Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("384.319");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.5.b.b.319.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 12.0000i | − 0.480000i | −0.970773 | − | 0.240000i | \(-0.922853\pi\) | ||||
0.970773 | − | 0.240000i | \(-0.0771474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 62.3538i | − 1.27253i | −0.771472 | − | 0.636264i | \(-0.780479\pi\) | ||||
0.771472 | − | 0.636264i | \(-0.219521\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.7846 | −0.171774 | −0.0858868 | − | 0.996305i | \(-0.527372\pi\) | ||||
−0.0858868 | + | 0.996305i | \(0.527372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 264.000i | − 1.56213i | −0.624450 | − | 0.781065i | \(-0.714677\pi\) | ||||
0.624450 | − | 0.781065i | \(-0.285323\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 62.3538i | 0.277128i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 110.000 | 0.380623 | 0.190311 | − | 0.981724i | \(-0.439050\pi\) | ||||
0.190311 | + | 0.981724i | \(0.439050\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −103.923 | −0.287875 | −0.143938 | − | 0.989587i | \(-0.545977\pi\) | ||||
−0.143938 | + | 0.989587i | \(0.545977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 324.000i | 0.734694i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 124.708i | 0.235742i | 0.993029 | + | 0.117871i | \(0.0376070\pi\) | ||||
−0.993029 | + | 0.117871i | \(0.962393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 481.000 | 0.769600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 228.000i | 0.271106i | 0.990770 | + | 0.135553i | \(0.0432811\pi\) | ||||
−0.990770 | + | 0.135553i | \(0.956719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1434.14i | − 1.49234i | −0.665756 | − | 0.746170i | \(-0.731891\pi\) | ||||
0.665756 | − | 0.746170i | \(-0.268109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 108.000 | 0.0991736 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −748.246 | −0.610813 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1392.00i | 1.01680i | 0.861121 | + | 0.508400i | \(0.169763\pi\) | ||||
−0.861121 | + | 0.508400i | \(0.830237\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1371.78i | 0.901896i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1282.00 | 0.762641 | 0.381321 | − | 0.924443i | \(-0.375469\pi\) | ||||
0.381321 | + | 0.924443i | \(0.375469\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2514.94 | −1.36016 | −0.680081 | − | 0.733137i | \(-0.738055\pi\) | ||||
−0.680081 | + | 0.733137i | \(0.738055\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 324.000i | − 0.160000i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2618.86i | 1.18554i | 0.805371 | + | 0.592771i | \(0.201966\pi\) | ||||
−0.805371 | + | 0.592771i | \(0.798034\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1487.00 | −0.619325 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −571.577 | −0.219753 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4500.00i | − 1.60199i | −0.598669 | − | 0.800997i | \(-0.704303\pi\) | ||||
0.598669 | − | 0.800997i | \(-0.295697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 249.415i | 0.0824513i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 540.000 | 0.166205 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6339.31 | −1.82112 | −0.910558 | − | 0.413381i | \(-0.864348\pi\) | ||||
−0.910558 | + | 0.413381i | \(0.864348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 960.000i | 0.257995i | 0.991645 | + | 0.128998i | \(0.0411759\pi\) | ||||
−0.991645 | + | 0.128998i | \(0.958824\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1683.55i | − 0.424176i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3168.00 | −0.749822 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3263.18 | −0.726929 | −0.363464 | − | 0.931608i | \(-0.618406\pi\) | ||||
−0.363464 | + | 0.931608i | \(0.618406\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 648.000i | − 0.136106i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 6110.68i | − 1.21220i | −0.795390 | − | 0.606098i | \(-0.792734\pi\) | ||||
0.795390 | − | 0.606098i | \(-0.207266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3170.00 | −0.594858 | −0.297429 | − | 0.954744i | \(-0.596129\pi\) | ||||
−0.297429 | + | 0.954744i | \(0.596129\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2499.35 | −0.444329 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1296.00i | 0.218587i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1558.85i | 0.249775i | 0.992171 | + | 0.124887i | \(0.0398570\pi\) | ||||
−0.992171 | + | 0.124887i | \(0.960143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4427.12 | −0.642636 | −0.321318 | − | 0.946971i | \(-0.604126\pi\) | ||||
−0.321318 | + | 0.946971i | \(0.604126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1320.00i | − 0.182699i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1184.72i | − 0.156523i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1550.00 | 0.195682 | 0.0978412 | − | 0.995202i | \(-0.468806\pi\) | ||||
0.0978412 | + | 0.995202i | \(0.468806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16461.4 | −1.98785 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7452.00i | 0.861602i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1247.08i | 0.138180i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8018.00 | −0.852163 | −0.426081 | − | 0.904685i | \(-0.640106\pi\) | ||||
−0.426081 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −561.184 | −0.0572579 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15516.0i | 1.52103i | 0.649322 | + | 0.760514i | \(0.275053\pi\) | ||||
−0.649322 | + | 0.760514i | \(0.724947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11535.5i | 1.08733i | 0.839303 | + | 0.543664i | \(0.182963\pi\) | ||||
−0.839303 | + | 0.543664i | \(0.817037\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3888.00 | 0.352653 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19059.5 | −1.66473 | −0.832365 | − | 0.554228i | \(-0.813013\pi\) | ||||
−0.832365 | + | 0.554228i | \(0.813013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 10968.0i | − 0.923155i | −0.887100 | − | 0.461577i | \(-0.847284\pi\) | ||||
0.887100 | − | 0.461577i | \(-0.152716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 7233.04i | − 0.587050i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10786.0 | 0.844702 | 0.422351 | − | 0.906432i | \(-0.361205\pi\) | ||||
0.422351 | + | 0.906432i | \(0.361205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1496.49 | 0.113156 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 7128.00i | − 0.520710i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 6858.92i | − 0.484353i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14209.0 | −0.970494 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6661.47 | −0.440311 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 13272.0i | − 0.849408i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6422.44i | 0.398192i | 0.979980 | + | 0.199096i | \(0.0638006\pi\) | ||||
−0.979980 | + | 0.199096i | \(0.936199\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13068.0 | 0.785289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16024.9 | 0.933800 | 0.466900 | − | 0.884310i | \(-0.345371\pi\) | ||||
0.466900 | + | 0.884310i | \(0.345371\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6480.00i | 0.366329i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1683.55i | 0.0923760i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17794.0 | 0.948053 | 0.474026 | − | 0.880511i | \(-0.342800\pi\) | ||||
0.474026 | + | 0.880511i | \(0.342800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17313.6 | −0.896102 | −0.448051 | − | 0.894008i | \(-0.647882\pi\) | ||||
−0.448051 | + | 0.894008i | \(0.647882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 13608.0i | − 0.684473i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5487.14i | 0.268333i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2736.00 | 0.130131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7726.68 | 0.357568 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 13596.0i | − 0.612405i | −0.951966 | − | 0.306202i | \(-0.900942\pi\) | ||||
0.951966 | − | 0.306202i | \(-0.0990584\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 20763.8i | − 0.910654i | −0.890324 | − | 0.455327i | \(-0.849522\pi\) | ||||
0.890324 | − | 0.455327i | \(-0.150478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2970.00 | 0.126874 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17209.7 | −0.716323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12432.0i | 0.504361i | 0.967680 | + | 0.252181i | \(0.0811477\pi\) | ||||
−0.967680 | + | 0.252181i | \(0.918852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23382.7i | 0.924911i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7776.00 | 0.299988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 43710.0 | 1.64515 | 0.822576 | − | 0.568655i | \(-0.192536\pi\) | ||||
0.822576 | + | 0.568655i | \(0.192536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1296.00i | − 0.0476033i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 43148.8i | 1.54716i | 0.633696 | + | 0.773582i | \(0.281537\pi\) | ||||
−0.633696 | + | 0.773582i | \(0.718463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −41135.0 | −1.44025 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2805.92 | −0.0959585 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 53628.0i | 1.79184i | 0.444215 | + | 0.895920i | \(0.353483\pi\) | ||||
−0.444215 | + | 0.895920i | \(0.646517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 29992.2i | − 0.979337i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32940.0 | 1.05142 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 40717.1 | 1.27078 | 0.635390 | − | 0.772192i | \(-0.280839\pi\) | ||||
0.635390 | + | 0.772192i | \(0.280839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8568.00i | 0.261530i | 0.991413 | + | 0.130765i | \(0.0417434\pi\) | ||||
−0.991413 | + | 0.130765i | \(0.958257\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 4988.31i | − 0.148954i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16704.0 | 0.488064 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2286.31 | −0.0653810 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8748.00i | 0.244898i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 67092.7i | − 1.83911i | −0.392957 | − | 0.919557i | \(-0.628548\pi\) | ||||
0.392957 | − | 0.919557i | \(-0.371452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −59234.0 | −1.59022 | −0.795109 | − | 0.606467i | \(-0.792586\pi\) | ||||
−0.795109 | + | 0.606467i | \(0.792586\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16461.4 | 0.432910 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 24996.0i | − 0.644077i | −0.946727 | − | 0.322039i | \(-0.895632\pi\) | ||||
0.946727 | − | 0.322039i | \(-0.104368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 28371.0i | − 0.716421i | −0.933641 | − | 0.358211i | \(-0.883387\pi\) | ||||
0.933641 | − | 0.358211i | \(-0.116613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16956.0 | 0.419693 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14216.7 | 0.344990 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 15384.0i | − 0.366068i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3367.11i | 0.0785808i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2160.00 | 0.0494494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 54684.3 | 1.22828 | 0.614141 | − | 0.789197i | \(-0.289503\pi\) | ||||
0.614141 | + | 0.789197i | \(0.289503\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31752.0i | 0.699861i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30179.3i | 0.652877i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −89424.0 | −1.89904 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16471.8 | 0.343442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 29040.0i | − 0.594582i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 38098.2i | 0.766116i | 0.923724 | + | 0.383058i | \(0.125129\pi\) | ||||
−0.923724 | + | 0.383058i | \(0.874871\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12987.0 | 0.256533 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 92678.6 | 1.79857 | 0.899286 | − | 0.437362i | \(-0.144087\pi\) | ||||
0.899286 | + | 0.437362i | \(0.144087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 66072.0i | − 1.25993i | −0.776623 | − | 0.629965i | \(-0.783069\pi\) | ||||
0.776623 | − | 0.629965i | \(-0.216931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 6734.21i | − 0.126201i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 72686.0 | 1.33887 | 0.669436 | − | 0.742870i | \(-0.266536\pi\) | ||||
0.669436 | + | 0.742870i | \(0.266536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31426.3 | 0.569060 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8100.00i | − 0.144208i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 83304.7i | 1.45839i | 0.684306 | + | 0.729195i | \(0.260105\pi\) | ||||
−0.684306 | + | 0.729195i | \(0.739895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −44738.0 | −0.770269 | −0.385135 | − | 0.922860i | \(-0.625845\pi\) | ||||
−0.385135 | + | 0.922860i | \(0.625845\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17844.0i | 0.297276i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27435.7i | 0.449699i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23004.0 | 0.371026 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20181.9 | 0.320342 | 0.160171 | − | 0.987089i | \(-0.448795\pi\) | ||||
0.160171 | + | 0.987089i | \(0.448795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2592.00i | − 0.0404943i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6858.92i | 0.105481i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −55166.0 | −0.835228 | −0.417614 | − | 0.908624i | \(-0.637134\pi\) | ||||
−0.417614 | + | 0.908624i | \(0.637134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 86796.5 | 1.29391 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6156.00i | 0.0903686i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 113733.i | − 1.64428i | −0.569283 | − | 0.822141i | \(-0.692779\pi\) | ||||
0.569283 | − | 0.822141i | \(-0.307221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −54000.0 | −0.768957 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8054.04 | −0.112977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 92460.0i | − 1.27776i | −0.769306 | − | 0.638880i | \(-0.779398\pi\) | ||||
0.769306 | − | 0.638880i | \(-0.220602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 50569.0i | 0.688566i | 0.938866 | + | 0.344283i | \(0.111878\pi\) | ||||
−0.938866 | + | 0.344283i | \(0.888122\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 85536.0 | 1.14769 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9997.40 | −0.132197 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 125208.i | 1.63182i | 0.578178 | + | 0.815911i | \(0.303764\pi\) | ||||
−0.578178 | + | 0.815911i | \(0.696236\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 38721.7i | − 0.497446i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 130670. | 1.65487 | 0.827434 | − | 0.561563i | \(-0.189800\pi\) | ||||
0.827434 | + | 0.561563i | \(0.189800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12408.4 | −0.154933 | −0.0774664 | − | 0.996995i | \(-0.524683\pi\) | ||||
−0.0774664 | + | 0.996995i | \(0.524683\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 6480.00i | − 0.0797784i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 79937.6i | − 0.970482i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −71421.0 | −0.855126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41662.8 | 0.491996 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 60204.0i | 0.701278i | 0.936511 | + | 0.350639i | \(0.114036\pi\) | ||||
−0.936511 | + | 0.350639i | \(0.885964\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 76071.7i | 0.874136i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2916.00 | 0.0330579 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32922.8 | 0.368260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 156816.i | 1.73084i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 80623.5i | − 0.878166i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11520.0 | 0.123838 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −88563.2 | −0.939673 | −0.469836 | − | 0.882754i | \(-0.655687\pi\) | ||||
−0.469836 | + | 0.882754i | \(0.655687\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 59940.0i | − 0.627769i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 78067.0i | 0.807136i | 0.914950 | + | 0.403568i | \(0.132230\pi\) | ||||
−0.914950 | + | 0.403568i | \(0.867770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −76366.0 | −0.779491 | −0.389746 | − | 0.920923i | \(-0.627437\pi\) | ||||
−0.389746 | + | 0.920923i | \(0.627437\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20202.6 | −0.203604 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13836.0i | − 0.137687i | −0.997627 | − | 0.0688434i | \(-0.978069\pi\) | ||||
0.997627 | − | 0.0688434i | \(-0.0219309\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4738.89i | − 0.0465688i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 99036.0 | 0.961132 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11431.5 | −0.109572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 126984.i | − 1.20222i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 56991.4i | 0.532984i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 163296. | 1.50863 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 44458.3 | 0.405786 | 0.202893 | − | 0.979201i | \(-0.434966\pi\) | ||||
0.202893 | + | 0.979201i | \(0.434966\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 37584.0i | 0.338934i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39158.2i | 0.348926i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6386.00 | 0.0562301 | 0.0281151 | − | 0.999605i | \(-0.491050\pi\) | ||||
0.0281151 | + | 0.999605i | \(0.491050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −56045.7 | −0.487689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29808.0i | 0.256345i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 56991.4i | − 0.484419i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7776.00 | −0.0653308 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −54642.7 | −0.453809 | −0.226905 | − | 0.973917i | \(-0.572861\pi\) | ||||
−0.226905 | + | 0.973917i | \(0.572861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 96192.0i | − 0.789747i | −0.918735 | − | 0.394874i | \(-0.870788\pi\) | ||||
0.918735 | − | 0.394874i | \(-0.129212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37038.2i | 0.300632i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −73502.0 | −0.589861 | −0.294931 | − | 0.955519i | \(-0.595297\pi\) | ||||
−0.294931 | + | 0.955519i | \(0.595297\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −73328.1 | −0.581854 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35640.0i | 0.279641i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 127327.i | − 0.987939i | −0.869479 | − | 0.493969i | \(-0.835546\pi\) | ||||
0.869479 | − | 0.493969i | \(-0.164454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −119521. | −0.917128 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 73832.1 | 0.560315 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38040.0i | 0.285532i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 227404.i | − 1.68837i | −0.536055 | − | 0.844183i | \(-0.680086\pi\) | ||||
0.536055 | − | 0.844183i | \(-0.319914\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 34614.0 | 0.254214 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −280592. | −2.03858 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 196704.i | − 1.41382i | −0.707301 | − | 0.706912i | \(-0.750088\pi\) | ||||
0.707301 | − | 0.706912i | \(-0.249912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 68963.3i | 0.490406i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 60192.0 | 0.423503 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −53395.7 | −0.371730 | −0.185865 | − | 0.982575i | \(-0.559509\pi\) | ||||
−0.185865 | + | 0.982575i | \(0.559509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 33372.0i | − 0.229896i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 193796.i | 1.32113i | 0.750767 | + | 0.660567i | \(0.229684\pi\) | ||||
−0.750767 | + | 0.660567i | \(0.770316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15552.0 | 0.104922 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −67903.3 | −0.453387 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 109404.i | − 0.722993i | −0.932373 | − | 0.361496i | \(-0.882266\pi\) | ||||
0.932373 | − | 0.361496i | \(-0.117734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13717.8i | 0.0897289i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −83268.0 | −0.539129 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18706.1 | 0.119892 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 113952.i | − 0.723004i | −0.932371 | − | 0.361502i | \(-0.882264\pi\) | ||||
0.932371 | − | 0.361502i | \(-0.117736\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 33671.1i | − 0.211500i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −112594. | −0.700207 | −0.350104 | − | 0.936711i | \(-0.613854\pi\) | ||||
−0.350104 | + | 0.936711i | \(0.613854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −378612. | −2.33123 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 8748.00i | − 0.0533333i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 28932.2i | − 0.174660i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −187870. | −1.12308 | −0.561540 | − | 0.827449i | \(-0.689791\pi\) | ||||
−0.561540 | + | 0.827449i | \(0.689791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −92460.3 | −0.547358 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 395280.i | 2.31742i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 53125.5i | 0.308465i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 89964.0 | 0.517365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −97957.9 | −0.557971 | −0.278985 | − | 0.960295i | \(-0.589998\pi\) | ||||
−0.278985 | + | 0.960295i | \(0.589998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 307992.i | 1.73770i | 0.495074 | + | 0.868851i | \(0.335141\pi\) | ||||
−0.495074 | + | 0.868851i | \(0.664859\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 70709.2i | 0.395180i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 52910.0 | 0.292927 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 59859.7 | 0.328306 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 28512.0i | − 0.154922i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 93655.5i | 0.504172i | 0.967705 | + | 0.252086i | \(0.0811165\pi\) | ||||
−0.967705 | + | 0.252086i | \(0.918883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 54574.0 | 0.291078 | 0.145539 | − | 0.989352i | \(-0.453508\pi\) | ||||
0.145539 | + | 0.989352i | \(0.453508\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14216.7 | −0.0751311 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 12960.0i | − 0.0678644i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 41215.9i | 0.213863i | 0.994266 | + | 0.106931i | \(0.0341025\pi\) | ||||
−0.994266 | + | 0.106931i | \(0.965897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40149.0 | −0.206442 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −61210.7 | −0.311903 | −0.155952 | − | 0.987765i | \(-0.549844\pi\) | ||||
−0.155952 | + | 0.987765i | \(0.549844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 18600.0i | − 0.0939275i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 70646.9i | 0.353572i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −128914. | −0.639451 | −0.319726 | − | 0.947510i | \(-0.603591\pi\) | ||||
−0.319726 | + | 0.947510i | \(0.603591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26645.9 | −0.131002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 107892.i | 0.525766i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 197537.i | 0.954169i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −160030. | −0.766247 | −0.383124 | − | 0.923697i | \(-0.625152\pi\) | ||||
−0.383124 | + | 0.923697i | \(0.625152\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15432.6 | −0.0732509 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 299988.i | − 1.41157i | −0.708427 | − | 0.705784i | \(-0.750595\pi\) | ||||
0.708427 | − | 0.705784i | \(-0.249405\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 60670.3i | − 0.283018i | −0.989937 | − | 0.141509i | \(-0.954805\pi\) | ||||
0.989937 | − | 0.141509i | \(-0.0451954\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 89424.0 | 0.413569 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −351031. | −1.60958 | −0.804789 | − | 0.593561i | \(-0.797722\pi\) | ||||
−0.804789 | + | 0.593561i | \(0.797722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 203472.i | 0.925037i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 64598.6i | − 0.291193i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52272.0 | 0.233640 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −49987.0 | −0.221549 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 121500.i | − 0.533998i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 348059.i | − 1.51699i | −0.651680 | − | 0.758494i | \(-0.725936\pi\) | ||||
0.651680 | − | 0.758494i | \(-0.274064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 367488. | 1.58837 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −40405.3 | −0.173198 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 96216.0i | 0.409038i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 247732.i | − 1.04454i | −0.852781 | − | 0.522268i | \(-0.825086\pi\) | ||||
0.852781 | − | 0.522268i | \(-0.174914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −227124. | −0.949829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 243409. | 1.00965 | 0.504827 | − | 0.863220i | \(-0.331556\pi\) | ||||
0.504827 | + | 0.863220i | \(0.331556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25080.0i | 0.103189i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6734.21i | 0.0274838i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −381024. | −1.54255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −341055. | −1.36969 | −0.684846 | − | 0.728688i | \(-0.740131\pi\) | ||||
−0.684846 | + | 0.728688i | \(0.740131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 224208.i | − 0.893255i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 44021.8i | − 0.173993i | −0.996209 | − | 0.0869965i | \(-0.972273\pi\) | ||||
0.996209 | − | 0.0869965i | \(-0.0277269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 186192. | 0.730093 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 213744. | 0.831529 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 166428.i | − 0.642378i | −0.947015 | − | 0.321189i | \(-0.895917\pi\) | ||||
0.947015 | − | 0.321189i | \(-0.104083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 197662.i | 0.756973i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14580.0 | 0.0554017 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 138426. | 0.521917 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 54432.0i | − 0.203645i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 278659.i | − 1.03452i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 444130. | 1.63619 | 0.818097 | − | 0.575081i | \(-0.195029\pi\) | ||||
0.818097 | + | 0.575081i | \(0.195029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 175152. | 0.640341 | 0.320171 | − | 0.947360i | \(-0.396260\pi\) | ||||
0.320171 | + | 0.947360i | \(0.396260\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 155844.i | 0.565420i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 157755.i | − 0.568018i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 264289. | 0.944426 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −171161. | −0.607039 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 338448.i | − 1.19134i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 228714.i | 0.799070i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −211572. | −0.733685 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30906.7 | 0.106384 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 138360.i | − 0.472733i | −0.971664 | − | 0.236367i | \(-0.924043\pi\) | ||||
0.971664 | − | 0.236367i | \(-0.0759566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 44520.6i | − 0.150995i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −131616. | −0.443114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 341096. | 1.13999 | 0.569997 | − | 0.821647i | \(-0.306945\pi\) | ||||
0.569997 | + | 0.821647i | \(0.306945\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25920.0i | 0.0859984i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 23694.5i | − 0.0780447i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 97200.0 | 0.317845 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −86796.5 | −0.281784 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 61260.0i | 0.197454i | 0.995115 | + | 0.0987272i | \(0.0314771\pi\) | ||||
−0.995115 | + | 0.0987272i | \(0.968523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 663944.i | 2.12475i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11880.0 | 0.0377477 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −331577. | −1.04609 | −0.523043 | − | 0.852306i | \(-0.675203\pi\) | ||||
−0.523043 | + | 0.852306i | \(0.675203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 129432.i | − 0.405457i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 45455.9i | − 0.141392i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 137026. | 0.423232 | 0.211616 | − | 0.977353i | \(-0.432127\pi\) | ||||
0.211616 | + | 0.977353i | \(0.432127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 259122. | 0.794752 | 0.397376 | − | 0.917656i | \(-0.369921\pi\) | ||||
0.397376 | + | 0.917656i | \(0.369921\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 348624.i | 1.06181i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 59984.4i | 0.181427i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 276050. | 0.829156 | 0.414578 | − | 0.910014i | \(-0.363929\pi\) | ||||
0.414578 | + | 0.910014i | \(0.363929\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 307789. | 0.918112 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 276048.i | 0.817772i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 93530.7i | 0.275180i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −85536.0 | −0.249941 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 405944. | 1.17812 | 0.589061 | − | 0.808089i | \(-0.299498\pi\) | ||||
0.589061 | + | 0.808089i | \(0.299498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 149040.i | 0.429608i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 129883.i | 0.371858i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −430238. | −1.22349 | −0.611744 | − | 0.791056i | \(-0.709532\pi\) | ||||
−0.611744 | + | 0.791056i | \(0.709532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −82307.1 | −0.232489 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 147420.i | 0.413626i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 50007.8i | − 0.139375i | −0.997569 | − | 0.0696873i | \(-0.977800\pi\) | ||||
0.997569 | − | 0.0696873i | \(-0.0222002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 530110. | 1.46763 | 0.733816 | − | 0.679348i | \(-0.237738\pi\) | ||||
0.733816 | + | 0.679348i | \(0.237738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −88106.0 | −0.242310 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 170508.i | 0.465837i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 516851.i | − 1.40277i | −0.712780 | − | 0.701387i | \(-0.752564\pi\) | ||||
0.712780 | − | 0.701387i | \(-0.247436\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −73872.0 | −0.199180 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 691379. | 1.85197 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 411840.i | − 1.09599i | −0.836481 | − | 0.547996i | \(-0.815391\pi\) | ||||
0.836481 | − | 0.547996i | \(-0.184609\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 79937.6i | 0.211349i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −150610. | −0.395625 | −0.197812 | − | 0.980240i | \(-0.563384\pi\) | ||||
−0.197812 | + | 0.980240i | \(0.563384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 314492. | 0.820783 | 0.410391 | − | 0.911909i | \(-0.365392\pi\) | ||||
0.410391 | + | 0.911909i | \(0.365392\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 17496.0i | − 0.0453686i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 96648.4i | − 0.249011i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 141361. | 0.361884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11223.7 | −0.0285496 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 153120.i | 0.387018i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 381418.i | − 0.957950i | −0.877829 | − | 0.478975i | \(-0.841008\pi\) | ||||
0.877829 | − | 0.478975i | \(-0.158992\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −284148. | −0.709148 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 77069.3 | 0.191132 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 392568.i | 0.967467i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 164988.i | − 0.404065i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −264754. | −0.644357 | −0.322178 | − | 0.946679i | \(-0.604415\pi\) | ||||
−0.322178 | + | 0.946679i | \(0.604415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 655360. | 1.58510 | 0.792552 | − | 0.609805i | \(-0.208752\pi\) | ||||
0.792552 | + | 0.609805i | \(0.208752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 156816.i | − 0.376939i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 593733.i | 1.41835i | 0.705034 | + | 0.709174i | \(0.250932\pi\) | ||||
−0.705034 | + | 0.709174i | \(0.749068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 131760. | 0.312820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 464661. | 1.09641 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 72612.0i | − 0.170287i | −0.996369 | − | 0.0851436i | \(-0.972865\pi\) | ||||
0.996369 | − | 0.0851436i | \(-0.0271349\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 192299.i | − 0.448224i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −85590.0 | −0.198286 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 163429. | 0.376322 | 0.188161 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188161 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 360816.i | 0.825815i | 0.910773 | + | 0.412908i | \(0.135487\pi\) | ||||
−0.910773 | + | 0.412908i | \(0.864513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 150896.i | 0.343282i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 77760.0 | 0.175838 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28433.3 | −0.0639111 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 197964.i | − 0.442317i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 19953.2i | − 0.0443168i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 406702. | 0.897938 | 0.448969 | − | 0.893547i | \(-0.351791\pi\) | ||||
0.448969 | + | 0.893547i | \(0.351791\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −67482.4 | −0.148110 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 181548.i | − 0.396108i | −0.980191 | − | 0.198054i | \(-0.936538\pi\) | ||||
0.980191 | − | 0.198054i | \(-0.0634622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 499953.i | 1.08440i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −481572. | −1.03841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15567.7 | −0.0333720 | −0.0166860 | − | 0.999861i | \(-0.505312\pi\) | ||||
−0.0166860 | + | 0.999861i | \(0.505312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 213528.i | − 0.455065i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 343320.i | 0.727421i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.18800e6 | −2.50252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5674.20 | −0.0118836 | −0.00594181 | − | 0.999982i | \(-0.501891\pi\) | ||||
−0.00594181 | + | 0.999982i | \(0.501891\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 34992.0i | 0.0728622i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 207763.i | 0.430129i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 141020. | 0.290279 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −377688. | −0.772998 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 868188.i | − 1.76676i | −0.468657 | − | 0.883380i | \(-0.655262\pi\) | ||||
0.468657 | − | 0.883380i | \(-0.344738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 144661.i | − 0.292712i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −163296. | −0.328547 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 967482. | 1.93555 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47112.0i | 0.0937215i | 0.998901 | + | 0.0468607i | \(0.0149217\pi\) | ||||
−0.998901 | + | 0.0468607i | \(0.985078\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42088.8i | 0.0832583i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 178848. | 0.351807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 65845.6 | 0.128800 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 432864.i | − 0.842002i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 324365.i | − 0.627445i | −0.949515 | − | 0.313723i | \(-0.898424\pi\) | ||||
0.949515 | − | 0.313723i | \(-0.101576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 719280. | 1.38365 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 232465. | 0.444715 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 109668.i | 0.208643i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 544287.i | − 1.02981i | −0.857246 | − | 0.514907i | \(-0.827826\pi\) | ||||
0.857246 | − | 0.514907i | \(-0.172174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −276643. | −0.517708 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 455976.i | − 0.848661i | −0.905507 | − | 0.424330i | \(-0.860510\pi\) | ||||
0.905507 | − | 0.424330i | \(-0.139490\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 92720.1i | − 0.171632i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 67824.0 | 0.124867 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 684042. | 1.25255 | 0.626274 | − | 0.779603i | \(-0.284579\pi\) | ||||
0.626274 | + | 0.779603i | \(0.284579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 142560.i | − 0.259634i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 863476.i | − 1.56413i | −0.623198 | − | 0.782064i | \(-0.714167\pi\) | ||||
0.623198 | − | 0.782064i | \(-0.285833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −163152. | −0.293954 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −119532. | −0.214212 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.18843e6i | 2.11841i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 546905.i | − 0.969689i | −0.874600 | − | 0.484844i | \(-0.838876\pi\) | ||||
0.874600 | − | 0.484844i | \(-0.161124\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −104868. | −0.184949 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −249166. | −0.437114 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 359496.i | 0.627339i | 0.949532 | + | 0.313670i | \(0.101558\pi\) | ||||
−0.949532 | + | 0.313670i | \(0.898442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13468.4i | 0.0233794i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −315806. | −0.545320 | −0.272660 | − | 0.962111i | \(-0.587903\pi\) | ||||
−0.272660 | + | 0.962111i | \(0.587903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −683897. | −1.17474 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 35640.0i | − 0.0608997i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.67358e6i | 2.84482i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 303070. | 0.512496 | 0.256248 | − | 0.966611i | \(-0.417514\pi\) | ||||
0.256248 | + | 0.966611i | \(0.417514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 286651. | 0.482219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 379668.i | − 0.635397i | −0.948192 | − | 0.317698i | \(-0.897090\pi\) | ||||
0.948192 | − | 0.317698i | \(-0.102910\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 689820.i | − 1.14850i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −451008. | −0.747037 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −133229. | −0.219546 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 127008.i | 0.208223i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 31987.5i | − 0.0521743i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 149184. | 0.242093 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52689.0 | 0.0850688 | 0.0425344 | − | 0.999095i | \(-0.486457\pi\) | ||||
0.0425344 | + | 0.999095i | \(0.486457\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 590976.i | 0.949327i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 672548.i | − 1.07491i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 253440. | 0.403022 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 280592. | 0.443957 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51900.0i | 0.0817054i | 0.999165 | + | 0.0408527i | \(0.0130074\pi\) | ||||
−0.999165 | + | 0.0408527i | \(0.986993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 288075.i | 0.451244i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41850.0 | 0.0652275 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 65887.2 | 0.102181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 93312.0i | − 0.143994i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 480436.i | 0.737715i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 498562. | 0.761767 | 0.380883 | − | 0.924623i | \(-0.375620\pi\) | ||||
0.380883 | + | 0.924623i | \(0.375620\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −69441.4 | −0.105579 | −0.0527894 | − | 0.998606i | \(-0.516811\pi\) | ||||
−0.0527894 | + | 0.998606i | \(0.516811\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 262764.i | − 0.397544i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 524520.i | − 0.789673i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 261360. | 0.391557 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −444458. | −0.662618 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 763068.i | 1.13208i | 0.824378 | + | 0.566040i | \(0.191525\pi\) | ||||
−0.824378 | + | 0.566040i | \(0.808475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.23404e6i | 1.82193i | 0.412486 | + | 0.910964i | \(0.364661\pi\) | ||||
−0.412486 | + | 0.910964i | \(0.635339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 51948.0 | 0.0763240 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −587560. | −0.859095 | −0.429548 | − | 0.903044i | \(-0.641327\pi\) | ||||
−0.429548 | + | 0.903044i | \(0.641327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 518184.i | 0.754006i | 0.926212 | + | 0.377003i | \(0.123045\pi\) | ||||
−0.926212 | + | 0.377003i | \(0.876955\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 650600.i | − 0.942132i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −163570. | −0.235729 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 517786. | 0.742639 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 201204.i | 0.287201i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 608698.i | 0.864725i | 0.901700 | + | 0.432362i | \(0.142320\pi\) | ||||
−0.901700 | + | 0.432362i | \(0.857680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 655297. | 0.926502 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −678981. | −0.955438 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 493620.i | 0.691320i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 885986.i | 1.23498i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 64476.0 | 0.0894505 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −173593. | −0.239703 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.28203e6i | − 1.76198i | −0.473136 | − | 0.880990i | \(-0.656878\pi\) | ||||
0.473136 | − | 0.880990i | \(-0.343122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33671.1i | 0.0460601i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.15264e6 | −1.56939 | −0.784696 | − | 0.619881i | \(-0.787181\pi\) | ||||
−0.784696 | + | 0.619881i | \(0.787181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.24011e6 | −1.68064 | −0.840321 | − | 0.542089i | \(-0.817633\pi\) | ||||
−0.840321 | + | 0.542089i | \(0.817633\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 415368.i | 0.560308i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 251161.i | 0.337234i | 0.985682 | + | 0.168617i | \(0.0539301\pi\) | ||||
−0.985682 | + | 0.168617i | \(0.946070\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 643536. | 0.860084 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 371114. | 0.493707 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 32400.0i | − 0.0429048i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 861481.i | 1.13556i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −216486. | −0.284054 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −827560. | −1.08089 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 661728.i | − 0.860360i | −0.902743 | − | 0.430180i | \(-0.858450\pi\) | ||||
0.902743 | − | 0.430180i | \(-0.141550\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 312829.i | − 0.404883i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 858562. | 1.10616 | 0.553082 | − | 0.833127i | \(-0.313451\pi\) | ||||
0.553082 | + | 0.833127i | \(0.313451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.09620e6 | −1.40595 | −0.702973 | − | 0.711216i | \(-0.748145\pi\) | ||||
−0.702973 | + | 0.711216i | \(0.748145\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 395280.i | − 0.504683i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 937802.i | − 1.19197i | −0.802997 | − | 0.595983i | \(-0.796763\pi\) | ||||
0.802997 | − | 0.595983i | \(-0.203237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 400464. | 0.506711 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15152.0 | −0.0190860 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 272160.i | − 0.341288i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 488605.i | − 0.609974i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −171072. | −0.212615 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 326983. | 0.404582 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 495000.i | − 0.609755i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 814840.i | − 0.999302i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 102816. | 0.125535 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −533104. | −0.648034 | −0.324017 | − | 0.946051i | \(-0.605033\pi\) | ||||
−0.324017 | + | 0.946051i | \(0.605033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 418932.i | 0.507009i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 148153.i | − 0.178514i | −0.996009 | − | 0.0892571i | \(-0.971551\pi\) | ||||
0.996009 | − | 0.0892571i | \(-0.0284493\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 92016.0 | 0.110388 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −59859.7 | −0.0714977 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 999216.i | − 1.18829i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 183008.i | 0.216691i | 0.994113 | + | 0.108345i | \(0.0345552\pi\) | ||||
−0.994113 | + | 0.108345i | \(0.965445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 460188. | 0.542520 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.61322e6 | −1.89361 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 669552.i | 0.782530i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 311457.i | 0.362443i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23122.0 | −0.0267913 | −0.0133957 | − | 0.999910i | \(-0.504264\pi\) | ||||
−0.0133957 | + | 0.999910i | \(0.504264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 154534. | 0.178289 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 405648.i | − 0.466000i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27435.7i | 0.0313829i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.03090e6 | −1.17418 | −0.587092 | − | 0.809520i | \(-0.699728\pi\) | ||||
−0.587092 | + | 0.809520i | \(0.699728\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 396809. | 0.450040 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.68690e6i | − 1.90507i | −0.304435 | − | 0.952533i | \(-0.598468\pi\) | ||||
0.304435 | − | 0.952533i | \(-0.401532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 159875.i | 0.179787i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 104976. | 0.117551 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −381876. | −0.425816 | −0.212908 | − | 0.977072i | \(-0.568293\pi\) | ||||
−0.212908 | + | 0.977072i | \(0.568293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 836880.i | 0.929246i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 71894.0i | 0.0794935i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 88738.0 | 0.0977066 | 0.0488533 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488533 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −805113. | −0.882775 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24624.0i | 0.0268865i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1.10952e6i | − 1.20642i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.13323e6 | −1.22708 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −514606. | −0.554910 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 710808.i | 0.763304i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.31062e6i | − 1.40159i | −0.713361 | − | 0.700797i | \(-0.752828\pi\) | ||||
0.713361 | − | 0.700797i | \(-0.247172\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 59400.0 | 0.0632614 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 190616. | 0.202172 | 0.101086 | − | 0.994878i | \(-0.467768\pi\) | ||||
0.101086 | + | 0.994878i | \(0.467768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.07957e6i | 1.14031i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 659828.i | 0.694099i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7186.00 | −0.00752832 | −0.00376416 | − | 0.999993i | \(-0.501198\pi\) | ||||
−0.00376416 | + | 0.999993i | \(0.501198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32216.1 | −0.0336131 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 296136.i | − 0.307718i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 810101.i | 0.838363i | 0.907902 | + | 0.419182i | \(0.137683\pi\) | ||||
−0.907902 | + | 0.419182i | \(0.862317\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −299952. | −0.309157 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −848511. | −0.871010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 313632.i | − 0.320647i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 313079.i | 0.318791i | 0.987215 | + | 0.159395i | \(0.0509545\pi\) | ||||
−0.987215 | + | 0.159395i | \(0.949045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −231012. | −0.234280 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −340452. | −0.343882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.13174e6i | 1.13857i | 0.822142 | + | 0.569283i | \(0.192779\pi\) | ||||
−0.822142 | + | 0.569283i | \(0.807221\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 195292.i | − 0.195683i |
(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 | 384.5.b.b.319.1 | ✓ | 4 | |
3.2 | odd | 2 | 1152.5.b.e.703.3 | 4 | |||
4.3 | odd | 2 | inner | 384.5.b.b.319.3 | yes | 4 | |
8.3 | odd | 2 | inner | 384.5.b.b.319.2 | yes | 4 | |
8.5 | even | 2 | inner | 384.5.b.b.319.4 | yes | 4 | |
12.11 | even | 2 | 1152.5.b.e.703.4 | 4 | |||
16.3 | odd | 4 | 768.5.g.a.511.2 | 2 | |||
16.5 | even | 4 | 768.5.g.b.511.2 | 2 | |||
16.11 | odd | 4 | 768.5.g.b.511.1 | 2 | |||
16.13 | even | 4 | 768.5.g.a.511.1 | 2 | |||
24.5 | odd | 2 | 1152.5.b.e.703.1 | 4 | |||
24.11 | even | 2 | 1152.5.b.e.703.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.b.b.319.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
384.5.b.b.319.2 | yes | 4 | 8.3 | odd | 2 | inner | |
384.5.b.b.319.3 | yes | 4 | 4.3 | odd | 2 | inner | |
384.5.b.b.319.4 | yes | 4 | 8.5 | even | 2 | inner | |
768.5.g.a.511.1 | 2 | 16.13 | even | 4 | |||
768.5.g.a.511.2 | 2 | 16.3 | odd | 4 | |||
768.5.g.b.511.1 | 2 | 16.11 | odd | 4 | |||
768.5.g.b.511.2 | 2 | 16.5 | even | 4 | |||
1152.5.b.e.703.1 | 4 | 24.5 | odd | 2 | |||
1152.5.b.e.703.2 | 4 | 24.11 | even | 2 | |||
1152.5.b.e.703.3 | 4 | 3.2 | odd | 2 | |||
1152.5.b.e.703.4 | 4 | 12.11 | even | 2 |