409894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42324.0 | −1.83255 | −0.916274 | − | 0.400552i | \(-0.868818\pi\) | ||||
−0.916274 | + | 0.400552i | \(0.868818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39050.0 | 1.68456 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3744.00 | 0.160326 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 644.000 | 0.0274764 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3240.00 | −0.137731 | −0.0688653 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688653 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9618.00 | 0.407366 | 0.203683 | − | 0.979037i | \(-0.434709\pi\) | ||||
0.203683 | + | 0.979037i | \(0.434709\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4721.00 | 0.198507 | 0.0992535 | − | 0.995062i | \(-0.468355\pi\) | ||||
0.0992535 | + | 0.995062i | \(0.468355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26996.0 | −1.13101 | −0.565507 | − | 0.824744i | \(-0.691319\pi\) | ||||
−0.565507 | + | 0.824744i | \(0.691319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 40130.0 | 1.67520 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6223.00 | 0.258841 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42340.0 | 1.74849 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12262.0 | −0.504566 | −0.252283 | − | 0.967653i | \(-0.581181\pi\) | ||||
−0.252283 | + | 0.967653i | \(0.581181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23233.0 | −0.952602 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17930.0 | −0.732553 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8470.00 | −0.343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8735.00 | 0.353103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30080.0 | −1.21167 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22982.0 | 0.922496 | 0.461248 | − | 0.887271i | \(-0.347402\pi\) | ||||
0.461248 | + | 0.887271i | \(0.347402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22381.0 | −0.892089 | −0.446045 | − | 0.895011i | \(-0.647168\pi\) | ||||
−0.446045 | + | 0.895011i | \(0.647168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18555.0 | −0.737006 | −0.368503 | − | 0.929626i | \(-0.620130\pi\) | ||||
−0.368503 | + | 0.929626i | \(0.620130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17745.0 | 0.702379 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6452.00 | 0.254494 | 0.127247 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127247 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 56080.0 | 2.19674 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 594.000 | 0.0231877 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9522.00 | 0.370426 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −364.000 | −0.0141117 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3632.00 | −0.139845 | −0.0699224 | − | 0.997552i | \(-0.522275\pi\) | ||||
−0.0699224 | + | 0.997552i | \(0.522275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2530.00 | 0.0970817 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1542.00 | −0.0589686 | −0.0294843 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294843 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38145.0 | −1.45377 | −0.726886 | − | 0.686758i | \(-0.759033\pi\) | ||||
−0.726886 | + | 0.686758i | \(0.759033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23898.0 | −0.904641 | −0.452320 | − | 0.891856i | \(-0.649404\pi\) | ||||
−0.452320 | + | 0.891856i | \(0.649404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 742.000 | 0.0279931 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7381.00 | −0.277523 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15678.0 | −0.587508 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18400.0 | −0.684903 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9928.00 | −0.368317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 77724.0 | 2.87388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1120.00 | 0.0412749 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43324.0 | −1.58605 | −0.793026 | − | 0.609187i | \(-0.791496\pi\) | ||||
−0.793026 | + | 0.609187i | \(0.791496\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2304.00 | −0.0840691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21756.0 | −0.791228 | −0.395614 | − | 0.918417i | \(-0.629468\pi\) | ||||
−0.395614 | + | 0.918417i | \(0.629468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3399.00 | −0.123210 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8064.00 | −0.290400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19290.0 | −0.692403 | −0.346202 | − | 0.938160i | \(-0.612529\pi\) | ||||
−0.346202 | + | 0.938160i | \(0.612529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13305.0 | 0.476020 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32292.0 | −1.15158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3176.00 | −0.112528 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34990.0 | 1.23572 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5733.00 | 0.201817 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29190.0 | 1.02426 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14415.0 | −0.502580 | −0.251290 | − | 0.967912i | \(-0.580855\pi\) | ||||
−0.251290 | + | 0.967912i | \(0.580855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9090.00 | −0.315912 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9336.00 | 0.323427 | 0.161714 | − | 0.986838i | \(-0.448298\pi\) | ||||
0.161714 | + | 0.986838i | \(0.448298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40560.0 | 1.40065 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3636.00 | 0.124767 | 0.0623834 | − | 0.998052i | \(-0.480130\pi\) | ||||
0.0623834 | + | 0.998052i | \(0.480130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −54510.0 | −1.86456 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33900.0 | −1.15592 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5247.00 | −0.178349 | −0.0891747 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891747 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1870.00 | 0.0631646 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10899.0 | 0.366994 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55473.0 | 1.86207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3322.00 | 0.111163 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42182.0 | 1.40277 | 0.701387 | − | 0.712781i | \(-0.252565\pi\) | ||||
0.701387 | + | 0.712781i | \(0.252565\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 74295.0 | 2.46305 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23227.0 | −0.767652 | −0.383826 | − | 0.923405i | \(-0.625394\pi\) | ||||
−0.383826 | + | 0.923405i | \(0.625394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5131.00 | 0.169057 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11821.0 | 0.387090 | 0.193545 | − | 0.981091i | \(-0.438001\pi\) | ||||
0.193545 | + | 0.981091i | \(0.438001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3729.00 | −0.121736 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −140.000 | −0.00455643 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3420.00 | 0.110968 | 0.0554838 | − | 0.998460i | \(-0.482330\pi\) | ||||
0.0554838 | + | 0.998460i | \(0.482330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4690.00 | −0.151251 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2560.00 | 0.0823087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4636.00 | −0.148605 | −0.0743024 | − | 0.997236i | \(-0.523673\pi\) | ||||
−0.0743024 | + | 0.997236i | \(0.523673\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4645.00 | −0.148444 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14722.0 | −0.467653 | −0.233827 | − | 0.972278i | \(-0.575125\pi\) | ||||
−0.233827 | + | 0.972278i | \(0.575125\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54520.0 | 1.72666 |
(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 | 1400.4.a.h.1.1 | yes | 1 | |
5.2 | odd | 4 | 1400.4.g.d.449.1 | 2 | |||
5.3 | odd | 4 | 1400.4.g.d.449.2 | 2 | |||
5.4 | even | 2 | 1400.4.a.c.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.4.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
1400.4.a.h.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1400.4.g.d.449.1 | 2 | 5.2 | odd | 4 | |||
1400.4.g.d.449.2 | 2 | 5.3 | odd | 4 |