Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,5,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.197");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (of order \(2\), degree \(1\), 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: | \(91.1723074400\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.224054542336.12 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 199x^{4} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.7 | ||
Root | \(1.96485 + 2.67196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.5.b.j.197.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 12.6723i | 0.506893i | 0.967349 | + | 0.253446i | \(0.0815641\pi\) | ||||
−0.967349 | + | 0.253446i | \(0.918436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −35.8427 | −0.358427 | ||||||||
\(11\) | − 166.462i | − 1.37572i | −0.725845 | − | 0.687858i | \(-0.758551\pi\) | ||||
0.725845 | − | 0.687858i | \(-0.241449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 140.982 | 0.834212 | 0.417106 | − | 0.908858i | \(-0.363044\pi\) | ||||
0.417106 | + | 0.908858i | \(0.363044\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 38.7401i | 0.134049i | 0.997751 | + | 0.0670244i | \(0.0213505\pi\) | ||||
−0.997751 | + | 0.0670244i | \(0.978649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −359.282 | −0.995241 | −0.497621 | − | 0.867395i | \(-0.665793\pi\) | ||||
−0.497621 | + | 0.867395i | \(0.665793\pi\) | |||||||
\(20\) | − 101.379i | − 0.253446i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 470.825 | 0.972779 | ||||||||
\(23\) | 22.2119i | 0.0419885i | 0.999780 | + | 0.0209943i | \(0.00668317\pi\) | ||||
−0.999780 | + | 0.0209943i | \(0.993317\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 464.412 | 0.743060 | ||||||||
\(26\) | 398.757i | 0.589877i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 83.2708i | 0.0990141i | 0.998774 | + | 0.0495070i | \(0.0157650\pi\) | ||||
−0.998774 | + | 0.0495070i | \(0.984235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.6539 | −0.0214921 | −0.0107461 | − | 0.999942i | \(-0.503421\pi\) | ||||
−0.0107461 | + | 0.999942i | \(0.503421\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −109.574 | −0.0947868 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1361.06 | −0.994202 | −0.497101 | − | 0.867693i | \(-0.665602\pi\) | ||||
−0.497101 | + | 0.867693i | \(0.665602\pi\) | |||||||
\(38\) | − 1016.20i | − 0.703742i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 286.742 | 0.179214 | ||||||||
\(41\) | 2210.66i | 1.31509i | 0.753417 | + | 0.657543i | \(0.228404\pi\) | ||||
−0.753417 | + | 0.657543i | \(0.771596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1459.06 | −0.789109 | −0.394554 | − | 0.918873i | \(-0.629101\pi\) | ||||
−0.394554 | + | 0.918873i | \(0.629101\pi\) | |||||||
\(44\) | 1331.69i | 0.687858i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −62.8248 | −0.0296904 | ||||||||
\(47\) | 1415.45i | 0.640763i | 0.947289 | + | 0.320382i | \(0.103811\pi\) | ||||
−0.947289 | + | 0.320382i | \(0.896189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1313.56i | 0.525423i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1127.86 | −0.417106 | ||||||||
\(53\) | 2591.76i | 0.922662i | 0.887228 | + | 0.461331i | \(0.152628\pi\) | ||||
−0.887228 | + | 0.461331i | \(0.847372\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2109.46 | 0.697341 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −235.525 | −0.0700135 | ||||||||
\(59\) | − 2773.93i | − 0.796878i | −0.917195 | − | 0.398439i | \(-0.869552\pi\) | ||||
0.917195 | − | 0.398439i | \(-0.130448\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1734.29 | −0.466081 | −0.233041 | − | 0.972467i | \(-0.574868\pi\) | ||||
−0.233041 | + | 0.972467i | \(0.574868\pi\) | |||||||
\(62\) | − 58.4181i | − 0.0151972i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 1786.57i | 0.422856i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −952.113 | −0.212099 | −0.106050 | − | 0.994361i | \(-0.533820\pi\) | ||||
−0.106050 | + | 0.994361i | \(0.533820\pi\) | |||||||
\(68\) | − 309.921i | − 0.0670244i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3845.91i | 0.762926i | 0.924384 | + | 0.381463i | \(0.124580\pi\) | ||||
−0.924384 | + | 0.381463i | \(0.875420\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3605.64 | −0.676607 | −0.338303 | − | 0.941037i | \(-0.609853\pi\) | ||||
−0.338303 | + | 0.941037i | \(0.609853\pi\) | |||||||
\(74\) | − 3849.66i | − 0.703007i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2874.26 | 0.497621 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6839.18 | −1.09585 | −0.547923 | − | 0.836529i | \(-0.684581\pi\) | ||||
−0.547923 | + | 0.836529i | \(0.684581\pi\) | |||||||
\(80\) | 811.028i | 0.126723i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6252.69 | −0.929907 | ||||||||
\(83\) | − 9448.26i | − 1.37150i | −0.727837 | − | 0.685750i | \(-0.759474\pi\) | ||||
0.727837 | − | 0.685750i | \(-0.240526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −490.927 | −0.0679483 | ||||||||
\(86\) | − 4126.85i | − 0.557984i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3766.60 | −0.486389 | ||||||||
\(89\) | 13655.2i | 1.72392i | 0.506976 | + | 0.861960i | \(0.330763\pi\) | ||||
−0.506976 | + | 0.861960i | \(0.669237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 177.695i | − 0.0209943i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4003.49 | −0.453088 | ||||||||
\(95\) | − 4552.94i | − 0.504481i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10360.4 | 1.10112 | 0.550561 | − | 0.834795i | \(-0.314414\pi\) | ||||
0.550561 | + | 0.834795i | \(0.314414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3715.30 | −0.371530 | ||||||||
\(101\) | − 13850.7i | − 1.35778i | −0.734240 | − | 0.678890i | \(-0.762461\pi\) | ||||
0.734240 | − | 0.678890i | \(-0.237539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15678.8 | 1.47788 | 0.738941 | − | 0.673771i | \(-0.235326\pi\) | ||||
0.738941 | + | 0.673771i | \(0.235326\pi\) | |||||||
\(104\) | − 3190.06i | − 0.294939i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7330.60 | −0.652421 | ||||||||
\(107\) | − 9059.88i | − 0.791325i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8842.23 | −0.744232 | −0.372116 | − | 0.928186i | \(-0.621368\pi\) | ||||
−0.372116 | + | 0.928186i | \(0.621368\pi\) | |||||||
\(110\) | 5966.44i | 0.493094i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11117.8i | 0.870688i | 0.900264 | + | 0.435344i | \(0.143373\pi\) | ||||
−0.900264 | + | 0.435344i | \(0.856627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −281.477 | −0.0212837 | ||||||||
\(116\) | − 666.167i | − 0.0495070i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7845.87 | 0.563478 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13068.5 | −0.892596 | ||||||||
\(122\) | − 4905.31i | − 0.329569i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 165.231 | 0.0107461 | ||||||||
\(125\) | 13805.4i | 0.883544i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −26937.3 | −1.67012 | −0.835059 | − | 0.550160i | \(-0.814567\pi\) | ||||
−0.835059 | + | 0.550160i | \(0.814567\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5053.18 | −0.299004 | ||||||||
\(131\) | 10883.3i | 0.634191i | 0.948394 | + | 0.317095i | \(0.102708\pi\) | ||||
−0.948394 | + | 0.317095i | \(0.897292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 2692.98i | − 0.149977i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 876.588 | 0.0473934 | ||||||||
\(137\) | 6806.31i | 0.362636i | 0.983425 | + | 0.181318i | \(0.0580363\pi\) | ||||
−0.983425 | + | 0.181318i | \(0.941964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18840.7 | −0.975139 | −0.487570 | − | 0.873084i | \(-0.662116\pi\) | ||||
−0.487570 | + | 0.873084i | \(0.662116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10877.9 | −0.539470 | ||||||||
\(143\) | − 23468.1i | − 1.14764i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1055.23 | −0.0501895 | ||||||||
\(146\) | − 10198.3i | − 0.478433i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10888.5 | 0.497101 | ||||||||
\(149\) | − 15302.7i | − 0.689279i | −0.938735 | − | 0.344640i | \(-0.888001\pi\) | ||||
0.938735 | − | 0.344640i | \(-0.111999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −44025.0 | −1.93084 | −0.965418 | − | 0.260708i | \(-0.916044\pi\) | ||||
−0.965418 | + | 0.260708i | \(0.916044\pi\) | |||||||
\(152\) | 8129.63i | 0.351871i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 261.733i | − 0.0108942i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −45077.6 | −1.82878 | −0.914390 | − | 0.404834i | \(-0.867329\pi\) | ||||
−0.914390 | + | 0.404834i | \(0.867329\pi\) | |||||||
\(158\) | − 19344.1i | − 0.774880i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2293.93 | −0.0896068 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −49796.7 | −1.87424 | −0.937119 | − | 0.349009i | \(-0.886518\pi\) | ||||
−0.937119 | + | 0.349009i | \(0.886518\pi\) | |||||||
\(164\) | − 17685.3i | − 0.657543i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26723.7 | 0.969797 | ||||||||
\(167\) | 19878.6i | 0.712775i | 0.934338 | + | 0.356388i | \(0.115992\pi\) | ||||
−0.934338 | + | 0.356388i | \(0.884008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8685.10 | −0.304090 | ||||||||
\(170\) | − 1388.55i | − 0.0480467i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11672.5 | 0.394554 | ||||||||
\(173\) | 2800.14i | 0.0935595i | 0.998905 | + | 0.0467797i | \(0.0148959\pi\) | ||||
−0.998905 | + | 0.0467797i | \(0.985104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 10653.5i | − 0.343929i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −38622.7 | −1.21900 | ||||||||
\(179\) | − 38943.0i | − 1.21541i | −0.794163 | − | 0.607705i | \(-0.792090\pi\) | ||||
0.794163 | − | 0.607705i | \(-0.207910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45313.6 | 1.38316 | 0.691578 | − | 0.722302i | \(-0.256916\pi\) | ||||
0.691578 | + | 0.722302i | \(0.256916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 502.599 | 0.0148452 | ||||||||
\(185\) | − 17247.8i | − 0.503953i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6448.74 | 0.184413 | ||||||||
\(188\) | − 11323.6i | − 0.320382i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12877.6 | 0.356722 | ||||||||
\(191\) | − 14139.4i | − 0.387582i | −0.981043 | − | 0.193791i | \(-0.937922\pi\) | ||||
0.981043 | − | 0.193791i | \(-0.0620783\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18480.7 | −0.496138 | −0.248069 | − | 0.968742i | \(-0.579796\pi\) | ||||
−0.248069 | + | 0.968742i | \(0.579796\pi\) | |||||||
\(194\) | 29303.8i | 0.778610i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 29573.5i | − 0.762027i | −0.924569 | − | 0.381014i | \(-0.875575\pi\) | ||||
0.924569 | − | 0.381014i | \(-0.124425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −41458.1 | −1.04690 | −0.523448 | − | 0.852058i | \(-0.675355\pi\) | ||||
−0.523448 | + | 0.852058i | \(0.675355\pi\) | |||||||
\(200\) | − 10508.5i | − 0.262711i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39175.7 | 0.960095 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28014.2 | −0.666608 | ||||||||
\(206\) | 44346.5i | 1.04502i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9022.84 | 0.208553 | ||||||||
\(209\) | 59806.7i | 1.36917i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 29165.3 | 0.655090 | 0.327545 | − | 0.944836i | \(-0.393779\pi\) | ||||
0.327545 | + | 0.944836i | \(0.393779\pi\) | |||||||
\(212\) | − 20734.1i | − 0.461331i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25625.2 | 0.559551 | ||||||||
\(215\) | − 18489.7i | − 0.399993i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 25009.6i | − 0.526252i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −16875.6 | −0.348670 | ||||||||
\(221\) | 5461.65i | 0.111825i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18360.3 | −0.369208 | −0.184604 | − | 0.982813i | \(-0.559100\pi\) | ||||
−0.184604 | + | 0.982813i | \(0.559100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31445.9 | −0.615670 | ||||||||
\(227\) | − 59117.7i | − 1.14727i | −0.819111 | − | 0.573635i | \(-0.805533\pi\) | ||||
0.819111 | − | 0.573635i | \(-0.194467\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 95795.1 | 1.82672 | 0.913361 | − | 0.407150i | \(-0.133478\pi\) | ||||
0.913361 | + | 0.407150i | \(0.133478\pi\) | |||||||
\(230\) | − 796.136i | − 0.0150498i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1884.20 | 0.0350068 | ||||||||
\(233\) | − 33711.0i | − 0.620955i | −0.950581 | − | 0.310478i | \(-0.899511\pi\) | ||||
0.950581 | − | 0.310478i | \(-0.100489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17937.0 | −0.324798 | ||||||||
\(236\) | 22191.5i | 0.398439i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 5136.58i | − 0.0899246i | −0.998989 | − | 0.0449623i | \(-0.985683\pi\) | ||||
0.998989 | − | 0.0449623i | \(-0.0143168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −46159.8 | −0.794748 | −0.397374 | − | 0.917657i | \(-0.630078\pi\) | ||||
−0.397374 | + | 0.917657i | \(0.630078\pi\) | |||||||
\(242\) | − 36963.3i | − 0.631161i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13874.3 | 0.233041 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −50652.3 | −0.830243 | ||||||||
\(248\) | 467.345i | 0.00759861i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −39047.5 | −0.624760 | ||||||||
\(251\) | 97957.3i | 1.55485i | 0.628974 | + | 0.777426i | \(0.283475\pi\) | ||||
−0.628974 | + | 0.777426i | \(0.716525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3697.44 | 0.0577643 | ||||||||
\(254\) | − 76190.3i | − 1.18095i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 77010.2i | − 1.16596i | −0.812488 | − | 0.582978i | \(-0.801887\pi\) | ||||
0.812488 | − | 0.582978i | \(-0.198113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 14292.5i | − 0.211428i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −30782.7 | −0.448440 | ||||||||
\(263\) | 82173.7i | 1.18801i | 0.804460 | + | 0.594007i | \(0.202455\pi\) | ||||
−0.804460 | + | 0.594007i | \(0.797545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32843.6 | −0.467691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7616.90 | 0.106050 | ||||||||
\(269\) | − 115507.i | − 1.59626i | −0.602488 | − | 0.798128i | \(-0.705824\pi\) | ||||
0.602488 | − | 0.798128i | \(-0.294176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 60189.3 | 0.819559 | 0.409780 | − | 0.912185i | \(-0.365606\pi\) | ||||
0.409780 | + | 0.912185i | \(0.365606\pi\) | |||||||
\(272\) | 2479.37i | 0.0335122i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19251.2 | −0.256422 | ||||||||
\(275\) | − 77306.9i | − 1.02224i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −113652. | −1.48122 | −0.740609 | − | 0.671936i | \(-0.765463\pi\) | ||||
−0.740609 | + | 0.671936i | \(0.765463\pi\) | |||||||
\(278\) | − 53289.4i | − 0.689528i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 64605.4i | 0.818194i | 0.912491 | + | 0.409097i | \(0.134156\pi\) | ||||
−0.912491 | + | 0.409097i | \(0.865844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −75243.4 | −0.939497 | −0.469749 | − | 0.882800i | \(-0.655655\pi\) | ||||
−0.469749 | + | 0.882800i | \(0.655655\pi\) | |||||||
\(284\) | − 30767.3i | − 0.381463i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 66377.8 | 0.811504 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 82020.2 | 0.982031 | ||||||||
\(290\) | − 2984.65i | − 0.0354893i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 28845.1 | 0.338303 | ||||||||
\(293\) | 62577.9i | 0.728930i | 0.931217 | + | 0.364465i | \(0.118748\pi\) | ||||
−0.931217 | + | 0.364465i | \(0.881252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35152.1 | 0.403932 | ||||||||
\(296\) | 30797.3i | 0.351503i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 43282.6 | 0.487394 | ||||||||
\(299\) | 3131.48i | 0.0350274i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 124521.i | − 1.36531i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22994.1 | −0.248810 | ||||||||
\(305\) | − 21977.5i | − 0.236253i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −41292.1 | −0.438117 | −0.219059 | − | 0.975712i | \(-0.570299\pi\) | ||||
−0.219059 | + | 0.975712i | \(0.570299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 740.293 | 0.00770336 | ||||||||
\(311\) | 18468.2i | 0.190943i | 0.995432 | + | 0.0954715i | \(0.0304359\pi\) | ||||
−0.995432 | + | 0.0954715i | \(0.969564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 70159.4 | 0.716139 | 0.358069 | − | 0.933695i | \(-0.383435\pi\) | ||||
0.358069 | + | 0.933695i | \(0.383435\pi\) | |||||||
\(314\) | − 127499.i | − 1.29314i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 54713.4 | 0.547923 | ||||||||
\(317\) | 36037.5i | 0.358622i | 0.983792 | + | 0.179311i | \(0.0573868\pi\) | ||||
−0.983792 | + | 0.179311i | \(0.942613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13861.4 | 0.136215 | ||||||||
\(320\) | − 6488.23i | − 0.0633616i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 13918.6i | − 0.133411i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 65473.7 | 0.619870 | ||||||||
\(326\) | − 140846.i | − 1.32529i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 50021.5 | 0.464953 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32479.8 | 0.296454 | 0.148227 | − | 0.988953i | \(-0.452643\pi\) | ||||
0.148227 | + | 0.988953i | \(0.452643\pi\) | |||||||
\(332\) | 75586.1i | 0.685750i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −56225.1 | −0.504008 | ||||||||
\(335\) | − 12065.5i | − 0.107511i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −156861. | −1.38119 | −0.690597 | − | 0.723240i | \(-0.742652\pi\) | ||||
−0.690597 | + | 0.723240i | \(0.742652\pi\) | |||||||
\(338\) | − 24565.2i | − 0.215024i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3927.41 | 0.0339742 | ||||||||
\(341\) | 3438.09i | 0.0295671i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 33014.8i | 0.278992i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7920.00 | −0.0661565 | ||||||||
\(347\) | 97556.6i | 0.810210i | 0.914270 | + | 0.405105i | \(0.132765\pi\) | ||||
−0.914270 | + | 0.405105i | \(0.867235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −84314.3 | −0.692230 | −0.346115 | − | 0.938192i | \(-0.612499\pi\) | ||||
−0.346115 | + | 0.938192i | \(0.612499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30132.8 | 0.243195 | ||||||||
\(353\) | 161034.i | 1.29232i | 0.763204 | + | 0.646158i | \(0.223625\pi\) | ||||
−0.763204 | + | 0.646158i | \(0.776375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48736.6 | −0.386722 | ||||||||
\(356\) | − 109241.i | − 0.861960i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 110147. | 0.859425 | ||||||||
\(359\) | − 124144.i | − 0.963246i | −0.876378 | − | 0.481623i | \(-0.840047\pi\) | ||||
0.876378 | − | 0.481623i | \(-0.159953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1237.34 | −0.00949457 | ||||||||
\(362\) | 128166.i | 0.978039i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 45691.8i | − 0.342967i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 94483.2 | 0.701492 | 0.350746 | − | 0.936471i | \(-0.385928\pi\) | ||||
0.350746 | + | 0.936471i | \(0.385928\pi\) | |||||||
\(368\) | 1421.56i | 0.0104971i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 48784.2 | 0.356349 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −248173. | −1.78376 | −0.891881 | − | 0.452270i | \(-0.850615\pi\) | ||||
−0.891881 | + | 0.452270i | \(0.850615\pi\) | |||||||
\(374\) | 18239.8i | 0.130400i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32027.9 | 0.226544 | ||||||||
\(377\) | 11739.7i | 0.0825988i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16745.0 | −0.116575 | −0.0582877 | − | 0.998300i | \(-0.518564\pi\) | ||||
−0.0582877 | + | 0.998300i | \(0.518564\pi\) | |||||||
\(380\) | 36423.5i | 0.252240i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 39992.2 | 0.274062 | ||||||||
\(383\) | − 130421.i | − 0.889101i | −0.895754 | − | 0.444550i | \(-0.853363\pi\) | ||||
0.895754 | − | 0.444550i | \(-0.146637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 52271.2i | − 0.350823i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −82883.6 | −0.550561 | ||||||||
\(389\) | 45385.9i | 0.299931i | 0.988691 | + | 0.149966i | \(0.0479163\pi\) | ||||
−0.988691 | + | 0.149966i | \(0.952084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −860.493 | −0.00562851 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 83646.5 | 0.538835 | ||||||||
\(395\) | − 86668.2i | − 0.555476i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 58752.9 | 0.372776 | 0.186388 | − | 0.982476i | \(-0.440322\pi\) | ||||
0.186388 | + | 0.982476i | \(0.440322\pi\) | |||||||
\(398\) | − 117261.i | − 0.740267i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 29722.4 | 0.185765 | ||||||||
\(401\) | 269379.i | 1.67523i | 0.546258 | + | 0.837617i | \(0.316052\pi\) | ||||
−0.546258 | + | 0.837617i | \(0.683948\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2911.83 | −0.0179290 | ||||||||
\(404\) | 110806.i | 0.678890i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 226565.i | 1.36774i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 308049. | 1.84150 | 0.920752 | − | 0.390148i | \(-0.127576\pi\) | ||||
0.920752 | + | 0.390148i | \(0.127576\pi\) | |||||||
\(410\) | − 79236.1i | − 0.471363i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −125431. | −0.738941 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 119731. | 0.695203 | ||||||||
\(416\) | 25520.5i | 0.147469i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −169159. | −0.968150 | ||||||||
\(419\) | 234381.i | 1.33504i | 0.744592 | + | 0.667520i | \(0.232644\pi\) | ||||
−0.744592 | + | 0.667520i | \(0.767356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −120240. | −0.678401 | −0.339200 | − | 0.940714i | \(-0.610156\pi\) | ||||
−0.339200 | + | 0.940714i | \(0.610156\pi\) | |||||||
\(422\) | 82491.8i | 0.463219i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 58644.8 | 0.326210 | ||||||||
\(425\) | 17991.4i | 0.0996063i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 72479.1i | 0.395663i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 52296.8 | 0.282838 | ||||||||
\(431\) | 229940.i | 1.23783i | 0.785460 | + | 0.618913i | \(0.212427\pi\) | ||||
−0.785460 | + | 0.618913i | \(0.787573\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −297018. | −1.58419 | −0.792095 | − | 0.610398i | \(-0.791010\pi\) | ||||
−0.792095 | + | 0.610398i | \(0.791010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 70737.8 | 0.372116 | ||||||||
\(437\) | − 7980.35i | − 0.0417887i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −281472. | −1.46051 | −0.730257 | − | 0.683172i | \(-0.760600\pi\) | ||||
−0.730257 | + | 0.683172i | \(0.760600\pi\) | |||||||
\(440\) | − 47731.5i | − 0.246547i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15447.9 | −0.0790723 | ||||||||
\(443\) | 332821.i | 1.69591i | 0.530068 | + | 0.847955i | \(0.322167\pi\) | ||||
−0.530068 | + | 0.847955i | \(0.677833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −173043. | −0.873842 | ||||||||
\(446\) | − 51930.9i | − 0.261069i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13253.5i | 0.0657413i | 0.999460 | + | 0.0328706i | \(0.0104649\pi\) | ||||
−0.999460 | + | 0.0328706i | \(0.989535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 367990. | 1.80919 | ||||||||
\(452\) | − 88942.6i | − 0.435344i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 167210. | 0.811243 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 267097. | 1.27890 | 0.639449 | − | 0.768833i | \(-0.279162\pi\) | ||||
0.639449 | + | 0.768833i | \(0.279162\pi\) | |||||||
\(458\) | 270950.i | 1.29169i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2251.81 | 0.0106418 | ||||||||
\(461\) | − 3390.66i | − 0.0159545i | −0.999968 | − | 0.00797724i | \(-0.997461\pi\) | ||||
0.999968 | − | 0.00797724i | \(-0.00253926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −102480. | −0.478054 | −0.239027 | − | 0.971013i | \(-0.576828\pi\) | ||||
−0.239027 | + | 0.971013i | \(0.576828\pi\) | |||||||
\(464\) | 5329.33i | 0.0247535i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 95349.2 | 0.439082 | ||||||||
\(467\) | 62515.0i | 0.286649i | 0.989676 | + | 0.143324i | \(0.0457793\pi\) | ||||
−0.989676 | + | 0.143324i | \(0.954221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 50733.4i | − 0.229667i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −62766.9 | −0.281739 | ||||||||
\(473\) | 242878.i | 1.08559i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −166855. | −0.739524 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14528.5 | 0.0635863 | ||||||||
\(479\) | − 247519.i | − 1.07879i | −0.842052 | − | 0.539396i | \(-0.818653\pi\) | ||||
0.842052 | − | 0.539396i | \(-0.181347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −191885. | −0.829375 | ||||||||
\(482\) | − 130560.i | − 0.561972i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 104548. | 0.446298 | ||||||||
\(485\) | 131291.i | 0.558150i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 258363. | 1.08936 | 0.544680 | − | 0.838644i | \(-0.316651\pi\) | ||||
0.544680 | + | 0.838644i | \(0.316651\pi\) | |||||||
\(488\) | 39242.5i | 0.164785i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 239798.i | 0.994676i | 0.867557 | + | 0.497338i | \(0.165689\pi\) | ||||
−0.867557 | + | 0.497338i | \(0.834311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3225.92 | −0.0132727 | ||||||||
\(494\) | − 143266.i | − 0.587070i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1321.85 | −0.00537303 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33013.7 | 0.132584 | 0.0662922 | − | 0.997800i | \(-0.478883\pi\) | ||||
0.0662922 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(500\) | − 110443.i | − 0.441772i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −277065. | −1.09945 | ||||||||
\(503\) | − 260862.i | − 1.03104i | −0.856878 | − | 0.515519i | \(-0.827599\pi\) | ||||
0.856878 | − | 0.515519i | \(-0.172401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 175521. | 0.688248 | ||||||||
\(506\) | 10457.9i | 0.0408455i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 215499. | 0.835059 | ||||||||
\(509\) | 60997.8i | 0.235439i | 0.993047 | + | 0.117720i | \(0.0375584\pi\) | ||||
−0.993047 | + | 0.117720i | \(0.962442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 217818. | 0.824455 | ||||||||
\(515\) | 198687.i | 0.749127i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 235618. | 0.881509 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 40425.4 | 0.149502 | ||||||||
\(521\) | 365690.i | 1.34722i | 0.739087 | + | 0.673609i | \(0.235257\pi\) | ||||
−0.739087 | + | 0.673609i | \(0.764743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −101715. | −0.371863 | −0.185931 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185931 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(524\) | − 87066.8i | − 0.317095i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −232422. | −0.840053 | ||||||||
\(527\) | − 800.135i | − 0.00288099i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279348. | 0.998237 | ||||||||
\(530\) | − 92895.7i | − 0.330707i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 311663.i | 1.09706i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 114810. | 0.401117 | ||||||||
\(536\) | 21543.9i | 0.0749884i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 326702. | 1.12872 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 288439. | 0.985508 | 0.492754 | − | 0.870169i | \(-0.335990\pi\) | ||||
0.492754 | + | 0.870169i | \(0.335990\pi\) | |||||||
\(542\) | 170241.i | 0.579516i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7012.71 | −0.0236967 | ||||||||
\(545\) | − 112051.i | − 0.377246i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 122429. | 0.409175 | 0.204587 | − | 0.978848i | \(-0.434415\pi\) | ||||
0.204587 | + | 0.978848i | \(0.434415\pi\) | |||||||
\(548\) | − 54450.5i | − 0.181318i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 218657. | 0.722833 | ||||||||
\(551\) | − 29917.7i | − 0.0985429i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 321457.i | − 1.04738i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 150725. | 0.487570 | ||||||||
\(557\) | 188468.i | 0.607473i | 0.952756 | + | 0.303736i | \(0.0982342\pi\) | ||||
−0.952756 | + | 0.303736i | \(0.901766\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −205701. | −0.658284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −182732. | −0.578550 | ||||||||
\(563\) | 274483.i | 0.865960i | 0.901403 | + | 0.432980i | \(0.142538\pi\) | ||||
−0.901403 | + | 0.432980i | \(0.857462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −140889. | −0.441346 | ||||||||
\(566\) | − 212820.i | − 0.664325i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 87023.0 | 0.269735 | ||||||||
\(569\) | 296571.i | 0.916018i | 0.888948 | + | 0.458009i | \(0.151437\pi\) | ||||
−0.888948 | + | 0.458009i | \(0.848563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34109.6 | 0.104618 | 0.0523088 | − | 0.998631i | \(-0.483342\pi\) | ||||
0.0523088 | + | 0.998631i | \(0.483342\pi\) | |||||||
\(572\) | 187745.i | 0.573820i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10315.5i | 0.0312000i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 304240. | 0.913828 | 0.456914 | − | 0.889511i | \(-0.348955\pi\) | ||||
0.456914 | + | 0.889511i | \(0.348955\pi\) | |||||||
\(578\) | 231988.i | 0.694401i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8441.87 | 0.0250948 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 431428. | 1.26932 | ||||||||
\(584\) | 81586.3i | 0.239217i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −176997. | −0.515431 | ||||||||
\(587\) | 200013.i | 0.580474i | 0.956955 | + | 0.290237i | \(0.0937341\pi\) | ||||
−0.956955 | + | 0.290237i | \(0.906266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7420.59 | 0.0213898 | ||||||||
\(590\) | 99425.3i | 0.285623i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −87108.0 | −0.248550 | ||||||||
\(593\) | − 472577.i | − 1.34389i | −0.740602 | − | 0.671944i | \(-0.765460\pi\) | ||||
0.740602 | − | 0.671944i | \(-0.234540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 122422.i | 0.344640i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8857.17 | −0.0247681 | ||||||||
\(599\) | − 254544.i | − 0.709429i | −0.934975 | − | 0.354714i | \(-0.884578\pi\) | ||||
0.934975 | − | 0.354714i | \(-0.115422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46871.2 | −0.129765 | −0.0648824 | − | 0.997893i | \(-0.520667\pi\) | ||||
−0.0648824 | + | 0.997893i | \(0.520667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 352200. | 0.965418 | ||||||||
\(605\) | − 165608.i | − 0.452451i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 299526. | 0.812937 | 0.406468 | − | 0.913665i | \(-0.366760\pi\) | ||||
0.406468 | + | 0.913665i | \(0.366760\pi\) | |||||||
\(608\) | − 65037.0i | − 0.175935i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 62161.6 | 0.167056 | ||||||||
\(611\) | 199552.i | 0.534533i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −192711. | −0.512845 | −0.256422 | − | 0.966565i | \(-0.582544\pi\) | ||||
−0.256422 | + | 0.966565i | \(0.582544\pi\) | |||||||
\(614\) | − 116792.i | − 0.309796i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 470863.i | 1.23687i | 0.785835 | + | 0.618436i | \(0.212233\pi\) | ||||
−0.785835 | + | 0.618436i | \(0.787767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 518245. | 1.35255 | 0.676276 | − | 0.736648i | \(-0.263593\pi\) | ||||
0.676276 | + | 0.736648i | \(0.263593\pi\) | |||||||
\(620\) | 2093.86i | 0.00544710i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −52235.9 | −0.135017 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 115312. | 0.295198 | ||||||||
\(626\) | 198441.i | 0.506386i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 360621. | 0.914390 | ||||||||
\(629\) | − 52727.7i | − 0.133272i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −264043. | −0.663157 | −0.331578 | − | 0.943428i | \(-0.607581\pi\) | ||||
−0.331578 | + | 0.943428i | \(0.607581\pi\) | |||||||
\(632\) | 154753.i | 0.387440i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −101930. | −0.253584 | ||||||||
\(635\) | − 341358.i | − 0.846570i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 39206.0i | 0.0963188i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18351.5 | 0.0448034 | ||||||||
\(641\) | 757333.i | 1.84319i | 0.388149 | + | 0.921597i | \(0.373115\pi\) | ||||
−0.388149 | + | 0.921597i | \(0.626885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −317514. | −0.767965 | −0.383982 | − | 0.923340i | \(-0.625448\pi\) | ||||
−0.383982 | + | 0.923340i | \(0.625448\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39367.8 | 0.0943358 | ||||||||
\(647\) | − 41488.0i | − 0.0991092i | −0.998771 | − | 0.0495546i | \(-0.984220\pi\) | ||||
0.998771 | − | 0.0495546i | \(-0.0157802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −461754. | −1.09628 | ||||||||
\(650\) | 185188.i | 0.438314i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 398373. | 0.937119 | ||||||||
\(653\) | − 226789.i | − 0.531857i | −0.963993 | − | 0.265928i | \(-0.914321\pi\) | ||||
0.963993 | − | 0.265928i | \(-0.0856785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −137917. | −0.321467 | ||||||||
\(656\) | 141482.i | 0.328772i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 348934.i | − 0.803474i | −0.915755 | − | 0.401737i | \(-0.868407\pi\) | ||||
0.915755 | − | 0.401737i | \(-0.131593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −739225. | −1.69190 | −0.845948 | − | 0.533266i | \(-0.820964\pi\) | ||||
−0.845948 | + | 0.533266i | \(0.820964\pi\) | |||||||
\(662\) | 91866.7i | 0.209624i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −213790. | −0.484898 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1849.61 | −0.00415746 | ||||||||
\(668\) | − 159029.i | − 0.356388i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 34126.3 | 0.0760221 | ||||||||
\(671\) | 288693.i | 0.641196i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4304.77 | −0.00950429 | −0.00475214 | − | 0.999989i | \(-0.501513\pi\) | ||||
−0.00475214 | + | 0.999989i | \(0.501513\pi\) | |||||||
\(674\) | − 443670.i | − 0.976652i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 69480.8 | 0.152045 | ||||||||
\(677\) | − 392165.i | − 0.855641i | −0.903864 | − | 0.427820i | \(-0.859282\pi\) | ||||
0.903864 | − | 0.427820i | \(-0.140718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11108.4i | 0.0240234i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9724.38 | −0.0209071 | ||||||||
\(683\) | − 881336.i | − 1.88930i | −0.328085 | − | 0.944648i | \(-0.606403\pi\) | ||||
0.328085 | − | 0.944648i | \(-0.393597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −86251.8 | −0.183817 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −93380.0 | −0.197277 | ||||||||
\(689\) | 365391.i | 0.769696i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −244166. | −0.511364 | −0.255682 | − | 0.966761i | \(-0.582300\pi\) | ||||
−0.255682 | + | 0.966761i | \(0.582300\pi\) | |||||||
\(692\) | − 22401.1i | − 0.0467797i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −275932. | −0.572905 | ||||||||
\(695\) | − 238755.i | − 0.494291i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −85641.2 | −0.176286 | ||||||||
\(698\) | − 238477.i | − 0.489480i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 651477.i | − 1.32575i | −0.748728 | − | 0.662877i | \(-0.769335\pi\) | ||||
0.748728 | − | 0.662877i | \(-0.230665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 489005. | 0.989471 | ||||||||
\(704\) | 85228.4i | 0.171965i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −455473. | −0.913805 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −509544. | −1.01365 | −0.506827 | − | 0.862048i | \(-0.669182\pi\) | ||||
−0.506827 | + | 0.862048i | \(0.669182\pi\) | |||||||
\(710\) | − 137848.i | − 0.273453i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 308981. | 0.609498 | ||||||||
\(713\) | − 458.764i | 0 0.000902422i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 297395. | 0.581730 | ||||||||
\(716\) | 311544.i | 0.607705i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 351133. | 0.681118 | ||||||||
\(719\) | 449003.i | 0.868544i | 0.900782 | + | 0.434272i | \(0.142994\pi\) | ||||
−0.900782 | + | 0.434272i | \(0.857006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 3499.73i | − 0.00671367i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −362509. | −0.691578 | ||||||||
\(725\) | 38672.0i | 0.0735734i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −154130. | −0.291620 | −0.145810 | − | 0.989313i | \(-0.546579\pi\) | ||||
−0.145810 | + | 0.989313i | \(0.546579\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 129236. | 0.242514 | ||||||||
\(731\) | − 56524.2i | − 0.105779i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 807161. | 1.50228 | 0.751142 | − | 0.660141i | \(-0.229503\pi\) | ||||
0.751142 | + | 0.660141i | \(0.229503\pi\) | |||||||
\(734\) | 267239.i | 0.496030i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4020.79 | −0.00742259 | ||||||||
\(737\) | 158490.i | 0.291788i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 127146. | 0.232816 | 0.116408 | − | 0.993201i | \(-0.462862\pi\) | ||||
0.116408 | + | 0.993201i | \(0.462862\pi\) | |||||||
\(740\) | 137982.i | 0.251977i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 930586.i | − 1.68569i | −0.538153 | − | 0.842847i | \(-0.680878\pi\) | ||||
0.538153 | − | 0.842847i | \(-0.319122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 193921. | 0.349391 | ||||||||
\(746\) | − 701940.i | − 1.26131i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −51590.0 | −0.0922066 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 353228. | 0.626289 | 0.313145 | − | 0.949705i | \(-0.398618\pi\) | ||||
0.313145 | + | 0.949705i | \(0.398618\pi\) | |||||||
\(752\) | 90588.6i | 0.160191i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33204.8 | −0.0584062 | ||||||||
\(755\) | − 557898.i | − 0.978726i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 258673. | 0.451398 | 0.225699 | − | 0.974197i | \(-0.427533\pi\) | ||||
0.225699 | + | 0.974197i | \(0.427533\pi\) | |||||||
\(758\) | − 47362.1i | − 0.0824313i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −103021. | −0.178361 | ||||||||
\(761\) | − 44043.2i | − 0.0760518i | −0.999277 | − | 0.0380259i | \(-0.987893\pi\) | ||||
0.999277 | − | 0.0380259i | \(-0.0121069\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 113115.i | 0.193791i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 368887. | 0.628689 | ||||||||
\(767\) | − 391074.i | − 0.664766i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 438155. | 0.740927 | 0.370463 | − | 0.928847i | \(-0.379199\pi\) | ||||
0.370463 | + | 0.928847i | \(0.379199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 147845. | 0.248069 | ||||||||
\(773\) | 759856.i | 1.27166i | 0.771827 | + | 0.635832i | \(0.219343\pi\) | ||||
−0.771827 | + | 0.635832i | \(0.780657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9591.94 | −0.0159699 | ||||||||
\(776\) | − 234430.i | − 0.389305i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −128371. | −0.212083 | ||||||||
\(779\) | − 794251.i | − 1.30883i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 640197. | 1.04957 | ||||||||
\(782\) | − 2433.84i | − 0.00397996i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 571238.i | − 0.926995i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −865390. | −1.39721 | −0.698606 | − | 0.715507i | \(-0.746196\pi\) | ||||
−0.698606 | + | 0.715507i | \(0.746196\pi\) | |||||||
\(788\) | 236588.i | 0.381014i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 245135. | 0.392781 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −244503. | −0.388811 | ||||||||
\(794\) | 166178.i | 0.263593i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 331665. | 0.523448 | ||||||||
\(797\) | 435436.i | 0.685501i | 0.939427 | + | 0.342750i | \(0.111358\pi\) | ||||
−0.939427 | + | 0.342750i | \(0.888642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54834.5 | −0.0858936 | ||||||||
\(800\) | 84067.6i | 0.131356i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −761920. | −1.18457 | ||||||||
\(803\) | 600201.i | 0.930819i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 8235.90i | − 0.0126777i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −313406. | −0.480047 | ||||||||
\(809\) | − 593479.i | − 0.906794i | −0.891309 | − | 0.453397i | \(-0.850212\pi\) | ||||
0.891309 | − | 0.453397i | \(-0.149788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 95960.2 | 0.145898 | 0.0729490 | − | 0.997336i | \(-0.476759\pi\) | ||||
0.0729490 | + | 0.997336i | \(0.476759\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −640822. | −0.967138 | ||||||||
\(815\) | − 631039.i | − 0.950038i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 524215. | 0.785354 | ||||||||
\(818\) | 871293.i | 1.30214i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 224114. | 0.333304 | ||||||||
\(821\) | − 280951.i | − 0.416816i | −0.978042 | − | 0.208408i | \(-0.933172\pi\) | ||||
0.978042 | − | 0.208408i | \(-0.0668282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −579343. | −0.855335 | −0.427668 | − | 0.903936i | \(-0.640665\pi\) | ||||
−0.427668 | + | 0.903936i | \(0.640665\pi\) | |||||||
\(824\) | − 354772.i | − 0.522510i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 73153.5i | − 0.106961i | −0.998569 | − | 0.0534803i | \(-0.982969\pi\) | ||||
0.998569 | − | 0.0534803i | \(-0.0170314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.13687e6 | −1.65425 | −0.827125 | − | 0.562018i | \(-0.810025\pi\) | ||||
−0.827125 | + | 0.562018i | \(0.810025\pi\) | |||||||
\(830\) | 338651.i | 0.491583i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −72182.7 | −0.104277 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −251908. | −0.361300 | ||||||||
\(836\) | − 478454.i | − 0.684585i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −662929. | −0.944015 | ||||||||
\(839\) | 530489.i | 0.753620i | 0.926291 | + | 0.376810i | \(0.122979\pi\) | ||||
−0.926291 | + | 0.376810i | \(0.877021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 700347. | 0.990196 | ||||||||
\(842\) | − 340091.i | − 0.479702i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −233322. | −0.327545 | ||||||||
\(845\) | − 110060.i | − 0.154141i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 165873.i | 0.230666i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −50887.3 | −0.0704323 | ||||||||
\(851\) | − 30231.8i | − 0.0417451i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 160401. | 0.220450 | 0.110225 | − | 0.993907i | \(-0.464843\pi\) | ||||
0.110225 | + | 0.993907i | \(0.464843\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −205002. | −0.279776 | ||||||||
\(857\) | − 566167.i | − 0.770873i | −0.922734 | − | 0.385436i | \(-0.874051\pi\) | ||||
0.922734 | − | 0.385436i | \(-0.125949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 993543. | 1.34648 | 0.673241 | − | 0.739424i | \(-0.264902\pi\) | ||||
0.673241 | + | 0.739424i | \(0.264902\pi\) | |||||||
\(860\) | 147918.i | 0.199997i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −650368. | −0.875275 | ||||||||
\(863\) | − 341066.i | − 0.457949i | −0.973432 | − | 0.228974i | \(-0.926463\pi\) | ||||
0.973432 | − | 0.228974i | \(-0.0735372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35484.3 | −0.0474246 | ||||||||
\(866\) | − 840094.i | − 1.12019i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.13846e6i | 1.50757i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −134231. | −0.176936 | ||||||||
\(872\) | 200077.i | 0.263126i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22571.8 | 0.0295491 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.40566e6 | −1.82760 | −0.913798 | − | 0.406169i | \(-0.866864\pi\) | ||||
−0.913798 | + | 0.406169i | \(0.866864\pi\) | |||||||
\(878\) | − 796123.i | − 1.03274i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 135005. | 0.174335 | ||||||||
\(881\) | − 1.09152e6i | − 1.40631i | −0.711036 | − | 0.703155i | \(-0.751774\pi\) | ||||
0.711036 | − | 0.703155i | \(-0.248226\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 60422.5 | 0.0774957 | 0.0387478 | − | 0.999249i | \(-0.487663\pi\) | ||||
0.0387478 | + | 0.999249i | \(0.487663\pi\) | |||||||
\(884\) | − 43693.2i | − 0.0559126i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −941359. | −1.19919 | ||||||||
\(887\) | 362657.i | 0.460945i | 0.973079 | + | 0.230472i | \(0.0740271\pi\) | ||||
−0.973079 | + | 0.230472i | \(0.925973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 489438.i | − 0.617900i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 146883. | 0.184604 | ||||||||
\(893\) | − 508545.i | − 0.637714i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 493498. | 0.616083 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37486.6 | −0.0464861 | ||||||||
\(899\) | − 1719.87i | − 0.00212802i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −100405. | −0.123682 | ||||||||
\(902\) | 1.04083e6i | 1.27929i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 251568. | 0.307835 | ||||||||
\(905\) | 574228.i | 0.701112i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24950.6 | −0.0303296 | −0.0151648 | − | 0.999885i | \(-0.504827\pi\) | ||||
−0.0151648 | + | 0.999885i | \(0.504827\pi\) | |||||||
\(908\) | 472942.i | 0.573635i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 657747.i | 0.792542i | 0.918134 | + | 0.396271i | \(0.129696\pi\) | ||||
−0.918134 | + | 0.396271i | \(0.870304\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.57277e6 | −1.88679 | ||||||||
\(914\) | 755464.i | 0.904318i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −766361. | −0.913361 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 565588. | 0.669683 | 0.334842 | − | 0.942274i | \(-0.391317\pi\) | ||||
0.334842 | + | 0.942274i | \(0.391317\pi\) | |||||||
\(920\) | 6369.09i | 0.00752492i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9590.25 | 0.0112815 | ||||||||
\(923\) | 542204.i | 0.636442i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −632094. | −0.738751 | ||||||||
\(926\) | − 289857.i | − 0.338035i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15073.6 | −0.0175034 | ||||||||
\(929\) | − 338139.i | − 0.391800i | −0.980624 | − | 0.195900i | \(-0.937237\pi\) | ||||
0.980624 | − | 0.195900i | \(-0.0627628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 269688.i | 0.310478i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −176819. | −0.202691 | ||||||||
\(935\) | 81720.5i | 0.0934777i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 600379. | 0.683827 | 0.341914 | − | 0.939731i | \(-0.388925\pi\) | ||||
0.341914 | + | 0.939731i | \(0.388925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 143496. | 0.162399 | ||||||||
\(941\) | − 84374.7i | − 0.0952869i | −0.998864 | − | 0.0476434i | \(-0.984829\pi\) | ||||
0.998864 | − | 0.0476434i | \(-0.0151711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49103.1 | −0.0552186 | ||||||||
\(944\) | − 177532.i | − 0.199219i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −686963. | −0.767628 | ||||||||
\(947\) | − 1.71415e6i | − 1.91138i | −0.294369 | − | 0.955692i | \(-0.595109\pi\) | ||||
0.294369 | − | 0.955692i | \(-0.404891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −508330. | −0.564434 | ||||||||
\(950\) | − 471937.i | − 0.522922i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 928678.i | − 1.02254i | −0.859421 | − | 0.511269i | \(-0.829176\pi\) | ||||
0.859421 | − | 0.511269i | \(-0.170824\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 179179. | 0.196462 | ||||||||
\(956\) | 41092.7i | 0.0449623i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 700090. | 0.762821 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −923094. | −0.999538 | ||||||||
\(962\) | − 542733.i | − 0.586457i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 369278. | 0.397374 | ||||||||
\(965\) | − 234193.i | − 0.251489i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −729610. | −0.780257 | −0.390129 | − | 0.920760i | \(-0.627569\pi\) | ||||
−0.390129 | + | 0.920760i | \(0.627569\pi\) | |||||||
\(968\) | 295706.i | 0.315580i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −371347. | −0.394672 | ||||||||
\(971\) | 1.56670e6i | 1.66168i | 0.556511 | + | 0.830841i | \(0.312140\pi\) | ||||
−0.556511 | + | 0.830841i | \(0.687860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 730760.i | 0.770294i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −110995. | −0.116520 | ||||||||
\(977\) | − 239837.i | − 0.251263i | −0.992077 | − | 0.125631i | \(-0.959904\pi\) | ||||
0.992077 | − | 0.125631i | \(-0.0400956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.27306e6 | 2.37163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −678250. | −0.703342 | ||||||||
\(983\) | − 1.42682e6i | − 1.47660i | −0.674472 | − | 0.738300i | \(-0.735629\pi\) | ||||
0.674472 | − | 0.738300i | \(-0.264371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 374765. | 0.386266 | ||||||||
\(986\) | − 9124.28i | − 0.00938523i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 405218. | 0.415121 | ||||||||
\(989\) | − 32408.6i | − 0.0331335i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.57484e6 | 1.60357 | 0.801786 | − | 0.597612i | \(-0.203884\pi\) | ||||
0.801786 | + | 0.597612i | \(0.203884\pi\) | |||||||
\(992\) | − 3738.76i | − 0.00379931i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 525370.i | − 0.530664i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −612478. | −0.616169 | −0.308084 | − | 0.951359i | \(-0.599688\pi\) | ||||
−0.308084 | + | 0.951359i | \(0.599688\pi\) | |||||||
\(998\) | 93376.7i | 0.0937514i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.5.b.j.197.7 | yes | 8 | |
3.2 | odd | 2 | inner | 882.5.b.j.197.2 | ✓ | 8 | |
7.6 | odd | 2 | inner | 882.5.b.j.197.6 | yes | 8 | |
21.20 | even | 2 | inner | 882.5.b.j.197.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.5.b.j.197.2 | ✓ | 8 | 3.2 | odd | 2 | inner | |
882.5.b.j.197.3 | yes | 8 | 21.20 | even | 2 | inner | |
882.5.b.j.197.6 | yes | 8 | 7.6 | odd | 2 | inner | |
882.5.b.j.197.7 | yes | 8 | 1.1 | even | 1 | trivial |