Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,6,Mod(499,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.499");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(120.287864860\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} + 1810x^{4} + 801025 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 499.4 | ||
Root | \(3.72585 - 3.72585i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.499 |
Dual form | 750.6.c.a.499.5 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | − 9.00000i | − 0.577350i | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 121.516i | 0.937320i | 0.883379 | + | 0.468660i | \(0.155263\pi\) | ||||
−0.883379 | + | 0.468660i | \(0.844737\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −181.652 | −0.452645 | −0.226323 | − | 0.974052i | \(-0.572670\pi\) | ||||
−0.226323 | + | 0.974052i | \(0.572670\pi\) | |||||||
\(12\) | 144.000i | 0.288675i | ||||||||
\(13\) | 775.680i | 1.27299i | 0.771282 | + | 0.636494i | \(0.219616\pi\) | ||||
−0.771282 | + | 0.636494i | \(0.780384\pi\) | |||||||
\(14\) | 486.063 | 0.662785 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 973.827i | 0.817259i | 0.912700 | + | 0.408629i | \(0.133993\pi\) | ||||
−0.912700 | + | 0.408629i | \(0.866007\pi\) | |||||||
\(18\) | 324.000i | 0.235702i | ||||||||
\(19\) | −573.377 | −0.364382 | −0.182191 | − | 0.983263i | \(-0.558319\pi\) | ||||
−0.182191 | + | 0.983263i | \(0.558319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1093.64 | 0.541162 | ||||||||
\(22\) | 726.607i | 0.320069i | ||||||||
\(23\) | 1098.54i | 0.433009i | 0.976282 | + | 0.216504i | \(0.0694656\pi\) | ||||
−0.976282 | + | 0.216504i | \(0.930534\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3102.72 | 0.900138 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | − 1944.25i | − 0.468660i | ||||||||
\(29\) | −447.258 | −0.0987559 | −0.0493779 | − | 0.998780i | \(-0.515724\pi\) | ||||
−0.0493779 | + | 0.998780i | \(0.515724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.1857 | −0.00227744 | −0.00113872 | − | 0.999999i | \(-0.500362\pi\) | ||||
−0.00113872 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | 1634.87i | 0.261335i | ||||||||
\(34\) | 3895.31 | 0.577889 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | − 8772.25i | − 1.05343i | −0.850041 | − | 0.526716i | \(-0.823423\pi\) | ||||
0.850041 | − | 0.526716i | \(-0.176577\pi\) | |||||||
\(38\) | 2293.51i | 0.257657i | ||||||||
\(39\) | 6981.12 | 0.734960 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11607.8 | −1.07842 | −0.539212 | − | 0.842170i | \(-0.681278\pi\) | ||||
−0.539212 | + | 0.842170i | \(0.681278\pi\) | |||||||
\(42\) | − 4374.57i | − 0.382659i | ||||||||
\(43\) | 6856.51i | 0.565500i | 0.959194 | + | 0.282750i | \(0.0912466\pi\) | ||||
−0.959194 | + | 0.282750i | \(0.908753\pi\) | |||||||
\(44\) | 2906.43 | 0.226323 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4394.17 | 0.306184 | ||||||||
\(47\) | 1423.86i | 0.0940207i | 0.998894 | + | 0.0470103i | \(0.0149694\pi\) | ||||
−0.998894 | + | 0.0470103i | \(0.985031\pi\) | |||||||
\(48\) | − 2304.00i | − 0.144338i | ||||||||
\(49\) | 2040.91 | 0.121432 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8764.45 | 0.471845 | ||||||||
\(52\) | − 12410.9i | − 0.636494i | ||||||||
\(53\) | − 17405.8i | − 0.851148i | −0.904924 | − | 0.425574i | \(-0.860072\pi\) | ||||
0.904924 | − | 0.425574i | \(-0.139928\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7777.01 | −0.331393 | ||||||||
\(57\) | 5160.40i | 0.210376i | ||||||||
\(58\) | 1789.03i | 0.0698309i | ||||||||
\(59\) | −1303.16 | −0.0487378 | −0.0243689 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243689 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1336.54 | −0.0459893 | −0.0229947 | − | 0.999736i | \(-0.507320\pi\) | ||||
−0.0229947 | + | 0.999736i | \(0.507320\pi\) | |||||||
\(62\) | 48.7429i | 0.00161039i | ||||||||
\(63\) | − 9842.78i | − 0.312440i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6539.46 | 0.184792 | ||||||||
\(67\) | − 36470.3i | − 0.992550i | −0.868165 | − | 0.496275i | \(-0.834701\pi\) | ||||
0.868165 | − | 0.496275i | \(-0.165299\pi\) | |||||||
\(68\) | − 15581.2i | − 0.408629i | ||||||||
\(69\) | 9886.87 | 0.249998 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −54059.4 | −1.27270 | −0.636349 | − | 0.771402i | \(-0.719556\pi\) | ||||
−0.636349 | + | 0.771402i | \(0.719556\pi\) | |||||||
\(72\) | − 5184.00i | − 0.117851i | ||||||||
\(73\) | − 10191.7i | − 0.223840i | −0.993717 | − | 0.111920i | \(-0.964300\pi\) | ||||
0.993717 | − | 0.111920i | \(-0.0357001\pi\) | |||||||
\(74\) | −35089.0 | −0.744889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9174.04 | 0.182191 | ||||||||
\(77\) | − 22073.6i | − 0.424273i | ||||||||
\(78\) | − 27924.5i | − 0.519695i | ||||||||
\(79\) | 48131.3 | 0.867681 | 0.433840 | − | 0.900990i | \(-0.357158\pi\) | ||||
0.433840 | + | 0.900990i | \(0.357158\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 46431.1i | 0.762561i | ||||||||
\(83\) | − 90905.1i | − 1.44841i | −0.689582 | − | 0.724207i | \(-0.742206\pi\) | ||||
0.689582 | − | 0.724207i | \(-0.257794\pi\) | |||||||
\(84\) | −17498.3 | −0.270581 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 27426.1 | 0.399869 | ||||||||
\(87\) | 4025.32i | 0.0570167i | ||||||||
\(88\) | − 11625.7i | − 0.160034i | ||||||||
\(89\) | −8917.29 | −0.119332 | −0.0596661 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596661 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −94257.4 | −1.19320 | ||||||||
\(92\) | − 17576.7i | − 0.216504i | ||||||||
\(93\) | 109.672i | 0.00131488i | ||||||||
\(94\) | 5695.45 | 0.0664827 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | − 55700.1i | − 0.601072i | −0.953770 | − | 0.300536i | \(-0.902834\pi\) | ||||
0.953770 | − | 0.300536i | \(-0.0971656\pi\) | |||||||
\(98\) | − 8163.63i | − 0.0858654i | ||||||||
\(99\) | 14713.8 | 0.150882 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 24249.0 | 0.236532 | 0.118266 | − | 0.992982i | \(-0.462266\pi\) | ||||
0.118266 | + | 0.992982i | \(0.462266\pi\) | |||||||
\(102\) | − 35057.8i | − 0.333645i | ||||||||
\(103\) | − 195610.i | − 1.81676i | −0.418143 | − | 0.908381i | \(-0.637319\pi\) | ||||
0.418143 | − | 0.908381i | \(-0.362681\pi\) | |||||||
\(104\) | −49643.5 | −0.450069 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −69623.3 | −0.601852 | ||||||||
\(107\) | − 24155.7i | − 0.203967i | −0.994786 | − | 0.101983i | \(-0.967481\pi\) | ||||
0.994786 | − | 0.101983i | \(-0.0325189\pi\) | |||||||
\(108\) | − 11664.0i | − 0.0962250i | ||||||||
\(109\) | 183775. | 1.48157 | 0.740783 | − | 0.671744i | \(-0.234455\pi\) | ||||
0.740783 | + | 0.671744i | \(0.234455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −78950.3 | −0.608200 | ||||||||
\(112\) | 31108.0i | 0.234330i | ||||||||
\(113\) | 52987.5i | 0.390371i | 0.980766 | + | 0.195185i | \(0.0625308\pi\) | ||||
−0.980766 | + | 0.195185i | \(0.937469\pi\) | |||||||
\(114\) | 20641.6 | 0.148758 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7156.12 | 0.0493779 | ||||||||
\(117\) | − 62830.1i | − 0.424329i | ||||||||
\(118\) | 5212.62i | 0.0344628i | ||||||||
\(119\) | −118335. | −0.766033 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −128054. | −0.795112 | ||||||||
\(122\) | 5346.16i | 0.0325194i | ||||||||
\(123\) | 104470.i | 0.622629i | ||||||||
\(124\) | 194.972 | 0.00113872 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −39371.1 | −0.220928 | ||||||||
\(127\) | − 147089.i | − 0.809227i | −0.914488 | − | 0.404614i | \(-0.867406\pi\) | ||||
0.914488 | − | 0.404614i | \(-0.132594\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 61708.6 | 0.326491 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −94832.5 | −0.482813 | −0.241407 | − | 0.970424i | \(-0.577609\pi\) | ||||
−0.241407 | + | 0.970424i | \(0.577609\pi\) | |||||||
\(132\) | − 26157.9i | − 0.130667i | ||||||||
\(133\) | − 69674.4i | − 0.341542i | ||||||||
\(134\) | −145881. | −0.701839 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −62325.0 | −0.288945 | ||||||||
\(137\) | 209273.i | 0.952603i | 0.879282 | + | 0.476302i | \(0.158023\pi\) | ||||
−0.879282 | + | 0.476302i | \(0.841977\pi\) | |||||||
\(138\) | − 39547.5i | − 0.176775i | ||||||||
\(139\) | −79747.4 | −0.350090 | −0.175045 | − | 0.984560i | \(-0.556007\pi\) | ||||
−0.175045 | + | 0.984560i | \(0.556007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12814.8 | 0.0542829 | ||||||||
\(142\) | 216238.i | 0.899933i | ||||||||
\(143\) | − 140904.i | − 0.576212i | ||||||||
\(144\) | −20736.0 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −40766.7 | −0.158279 | ||||||||
\(147\) | − 18368.2i | − 0.0701088i | ||||||||
\(148\) | 140356.i | 0.526716i | ||||||||
\(149\) | −293213. | −1.08198 | −0.540988 | − | 0.841030i | \(-0.681950\pi\) | ||||
−0.540988 | + | 0.841030i | \(0.681950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −278690. | −0.994672 | −0.497336 | − | 0.867558i | \(-0.665688\pi\) | ||||
−0.497336 | + | 0.867558i | \(0.665688\pi\) | |||||||
\(152\) | − 36696.1i | − 0.128828i | ||||||||
\(153\) | − 78880.0i | − 0.272420i | ||||||||
\(154\) | −88294.3 | −0.300006 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −111698. | −0.367480 | ||||||||
\(157\) | 116196.i | 0.376220i | 0.982148 | + | 0.188110i | \(0.0602362\pi\) | ||||
−0.982148 | + | 0.188110i | \(0.939764\pi\) | |||||||
\(158\) | − 192525.i | − 0.613543i | ||||||||
\(159\) | −156652. | −0.491410 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −133490. | −0.405868 | ||||||||
\(162\) | − 26244.0i | − 0.0785674i | ||||||||
\(163\) | 60540.0i | 0.178473i | 0.996010 | + | 0.0892367i | \(0.0284428\pi\) | ||||
−0.996010 | + | 0.0892367i | \(0.971557\pi\) | |||||||
\(164\) | 185725. | 0.539212 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −363620. | −1.02418 | ||||||||
\(167\) | 613483.i | 1.70220i | 0.525001 | + | 0.851102i | \(0.324065\pi\) | ||||
−0.525001 | + | 0.851102i | \(0.675935\pi\) | |||||||
\(168\) | 69993.1i | 0.191330i | ||||||||
\(169\) | −230387. | −0.620498 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46443.6 | 0.121461 | ||||||||
\(172\) | − 109704.i | − 0.282750i | ||||||||
\(173\) | 58116.5i | 0.147633i | 0.997272 | + | 0.0738167i | \(0.0235180\pi\) | ||||
−0.997272 | + | 0.0738167i | \(0.976482\pi\) | |||||||
\(174\) | 16101.3 | 0.0403169 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −46502.9 | −0.113161 | ||||||||
\(177\) | 11728.4i | 0.0281388i | ||||||||
\(178\) | 35669.1i | 0.0843806i | ||||||||
\(179\) | 496418. | 1.15802 | 0.579008 | − | 0.815322i | \(-0.303440\pi\) | ||||
0.579008 | + | 0.815322i | \(0.303440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 563042. | 1.27745 | 0.638725 | − | 0.769435i | \(-0.279462\pi\) | ||||
0.638725 | + | 0.769435i | \(0.279462\pi\) | |||||||
\(182\) | 377030.i | 0.843717i | ||||||||
\(183\) | 12028.8i | 0.0265519i | ||||||||
\(184\) | −70306.6 | −0.153092 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 438.686 | 0.000929762 0 | ||||||||
\(187\) | − 176897.i | − 0.369928i | ||||||||
\(188\) | − 22781.8i | − 0.0470103i | ||||||||
\(189\) | −88585.0 | −0.180387 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −562696. | −1.11607 | −0.558033 | − | 0.829819i | \(-0.688444\pi\) | ||||
−0.558033 | + | 0.829819i | \(0.688444\pi\) | |||||||
\(192\) | 36864.0i | 0.0721688i | ||||||||
\(193\) | − 528085.i | − 1.02049i | −0.860028 | − | 0.510247i | \(-0.829554\pi\) | ||||
0.860028 | − | 0.510247i | \(-0.170446\pi\) | |||||||
\(194\) | −222800. | −0.425022 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32654.5 | −0.0607160 | ||||||||
\(197\) | − 895318.i | − 1.64366i | −0.569733 | − | 0.821830i | \(-0.692953\pi\) | ||||
0.569733 | − | 0.821830i | \(-0.307047\pi\) | |||||||
\(198\) | − 58855.2i | − 0.106690i | ||||||||
\(199\) | 907778. | 1.62498 | 0.812488 | − | 0.582978i | \(-0.198113\pi\) | ||||
0.812488 | + | 0.582978i | \(0.198113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −328233. | −0.573049 | ||||||||
\(202\) | − 96995.9i | − 0.167253i | ||||||||
\(203\) | − 54348.9i | − 0.0925658i | ||||||||
\(204\) | −140231. | −0.235922 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −782440. | −1.28465 | ||||||||
\(207\) | − 88981.8i | − 0.144336i | ||||||||
\(208\) | 198574.i | 0.318247i | ||||||||
\(209\) | 104155. | 0.164936 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −826317. | −1.27773 | −0.638867 | − | 0.769317i | \(-0.720597\pi\) | ||||
−0.638867 | + | 0.769317i | \(0.720597\pi\) | |||||||
\(212\) | 278493.i | 0.425574i | ||||||||
\(213\) | 486534.i | 0.734792i | ||||||||
\(214\) | −96622.7 | −0.144226 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | − 1480.76i | − 0.00213469i | ||||||||
\(218\) | − 735101.i | − 1.04763i | ||||||||
\(219\) | −91725.1 | −0.129234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −755379. | −1.04036 | ||||||||
\(222\) | 315801.i | 0.430062i | ||||||||
\(223\) | 198690.i | 0.267555i | 0.991011 | + | 0.133778i | \(0.0427108\pi\) | ||||
−0.991011 | + | 0.133778i | \(0.957289\pi\) | |||||||
\(224\) | 124432. | 0.165696 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 211950. | 0.276034 | ||||||||
\(227\) | 474777.i | 0.611541i | 0.952105 | + | 0.305770i | \(0.0989140\pi\) | ||||
−0.952105 | + | 0.305770i | \(0.901086\pi\) | |||||||
\(228\) | − 82566.3i | − 0.105188i | ||||||||
\(229\) | 235056. | 0.296199 | 0.148099 | − | 0.988972i | \(-0.452684\pi\) | ||||
0.148099 | + | 0.988972i | \(0.452684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −198662. | −0.244954 | ||||||||
\(232\) | − 28624.5i | − 0.0349155i | ||||||||
\(233\) | 451110.i | 0.544368i | 0.962245 | + | 0.272184i | \(0.0877460\pi\) | ||||
−0.962245 | + | 0.272184i | \(0.912254\pi\) | |||||||
\(234\) | −251320. | −0.300046 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 20850.5 | 0.0243689 | ||||||||
\(237\) | − 433182.i | − 0.500956i | ||||||||
\(238\) | 473342.i | 0.541667i | ||||||||
\(239\) | 922502. | 1.04465 | 0.522327 | − | 0.852745i | \(-0.325064\pi\) | ||||
0.522327 | + | 0.852745i | \(0.325064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.23628e6 | −1.37111 | −0.685555 | − | 0.728020i | \(-0.740441\pi\) | ||||
−0.685555 | + | 0.728020i | \(0.740441\pi\) | |||||||
\(242\) | 512215.i | 0.562229i | ||||||||
\(243\) | − 59049.0i | − 0.0641500i | ||||||||
\(244\) | 21384.6 | 0.0229947 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 417880. | 0.440265 | ||||||||
\(247\) | − 444757.i | − 0.463853i | ||||||||
\(248\) | − 779.887i | 0 0.000805197i | ||||||||
\(249\) | −818146. | −0.836243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.89718e6 | −1.90075 | −0.950373 | − | 0.311114i | \(-0.899298\pi\) | ||||
−0.950373 | + | 0.311114i | \(0.899298\pi\) | |||||||
\(252\) | 157484.i | 0.156220i | ||||||||
\(253\) | − 199552.i | − 0.195999i | ||||||||
\(254\) | −588356. | −0.572210 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 211391.i | 0.199643i | 0.995005 | + | 0.0998215i | \(0.0318272\pi\) | ||||
−0.995005 | + | 0.0998215i | \(0.968173\pi\) | |||||||
\(258\) | − 246835.i | − 0.230864i | ||||||||
\(259\) | 1.06597e6 | 0.987403 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36227.9 | 0.0329186 | ||||||||
\(262\) | 379330.i | 0.341400i | ||||||||
\(263\) | 11971.3i | 0.0106721i | 0.999986 | + | 0.00533607i | \(0.00169853\pi\) | ||||
−0.999986 | + | 0.00533607i | \(0.998301\pi\) | |||||||
\(264\) | −104631. | −0.0923958 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −278698. | −0.241507 | ||||||||
\(267\) | 80255.6i | 0.0688965i | ||||||||
\(268\) | 583525.i | 0.496275i | ||||||||
\(269\) | −600883. | −0.506302 | −0.253151 | − | 0.967427i | \(-0.581467\pi\) | ||||
−0.253151 | + | 0.967427i | \(0.581467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.06392e6 | −0.880010 | −0.440005 | − | 0.897995i | \(-0.645023\pi\) | ||||
−0.440005 | + | 0.897995i | \(0.645023\pi\) | |||||||
\(272\) | 249300.i | 0.204315i | ||||||||
\(273\) | 848317.i | 0.688892i | ||||||||
\(274\) | 837093. | 0.673592 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −158190. | −0.124999 | ||||||||
\(277\) | 355101.i | 0.278069i | 0.990288 | + | 0.139035i | \(0.0443999\pi\) | ||||
−0.990288 | + | 0.139035i | \(0.955600\pi\) | |||||||
\(278\) | 318990.i | 0.247551i | ||||||||
\(279\) | 987.044 | 0.000759147 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.30120e6 | −0.983053 | −0.491527 | − | 0.870862i | \(-0.663561\pi\) | ||||
−0.491527 | + | 0.870862i | \(0.663561\pi\) | |||||||
\(282\) | − 51259.0i | − 0.0383838i | ||||||||
\(283\) | 1.56975e6i | 1.16510i | 0.812795 | + | 0.582550i | \(0.197945\pi\) | ||||
−0.812795 | + | 0.582550i | \(0.802055\pi\) | |||||||
\(284\) | 864950. | 0.636349 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −563615. | −0.407443 | ||||||||
\(287\) | − 1.41053e6i | − 1.01083i | ||||||||
\(288\) | 82944.0i | 0.0589256i | ||||||||
\(289\) | 471517. | 0.332088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −501301. | −0.347029 | ||||||||
\(292\) | 163067.i | 0.111920i | ||||||||
\(293\) | 476235.i | 0.324080i | 0.986784 | + | 0.162040i | \(0.0518073\pi\) | ||||
−0.986784 | + | 0.162040i | \(0.948193\pi\) | |||||||
\(294\) | −73472.7 | −0.0495744 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 561424. | 0.372445 | ||||||||
\(297\) | − 132424.i | − 0.0871116i | ||||||||
\(298\) | 1.17285e6i | 0.765073i | ||||||||
\(299\) | −852117. | −0.551215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −833175. | −0.530054 | ||||||||
\(302\) | 1.11476e6i | 0.703339i | ||||||||
\(303\) | − 218241.i | − 0.136562i | ||||||||
\(304\) | −146785. | −0.0910954 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −315520. | −0.192630 | ||||||||
\(307\) | 279929.i | 0.169513i | 0.996402 | + | 0.0847563i | \(0.0270112\pi\) | ||||
−0.996402 | + | 0.0847563i | \(0.972989\pi\) | |||||||
\(308\) | 353177.i | 0.212137i | ||||||||
\(309\) | −1.76049e6 | −1.04891 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.68143e6 | 0.985774 | 0.492887 | − | 0.870093i | \(-0.335942\pi\) | ||||
0.492887 | + | 0.870093i | \(0.335942\pi\) | |||||||
\(312\) | 446792.i | 0.259848i | ||||||||
\(313\) | 2.34993e6i | 1.35579i | 0.735157 | + | 0.677897i | \(0.237108\pi\) | ||||
−0.735157 | + | 0.677897i | \(0.762892\pi\) | |||||||
\(314\) | 464784. | 0.266028 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −770101. | −0.433840 | ||||||||
\(317\) | − 3.36066e6i | − 1.87835i | −0.343443 | − | 0.939174i | \(-0.611593\pi\) | ||||
0.343443 | − | 0.939174i | \(-0.388407\pi\) | |||||||
\(318\) | 626610.i | 0.347480i | ||||||||
\(319\) | 81245.2 | 0.0447014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −217401. | −0.117760 | ||||||||
\(322\) | 533961.i | 0.286992i | ||||||||
\(323\) | − 558371.i | − 0.297794i | ||||||||
\(324\) | −104976. | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 242160. | 0.126200 | ||||||||
\(327\) | − 1.65398e6i | − 0.855383i | ||||||||
\(328\) | − 742898.i | − 0.381281i | ||||||||
\(329\) | −173022. | −0.0881274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.08666e6 | 0.545157 | 0.272579 | − | 0.962134i | \(-0.412124\pi\) | ||||
0.272579 | + | 0.962134i | \(0.412124\pi\) | |||||||
\(332\) | 1.45448e6i | 0.724207i | ||||||||
\(333\) | 710552.i | 0.351144i | ||||||||
\(334\) | 2.45393e6 | 1.20364 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 279972. | 0.135290 | ||||||||
\(337\) | − 2.38152e6i | − 1.14230i | −0.820847 | − | 0.571148i | \(-0.806498\pi\) | ||||
0.820847 | − | 0.571148i | \(-0.193502\pi\) | |||||||
\(338\) | 921546.i | 0.438758i | ||||||||
\(339\) | 476887. | 0.225381 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2213.56 | 0.00103087 | ||||||||
\(342\) | − 185774.i | − 0.0858856i | ||||||||
\(343\) | 2.29032e6i | 1.05114i | ||||||||
\(344\) | −438817. | −0.199934 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 232466. | 0.104393 | ||||||||
\(347\) | − 1.86294e6i | − 0.830570i | −0.909691 | − | 0.415285i | \(-0.863682\pi\) | ||||
0.909691 | − | 0.415285i | \(-0.136318\pi\) | |||||||
\(348\) | − 64405.1i | − 0.0285084i | ||||||||
\(349\) | −3.30379e6 | −1.45194 | −0.725969 | − | 0.687727i | \(-0.758609\pi\) | ||||
−0.725969 | + | 0.687727i | \(0.758609\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −565471. | −0.244987 | ||||||||
\(352\) | 186011.i | 0.0800171i | ||||||||
\(353\) | − 2.53715e6i | − 1.08370i | −0.840475 | − | 0.541851i | \(-0.817724\pi\) | ||||
0.840475 | − | 0.541851i | \(-0.182276\pi\) | |||||||
\(354\) | 46913.6 | 0.0198971 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 142677. | 0.0596661 | ||||||||
\(357\) | 1.06502e6i | 0.442269i | ||||||||
\(358\) | − 1.98567e6i | − 0.818842i | ||||||||
\(359\) | −4.02351e6 | −1.64766 | −0.823832 | − | 0.566835i | \(-0.808168\pi\) | ||||
−0.823832 | + | 0.566835i | \(0.808168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.14734e6 | −0.867226 | ||||||||
\(362\) | − 2.25217e6i | − 0.903294i | ||||||||
\(363\) | 1.15248e6i | 0.459058i | ||||||||
\(364\) | 1.50812e6 | 0.596598 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 48115.4 | 0.0187751 | ||||||||
\(367\) | − 2.78489e6i | − 1.07930i | −0.841888 | − | 0.539652i | \(-0.818556\pi\) | ||||
0.841888 | − | 0.539652i | \(-0.181444\pi\) | |||||||
\(368\) | 281227.i | 0.108252i | ||||||||
\(369\) | 940231. | 0.359475 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.11508e6 | 0.797797 | ||||||||
\(372\) | − 1754.75i | 0 0.000657441i | ||||||||
\(373\) | − 2.86936e6i | − 1.06786i | −0.845530 | − | 0.533928i | \(-0.820715\pi\) | ||||
0.845530 | − | 0.533928i | \(-0.179285\pi\) | |||||||
\(374\) | −707590. | −0.261579 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −91127.2 | −0.0332413 | ||||||||
\(377\) | − 346929.i | − 0.125715i | ||||||||
\(378\) | 354340.i | 0.127553i | ||||||||
\(379\) | 4.08007e6 | 1.45905 | 0.729524 | − | 0.683955i | \(-0.239742\pi\) | ||||
0.729524 | + | 0.683955i | \(0.239742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.32380e6 | −0.467208 | ||||||||
\(382\) | 2.25078e6i | 0.789178i | ||||||||
\(383\) | − 5.20039e6i | − 1.81150i | −0.423810 | − | 0.905751i | \(-0.639307\pi\) | ||||
0.423810 | − | 0.905751i | \(-0.360693\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.11234e6 | −0.721599 | ||||||||
\(387\) | − 555378.i | − 0.188500i | ||||||||
\(388\) | 891202.i | 0.300536i | ||||||||
\(389\) | −1.51547e6 | −0.507777 | −0.253888 | − | 0.967234i | \(-0.581710\pi\) | ||||
−0.253888 | + | 0.967234i | \(0.581710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.06979e6 | −0.353880 | ||||||||
\(392\) | 130618.i | 0.0429327i | ||||||||
\(393\) | 853493.i | 0.278752i | ||||||||
\(394\) | −3.58127e6 | −1.16224 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −235421. | −0.0754409 | ||||||||
\(397\) | − 20619.2i | − 0.00656592i | −0.999995 | − | 0.00328296i | \(-0.998955\pi\) | ||||
0.999995 | − | 0.00328296i | \(-0.00104500\pi\) | |||||||
\(398\) | − 3.63111e6i | − 1.14903i | ||||||||
\(399\) | −627070. | −0.197189 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.73600e6 | 0.849678 | 0.424839 | − | 0.905269i | \(-0.360331\pi\) | ||||
0.424839 | + | 0.905269i | \(0.360331\pi\) | |||||||
\(402\) | 1.31293e6i | 0.405207i | ||||||||
\(403\) | − 9452.23i | − 0.00289916i | ||||||||
\(404\) | −387984. | −0.118266 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −217396. | −0.0654539 | ||||||||
\(407\) | 1.59350e6i | 0.476831i | ||||||||
\(408\) | 560925.i | 0.166822i | ||||||||
\(409\) | 3.06698e6 | 0.906573 | 0.453286 | − | 0.891365i | \(-0.350252\pi\) | ||||
0.453286 | + | 0.891365i | \(0.350252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.88346e6 | 0.549986 | ||||||||
\(412\) | 3.12976e6i | 0.908381i | ||||||||
\(413\) | − 158354.i | − 0.0456829i | ||||||||
\(414\) | −355927. | −0.102061 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 794296. | 0.225035 | ||||||||
\(417\) | 717727.i | 0.202125i | ||||||||
\(418\) | − 416620.i | − 0.116627i | ||||||||
\(419\) | −1.72617e6 | −0.480339 | −0.240170 | − | 0.970731i | \(-0.577203\pi\) | ||||
−0.240170 | + | 0.970731i | \(0.577203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.87229e6 | 1.33976 | 0.669882 | − | 0.742468i | \(-0.266345\pi\) | ||||
0.669882 | + | 0.742468i | \(0.266345\pi\) | |||||||
\(422\) | 3.30527e6i | 0.903494i | ||||||||
\(423\) | − 115333.i | − 0.0313402i | ||||||||
\(424\) | 1.11397e6 | 0.300926 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.94614e6 | 0.519577 | ||||||||
\(427\) | − 162411.i | − 0.0431067i | ||||||||
\(428\) | 386491.i | 0.101983i | ||||||||
\(429\) | −1.26813e6 | −0.332676 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.20696e6 | −0.572271 | −0.286136 | − | 0.958189i | \(-0.592371\pi\) | ||||
−0.286136 | + | 0.958189i | \(0.592371\pi\) | |||||||
\(432\) | 186624.i | 0.0481125i | ||||||||
\(433\) | − 2.00729e6i | − 0.514507i | −0.966344 | − | 0.257253i | \(-0.917182\pi\) | ||||
0.966344 | − | 0.257253i | \(-0.0828175\pi\) | |||||||
\(434\) | −5923.04 | −0.00150945 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.94041e6 | −0.740783 | ||||||||
\(437\) | − 629879.i | − 0.157781i | ||||||||
\(438\) | 366900.i | 0.0913824i | ||||||||
\(439\) | −161997. | −0.0401186 | −0.0200593 | − | 0.999799i | \(-0.506386\pi\) | ||||
−0.0200593 | + | 0.999799i | \(0.506386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −165314. | −0.0404773 | ||||||||
\(442\) | 3.02151e6i | 0.735646i | ||||||||
\(443\) | − 4.88655e6i | − 1.18302i | −0.806296 | − | 0.591512i | \(-0.798531\pi\) | ||||
0.806296 | − | 0.591512i | \(-0.201469\pi\) | |||||||
\(444\) | 1.26320e6 | 0.304100 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 794759. | 0.189190 | ||||||||
\(447\) | 2.63892e6i | 0.624679i | ||||||||
\(448\) | − 497729.i | − 0.117165i | ||||||||
\(449\) | 1.73015e6 | 0.405012 | 0.202506 | − | 0.979281i | \(-0.435091\pi\) | ||||
0.202506 | + | 0.979281i | \(0.435091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.10858e6 | 0.488144 | ||||||||
\(452\) | − 847800.i | − 0.195185i | ||||||||
\(453\) | 2.50821e6i | 0.574274i | ||||||||
\(454\) | 1.89911e6 | 0.432425 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −330265. | −0.0743791 | ||||||||
\(457\) | 438403.i | 0.0981936i | 0.998794 | + | 0.0490968i | \(0.0156343\pi\) | ||||
−0.998794 | + | 0.0490968i | \(0.984366\pi\) | |||||||
\(458\) | − 940225.i | − 0.209444i | ||||||||
\(459\) | −709920. | −0.157282 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −242647. | −0.0531768 | −0.0265884 | − | 0.999646i | \(-0.508464\pi\) | ||||
−0.0265884 | + | 0.999646i | \(0.508464\pi\) | |||||||
\(462\) | 794648.i | 0.173209i | ||||||||
\(463\) | 5.98909e6i | 1.29840i | 0.760618 | + | 0.649199i | \(0.224896\pi\) | ||||
−0.760618 | + | 0.649199i | \(0.775104\pi\) | |||||||
\(464\) | −114498. | −0.0246890 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.80444e6 | 0.384927 | ||||||||
\(467\) | − 3.29307e6i | − 0.698729i | −0.936987 | − | 0.349364i | \(-0.886398\pi\) | ||||
0.936987 | − | 0.349364i | \(-0.113602\pi\) | |||||||
\(468\) | 1.00528e6i | 0.212165i | ||||||||
\(469\) | 4.43172e6 | 0.930337 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.04576e6 | 0.217211 | ||||||||
\(472\) | − 83401.9i | − 0.0172314i | ||||||||
\(473\) | − 1.24550e6i | − 0.255971i | ||||||||
\(474\) | −1.73273e6 | −0.354229 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.89337e6 | 0.383016 | ||||||||
\(477\) | 1.40987e6i | 0.283716i | ||||||||
\(478\) | − 3.69001e6i | − 0.738682i | ||||||||
\(479\) | −2.48892e6 | −0.495647 | −0.247824 | − | 0.968805i | \(-0.579715\pi\) | ||||
−0.247824 | + | 0.968805i | \(0.579715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.80446e6 | 1.34101 | ||||||||
\(482\) | 4.94510e6i | 0.969522i | ||||||||
\(483\) | 1.20141e6i | 0.234328i | ||||||||
\(484\) | 2.04886e6 | 0.397556 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | − 8.13337e6i | − 1.55399i | −0.629507 | − | 0.776994i | \(-0.716743\pi\) | ||||
0.629507 | − | 0.776994i | \(-0.283257\pi\) | |||||||
\(488\) | − 85538.5i | − 0.0162597i | ||||||||
\(489\) | 544860. | 0.103042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.23929e6 | −0.419186 | −0.209593 | − | 0.977789i | \(-0.567214\pi\) | ||||
−0.209593 | + | 0.977789i | \(0.567214\pi\) | |||||||
\(492\) | − 1.67152e6i | − 0.311314i | ||||||||
\(493\) | − 435552.i | − 0.0807091i | ||||||||
\(494\) | −1.77903e6 | −0.327994 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3119.55 | −0.000569361 0 | ||||||||
\(497\) | − 6.56907e6i | − 1.19292i | ||||||||
\(498\) | 3.27258e6i | 0.591313i | ||||||||
\(499\) | 2.06377e6 | 0.371031 | 0.185516 | − | 0.982641i | \(-0.440604\pi\) | ||||
0.185516 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.52135e6 | 0.982768 | ||||||||
\(502\) | 7.58871e6i | 1.34403i | ||||||||
\(503\) | − 5.71915e6i | − 1.00789i | −0.863737 | − | 0.503943i | \(-0.831882\pi\) | ||||
0.863737 | − | 0.503943i | \(-0.168118\pi\) | |||||||
\(504\) | 629938. | 0.110464 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −798208. | −0.138593 | ||||||||
\(507\) | 2.07348e6i | 0.358245i | ||||||||
\(508\) | 2.35342e6i | 0.404614i | ||||||||
\(509\) | −6.52514e6 | −1.11634 | −0.558168 | − | 0.829728i | \(-0.688496\pi\) | ||||
−0.558168 | + | 0.829728i | \(0.688496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.23845e6 | 0.209810 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | − 417992.i | − 0.0701253i | ||||||||
\(514\) | 845565. | 0.141169 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −987338. | −0.163246 | ||||||||
\(517\) | − 258647.i | − 0.0425580i | ||||||||
\(518\) | − 4.26387e6i | − 0.698199i | ||||||||
\(519\) | 523049. | 0.0852361 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.48021e6 | 0.561709 | 0.280855 | − | 0.959750i | \(-0.409382\pi\) | ||||
0.280855 | + | 0.959750i | \(0.409382\pi\) | |||||||
\(522\) | − 144912.i | − 0.0232770i | ||||||||
\(523\) | 4.85070e6i | 0.775443i | 0.921777 | + | 0.387722i | \(0.126738\pi\) | ||||
−0.921777 | + | 0.387722i | \(0.873262\pi\) | |||||||
\(524\) | 1.51732e6 | 0.241407 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47885.1 | 0.00754634 | ||||||||
\(527\) | − 11866.8i | − 0.00186126i | ||||||||
\(528\) | 418526.i | 0.0653337i | ||||||||
\(529\) | 5.22955e6 | 0.812503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105556. | 0.0162459 | ||||||||
\(532\) | 1.11479e6i | 0.170771i | ||||||||
\(533\) | − 9.00393e6i | − 1.37282i | ||||||||
\(534\) | 321022. | 0.0487172 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.33410e6 | 0.350919 | ||||||||
\(537\) | − 4.46776e6i | − 0.668581i | ||||||||
\(538\) | 2.40353e6i | 0.358009i | ||||||||
\(539\) | −370735. | −0.0549656 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.21646e7 | 1.78691 | 0.893456 | − | 0.449152i | \(-0.148274\pi\) | ||||
0.893456 | + | 0.449152i | \(0.148274\pi\) | |||||||
\(542\) | 4.25570e6i | 0.622261i | ||||||||
\(543\) | − 5.06737e6i | − 0.737536i | ||||||||
\(544\) | 997199. | 0.144472 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.39327e6 | 0.487120 | ||||||||
\(547\) | − 6.48941e6i | − 0.927335i | −0.886009 | − | 0.463668i | \(-0.846533\pi\) | ||||
0.886009 | − | 0.463668i | \(-0.153467\pi\) | |||||||
\(548\) | − 3.34837e6i | − 0.476302i | ||||||||
\(549\) | 108260. | 0.0153298 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 256447. | 0.0359848 | ||||||||
\(552\) | 632760.i | 0.0883876i | ||||||||
\(553\) | 5.84871e6i | 0.813294i | ||||||||
\(554\) | 1.42041e6 | 0.196625 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.27596e6 | 0.175045 | ||||||||
\(557\) | 1.06703e6i | 0.145726i | 0.997342 | + | 0.0728629i | \(0.0232136\pi\) | ||||
−0.997342 | + | 0.0728629i | \(0.976786\pi\) | |||||||
\(558\) | − 3948.18i | 0 0.000536798i | ||||||||
\(559\) | −5.31846e6 | −0.719874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.59208e6 | −0.213578 | ||||||||
\(562\) | 5.20479e6i | 0.695124i | ||||||||
\(563\) | − 7.78244e6i | − 1.03477i | −0.855752 | − | 0.517386i | \(-0.826905\pi\) | ||||
0.855752 | − | 0.517386i | \(-0.173095\pi\) | |||||||
\(564\) | −205036. | −0.0271414 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.27898e6 | 0.823850 | ||||||||
\(567\) | 797265.i | 0.104147i | ||||||||
\(568\) | − 3.45980e6i | − 0.449966i | ||||||||
\(569\) | 8.69392e6 | 1.12573 | 0.562866 | − | 0.826548i | \(-0.309699\pi\) | ||||
0.562866 | + | 0.826548i | \(0.309699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.15530e6 | 0.661704 | 0.330852 | − | 0.943683i | \(-0.392664\pi\) | ||||
0.330852 | + | 0.943683i | \(0.392664\pi\) | |||||||
\(572\) | 2.25446e6i | 0.288106i | ||||||||
\(573\) | 5.06426e6i | 0.644361i | ||||||||
\(574\) | −5.64212e6 | −0.714764 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 1.10792e7i | 1.38538i | 0.721233 | + | 0.692692i | \(0.243576\pi\) | ||||
−0.721233 | + | 0.692692i | \(0.756424\pi\) | |||||||
\(578\) | − 1.88607e6i | − 0.234822i | ||||||||
\(579\) | −4.75277e6 | −0.589183 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.10464e7 | 1.35763 | ||||||||
\(582\) | 2.00520e6i | 0.245387i | ||||||||
\(583\) | 3.16180e6i | 0.385268i | ||||||||
\(584\) | 652267. | 0.0791395 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.90494e6 | 0.229159 | ||||||||
\(587\) | 2.70928e6i | 0.324533i | 0.986747 | + | 0.162267i | \(0.0518805\pi\) | ||||
−0.986747 | + | 0.162267i | \(0.948120\pi\) | |||||||
\(588\) | 293891.i | 0.0350544i | ||||||||
\(589\) | 6987.02 | 0.000829858 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.05786e6 | −0.948967 | ||||||||
\(592\) | − 2.24570e6i | − 0.263358i | ||||||||
\(593\) | − 4.21114e6i | − 0.491771i | −0.969299 | − | 0.245886i | \(-0.920921\pi\) | ||||
0.969299 | − | 0.245886i | \(-0.0790787\pi\) | |||||||
\(594\) | −529697. | −0.0615972 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.69141e6 | 0.540988 | ||||||||
\(597\) | − 8.17000e6i | − 0.938180i | ||||||||
\(598\) | 3.40847e6i | 0.389768i | ||||||||
\(599\) | 1.27576e7 | 1.45279 | 0.726396 | − | 0.687276i | \(-0.241194\pi\) | ||||
0.726396 | + | 0.687276i | \(0.241194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.01360e7 | 1.14467 | 0.572337 | − | 0.820018i | \(-0.306037\pi\) | ||||
0.572337 | + | 0.820018i | \(0.306037\pi\) | |||||||
\(602\) | 3.33270e6i | 0.374805i | ||||||||
\(603\) | 2.95409e6i | 0.330850i | ||||||||
\(604\) | 4.45905e6 | 0.497336 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −872963. | −0.0965638 | ||||||||
\(607\) | − 1.64475e6i | − 0.181188i | −0.995888 | − | 0.0905938i | \(-0.971123\pi\) | ||||
0.995888 | − | 0.0905938i | \(-0.0288765\pi\) | |||||||
\(608\) | 587138.i | 0.0644142i | ||||||||
\(609\) | −489140. | −0.0534429 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.10446e6 | −0.119687 | ||||||||
\(612\) | 1.26208e6i | 0.136210i | ||||||||
\(613\) | 7.44887e6i | 0.800644i | 0.916375 | + | 0.400322i | \(0.131102\pi\) | ||||
−0.916375 | + | 0.400322i | \(0.868898\pi\) | |||||||
\(614\) | 1.11972e6 | 0.119864 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.41271e6 | 0.150003 | ||||||||
\(617\) | − 4.07579e6i | − 0.431021i | −0.976502 | − | 0.215511i | \(-0.930858\pi\) | ||||
0.976502 | − | 0.215511i | \(-0.0691416\pi\) | |||||||
\(618\) | 7.04196e6i | 0.741690i | ||||||||
\(619\) | −1.52740e7 | −1.60224 | −0.801119 | − | 0.598505i | \(-0.795761\pi\) | ||||
−0.801119 | + | 0.598505i | \(0.795761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −800837. | −0.0833326 | ||||||||
\(622\) | − 6.72571e6i | − 0.697047i | ||||||||
\(623\) | − 1.08359e6i | − 0.111852i | ||||||||
\(624\) | 1.78717e6 | 0.183740 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.39971e6 | 0.958691 | ||||||||
\(627\) | − 937395.i | − 0.0952256i | ||||||||
\(628\) | − 1.85914e6i | − 0.188110i | ||||||||
\(629\) | 8.54266e6 | 0.860927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.21288e6 | −0.421216 | −0.210608 | − | 0.977571i | \(-0.567544\pi\) | ||||
−0.210608 | + | 0.977571i | \(0.567544\pi\) | |||||||
\(632\) | 3.08040e6i | 0.306771i | ||||||||
\(633\) | 7.43685e6i | 0.737700i | ||||||||
\(634\) | −1.34426e7 | −1.32819 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.50644e6 | 0.245705 | ||||||||
\(637\) | 1.58309e6i | 0.154582i | ||||||||
\(638\) | − 324981.i | − 0.0316086i | ||||||||
\(639\) | 4.37881e6 | 0.424232 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.38889e6 | 0.421900 | 0.210950 | − | 0.977497i | \(-0.432344\pi\) | ||||
0.210950 | + | 0.977497i | \(0.432344\pi\) | |||||||
\(642\) | 869605.i | 0.0832692i | ||||||||
\(643\) | − 1.40652e7i | − 1.34159i | −0.741644 | − | 0.670793i | \(-0.765954\pi\) | ||||
0.741644 | − | 0.670793i | \(-0.234046\pi\) | |||||||
\(644\) | 2.13584e6 | 0.202934 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.23348e6 | −0.210572 | ||||||||
\(647\) | − 6.58712e6i | − 0.618635i | −0.950959 | − | 0.309318i | \(-0.899899\pi\) | ||||
0.950959 | − | 0.309318i | \(-0.100101\pi\) | |||||||
\(648\) | 419904.i | 0.0392837i | ||||||||
\(649\) | 236720. | 0.0220609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13326.8 | −0.00123246 | ||||||||
\(652\) | − 968640.i | − 0.0892367i | ||||||||
\(653\) | − 1.94602e7i | − 1.78593i | −0.450128 | − | 0.892964i | \(-0.648622\pi\) | ||||
0.450128 | − | 0.892964i | \(-0.351378\pi\) | |||||||
\(654\) | −6.61591e6 | −0.604847 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.97159e6 | −0.269606 | ||||||||
\(657\) | 825526.i | 0.0746135i | ||||||||
\(658\) | 692087.i | 0.0623155i | ||||||||
\(659\) | 296399. | 0.0265867 | 0.0132933 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132933 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.82870e7 | −1.62794 | −0.813970 | − | 0.580906i | \(-0.802698\pi\) | ||||
−0.813970 | + | 0.580906i | \(0.802698\pi\) | |||||||
\(662\) | − 4.34662e6i | − 0.385484i | ||||||||
\(663\) | 6.79841e6i | 0.600653i | ||||||||
\(664\) | 5.81793e6 | 0.512092 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.84221e6 | 0.248296 | ||||||||
\(667\) | − 491331.i | − 0.0427622i | ||||||||
\(668\) | − 9.81573e6i | − 0.851102i | ||||||||
\(669\) | 1.78821e6 | 0.154473 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 242785. | 0.0208168 | ||||||||
\(672\) | − 1.11989e6i | − 0.0956648i | ||||||||
\(673\) | 1.09926e7i | 0.935541i | 0.883850 | + | 0.467770i | \(0.154943\pi\) | ||||
−0.883850 | + | 0.467770i | \(0.845057\pi\) | |||||||
\(674\) | −9.52606e6 | −0.807726 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.68619e6 | 0.310249 | ||||||||
\(677\) | − 9.07079e6i | − 0.760630i | −0.924857 | − | 0.380315i | \(-0.875816\pi\) | ||||
0.924857 | − | 0.380315i | \(-0.124184\pi\) | |||||||
\(678\) | − 1.90755e6i | − 0.159368i | ||||||||
\(679\) | 6.76844e6 | 0.563397 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.27300e6 | 0.353073 | ||||||||
\(682\) | − 8854.24i | 0 0.000728938i | ||||||||
\(683\) | − 8.50582e6i | − 0.697693i | −0.937180 | − | 0.348847i | \(-0.886573\pi\) | ||||
0.937180 | − | 0.348847i | \(-0.113427\pi\) | |||||||
\(684\) | −743097. | −0.0607303 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.16128e6 | 0.743268 | ||||||||
\(687\) | − 2.11551e6i | − 0.171010i | ||||||||
\(688\) | 1.75527e6i | 0.141375i | ||||||||
\(689\) | 1.35014e7 | 1.08350 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.89850e7 | 1.51257 | 0.756285 | − | 0.654243i | \(-0.227013\pi\) | ||||
0.756285 | + | 0.654243i | \(0.227013\pi\) | |||||||
\(692\) | − 929864.i | − 0.0738167i | ||||||||
\(693\) | 1.78796e6i | 0.141424i | ||||||||
\(694\) | −7.45177e6 | −0.587301 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −257620. | −0.0201585 | ||||||||
\(697\) | − 1.13040e7i | − 0.881352i | ||||||||
\(698\) | 1.32151e7i | 1.02668i | ||||||||
\(699\) | 4.05999e6 | 0.314291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.33898e7 | 1.79776 | 0.898878 | − | 0.438199i | \(-0.144384\pi\) | ||||
0.898878 | + | 0.438199i | \(0.144384\pi\) | |||||||
\(702\) | 2.26188e6i | 0.173232i | ||||||||
\(703\) | 5.02981e6i | 0.383852i | ||||||||
\(704\) | 744046. | 0.0565807 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.01486e7 | −0.766293 | ||||||||
\(707\) | 2.94663e6i | 0.221706i | ||||||||
\(708\) | − 187654.i | − 0.0140694i | ||||||||
\(709\) | −2.29816e7 | −1.71698 | −0.858490 | − | 0.512830i | \(-0.828597\pi\) | ||||
−0.858490 | + | 0.512830i | \(0.828597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.89864e6 | −0.289227 | ||||||||
\(712\) | − 570706.i | − 0.0421903i | ||||||||
\(713\) | − 13386.5i | 0 0.000986153i | ||||||||
\(714\) | 4.26008e6 | 0.312732 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.94269e6 | −0.579008 | ||||||||
\(717\) | − 8.30252e6i | − 0.603132i | ||||||||
\(718\) | 1.60940e7i | 1.16507i | ||||||||
\(719\) | −2.01205e7 | −1.45150 | −0.725751 | − | 0.687958i | \(-0.758508\pi\) | ||||
−0.725751 | + | 0.687958i | \(0.758508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.37697e7 | 1.70289 | ||||||||
\(722\) | 8.58935e6i | 0.613221i | ||||||||
\(723\) | 1.11265e7i | 0.791611i | ||||||||
\(724\) | −9.00867e6 | −0.638725 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.60993e6 | 0.324603 | ||||||||
\(727\) | − 1.34321e7i | − 0.942554i | −0.881985 | − | 0.471277i | \(-0.843793\pi\) | ||||
0.881985 | − | 0.471277i | \(-0.156207\pi\) | |||||||
\(728\) | − 6.03247e6i | − 0.421859i | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.67706e6 | −0.462160 | ||||||||
\(732\) | − 192462.i | − 0.0132760i | ||||||||
\(733\) | 1.65480e7i | 1.13759i | 0.822480 | + | 0.568794i | \(0.192590\pi\) | ||||
−0.822480 | + | 0.568794i | \(0.807410\pi\) | |||||||
\(734\) | −1.11396e7 | −0.763183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.12491e6 | 0.0765459 | ||||||||
\(737\) | 6.62490e6i | 0.449273i | ||||||||
\(738\) | − 3.76092e6i | − 0.254187i | ||||||||
\(739\) | 7.62922e6 | 0.513888 | 0.256944 | − | 0.966426i | \(-0.417284\pi\) | ||||
0.256944 | + | 0.966426i | \(0.417284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.00282e6 | −0.267806 | ||||||||
\(742\) | − 8.46033e6i | − 0.564128i | ||||||||
\(743\) | − 1.34847e7i | − 0.896127i | −0.894002 | − | 0.448064i | \(-0.852114\pi\) | ||||
0.894002 | − | 0.448064i | \(-0.147886\pi\) | |||||||
\(744\) | −7018.98 | −0.000464881 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.14774e7 | −0.755089 | ||||||||
\(747\) | 7.36331e6i | 0.482805i | ||||||||
\(748\) | 2.83036e6i | 0.184964i | ||||||||
\(749\) | 2.93530e6 | 0.191182 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.37365e7 | −0.888743 | −0.444372 | − | 0.895843i | \(-0.646573\pi\) | ||||
−0.444372 | + | 0.895843i | \(0.646573\pi\) | |||||||
\(752\) | 364509.i | 0.0235052i | ||||||||
\(753\) | 1.70746e7i | 1.09740i | ||||||||
\(754\) | −1.38772e6 | −0.0888939 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.41736e6 | 0.0901936 | ||||||||
\(757\) | 832827.i | 0.0528220i | 0.999651 | + | 0.0264110i | \(0.00840786\pi\) | ||||
−0.999651 | + | 0.0264110i | \(0.991592\pi\) | |||||||
\(758\) | − 1.63203e7i | − 1.03170i | ||||||||
\(759\) | −1.79597e6 | −0.113160 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.49849e7 | −1.56392 | −0.781961 | − | 0.623327i | \(-0.785780\pi\) | ||||
−0.781961 | + | 0.623327i | \(0.785780\pi\) | |||||||
\(762\) | 5.29520e6i | 0.330366i | ||||||||
\(763\) | 2.23316e7i | 1.38870i | ||||||||
\(764\) | 9.00313e6 | 0.558033 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.08016e7 | −1.28093 | ||||||||
\(767\) | − 1.01083e6i | − 0.0620427i | ||||||||
\(768\) | − 589824.i | − 0.0360844i | ||||||||
\(769\) | −261268. | −0.0159320 | −0.00796600 | − | 0.999968i | \(-0.502536\pi\) | ||||
−0.00796600 | + | 0.999968i | \(0.502536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.90252e6 | 0.115264 | ||||||||
\(772\) | 8.44936e6i | 0.510247i | ||||||||
\(773\) | 2.07535e7i | 1.24923i | 0.780934 | + | 0.624614i | \(0.214744\pi\) | ||||
−0.780934 | + | 0.624614i | \(0.785256\pi\) | |||||||
\(774\) | −2.22151e6 | −0.133290 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.56481e6 | 0.212511 | ||||||||
\(777\) | − 9.59371e6i | − 0.570077i | ||||||||
\(778\) | 6.06187e6i | 0.359052i | ||||||||
\(779\) | 6.65564e6 | 0.392958 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.81998e6 | 0.576080 | ||||||||
\(782\) | 4.27916e6i | 0.250231i | ||||||||
\(783\) | − 326051.i | − 0.0190056i | ||||||||
\(784\) | 522473. | 0.0303580 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.41397e6 | 0.197108 | ||||||||
\(787\) | 1.35079e7i | 0.777411i | 0.921362 | + | 0.388706i | \(0.127078\pi\) | ||||
−0.921362 | + | 0.388706i | \(0.872922\pi\) | |||||||
\(788\) | 1.43251e7i | 0.821830i | ||||||||
\(789\) | 107742. | 0.00616156 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.43882e6 | −0.365902 | ||||||||
\(792\) | 941683.i | 0.0533448i | ||||||||
\(793\) | − 1.03673e6i | − 0.0585438i | ||||||||
\(794\) | −82476.8 | −0.00464280 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.45244e7 | −0.812488 | ||||||||
\(797\) | 1.48523e7i | 0.828226i | 0.910225 | + | 0.414113i | \(0.135908\pi\) | ||||
−0.910225 | + | 0.414113i | \(0.864092\pi\) | |||||||
\(798\) | 2.50828e6i | 0.139434i | ||||||||
\(799\) | −1.38660e6 | −0.0768392 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 722300. | 0.0397774 | ||||||||
\(802\) | − 1.09440e7i | − 0.600813i | ||||||||
\(803\) | 1.85134e6i | 0.101320i | ||||||||
\(804\) | 5.25172e6 | 0.286525 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37808.9 | −0.00205001 | ||||||||
\(807\) | 5.40795e6i | 0.292314i | ||||||||
\(808\) | 1.55193e6i | 0.0836267i | ||||||||
\(809\) | −1.02647e7 | −0.551412 | −0.275706 | − | 0.961242i | \(-0.588912\pi\) | ||||
−0.275706 | + | 0.961242i | \(0.588912\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.19932e6 | −0.491138 | −0.245569 | − | 0.969379i | \(-0.578975\pi\) | ||||
−0.245569 | + | 0.969379i | \(0.578975\pi\) | |||||||
\(812\) | 869582.i | 0.0462829i | ||||||||
\(813\) | 9.57532e6i | 0.508074i | ||||||||
\(814\) | 6.37398e6 | 0.337171 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.24370e6 | 0.117961 | ||||||||
\(817\) | − 3.93137e6i | − 0.206058i | ||||||||
\(818\) | − 1.22679e7i | − 0.641044i | ||||||||
\(819\) | 7.63485e6 | 0.397732 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.14810e7 | −0.594460 | −0.297230 | − | 0.954806i | \(-0.596063\pi\) | ||||
−0.297230 | + | 0.954806i | \(0.596063\pi\) | |||||||
\(822\) | − 7.53383e6i | − 0.388899i | ||||||||
\(823\) | − 6.34501e6i | − 0.326537i | −0.986582 | − | 0.163269i | \(-0.947796\pi\) | ||||
0.986582 | − | 0.163269i | \(-0.0522037\pi\) | |||||||
\(824\) | 1.25190e7 | 0.642323 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −633416. | −0.0323027 | ||||||||
\(827\) | 8.47717e6i | 0.431010i | 0.976503 | + | 0.215505i | \(0.0691398\pi\) | ||||
−0.976503 | + | 0.215505i | \(0.930860\pi\) | |||||||
\(828\) | 1.42371e6i | 0.0721681i | ||||||||
\(829\) | −3.07145e6 | −0.155224 | −0.0776118 | − | 0.996984i | \(-0.524729\pi\) | ||||
−0.0776118 | + | 0.996984i | \(0.524729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.19591e6 | 0.160543 | ||||||||
\(832\) | − 3.17719e6i | − 0.159123i | ||||||||
\(833\) | 1.98749e6i | 0.0992414i | ||||||||
\(834\) | 2.87091e6 | 0.142924 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.66648e6 | −0.0824678 | ||||||||
\(837\) | − 8883.40i | 0 0.000438294i | ||||||||
\(838\) | 6.90467e6i | 0.339651i | ||||||||
\(839\) | 1.09247e7 | 0.535802 | 0.267901 | − | 0.963447i | \(-0.413670\pi\) | ||||
0.267901 | + | 0.963447i | \(0.413670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03111e7 | −0.990247 | ||||||||
\(842\) | − 1.94892e7i | − 0.947356i | ||||||||
\(843\) | 1.17108e7i | 0.567566i | ||||||||
\(844\) | 1.32211e7 | 0.638867 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −461331. | −0.0221609 | ||||||||
\(847\) | − 1.55605e7i | − 0.745274i | ||||||||
\(848\) | − 4.45589e6i | − 0.212787i | ||||||||
\(849\) | 1.41277e7 | 0.672671 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.63668e6 | 0.456146 | ||||||||
\(852\) | − 7.78455e6i | − 0.367396i | ||||||||
\(853\) | 1.07711e7i | 0.506860i | 0.967354 | + | 0.253430i | \(0.0815587\pi\) | ||||
−0.967354 | + | 0.253430i | \(0.918441\pi\) | |||||||
\(854\) | −649642. | −0.0304810 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.54596e6 | 0.0721132 | ||||||||
\(857\) | 2.21421e6i | 0.102983i | 0.998673 | + | 0.0514917i | \(0.0163976\pi\) | ||||
−0.998673 | + | 0.0514917i | \(0.983602\pi\) | |||||||
\(858\) | 5.07253e6i | 0.235238i | ||||||||
\(859\) | −1.83525e7 | −0.848618 | −0.424309 | − | 0.905517i | \(-0.639483\pi\) | ||||
−0.424309 | + | 0.905517i | \(0.639483\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.26948e7 | −0.583602 | ||||||||
\(862\) | 8.82786e6i | 0.404657i | ||||||||
\(863\) | − 3.69703e7i | − 1.68976i | −0.534954 | − | 0.844881i | \(-0.679671\pi\) | ||||
0.534954 | − | 0.844881i | \(-0.320329\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.02917e6 | −0.363811 | ||||||||
\(867\) | − 4.24365e6i | − 0.191731i | ||||||||
\(868\) | 23692.1i | 0.00106735i | ||||||||
\(869\) | −8.74314e6 | −0.392752 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.82893e7 | 1.26350 | ||||||||
\(872\) | 1.17616e7i | 0.523813i | ||||||||
\(873\) | 4.51171e6i | 0.200357i | ||||||||
\(874\) | −2.51951e6 | −0.111568 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.46760e6 | 0.0646171 | ||||||||
\(877\) | 2.21326e7i | 0.971705i | 0.874041 | + | 0.485852i | \(0.161491\pi\) | ||||
−0.874041 | + | 0.485852i | \(0.838509\pi\) | |||||||
\(878\) | 647988.i | 0.0283681i | ||||||||
\(879\) | 4.28611e6 | 0.187108 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.98284e7 | −0.860693 | −0.430346 | − | 0.902664i | \(-0.641609\pi\) | ||||
−0.430346 | + | 0.902664i | \(0.641609\pi\) | |||||||
\(882\) | 661254.i | 0.0286218i | ||||||||
\(883\) | − 2.92615e7i | − 1.26298i | −0.775385 | − | 0.631489i | \(-0.782444\pi\) | ||||
0.775385 | − | 0.631489i | \(-0.217556\pi\) | |||||||
\(884\) | 1.20861e7 | 0.520180 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.95462e7 | −0.836524 | ||||||||
\(887\) | 1.80630e7i | 0.770870i | 0.922735 | + | 0.385435i | \(0.125949\pi\) | ||||
−0.922735 | + | 0.385435i | \(0.874051\pi\) | |||||||
\(888\) | − 5.05282e6i | − 0.215031i | ||||||||
\(889\) | 1.78736e7 | 0.758505 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.19182e6 | −0.0502939 | ||||||||
\(892\) | − 3.17904e6i | − 0.133778i | ||||||||
\(893\) | − 816410.i | − 0.0342594i | ||||||||
\(894\) | 1.05557e7 | 0.441715 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.99091e6 | −0.0828481 | ||||||||
\(897\) | 7.66905e6i | 0.318244i | ||||||||
\(898\) | − 6.92059e6i | − 0.286386i | ||||||||
\(899\) | 5450.16 | 0.000224911 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.69503e7 | 0.695608 | ||||||||
\(902\) | − 8.43430e6i | − 0.345170i | ||||||||
\(903\) | 7.49857e6i | 0.306027i | ||||||||
\(904\) | −3.39120e6 | −0.138017 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.00329e7 | 0.406073 | ||||||||
\(907\) | − 7.19621e6i | − 0.290460i | −0.989398 | − | 0.145230i | \(-0.953608\pi\) | ||||
0.989398 | − | 0.145230i | \(-0.0463922\pi\) | |||||||
\(908\) | − 7.59644e6i | − 0.305770i | ||||||||
\(909\) | −1.96417e6 | −0.0788440 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.38536e7 | −1.75069 | −0.875346 | − | 0.483497i | \(-0.839366\pi\) | ||||
−0.875346 | + | 0.483497i | \(0.839366\pi\) | |||||||
\(912\) | 1.32106e6i | 0.0525940i | ||||||||
\(913\) | 1.65131e7i | 0.655618i | ||||||||
\(914\) | 1.75361e6 | 0.0694334 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.76090e6 | −0.148099 | ||||||||
\(917\) | − 1.15236e7i | − 0.452550i | ||||||||
\(918\) | 2.83968e6i | 0.111215i | ||||||||
\(919\) | −2.83993e7 | −1.10922 | −0.554612 | − | 0.832109i | \(-0.687133\pi\) | ||||
−0.554612 | + | 0.832109i | \(0.687133\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.51936e6 | 0.0978682 | ||||||||
\(922\) | 970588.i | 0.0376017i | ||||||||
\(923\) | − 4.19328e7i | − 1.62013i | ||||||||
\(924\) | 3.17859e6 | 0.122477 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.39563e7 | 0.918106 | ||||||||
\(927\) | 1.58444e7i | 0.605587i | ||||||||
\(928\) | 457992.i | 0.0174577i | ||||||||
\(929\) | 1.58918e7 | 0.604134 | 0.302067 | − | 0.953287i | \(-0.402323\pi\) | ||||
0.302067 | + | 0.953287i | \(0.402323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17021e6 | −0.0442476 | ||||||||
\(932\) | − 7.21777e6i | − 0.272184i | ||||||||
\(933\) | − 1.51329e7i | − 0.569137i | ||||||||
\(934\) | −1.31723e7 | −0.494076 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.02113e6 | 0.150023 | ||||||||
\(937\) | 2.35736e7i | 0.877158i | 0.898693 | + | 0.438579i | \(0.144518\pi\) | ||||
−0.898693 | + | 0.438579i | \(0.855482\pi\) | |||||||
\(938\) | − 1.77269e7i | − 0.657847i | ||||||||
\(939\) | 2.11494e7 | 0.782768 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.35257e7 | −0.866102 | −0.433051 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433051 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(942\) | − 4.18306e6i | − 0.153591i | ||||||||
\(943\) | − 1.27516e7i | − 0.466967i | ||||||||
\(944\) | −333608. | −0.0121845 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.98199e6 | −0.180999 | ||||||||
\(947\) | − 58494.7i | − 0.00211954i | −0.999999 | − | 0.00105977i | \(-0.999663\pi\) | ||||
0.999999 | − | 0.00105977i | \(-0.000337335\pi\) | |||||||
\(948\) | 6.93091e6i | 0.250478i | ||||||||
\(949\) | 7.90548e6 | 0.284946 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.02459e7 | −1.08446 | ||||||||
\(952\) | − 7.57347e6i | − 0.270833i | ||||||||
\(953\) | − 8.44025e6i | − 0.301039i | −0.988607 | − | 0.150520i | \(-0.951905\pi\) | ||||
0.988607 | − | 0.150520i | \(-0.0480947\pi\) | |||||||
\(954\) | 5.63949e6 | 0.200617 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.47600e7 | −0.522327 | ||||||||
\(957\) | − 731207.i | − 0.0258083i | ||||||||
\(958\) | 9.95569e6i | 0.350476i | ||||||||
\(959\) | −2.54300e7 | −0.892894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86290e7 | −0.999995 | ||||||||
\(962\) | − 2.72178e7i | − 0.948235i | ||||||||
\(963\) | 1.95661e6i | 0.0679890i | ||||||||
\(964\) | 1.97804e7 | 0.685555 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.80564e6 | 0.165695 | ||||||||
\(967\) | 2.11888e7i | 0.728685i | 0.931265 | + | 0.364342i | \(0.118706\pi\) | ||||
−0.931265 | + | 0.364342i | \(0.881294\pi\) | |||||||
\(968\) | − 8.19543e6i | − 0.281115i | ||||||||
\(969\) | −5.02534e6 | −0.171932 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.53719e7 | 0.523215 | 0.261608 | − | 0.965174i | \(-0.415747\pi\) | ||||
0.261608 | + | 0.965174i | \(0.415747\pi\) | |||||||
\(972\) | 944784.i | 0.0320750i | ||||||||
\(973\) | − 9.69057e6i | − 0.328146i | ||||||||
\(974\) | −3.25335e7 | −1.09884 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −342154. | −0.0114973 | ||||||||
\(977\) | 3.99264e7i | 1.33821i | 0.743168 | + | 0.669104i | \(0.233322\pi\) | ||||
−0.743168 | + | 0.669104i | \(0.766678\pi\) | |||||||
\(978\) | − 2.17944e6i | − 0.0728615i | ||||||||
\(979\) | 1.61984e6 | 0.0540152 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.48858e7 | −0.493855 | ||||||||
\(982\) | 8.95717e6i | 0.296410i | ||||||||
\(983\) | 2.80060e7i | 0.924417i | 0.886771 | + | 0.462209i | \(0.152943\pi\) | ||||
−0.886771 | + | 0.462209i | \(0.847057\pi\) | |||||||
\(984\) | −6.68608e6 | −0.220132 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.74221e6 | −0.0570700 | ||||||||
\(987\) | 1.55720e6i | 0.0508804i | ||||||||
\(988\) | 7.11612e6i | 0.231927i | ||||||||
\(989\) | −7.53216e6 | −0.244866 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.81595e7 | −1.55775 | −0.778874 | − | 0.627180i | \(-0.784209\pi\) | ||||
−0.778874 | + | 0.627180i | \(0.784209\pi\) | |||||||
\(992\) | 12478.2i | 0 0.000402599i | ||||||||
\(993\) | − 9.77990e6i | − 0.314747i | ||||||||
\(994\) | −2.62763e7 | −0.843525 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.30903e7 | 0.418121 | ||||||||
\(997\) | 2.88893e7i | 0.920449i | 0.887803 | + | 0.460225i | \(0.152231\pi\) | ||||
−0.887803 | + | 0.460225i | \(0.847769\pi\) | |||||||
\(998\) | − 8.25510e6i | − 0.262359i | ||||||||
\(999\) | 6.39497e6 | 0.202733 |
(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 | 750.6.c.a.499.4 | 8 | ||
5.2 | odd | 4 | 750.6.a.e.1.1 | yes | 4 | ||
5.3 | odd | 4 | 750.6.a.d.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 750.6.c.a.499.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
750.6.a.d.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
750.6.a.e.1.1 | yes | 4 | 5.2 | odd | 4 | ||
750.6.c.a.499.4 | 8 | 1.1 | even | 1 | trivial | ||
750.6.c.a.499.5 | 8 | 5.4 | even | 2 | inner |