Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,6,Mod(1,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(1.76422201794\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −15.0000 | −0.962250 | −0.481125 | − | 0.876652i | \(-0.659772\pi\) | ||||
−0.481125 | + | 0.876652i | \(0.659772\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | −19.0000 | −0.339882 | −0.169941 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169941 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(6\) | 60.0000 | 0.680414 | ||||||||
\(7\) | 10.0000 | 0.0771356 | 0.0385678 | − | 0.999256i | \(-0.487720\pi\) | ||||
0.0385678 | + | 0.999256i | \(0.487720\pi\) | |||||||
\(8\) | 192.000 | 1.06066 | ||||||||
\(9\) | −18.0000 | −0.0740741 | ||||||||
\(10\) | 76.0000 | 0.240333 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 240.000 | 0.481125 | ||||||||
\(13\) | −1148.00 | −1.88401 | −0.942006 | − | 0.335597i | \(-0.891062\pi\) | ||||
−0.942006 | + | 0.335597i | \(0.891062\pi\) | |||||||
\(14\) | −40.0000 | −0.0545431 | ||||||||
\(15\) | 285.000 | 0.327052 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | 686.000 | 0.575707 | 0.287854 | − | 0.957674i | \(-0.407058\pi\) | ||||
0.287854 | + | 0.957674i | \(0.407058\pi\) | |||||||
\(18\) | 72.0000 | 0.0523783 | ||||||||
\(19\) | −384.000 | −0.244032 | −0.122016 | − | 0.992528i | \(-0.538936\pi\) | ||||
−0.122016 | + | 0.992528i | \(0.538936\pi\) | |||||||
\(20\) | 304.000 | 0.169941 | ||||||||
\(21\) | −150.000 | −0.0742238 | ||||||||
\(22\) | 484.000 | 0.213201 | ||||||||
\(23\) | 3709.00 | 1.46197 | 0.730983 | − | 0.682396i | \(-0.239062\pi\) | ||||
0.730983 | + | 0.682396i | \(0.239062\pi\) | |||||||
\(24\) | −2880.00 | −1.02062 | ||||||||
\(25\) | −2764.00 | −0.884480 | ||||||||
\(26\) | 4592.00 | 1.33220 | ||||||||
\(27\) | 3915.00 | 1.03353 | ||||||||
\(28\) | −160.000 | −0.0385678 | ||||||||
\(29\) | −5424.00 | −1.19764 | −0.598818 | − | 0.800885i | \(-0.704363\pi\) | ||||
−0.598818 | + | 0.800885i | \(0.704363\pi\) | |||||||
\(30\) | −1140.00 | −0.231261 | ||||||||
\(31\) | −6443.00 | −1.20416 | −0.602080 | − | 0.798436i | \(-0.705661\pi\) | ||||
−0.602080 | + | 0.798436i | \(0.705661\pi\) | |||||||
\(32\) | −5120.00 | −0.883883 | ||||||||
\(33\) | 1815.00 | 0.290129 | ||||||||
\(34\) | −2744.00 | −0.407087 | ||||||||
\(35\) | −190.000 | −0.0262170 | ||||||||
\(36\) | 288.000 | 0.0370370 | ||||||||
\(37\) | 12063.0 | 1.44861 | 0.724304 | − | 0.689481i | \(-0.242161\pi\) | ||||
0.724304 | + | 0.689481i | \(0.242161\pi\) | |||||||
\(38\) | 1536.00 | 0.172557 | ||||||||
\(39\) | 17220.0 | 1.81289 | ||||||||
\(40\) | −3648.00 | −0.360500 | ||||||||
\(41\) | −1528.00 | −0.141959 | −0.0709796 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709796 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(42\) | 600.000 | 0.0524841 | ||||||||
\(43\) | −4026.00 | −0.332049 | −0.166025 | − | 0.986122i | \(-0.553093\pi\) | ||||
−0.166025 | + | 0.986122i | \(0.553093\pi\) | |||||||
\(44\) | 1936.00 | 0.150756 | ||||||||
\(45\) | 342.000 | 0.0251765 | ||||||||
\(46\) | −14836.0 | −1.03377 | ||||||||
\(47\) | 7168.00 | 0.473318 | 0.236659 | − | 0.971593i | \(-0.423948\pi\) | ||||
0.236659 | + | 0.971593i | \(0.423948\pi\) | |||||||
\(48\) | 3840.00 | 0.240563 | ||||||||
\(49\) | −16707.0 | −0.994050 | ||||||||
\(50\) | 11056.0 | 0.625422 | ||||||||
\(51\) | −10290.0 | −0.553975 | ||||||||
\(52\) | 18368.0 | 0.942006 | ||||||||
\(53\) | −29862.0 | −1.46026 | −0.730128 | − | 0.683310i | \(-0.760540\pi\) | ||||
−0.730128 | + | 0.683310i | \(0.760540\pi\) | |||||||
\(54\) | −15660.0 | −0.730815 | ||||||||
\(55\) | 2299.00 | 0.102478 | ||||||||
\(56\) | 1920.00 | 0.0818147 | ||||||||
\(57\) | 5760.00 | 0.234820 | ||||||||
\(58\) | 21696.0 | 0.846856 | ||||||||
\(59\) | −6461.00 | −0.241640 | −0.120820 | − | 0.992674i | \(-0.538552\pi\) | ||||
−0.120820 | + | 0.992674i | \(0.538552\pi\) | |||||||
\(60\) | −4560.00 | −0.163526 | ||||||||
\(61\) | −16980.0 | −0.584269 | −0.292135 | − | 0.956377i | \(-0.594366\pi\) | ||||
−0.292135 | + | 0.956377i | \(0.594366\pi\) | |||||||
\(62\) | 25772.0 | 0.851469 | ||||||||
\(63\) | −180.000 | −0.00571375 | ||||||||
\(64\) | 28672.0 | 0.875000 | ||||||||
\(65\) | 21812.0 | 0.640342 | ||||||||
\(66\) | −7260.00 | −0.205152 | ||||||||
\(67\) | 29999.0 | 0.816432 | 0.408216 | − | 0.912885i | \(-0.366151\pi\) | ||||
0.408216 | + | 0.912885i | \(0.366151\pi\) | |||||||
\(68\) | −10976.0 | −0.287854 | ||||||||
\(69\) | −55635.0 | −1.40678 | ||||||||
\(70\) | 760.000 | 0.0185382 | ||||||||
\(71\) | 31023.0 | 0.730362 | 0.365181 | − | 0.930937i | \(-0.381007\pi\) | ||||
0.365181 | + | 0.930937i | \(0.381007\pi\) | |||||||
\(72\) | −3456.00 | −0.0785674 | ||||||||
\(73\) | 1924.00 | 0.0422569 | 0.0211285 | − | 0.999777i | \(-0.493274\pi\) | ||||
0.0211285 | + | 0.999777i | \(0.493274\pi\) | |||||||
\(74\) | −48252.0 | −1.02432 | ||||||||
\(75\) | 41460.0 | 0.851091 | ||||||||
\(76\) | 6144.00 | 0.122016 | ||||||||
\(77\) | −1210.00 | −0.0232573 | ||||||||
\(78\) | −68880.0 | −1.28191 | ||||||||
\(79\) | 65138.0 | 1.17427 | 0.587133 | − | 0.809490i | \(-0.300256\pi\) | ||||
0.587133 | + | 0.809490i | \(0.300256\pi\) | |||||||
\(80\) | 4864.00 | 0.0849706 | ||||||||
\(81\) | −54351.0 | −0.920439 | ||||||||
\(82\) | 6112.00 | 0.100380 | ||||||||
\(83\) | −102714. | −1.63657 | −0.818285 | − | 0.574813i | \(-0.805075\pi\) | ||||
−0.818285 | + | 0.574813i | \(0.805075\pi\) | |||||||
\(84\) | 2400.00 | 0.0371119 | ||||||||
\(85\) | −13034.0 | −0.195673 | ||||||||
\(86\) | 16104.0 | 0.234794 | ||||||||
\(87\) | 81360.0 | 1.15243 | ||||||||
\(88\) | −23232.0 | −0.319801 | ||||||||
\(89\) | 17415.0 | 0.233050 | 0.116525 | − | 0.993188i | \(-0.462825\pi\) | ||||
0.116525 | + | 0.993188i | \(0.462825\pi\) | |||||||
\(90\) | −1368.00 | −0.0178025 | ||||||||
\(91\) | −11480.0 | −0.145324 | ||||||||
\(92\) | −59344.0 | −0.730983 | ||||||||
\(93\) | 96645.0 | 1.15870 | ||||||||
\(94\) | −28672.0 | −0.334687 | ||||||||
\(95\) | 7296.00 | 0.0829422 | ||||||||
\(96\) | 76800.0 | 0.850517 | ||||||||
\(97\) | 66905.0 | 0.721987 | 0.360993 | − | 0.932568i | \(-0.382438\pi\) | ||||
0.360993 | + | 0.932568i | \(0.382438\pi\) | |||||||
\(98\) | 66828.0 | 0.702900 | ||||||||
\(99\) | 2178.00 | 0.0223342 | ||||||||
\(100\) | 44224.0 | 0.442240 | ||||||||
\(101\) | 96730.0 | 0.943534 | 0.471767 | − | 0.881723i | \(-0.343616\pi\) | ||||
0.471767 | + | 0.881723i | \(0.343616\pi\) | |||||||
\(102\) | 41160.0 | 0.391719 | ||||||||
\(103\) | −95704.0 | −0.888868 | −0.444434 | − | 0.895812i | \(-0.646595\pi\) | ||||
−0.444434 | + | 0.895812i | \(0.646595\pi\) | |||||||
\(104\) | −220416. | −1.99830 | ||||||||
\(105\) | 2850.00 | 0.0252273 | ||||||||
\(106\) | 119448. | 1.03256 | ||||||||
\(107\) | −32658.0 | −0.275759 | −0.137880 | − | 0.990449i | \(-0.544029\pi\) | ||||
−0.137880 | + | 0.990449i | \(0.544029\pi\) | |||||||
\(108\) | −62640.0 | −0.516764 | ||||||||
\(109\) | −185438. | −1.49497 | −0.747485 | − | 0.664279i | \(-0.768739\pi\) | ||||
−0.747485 | + | 0.664279i | \(0.768739\pi\) | |||||||
\(110\) | −9196.00 | −0.0724632 | ||||||||
\(111\) | −180945. | −1.39392 | ||||||||
\(112\) | −2560.00 | −0.0192839 | ||||||||
\(113\) | 72849.0 | 0.536695 | 0.268347 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268347 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(114\) | −23040.0 | −0.166043 | ||||||||
\(115\) | −70471.0 | −0.496896 | ||||||||
\(116\) | 86784.0 | 0.598818 | ||||||||
\(117\) | 20664.0 | 0.139556 | ||||||||
\(118\) | 25844.0 | 0.170866 | ||||||||
\(119\) | 6860.00 | 0.0444075 | ||||||||
\(120\) | 54720.0 | 0.346891 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 67920.0 | 0.413141 | ||||||||
\(123\) | 22920.0 | 0.136600 | ||||||||
\(124\) | 103088. | 0.602080 | ||||||||
\(125\) | 111891. | 0.640501 | ||||||||
\(126\) | 720.000 | 0.00404023 | ||||||||
\(127\) | −78184.0 | −0.430139 | −0.215069 | − | 0.976599i | \(-0.568998\pi\) | ||||
−0.215069 | + | 0.976599i | \(0.568998\pi\) | |||||||
\(128\) | 49152.0 | 0.265165 | ||||||||
\(129\) | 60390.0 | 0.319515 | ||||||||
\(130\) | −87248.0 | −0.452790 | ||||||||
\(131\) | −462.000 | −0.00235214 | −0.00117607 | − | 0.999999i | \(-0.500374\pi\) | ||||
−0.00117607 | + | 0.999999i | \(0.500374\pi\) | |||||||
\(132\) | −29040.0 | −0.145065 | ||||||||
\(133\) | −3840.00 | −0.0188236 | ||||||||
\(134\) | −119996. | −0.577304 | ||||||||
\(135\) | −74385.0 | −0.351278 | ||||||||
\(136\) | 131712. | 0.610630 | ||||||||
\(137\) | 296233. | 1.34844 | 0.674221 | − | 0.738530i | \(-0.264480\pi\) | ||||
0.674221 | + | 0.738530i | \(0.264480\pi\) | |||||||
\(138\) | 222540. | 0.994742 | ||||||||
\(139\) | −399818. | −1.75519 | −0.877597 | − | 0.479398i | \(-0.840855\pi\) | ||||
−0.877597 | + | 0.479398i | \(0.840855\pi\) | |||||||
\(140\) | 3040.00 | 0.0131085 | ||||||||
\(141\) | −107520. | −0.455451 | ||||||||
\(142\) | −124092. | −0.516444 | ||||||||
\(143\) | 138908. | 0.568051 | ||||||||
\(144\) | 4608.00 | 0.0185185 | ||||||||
\(145\) | 103056. | 0.407055 | ||||||||
\(146\) | −7696.00 | −0.0298802 | ||||||||
\(147\) | 250605. | 0.956525 | ||||||||
\(148\) | −193008. | −0.724304 | ||||||||
\(149\) | 72670.0 | 0.268157 | 0.134079 | − | 0.990971i | \(-0.457193\pi\) | ||||
0.134079 | + | 0.990971i | \(0.457193\pi\) | |||||||
\(150\) | −165840. | −0.601812 | ||||||||
\(151\) | −303082. | −1.08173 | −0.540864 | − | 0.841110i | \(-0.681902\pi\) | ||||
−0.540864 | + | 0.841110i | \(0.681902\pi\) | |||||||
\(152\) | −73728.0 | −0.258835 | ||||||||
\(153\) | −12348.0 | −0.0426450 | ||||||||
\(154\) | 4840.00 | 0.0164454 | ||||||||
\(155\) | 122417. | 0.409272 | ||||||||
\(156\) | −275520. | −0.906445 | ||||||||
\(157\) | −532987. | −1.72571 | −0.862854 | − | 0.505453i | \(-0.831326\pi\) | ||||
−0.862854 | + | 0.505453i | \(0.831326\pi\) | |||||||
\(158\) | −260552. | −0.830332 | ||||||||
\(159\) | 447930. | 1.40513 | ||||||||
\(160\) | 97280.0 | 0.300416 | ||||||||
\(161\) | 37090.0 | 0.112770 | ||||||||
\(162\) | 217404. | 0.650849 | ||||||||
\(163\) | 282076. | 0.831567 | 0.415783 | − | 0.909464i | \(-0.363507\pi\) | ||||
0.415783 | + | 0.909464i | \(0.363507\pi\) | |||||||
\(164\) | 24448.0 | 0.0709796 | ||||||||
\(165\) | −34485.0 | −0.0986099 | ||||||||
\(166\) | 410856. | 1.15723 | ||||||||
\(167\) | −573588. | −1.59151 | −0.795754 | − | 0.605620i | \(-0.792925\pi\) | ||||
−0.795754 | + | 0.605620i | \(0.792925\pi\) | |||||||
\(168\) | −28800.0 | −0.0787262 | ||||||||
\(169\) | 946611. | 2.54950 | ||||||||
\(170\) | 52136.0 | 0.138362 | ||||||||
\(171\) | 6912.00 | 0.0180765 | ||||||||
\(172\) | 64416.0 | 0.166025 | ||||||||
\(173\) | −386286. | −0.981282 | −0.490641 | − | 0.871362i | \(-0.663237\pi\) | ||||
−0.490641 | + | 0.871362i | \(0.663237\pi\) | |||||||
\(174\) | −325440. | −0.814888 | ||||||||
\(175\) | −27640.0 | −0.0682249 | ||||||||
\(176\) | 30976.0 | 0.0753778 | ||||||||
\(177\) | 96915.0 | 0.232519 | ||||||||
\(178\) | −69660.0 | −0.164791 | ||||||||
\(179\) | 545079. | 1.27153 | 0.635765 | − | 0.771882i | \(-0.280685\pi\) | ||||
0.635765 | + | 0.771882i | \(0.280685\pi\) | |||||||
\(180\) | −5472.00 | −0.0125882 | ||||||||
\(181\) | −279485. | −0.634106 | −0.317053 | − | 0.948408i | \(-0.602693\pi\) | ||||
−0.317053 | + | 0.948408i | \(0.602693\pi\) | |||||||
\(182\) | 45920.0 | 0.102760 | ||||||||
\(183\) | 254700. | 0.562213 | ||||||||
\(184\) | 712128. | 1.55065 | ||||||||
\(185\) | −229197. | −0.492356 | ||||||||
\(186\) | −386580. | −0.819327 | ||||||||
\(187\) | −83006.0 | −0.173582 | ||||||||
\(188\) | −114688. | −0.236659 | ||||||||
\(189\) | 39150.0 | 0.0797218 | ||||||||
\(190\) | −29184.0 | −0.0586490 | ||||||||
\(191\) | −444437. | −0.881509 | −0.440755 | − | 0.897628i | \(-0.645289\pi\) | ||||
−0.440755 | + | 0.897628i | \(0.645289\pi\) | |||||||
\(192\) | −430080. | −0.841969 | ||||||||
\(193\) | −18476.0 | −0.0357038 | −0.0178519 | − | 0.999841i | \(-0.505683\pi\) | ||||
−0.0178519 | + | 0.999841i | \(0.505683\pi\) | |||||||
\(194\) | −267620. | −0.510522 | ||||||||
\(195\) | −327180. | −0.616170 | ||||||||
\(196\) | 267312. | 0.497025 | ||||||||
\(197\) | 270182. | 0.496010 | 0.248005 | − | 0.968759i | \(-0.420225\pi\) | ||||
0.248005 | + | 0.968759i | \(0.420225\pi\) | |||||||
\(198\) | −8712.00 | −0.0157926 | ||||||||
\(199\) | 43320.0 | 0.0775453 | 0.0387727 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387727 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(200\) | −530688. | −0.938133 | ||||||||
\(201\) | −449985. | −0.785612 | ||||||||
\(202\) | −386920. | −0.667180 | ||||||||
\(203\) | −54240.0 | −0.0923803 | ||||||||
\(204\) | 164640. | 0.276987 | ||||||||
\(205\) | 29032.0 | 0.0482494 | ||||||||
\(206\) | 382816. | 0.628524 | ||||||||
\(207\) | −66762.0 | −0.108294 | ||||||||
\(208\) | 293888. | 0.471003 | ||||||||
\(209\) | 46464.0 | 0.0735785 | ||||||||
\(210\) | −11400.0 | −0.0178384 | ||||||||
\(211\) | 1.02968e6 | 1.59220 | 0.796100 | − | 0.605165i | \(-0.206893\pi\) | ||||
0.796100 | + | 0.605165i | \(0.206893\pi\) | |||||||
\(212\) | 477792. | 0.730128 | ||||||||
\(213\) | −465345. | −0.702791 | ||||||||
\(214\) | 130632. | 0.194991 | ||||||||
\(215\) | 76494.0 | 0.112858 | ||||||||
\(216\) | 751680. | 1.09622 | ||||||||
\(217\) | −64430.0 | −0.0928835 | ||||||||
\(218\) | 741752. | 1.05710 | ||||||||
\(219\) | −28860.0 | −0.0406617 | ||||||||
\(220\) | −36784.0 | −0.0512392 | ||||||||
\(221\) | −787528. | −1.08464 | ||||||||
\(222\) | 723780. | 0.985653 | ||||||||
\(223\) | 461281. | 0.621160 | 0.310580 | − | 0.950547i | \(-0.399477\pi\) | ||||
0.310580 | + | 0.950547i | \(0.399477\pi\) | |||||||
\(224\) | −51200.0 | −0.0681789 | ||||||||
\(225\) | 49752.0 | 0.0655170 | ||||||||
\(226\) | −291396. | −0.379501 | ||||||||
\(227\) | −855570. | −1.10202 | −0.551012 | − | 0.834497i | \(-0.685758\pi\) | ||||
−0.551012 | + | 0.834497i | \(0.685758\pi\) | |||||||
\(228\) | −92160.0 | −0.117410 | ||||||||
\(229\) | −665805. | −0.838993 | −0.419497 | − | 0.907757i | \(-0.637793\pi\) | ||||
−0.419497 | + | 0.907757i | \(0.637793\pi\) | |||||||
\(230\) | 281884. | 0.351359 | ||||||||
\(231\) | 18150.0 | 0.0223793 | ||||||||
\(232\) | −1.04141e6 | −1.27028 | ||||||||
\(233\) | 1.20934e6 | 1.45934 | 0.729671 | − | 0.683798i | \(-0.239673\pi\) | ||||
0.729671 | + | 0.683798i | \(0.239673\pi\) | |||||||
\(234\) | −82656.0 | −0.0986813 | ||||||||
\(235\) | −136192. | −0.160873 | ||||||||
\(236\) | 103376. | 0.120820 | ||||||||
\(237\) | −977070. | −1.12994 | ||||||||
\(238\) | −27440.0 | −0.0314009 | ||||||||
\(239\) | −571482. | −0.647154 | −0.323577 | − | 0.946202i | \(-0.604886\pi\) | ||||
−0.323577 | + | 0.946202i | \(0.604886\pi\) | |||||||
\(240\) | −72960.0 | −0.0817630 | ||||||||
\(241\) | −267080. | −0.296209 | −0.148105 | − | 0.988972i | \(-0.547317\pi\) | ||||
−0.148105 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(242\) | −58564.0 | −0.0642824 | ||||||||
\(243\) | −136080. | −0.147835 | ||||||||
\(244\) | 271680. | 0.292135 | ||||||||
\(245\) | 317433. | 0.337860 | ||||||||
\(246\) | −91680.0 | −0.0965910 | ||||||||
\(247\) | 440832. | 0.459760 | ||||||||
\(248\) | −1.23706e6 | −1.27720 | ||||||||
\(249\) | 1.54071e6 | 1.57479 | ||||||||
\(250\) | −447564. | −0.452903 | ||||||||
\(251\) | 1.38737e6 | 1.38998 | 0.694988 | − | 0.719022i | \(-0.255410\pi\) | ||||
0.694988 | + | 0.719022i | \(0.255410\pi\) | |||||||
\(252\) | 2880.00 | 0.00285687 | ||||||||
\(253\) | −448789. | −0.440799 | ||||||||
\(254\) | 312736. | 0.304154 | ||||||||
\(255\) | 195510. | 0.188286 | ||||||||
\(256\) | −1.11411e6 | −1.06250 | ||||||||
\(257\) | −885922. | −0.836686 | −0.418343 | − | 0.908289i | \(-0.637389\pi\) | ||||
−0.418343 | + | 0.908289i | \(0.637389\pi\) | |||||||
\(258\) | −241560. | −0.225931 | ||||||||
\(259\) | 120630. | 0.111739 | ||||||||
\(260\) | −348992. | −0.320171 | ||||||||
\(261\) | 97632.0 | 0.0887137 | ||||||||
\(262\) | 1848.00 | 0.00166322 | ||||||||
\(263\) | 1.44687e6 | 1.28986 | 0.644928 | − | 0.764243i | \(-0.276887\pi\) | ||||
0.644928 | + | 0.764243i | \(0.276887\pi\) | |||||||
\(264\) | 348480. | 0.307729 | ||||||||
\(265\) | 567378. | 0.496315 | ||||||||
\(266\) | 15360.0 | 0.0133103 | ||||||||
\(267\) | −261225. | −0.224252 | ||||||||
\(268\) | −479984. | −0.408216 | ||||||||
\(269\) | −353878. | −0.298176 | −0.149088 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149088 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(270\) | 297540. | 0.248391 | ||||||||
\(271\) | 525260. | 0.434461 | 0.217231 | − | 0.976120i | \(-0.430298\pi\) | ||||
0.217231 | + | 0.976120i | \(0.430298\pi\) | |||||||
\(272\) | −175616. | −0.143927 | ||||||||
\(273\) | 172200. | 0.139838 | ||||||||
\(274\) | −1.18493e6 | −0.953492 | ||||||||
\(275\) | 334444. | 0.266681 | ||||||||
\(276\) | 890160. | 0.703389 | ||||||||
\(277\) | −595610. | −0.466404 | −0.233202 | − | 0.972428i | \(-0.574920\pi\) | ||||
−0.233202 | + | 0.972428i | \(0.574920\pi\) | |||||||
\(278\) | 1.59927e6 | 1.24111 | ||||||||
\(279\) | 115974. | 0.0891970 | ||||||||
\(280\) | −36480.0 | −0.0278074 | ||||||||
\(281\) | 732318. | 0.553266 | 0.276633 | − | 0.960976i | \(-0.410781\pi\) | ||||
0.276633 | + | 0.960976i | \(0.410781\pi\) | |||||||
\(282\) | 430080. | 0.322052 | ||||||||
\(283\) | 2.23380e6 | 1.65798 | 0.828989 | − | 0.559264i | \(-0.188916\pi\) | ||||
0.828989 | + | 0.559264i | \(0.188916\pi\) | |||||||
\(284\) | −496368. | −0.365181 | ||||||||
\(285\) | −109440. | −0.0798112 | ||||||||
\(286\) | −555632. | −0.401673 | ||||||||
\(287\) | −15280.0 | −0.0109501 | ||||||||
\(288\) | 92160.0 | 0.0654729 | ||||||||
\(289\) | −949261. | −0.668561 | ||||||||
\(290\) | −412224. | −0.287831 | ||||||||
\(291\) | −1.00358e6 | −0.694732 | ||||||||
\(292\) | −30784.0 | −0.0211285 | ||||||||
\(293\) | −1.53108e6 | −1.04191 | −0.520953 | − | 0.853585i | \(-0.674423\pi\) | ||||
−0.520953 | + | 0.853585i | \(0.674423\pi\) | |||||||
\(294\) | −1.00242e6 | −0.676365 | ||||||||
\(295\) | 122759. | 0.0821293 | ||||||||
\(296\) | 2.31610e6 | 1.53648 | ||||||||
\(297\) | −473715. | −0.311620 | ||||||||
\(298\) | −290680. | −0.189616 | ||||||||
\(299\) | −4.25793e6 | −2.75436 | ||||||||
\(300\) | −663360. | −0.425546 | ||||||||
\(301\) | −40260.0 | −0.0256128 | ||||||||
\(302\) | 1.21233e6 | 0.764897 | ||||||||
\(303\) | −1.45095e6 | −0.907916 | ||||||||
\(304\) | 98304.0 | 0.0610081 | ||||||||
\(305\) | 322620. | 0.198583 | ||||||||
\(306\) | 49392.0 | 0.0301546 | ||||||||
\(307\) | −1.14268e6 | −0.691956 | −0.345978 | − | 0.938243i | \(-0.612453\pi\) | ||||
−0.345978 | + | 0.938243i | \(0.612453\pi\) | |||||||
\(308\) | 19360.0 | 0.0116286 | ||||||||
\(309\) | 1.43556e6 | 0.855313 | ||||||||
\(310\) | −489668. | −0.289399 | ||||||||
\(311\) | 586956. | 0.344116 | 0.172058 | − | 0.985087i | \(-0.444958\pi\) | ||||
0.172058 | + | 0.985087i | \(0.444958\pi\) | |||||||
\(312\) | 3.30624e6 | 1.92286 | ||||||||
\(313\) | −233857. | −0.134924 | −0.0674621 | − | 0.997722i | \(-0.521490\pi\) | ||||
−0.0674621 | + | 0.997722i | \(0.521490\pi\) | |||||||
\(314\) | 2.13195e6 | 1.22026 | ||||||||
\(315\) | 3420.00 | 0.00194200 | ||||||||
\(316\) | −1.04221e6 | −0.587133 | ||||||||
\(317\) | −935503. | −0.522874 | −0.261437 | − | 0.965221i | \(-0.584196\pi\) | ||||
−0.261437 | + | 0.965221i | \(0.584196\pi\) | |||||||
\(318\) | −1.79172e6 | −0.993579 | ||||||||
\(319\) | 656304. | 0.361101 | ||||||||
\(320\) | −544768. | −0.297397 | ||||||||
\(321\) | 489870. | 0.265349 | ||||||||
\(322\) | −148360. | −0.0797402 | ||||||||
\(323\) | −263424. | −0.140491 | ||||||||
\(324\) | 869616. | 0.460219 | ||||||||
\(325\) | 3.17307e6 | 1.66637 | ||||||||
\(326\) | −1.12830e6 | −0.588007 | ||||||||
\(327\) | 2.78157e6 | 1.43854 | ||||||||
\(328\) | −293376. | −0.150571 | ||||||||
\(329\) | 71680.0 | 0.0365097 | ||||||||
\(330\) | 137940. | 0.0697277 | ||||||||
\(331\) | −1.05823e6 | −0.530897 | −0.265449 | − | 0.964125i | \(-0.585520\pi\) | ||||
−0.265449 | + | 0.964125i | \(0.585520\pi\) | |||||||
\(332\) | 1.64342e6 | 0.818285 | ||||||||
\(333\) | −217134. | −0.107304 | ||||||||
\(334\) | 2.29435e6 | 1.12537 | ||||||||
\(335\) | −569981. | −0.277491 | ||||||||
\(336\) | 38400.0 | 0.0185559 | ||||||||
\(337\) | 506186. | 0.242793 | 0.121396 | − | 0.992604i | \(-0.461263\pi\) | ||||
0.121396 | + | 0.992604i | \(0.461263\pi\) | |||||||
\(338\) | −3.78644e6 | −1.80277 | ||||||||
\(339\) | −1.09274e6 | −0.516435 | ||||||||
\(340\) | 208544. | 0.0978364 | ||||||||
\(341\) | 779603. | 0.363068 | ||||||||
\(342\) | −27648.0 | −0.0127820 | ||||||||
\(343\) | −335140. | −0.153812 | ||||||||
\(344\) | −772992. | −0.352192 | ||||||||
\(345\) | 1.05706e6 | 0.478139 | ||||||||
\(346\) | 1.54514e6 | 0.693871 | ||||||||
\(347\) | 467636. | 0.208490 | 0.104245 | − | 0.994552i | \(-0.466757\pi\) | ||||
0.104245 | + | 0.994552i | \(0.466757\pi\) | |||||||
\(348\) | −1.30176e6 | −0.576213 | ||||||||
\(349\) | 304470. | 0.133808 | 0.0669038 | − | 0.997759i | \(-0.478688\pi\) | ||||
0.0669038 | + | 0.997759i | \(0.478688\pi\) | |||||||
\(350\) | 110560. | 0.0482423 | ||||||||
\(351\) | −4.49442e6 | −1.94718 | ||||||||
\(352\) | 619520. | 0.266501 | ||||||||
\(353\) | 2.51868e6 | 1.07581 | 0.537906 | − | 0.843005i | \(-0.319215\pi\) | ||||
0.537906 | + | 0.843005i | \(0.319215\pi\) | |||||||
\(354\) | −387660. | −0.164416 | ||||||||
\(355\) | −589437. | −0.248237 | ||||||||
\(356\) | −278640. | −0.116525 | ||||||||
\(357\) | −102900. | −0.0427312 | ||||||||
\(358\) | −2.18032e6 | −0.899108 | ||||||||
\(359\) | −3.01841e6 | −1.23607 | −0.618034 | − | 0.786151i | \(-0.712071\pi\) | ||||
−0.618034 | + | 0.786151i | \(0.712071\pi\) | |||||||
\(360\) | 65664.0 | 0.0267037 | ||||||||
\(361\) | −2.32864e6 | −0.940448 | ||||||||
\(362\) | 1.11794e6 | 0.448381 | ||||||||
\(363\) | −219615. | −0.0874773 | ||||||||
\(364\) | 183680. | 0.0726622 | ||||||||
\(365\) | −36556.0 | −0.0143624 | ||||||||
\(366\) | −1.01880e6 | −0.397545 | ||||||||
\(367\) | 994429. | 0.385397 | 0.192699 | − | 0.981258i | \(-0.438276\pi\) | ||||
0.192699 | + | 0.981258i | \(0.438276\pi\) | |||||||
\(368\) | −949504. | −0.365491 | ||||||||
\(369\) | 27504.0 | 0.0105155 | ||||||||
\(370\) | 916788. | 0.348149 | ||||||||
\(371\) | −298620. | −0.112638 | ||||||||
\(372\) | −1.54632e6 | −0.579351 | ||||||||
\(373\) | 1.72896e6 | 0.643446 | 0.321723 | − | 0.946834i | \(-0.395738\pi\) | ||||
0.321723 | + | 0.946834i | \(0.395738\pi\) | |||||||
\(374\) | 332024. | 0.122741 | ||||||||
\(375\) | −1.67836e6 | −0.616323 | ||||||||
\(376\) | 1.37626e6 | 0.502030 | ||||||||
\(377\) | 6.22675e6 | 2.25636 | ||||||||
\(378\) | −156600. | −0.0563718 | ||||||||
\(379\) | 454765. | 0.162626 | 0.0813128 | − | 0.996689i | \(-0.474089\pi\) | ||||
0.0813128 | + | 0.996689i | \(0.474089\pi\) | |||||||
\(380\) | −116736. | −0.0414711 | ||||||||
\(381\) | 1.17276e6 | 0.413901 | ||||||||
\(382\) | 1.77775e6 | 0.623321 | ||||||||
\(383\) | 2.27557e6 | 0.792673 | 0.396336 | − | 0.918105i | \(-0.370281\pi\) | ||||
0.396336 | + | 0.918105i | \(0.370281\pi\) | |||||||
\(384\) | −737280. | −0.255155 | ||||||||
\(385\) | 22990.0 | 0.00790473 | ||||||||
\(386\) | 73904.0 | 0.0252464 | ||||||||
\(387\) | 72468.0 | 0.0245962 | ||||||||
\(388\) | −1.07048e6 | −0.360993 | ||||||||
\(389\) | 389781. | 0.130601 | 0.0653005 | − | 0.997866i | \(-0.479199\pi\) | ||||
0.0653005 | + | 0.997866i | \(0.479199\pi\) | |||||||
\(390\) | 1.30872e6 | 0.435698 | ||||||||
\(391\) | 2.54437e6 | 0.841665 | ||||||||
\(392\) | −3.20774e6 | −1.05435 | ||||||||
\(393\) | 6930.00 | 0.00226335 | ||||||||
\(394\) | −1.08073e6 | −0.350732 | ||||||||
\(395\) | −1.23762e6 | −0.399112 | ||||||||
\(396\) | −34848.0 | −0.0111671 | ||||||||
\(397\) | −1.61933e6 | −0.515655 | −0.257827 | − | 0.966191i | \(-0.583007\pi\) | ||||
−0.257827 | + | 0.966191i | \(0.583007\pi\) | |||||||
\(398\) | −173280. | −0.0548328 | ||||||||
\(399\) | 57600.0 | 0.0181130 | ||||||||
\(400\) | 707584. | 0.221120 | ||||||||
\(401\) | −5.54368e6 | −1.72162 | −0.860810 | − | 0.508927i | \(-0.830042\pi\) | ||||
−0.860810 | + | 0.508927i | \(0.830042\pi\) | |||||||
\(402\) | 1.79994e6 | 0.555511 | ||||||||
\(403\) | 7.39656e6 | 2.26865 | ||||||||
\(404\) | −1.54768e6 | −0.471767 | ||||||||
\(405\) | 1.03267e6 | 0.312841 | ||||||||
\(406\) | 216960. | 0.0653228 | ||||||||
\(407\) | −1.45962e6 | −0.436772 | ||||||||
\(408\) | −1.97568e6 | −0.587579 | ||||||||
\(409\) | −2.70493e6 | −0.799553 | −0.399776 | − | 0.916613i | \(-0.630912\pi\) | ||||
−0.399776 | + | 0.916613i | \(0.630912\pi\) | |||||||
\(410\) | −116128. | −0.0341175 | ||||||||
\(411\) | −4.44350e6 | −1.29754 | ||||||||
\(412\) | 1.53126e6 | 0.444434 | ||||||||
\(413\) | −64610.0 | −0.0186391 | ||||||||
\(414\) | 267048. | 0.0765753 | ||||||||
\(415\) | 1.95157e6 | 0.556241 | ||||||||
\(416\) | 5.87776e6 | 1.66525 | ||||||||
\(417\) | 5.99727e6 | 1.68894 | ||||||||
\(418\) | −185856. | −0.0520279 | ||||||||
\(419\) | 3.37337e6 | 0.938705 | 0.469353 | − | 0.883011i | \(-0.344487\pi\) | ||||
0.469353 | + | 0.883011i | \(0.344487\pi\) | |||||||
\(420\) | −45600.0 | −0.0126137 | ||||||||
\(421\) | −4.52551e6 | −1.24441 | −0.622204 | − | 0.782855i | \(-0.713762\pi\) | ||||
−0.622204 | + | 0.782855i | \(0.713762\pi\) | |||||||
\(422\) | −4.11874e6 | −1.12586 | ||||||||
\(423\) | −129024. | −0.0350606 | ||||||||
\(424\) | −5.73350e6 | −1.54884 | ||||||||
\(425\) | −1.89610e6 | −0.509202 | ||||||||
\(426\) | 1.86138e6 | 0.496948 | ||||||||
\(427\) | −169800. | −0.0450680 | ||||||||
\(428\) | 522528. | 0.137880 | ||||||||
\(429\) | −2.08362e6 | −0.546607 | ||||||||
\(430\) | −305976. | −0.0798024 | ||||||||
\(431\) | −684534. | −0.177501 | −0.0887507 | − | 0.996054i | \(-0.528287\pi\) | ||||
−0.0887507 | + | 0.996054i | \(0.528287\pi\) | |||||||
\(432\) | −1.00224e6 | −0.258382 | ||||||||
\(433\) | −4.22591e6 | −1.08318 | −0.541589 | − | 0.840643i | \(-0.682177\pi\) | ||||
−0.541589 | + | 0.840643i | \(0.682177\pi\) | |||||||
\(434\) | 257720. | 0.0656786 | ||||||||
\(435\) | −1.54584e6 | −0.391689 | ||||||||
\(436\) | 2.96701e6 | 0.747485 | ||||||||
\(437\) | −1.42426e6 | −0.356767 | ||||||||
\(438\) | 115440. | 0.0287522 | ||||||||
\(439\) | −2.09185e6 | −0.518047 | −0.259023 | − | 0.965871i | \(-0.583401\pi\) | ||||
−0.259023 | + | 0.965871i | \(0.583401\pi\) | |||||||
\(440\) | 441408. | 0.108695 | ||||||||
\(441\) | 300726. | 0.0736333 | ||||||||
\(442\) | 3.15011e6 | 0.766956 | ||||||||
\(443\) | 1.56284e6 | 0.378361 | 0.189180 | − | 0.981942i | \(-0.439417\pi\) | ||||
0.189180 | + | 0.981942i | \(0.439417\pi\) | |||||||
\(444\) | 2.89512e6 | 0.696962 | ||||||||
\(445\) | −330885. | −0.0792095 | ||||||||
\(446\) | −1.84512e6 | −0.439226 | ||||||||
\(447\) | −1.09005e6 | −0.258034 | ||||||||
\(448\) | 286720. | 0.0674937 | ||||||||
\(449\) | −3.00449e6 | −0.703324 | −0.351662 | − | 0.936127i | \(-0.614383\pi\) | ||||
−0.351662 | + | 0.936127i | \(0.614383\pi\) | |||||||
\(450\) | −199008. | −0.0463275 | ||||||||
\(451\) | 184888. | 0.0428023 | ||||||||
\(452\) | −1.16558e6 | −0.268347 | ||||||||
\(453\) | 4.54623e6 | 1.04089 | ||||||||
\(454\) | 3.42228e6 | 0.779248 | ||||||||
\(455\) | 218120. | 0.0493932 | ||||||||
\(456\) | 1.10592e6 | 0.249064 | ||||||||
\(457\) | −2.44552e6 | −0.547747 | −0.273874 | − | 0.961766i | \(-0.588305\pi\) | ||||
−0.273874 | + | 0.961766i | \(0.588305\pi\) | |||||||
\(458\) | 2.66322e6 | 0.593258 | ||||||||
\(459\) | 2.68569e6 | 0.595010 | ||||||||
\(460\) | 1.12754e6 | 0.248448 | ||||||||
\(461\) | 7.79104e6 | 1.70743 | 0.853715 | − | 0.520741i | \(-0.174344\pi\) | ||||
0.853715 | + | 0.520741i | \(0.174344\pi\) | |||||||
\(462\) | −72600.0 | −0.0158246 | ||||||||
\(463\) | −1.05196e6 | −0.228059 | −0.114029 | − | 0.993477i | \(-0.536376\pi\) | ||||
−0.114029 | + | 0.993477i | \(0.536376\pi\) | |||||||
\(464\) | 1.38854e6 | 0.299409 | ||||||||
\(465\) | −1.83626e6 | −0.393823 | ||||||||
\(466\) | −4.83734e6 | −1.03191 | ||||||||
\(467\) | 3.97003e6 | 0.842369 | 0.421184 | − | 0.906975i | \(-0.361615\pi\) | ||||
0.421184 | + | 0.906975i | \(0.361615\pi\) | |||||||
\(468\) | −330624. | −0.0697782 | ||||||||
\(469\) | 299990. | 0.0629759 | ||||||||
\(470\) | 544768. | 0.113754 | ||||||||
\(471\) | 7.99480e6 | 1.66056 | ||||||||
\(472\) | −1.24051e6 | −0.256298 | ||||||||
\(473\) | 487146. | 0.100117 | ||||||||
\(474\) | 3.90828e6 | 0.798987 | ||||||||
\(475\) | 1.06138e6 | 0.215842 | ||||||||
\(476\) | −109760. | −0.0222038 | ||||||||
\(477\) | 537516. | 0.108167 | ||||||||
\(478\) | 2.28593e6 | 0.457607 | ||||||||
\(479\) | −8.53908e6 | −1.70048 | −0.850241 | − | 0.526393i | \(-0.823544\pi\) | ||||
−0.850241 | + | 0.526393i | \(0.823544\pi\) | |||||||
\(480\) | −1.45920e6 | −0.289076 | ||||||||
\(481\) | −1.38483e7 | −2.72919 | ||||||||
\(482\) | 1.06832e6 | 0.209452 | ||||||||
\(483\) | −556350. | −0.108513 | ||||||||
\(484\) | −234256. | −0.0454545 | ||||||||
\(485\) | −1.27120e6 | −0.245391 | ||||||||
\(486\) | 544320. | 0.104535 | ||||||||
\(487\) | −1.86487e6 | −0.356308 | −0.178154 | − | 0.984003i | \(-0.557013\pi\) | ||||
−0.178154 | + | 0.984003i | \(0.557013\pi\) | |||||||
\(488\) | −3.26016e6 | −0.619711 | ||||||||
\(489\) | −4.23114e6 | −0.800175 | ||||||||
\(490\) | −1.26973e6 | −0.238903 | ||||||||
\(491\) | 5.15727e6 | 0.965420 | 0.482710 | − | 0.875780i | \(-0.339653\pi\) | ||||
0.482710 | + | 0.875780i | \(0.339653\pi\) | |||||||
\(492\) | −366720. | −0.0683002 | ||||||||
\(493\) | −3.72086e6 | −0.689488 | ||||||||
\(494\) | −1.76333e6 | −0.325099 | ||||||||
\(495\) | −41382.0 | −0.00759099 | ||||||||
\(496\) | 1.64941e6 | 0.301040 | ||||||||
\(497\) | 310230. | 0.0563369 | ||||||||
\(498\) | −6.16284e6 | −1.11354 | ||||||||
\(499\) | 4.53340e6 | 0.815029 | 0.407514 | − | 0.913199i | \(-0.366396\pi\) | ||||
0.407514 | + | 0.913199i | \(0.366396\pi\) | |||||||
\(500\) | −1.79026e6 | −0.320251 | ||||||||
\(501\) | 8.60382e6 | 1.53143 | ||||||||
\(502\) | −5.54947e6 | −0.982861 | ||||||||
\(503\) | 1.71163e6 | 0.301641 | 0.150821 | − | 0.988561i | \(-0.451808\pi\) | ||||
0.150821 | + | 0.988561i | \(0.451808\pi\) | |||||||
\(504\) | −34560.0 | −0.00606035 | ||||||||
\(505\) | −1.83787e6 | −0.320691 | ||||||||
\(506\) | 1.79516e6 | 0.311692 | ||||||||
\(507\) | −1.41992e7 | −2.45326 | ||||||||
\(508\) | 1.25094e6 | 0.215069 | ||||||||
\(509\) | 9.73822e6 | 1.66604 | 0.833019 | − | 0.553244i | \(-0.186610\pi\) | ||||
0.833019 | + | 0.553244i | \(0.186610\pi\) | |||||||
\(510\) | −782040. | −0.133138 | ||||||||
\(511\) | 19240.0 | 0.00325951 | ||||||||
\(512\) | 2.88358e6 | 0.486136 | ||||||||
\(513\) | −1.50336e6 | −0.252214 | ||||||||
\(514\) | 3.54369e6 | 0.591627 | ||||||||
\(515\) | 1.81838e6 | 0.302110 | ||||||||
\(516\) | −966240. | −0.159757 | ||||||||
\(517\) | −867328. | −0.142711 | ||||||||
\(518\) | −482520. | −0.0790116 | ||||||||
\(519\) | 5.79429e6 | 0.944239 | ||||||||
\(520\) | 4.18790e6 | 0.679185 | ||||||||
\(521\) | 4.30279e6 | 0.694474 | 0.347237 | − | 0.937777i | \(-0.387120\pi\) | ||||
0.347237 | + | 0.937777i | \(0.387120\pi\) | |||||||
\(522\) | −390528. | −0.0627301 | ||||||||
\(523\) | 2.62280e6 | 0.419287 | 0.209643 | − | 0.977778i | \(-0.432770\pi\) | ||||
0.209643 | + | 0.977778i | \(0.432770\pi\) | |||||||
\(524\) | 7392.00 | 0.00117607 | ||||||||
\(525\) | 414600. | 0.0656494 | ||||||||
\(526\) | −5.78750e6 | −0.912066 | ||||||||
\(527\) | −4.41990e6 | −0.693243 | ||||||||
\(528\) | −464640. | −0.0725324 | ||||||||
\(529\) | 7.32034e6 | 1.13734 | ||||||||
\(530\) | −2.26951e6 | −0.350948 | ||||||||
\(531\) | 116298. | 0.0178993 | ||||||||
\(532\) | 61440.0 | 0.00941179 | ||||||||
\(533\) | 1.75414e6 | 0.267453 | ||||||||
\(534\) | 1.04490e6 | 0.158570 | ||||||||
\(535\) | 620502. | 0.0937257 | ||||||||
\(536\) | 5.75981e6 | 0.865956 | ||||||||
\(537\) | −8.17618e6 | −1.22353 | ||||||||
\(538\) | 1.41551e6 | 0.210842 | ||||||||
\(539\) | 2.02155e6 | 0.299717 | ||||||||
\(540\) | 1.19016e6 | 0.175639 | ||||||||
\(541\) | −2.49634e6 | −0.366700 | −0.183350 | − | 0.983048i | \(-0.558694\pi\) | ||||
−0.183350 | + | 0.983048i | \(0.558694\pi\) | |||||||
\(542\) | −2.10104e6 | −0.307211 | ||||||||
\(543\) | 4.19228e6 | 0.610169 | ||||||||
\(544\) | −3.51232e6 | −0.508858 | ||||||||
\(545\) | 3.52332e6 | 0.508114 | ||||||||
\(546\) | −688800. | −0.0988807 | ||||||||
\(547\) | 1.14323e7 | 1.63368 | 0.816838 | − | 0.576868i | \(-0.195725\pi\) | ||||
0.816838 | + | 0.576868i | \(0.195725\pi\) | |||||||
\(548\) | −4.73973e6 | −0.674221 | ||||||||
\(549\) | 305640. | 0.0432792 | ||||||||
\(550\) | −1.33778e6 | −0.188572 | ||||||||
\(551\) | 2.08282e6 | 0.292262 | ||||||||
\(552\) | −1.06819e7 | −1.49211 | ||||||||
\(553\) | 651380. | 0.0905778 | ||||||||
\(554\) | 2.38244e6 | 0.329798 | ||||||||
\(555\) | 3.43796e6 | 0.473770 | ||||||||
\(556\) | 6.39709e6 | 0.877597 | ||||||||
\(557\) | −9.81529e6 | −1.34049 | −0.670247 | − | 0.742138i | \(-0.733812\pi\) | ||||
−0.670247 | + | 0.742138i | \(0.733812\pi\) | |||||||
\(558\) | −463896. | −0.0630718 | ||||||||
\(559\) | 4.62185e6 | 0.625585 | ||||||||
\(560\) | 48640.0 | 0.00655426 | ||||||||
\(561\) | 1.24509e6 | 0.167030 | ||||||||
\(562\) | −2.92927e6 | −0.391218 | ||||||||
\(563\) | −8.19192e6 | −1.08922 | −0.544609 | − | 0.838690i | \(-0.683322\pi\) | ||||
−0.544609 | + | 0.838690i | \(0.683322\pi\) | |||||||
\(564\) | 1.72032e6 | 0.227725 | ||||||||
\(565\) | −1.38413e6 | −0.182413 | ||||||||
\(566\) | −8.93522e6 | −1.17237 | ||||||||
\(567\) | −543510. | −0.0709986 | ||||||||
\(568\) | 5.95642e6 | 0.774665 | ||||||||
\(569\) | −7.54286e6 | −0.976687 | −0.488344 | − | 0.872651i | \(-0.662399\pi\) | ||||
−0.488344 | + | 0.872651i | \(0.662399\pi\) | |||||||
\(570\) | 437760. | 0.0564351 | ||||||||
\(571\) | −8.69400e6 | −1.11591 | −0.557956 | − | 0.829871i | \(-0.688414\pi\) | ||||
−0.557956 | + | 0.829871i | \(0.688414\pi\) | |||||||
\(572\) | −2.22253e6 | −0.284025 | ||||||||
\(573\) | 6.66656e6 | 0.848233 | ||||||||
\(574\) | 61120.0 | 0.00774290 | ||||||||
\(575\) | −1.02517e7 | −1.29308 | ||||||||
\(576\) | −516096. | −0.0648148 | ||||||||
\(577\) | 2.03379e6 | 0.254312 | 0.127156 | − | 0.991883i | \(-0.459415\pi\) | ||||
0.127156 | + | 0.991883i | \(0.459415\pi\) | |||||||
\(578\) | 3.79704e6 | 0.472744 | ||||||||
\(579\) | 277140. | 0.0343560 | ||||||||
\(580\) | −1.64890e6 | −0.203528 | ||||||||
\(581\) | −1.02714e6 | −0.126238 | ||||||||
\(582\) | 4.01430e6 | 0.491250 | ||||||||
\(583\) | 3.61330e6 | 0.440284 | ||||||||
\(584\) | 369408. | 0.0448202 | ||||||||
\(585\) | −392616. | −0.0474328 | ||||||||
\(586\) | 6.12432e6 | 0.736739 | ||||||||
\(587\) | 3.51780e6 | 0.421381 | 0.210691 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210691 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(588\) | −4.00968e6 | −0.478263 | ||||||||
\(589\) | 2.47411e6 | 0.293854 | ||||||||
\(590\) | −491036. | −0.0580742 | ||||||||
\(591\) | −4.05273e6 | −0.477286 | ||||||||
\(592\) | −3.08813e6 | −0.362152 | ||||||||
\(593\) | −8.34535e6 | −0.974558 | −0.487279 | − | 0.873246i | \(-0.662011\pi\) | ||||
−0.487279 | + | 0.873246i | \(0.662011\pi\) | |||||||
\(594\) | 1.89486e6 | 0.220349 | ||||||||
\(595\) | −130340. | −0.0150933 | ||||||||
\(596\) | −1.16272e6 | −0.134079 | ||||||||
\(597\) | −649800. | −0.0746180 | ||||||||
\(598\) | 1.70317e7 | 1.94763 | ||||||||
\(599\) | 6.15022e6 | 0.700364 | 0.350182 | − | 0.936682i | \(-0.386120\pi\) | ||||
0.350182 | + | 0.936682i | \(0.386120\pi\) | |||||||
\(600\) | 7.96032e6 | 0.902719 | ||||||||
\(601\) | −6.86232e6 | −0.774970 | −0.387485 | − | 0.921876i | \(-0.626656\pi\) | ||||
−0.387485 | + | 0.921876i | \(0.626656\pi\) | |||||||
\(602\) | 161040. | 0.0181110 | ||||||||
\(603\) | −539982. | −0.0604764 | ||||||||
\(604\) | 4.84931e6 | 0.540864 | ||||||||
\(605\) | −278179. | −0.0308984 | ||||||||
\(606\) | 5.80380e6 | 0.641994 | ||||||||
\(607\) | −9.45536e6 | −1.04161 | −0.520807 | − | 0.853675i | \(-0.674369\pi\) | ||||
−0.520807 | + | 0.853675i | \(0.674369\pi\) | |||||||
\(608\) | 1.96608e6 | 0.215696 | ||||||||
\(609\) | 813600. | 0.0888930 | ||||||||
\(610\) | −1.29048e6 | −0.140419 | ||||||||
\(611\) | −8.22886e6 | −0.891737 | ||||||||
\(612\) | 197568. | 0.0213225 | ||||||||
\(613\) | −4.63658e6 | −0.498363 | −0.249182 | − | 0.968457i | \(-0.580162\pi\) | ||||
−0.249182 | + | 0.968457i | \(0.580162\pi\) | |||||||
\(614\) | 4.57072e6 | 0.489287 | ||||||||
\(615\) | −435480. | −0.0464280 | ||||||||
\(616\) | −232320. | −0.0246680 | ||||||||
\(617\) | 6.05704e6 | 0.640542 | 0.320271 | − | 0.947326i | \(-0.396226\pi\) | ||||
0.320271 | + | 0.947326i | \(0.396226\pi\) | |||||||
\(618\) | −5.74224e6 | −0.604798 | ||||||||
\(619\) | −5.63994e6 | −0.591626 | −0.295813 | − | 0.955246i | \(-0.595591\pi\) | ||||
−0.295813 | + | 0.955246i | \(0.595591\pi\) | |||||||
\(620\) | −1.95867e6 | −0.204636 | ||||||||
\(621\) | 1.45207e7 | 1.51098 | ||||||||
\(622\) | −2.34782e6 | −0.243327 | ||||||||
\(623\) | 174150. | 0.0179764 | ||||||||
\(624\) | −4.40832e6 | −0.453223 | ||||||||
\(625\) | 6.51157e6 | 0.666785 | ||||||||
\(626\) | 935428. | 0.0954057 | ||||||||
\(627\) | −696960. | −0.0708009 | ||||||||
\(628\) | 8.52779e6 | 0.862854 | ||||||||
\(629\) | 8.27522e6 | 0.833975 | ||||||||
\(630\) | −13680.0 | −0.00137320 | ||||||||
\(631\) | 1.12616e6 | 0.112597 | 0.0562987 | − | 0.998414i | \(-0.482070\pi\) | ||||
0.0562987 | + | 0.998414i | \(0.482070\pi\) | |||||||
\(632\) | 1.25065e7 | 1.24550 | ||||||||
\(633\) | −1.54453e7 | −1.53210 | ||||||||
\(634\) | 3.74201e6 | 0.369728 | ||||||||
\(635\) | 1.48550e6 | 0.146197 | ||||||||
\(636\) | −7.16688e6 | −0.702566 | ||||||||
\(637\) | 1.91796e7 | 1.87280 | ||||||||
\(638\) | −2.62522e6 | −0.255337 | ||||||||
\(639\) | −558414. | −0.0541009 | ||||||||
\(640\) | −933888. | −0.0901249 | ||||||||
\(641\) | −1.42020e7 | −1.36522 | −0.682611 | − | 0.730782i | \(-0.739156\pi\) | ||||
−0.682611 | + | 0.730782i | \(0.739156\pi\) | |||||||
\(642\) | −1.95948e6 | −0.187630 | ||||||||
\(643\) | 1.60794e6 | 0.153371 | 0.0766853 | − | 0.997055i | \(-0.475566\pi\) | ||||
0.0766853 | + | 0.997055i | \(0.475566\pi\) | |||||||
\(644\) | −593440. | −0.0563848 | ||||||||
\(645\) | −1.14741e6 | −0.108597 | ||||||||
\(646\) | 1.05370e6 | 0.0993423 | ||||||||
\(647\) | 3.10236e6 | 0.291361 | 0.145680 | − | 0.989332i | \(-0.453463\pi\) | ||||
0.145680 | + | 0.989332i | \(0.453463\pi\) | |||||||
\(648\) | −1.04354e7 | −0.976273 | ||||||||
\(649\) | 781781. | 0.0728573 | ||||||||
\(650\) | −1.26923e7 | −1.17830 | ||||||||
\(651\) | 966450. | 0.0893772 | ||||||||
\(652\) | −4.51322e6 | −0.415783 | ||||||||
\(653\) | 6.88852e6 | 0.632183 | 0.316091 | − | 0.948729i | \(-0.397629\pi\) | ||||
0.316091 | + | 0.948729i | \(0.397629\pi\) | |||||||
\(654\) | −1.11263e7 | −1.01720 | ||||||||
\(655\) | 8778.00 | 0.000799452 0 | ||||||||
\(656\) | 391168. | 0.0354898 | ||||||||
\(657\) | −34632.0 | −0.00313014 | ||||||||
\(658\) | −286720. | −0.0258163 | ||||||||
\(659\) | −1.24134e7 | −1.11347 | −0.556735 | − | 0.830690i | \(-0.687946\pi\) | ||||
−0.556735 | + | 0.830690i | \(0.687946\pi\) | |||||||
\(660\) | 551760. | 0.0493049 | ||||||||
\(661\) | −8.10994e6 | −0.721961 | −0.360980 | − | 0.932573i | \(-0.617558\pi\) | ||||
−0.360980 | + | 0.932573i | \(0.617558\pi\) | |||||||
\(662\) | 4.23292e6 | 0.375401 | ||||||||
\(663\) | 1.18129e7 | 1.04369 | ||||||||
\(664\) | −1.97211e7 | −1.73584 | ||||||||
\(665\) | 72960.0 | 0.00639780 | ||||||||
\(666\) | 868536. | 0.0758756 | ||||||||
\(667\) | −2.01176e7 | −1.75090 | ||||||||
\(668\) | 9.17741e6 | 0.795754 | ||||||||
\(669\) | −6.91922e6 | −0.597711 | ||||||||
\(670\) | 2.27992e6 | 0.196216 | ||||||||
\(671\) | 2.05458e6 | 0.176164 | ||||||||
\(672\) | 768000. | 0.0656052 | ||||||||
\(673\) | 1.78063e7 | 1.51543 | 0.757717 | − | 0.652584i | \(-0.226315\pi\) | ||||
0.757717 | + | 0.652584i | \(0.226315\pi\) | |||||||
\(674\) | −2.02474e6 | −0.171680 | ||||||||
\(675\) | −1.08211e7 | −0.914135 | ||||||||
\(676\) | −1.51458e7 | −1.27475 | ||||||||
\(677\) | 1.55179e7 | 1.30125 | 0.650626 | − | 0.759398i | \(-0.274507\pi\) | ||||
0.650626 | + | 0.759398i | \(0.274507\pi\) | |||||||
\(678\) | 4.37094e6 | 0.365175 | ||||||||
\(679\) | 669050. | 0.0556909 | ||||||||
\(680\) | −2.50253e6 | −0.207542 | ||||||||
\(681\) | 1.28336e7 | 1.06042 | ||||||||
\(682\) | −3.11841e6 | −0.256728 | ||||||||
\(683\) | −2.18106e6 | −0.178902 | −0.0894510 | − | 0.995991i | \(-0.528511\pi\) | ||||
−0.0894510 | + | 0.995991i | \(0.528511\pi\) | |||||||
\(684\) | −110592. | −0.00903823 | ||||||||
\(685\) | −5.62843e6 | −0.458311 | ||||||||
\(686\) | 1.34056e6 | 0.108762 | ||||||||
\(687\) | 9.98708e6 | 0.807321 | ||||||||
\(688\) | 1.03066e6 | 0.0830123 | ||||||||
\(689\) | 3.42816e7 | 2.75114 | ||||||||
\(690\) | −4.22826e6 | −0.338095 | ||||||||
\(691\) | 2.29892e7 | 1.83159 | 0.915795 | − | 0.401647i | \(-0.131562\pi\) | ||||
0.915795 | + | 0.401647i | \(0.131562\pi\) | |||||||
\(692\) | 6.18058e6 | 0.490641 | ||||||||
\(693\) | 21780.0 | 0.00172276 | ||||||||
\(694\) | −1.87054e6 | −0.147424 | ||||||||
\(695\) | 7.59654e6 | 0.596560 | ||||||||
\(696\) | 1.56211e7 | 1.22233 | ||||||||
\(697\) | −1.04821e6 | −0.0817270 | ||||||||
\(698\) | −1.21788e6 | −0.0946163 | ||||||||
\(699\) | −1.81400e7 | −1.40425 | ||||||||
\(700\) | 442240. | 0.0341125 | ||||||||
\(701\) | 2.34092e6 | 0.179925 | 0.0899626 | − | 0.995945i | \(-0.471325\pi\) | ||||
0.0899626 | + | 0.995945i | \(0.471325\pi\) | |||||||
\(702\) | 1.79777e7 | 1.37686 | ||||||||
\(703\) | −4.63219e6 | −0.353507 | ||||||||
\(704\) | −3.46931e6 | −0.263822 | ||||||||
\(705\) | 2.04288e6 | 0.154800 | ||||||||
\(706\) | −1.00747e7 | −0.760715 | ||||||||
\(707\) | 967300. | 0.0727801 | ||||||||
\(708\) | −1.55064e6 | −0.116259 | ||||||||
\(709\) | −1.92694e7 | −1.43964 | −0.719820 | − | 0.694161i | \(-0.755775\pi\) | ||||
−0.719820 | + | 0.694161i | \(0.755775\pi\) | |||||||
\(710\) | 2.35775e6 | 0.175530 | ||||||||
\(711\) | −1.17248e6 | −0.0869827 | ||||||||
\(712\) | 3.34368e6 | 0.247186 | ||||||||
\(713\) | −2.38971e7 | −1.76044 | ||||||||
\(714\) | 411600. | 0.0302155 | ||||||||
\(715\) | −2.63925e6 | −0.193070 | ||||||||
\(716\) | −8.72126e6 | −0.635765 | ||||||||
\(717\) | 8.57223e6 | 0.622724 | ||||||||
\(718\) | 1.20736e7 | 0.874032 | ||||||||
\(719\) | −2.14665e7 | −1.54860 | −0.774300 | − | 0.632819i | \(-0.781898\pi\) | ||||
−0.774300 | + | 0.632819i | \(0.781898\pi\) | |||||||
\(720\) | −87552.0 | −0.00629412 | ||||||||
\(721\) | −957040. | −0.0685633 | ||||||||
\(722\) | 9.31457e6 | 0.664997 | ||||||||
\(723\) | 4.00620e6 | 0.285028 | ||||||||
\(724\) | 4.47176e6 | 0.317053 | ||||||||
\(725\) | 1.49919e7 | 1.05928 | ||||||||
\(726\) | 878460. | 0.0618558 | ||||||||
\(727\) | −1.67705e7 | −1.17682 | −0.588411 | − | 0.808562i | \(-0.700246\pi\) | ||||
−0.588411 | + | 0.808562i | \(0.700246\pi\) | |||||||
\(728\) | −2.20416e6 | −0.154140 | ||||||||
\(729\) | 1.52485e7 | 1.06269 | ||||||||
\(730\) | 146224. | 0.0101557 | ||||||||
\(731\) | −2.76184e6 | −0.191163 | ||||||||
\(732\) | −4.07520e6 | −0.281107 | ||||||||
\(733\) | −1.75373e7 | −1.20560 | −0.602798 | − | 0.797894i | \(-0.705948\pi\) | ||||
−0.602798 | + | 0.797894i | \(0.705948\pi\) | |||||||
\(734\) | −3.97772e6 | −0.272517 | ||||||||
\(735\) | −4.76150e6 | −0.325106 | ||||||||
\(736\) | −1.89901e7 | −1.29221 | ||||||||
\(737\) | −3.62988e6 | −0.246163 | ||||||||
\(738\) | −110016. | −0.00743558 | ||||||||
\(739\) | 1.47387e7 | 0.992766 | 0.496383 | − | 0.868104i | \(-0.334661\pi\) | ||||
0.496383 | + | 0.868104i | \(0.334661\pi\) | |||||||
\(740\) | 3.66715e6 | 0.246178 | ||||||||
\(741\) | −6.61248e6 | −0.442404 | ||||||||
\(742\) | 1.19448e6 | 0.0796469 | ||||||||
\(743\) | −4.80946e6 | −0.319613 | −0.159806 | − | 0.987148i | \(-0.551087\pi\) | ||||
−0.159806 | + | 0.987148i | \(0.551087\pi\) | |||||||
\(744\) | 1.85558e7 | 1.22899 | ||||||||
\(745\) | −1.38073e6 | −0.0911419 | ||||||||
\(746\) | −6.91583e6 | −0.454985 | ||||||||
\(747\) | 1.84885e6 | 0.121227 | ||||||||
\(748\) | 1.32810e6 | 0.0867912 | ||||||||
\(749\) | −326580. | −0.0212709 | ||||||||
\(750\) | 6.71346e6 | 0.435806 | ||||||||
\(751\) | 8.29317e6 | 0.536563 | 0.268282 | − | 0.963341i | \(-0.413544\pi\) | ||||
0.268282 | + | 0.963341i | \(0.413544\pi\) | |||||||
\(752\) | −1.83501e6 | −0.118330 | ||||||||
\(753\) | −2.08105e7 | −1.33750 | ||||||||
\(754\) | −2.49070e7 | −1.59549 | ||||||||
\(755\) | 5.75856e6 | 0.367660 | ||||||||
\(756\) | −626400. | −0.0398609 | ||||||||
\(757\) | −352294. | −0.0223442 | −0.0111721 | − | 0.999938i | \(-0.503556\pi\) | ||||
−0.0111721 | + | 0.999938i | \(0.503556\pi\) | |||||||
\(758\) | −1.81906e6 | −0.114994 | ||||||||
\(759\) | 6.73184e6 | 0.424159 | ||||||||
\(760\) | 1.40083e6 | 0.0879735 | ||||||||
\(761\) | 1.68985e7 | 1.05776 | 0.528878 | − | 0.848698i | \(-0.322613\pi\) | ||||
0.528878 | + | 0.848698i | \(0.322613\pi\) | |||||||
\(762\) | −4.69104e6 | −0.292672 | ||||||||
\(763\) | −1.85438e6 | −0.115315 | ||||||||
\(764\) | 7.11099e6 | 0.440755 | ||||||||
\(765\) | 234612. | 0.0144943 | ||||||||
\(766\) | −9.10229e6 | −0.560504 | ||||||||
\(767\) | 7.41723e6 | 0.455253 | ||||||||
\(768\) | 1.67117e7 | 1.02239 | ||||||||
\(769\) | −36652.0 | −0.00223502 | −0.00111751 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111751 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(770\) | −91960.0 | −0.00558949 | ||||||||
\(771\) | 1.32888e7 | 0.805102 | ||||||||
\(772\) | 295616. | 0.0178519 | ||||||||
\(773\) | −3.17462e7 | −1.91093 | −0.955463 | − | 0.295113i | \(-0.904643\pi\) | ||||
−0.955463 | + | 0.295113i | \(0.904643\pi\) | |||||||
\(774\) | −289872. | −0.0173922 | ||||||||
\(775\) | 1.78085e7 | 1.06505 | ||||||||
\(776\) | 1.28458e7 | 0.765783 | ||||||||
\(777\) | −1.80945e6 | −0.107521 | ||||||||
\(778\) | −1.55912e6 | −0.0923489 | ||||||||
\(779\) | 586752. | 0.0346426 | ||||||||
\(780\) | 5.23488e6 | 0.308085 | ||||||||
\(781\) | −3.75378e6 | −0.220212 | ||||||||
\(782\) | −1.01775e7 | −0.595147 | ||||||||
\(783\) | −2.12350e7 | −1.23779 | ||||||||
\(784\) | 4.27699e6 | 0.248513 | ||||||||
\(785\) | 1.01268e7 | 0.586538 | ||||||||
\(786\) | −27720.0 | −0.00160043 | ||||||||
\(787\) | 2.01985e7 | 1.16247 | 0.581236 | − | 0.813735i | \(-0.302569\pi\) | ||||
0.581236 | + | 0.813735i | \(0.302569\pi\) | |||||||
\(788\) | −4.32291e6 | −0.248005 | ||||||||
\(789\) | −2.17031e7 | −1.24116 | ||||||||
\(790\) | 4.95049e6 | 0.282215 | ||||||||
\(791\) | 728490. | 0.0413983 | ||||||||
\(792\) | 418176. | 0.0236890 | ||||||||
\(793\) | 1.94930e7 | 1.10077 | ||||||||
\(794\) | 6.47732e6 | 0.364623 | ||||||||
\(795\) | −8.51067e6 | −0.477580 | ||||||||
\(796\) | −693120. | −0.0387727 | ||||||||
\(797\) | 1.55660e7 | 0.868023 | 0.434011 | − | 0.900907i | \(-0.357098\pi\) | ||||
0.434011 | + | 0.900907i | \(0.357098\pi\) | |||||||
\(798\) | −230400. | −0.0128078 | ||||||||
\(799\) | 4.91725e6 | 0.272493 | ||||||||
\(800\) | 1.41517e7 | 0.781777 | ||||||||
\(801\) | −313470. | −0.0172629 | ||||||||
\(802\) | 2.21747e7 | 1.21737 | ||||||||
\(803\) | −232804. | −0.0127409 | ||||||||
\(804\) | 7.19976e6 | 0.392806 | ||||||||
\(805\) | −704710. | −0.0383284 | ||||||||
\(806\) | −2.95863e7 | −1.60418 | ||||||||
\(807\) | 5.30817e6 | 0.286920 | ||||||||
\(808\) | 1.85722e7 | 1.00077 | ||||||||
\(809\) | −2.91667e7 | −1.56681 | −0.783404 | − | 0.621513i | \(-0.786518\pi\) | ||||
−0.783404 | + | 0.621513i | \(0.786518\pi\) | |||||||
\(810\) | −4.13068e6 | −0.221212 | ||||||||
\(811\) | −1.65215e7 | −0.882057 | −0.441029 | − | 0.897493i | \(-0.645386\pi\) | ||||
−0.441029 | + | 0.897493i | \(0.645386\pi\) | |||||||
\(812\) | 867840. | 0.0461902 | ||||||||
\(813\) | −7.87890e6 | −0.418061 | ||||||||
\(814\) | 5.83849e6 | 0.308844 | ||||||||
\(815\) | −5.35944e6 | −0.282635 | ||||||||
\(816\) | 2.63424e6 | 0.138494 | ||||||||
\(817\) | 1.54598e6 | 0.0810307 | ||||||||
\(818\) | 1.08197e7 | 0.565369 | ||||||||
\(819\) | 206640. | 0.0107648 | ||||||||
\(820\) | −464512. | −0.0241247 | ||||||||
\(821\) | 5.56614e6 | 0.288202 | 0.144101 | − | 0.989563i | \(-0.453971\pi\) | ||||
0.144101 | + | 0.989563i | \(0.453971\pi\) | |||||||
\(822\) | 1.77740e7 | 0.917498 | ||||||||
\(823\) | 1.18801e7 | 0.611391 | 0.305696 | − | 0.952129i | \(-0.401111\pi\) | ||||
0.305696 | + | 0.952129i | \(0.401111\pi\) | |||||||
\(824\) | −1.83752e7 | −0.942786 | ||||||||
\(825\) | −5.01666e6 | −0.256614 | ||||||||
\(826\) | 258440. | 0.0131798 | ||||||||
\(827\) | −1.32856e7 | −0.675489 | −0.337745 | − | 0.941238i | \(-0.609664\pi\) | ||||
−0.337745 | + | 0.941238i | \(0.609664\pi\) | |||||||
\(828\) | 1.06819e6 | 0.0541469 | ||||||||
\(829\) | −653987. | −0.0330509 | −0.0165254 | − | 0.999863i | \(-0.505260\pi\) | ||||
−0.0165254 | + | 0.999863i | \(0.505260\pi\) | |||||||
\(830\) | −7.80626e6 | −0.393322 | ||||||||
\(831\) | 8.93415e6 | 0.448798 | ||||||||
\(832\) | −3.29155e7 | −1.64851 | ||||||||
\(833\) | −1.14610e7 | −0.572282 | ||||||||
\(834\) | −2.39891e7 | −1.19426 | ||||||||
\(835\) | 1.08982e7 | 0.540926 | ||||||||
\(836\) | −743424. | −0.0367892 | ||||||||
\(837\) | −2.52243e7 | −1.24453 | ||||||||
\(838\) | −1.34935e7 | −0.663765 | ||||||||
\(839\) | 2.47747e7 | 1.21508 | 0.607538 | − | 0.794290i | \(-0.292157\pi\) | ||||
0.607538 | + | 0.794290i | \(0.292157\pi\) | |||||||
\(840\) | 547200. | 0.0267576 | ||||||||
\(841\) | 8.90863e6 | 0.434331 | ||||||||
\(842\) | 1.81021e7 | 0.879929 | ||||||||
\(843\) | −1.09848e7 | −0.532380 | ||||||||
\(844\) | −1.64749e7 | −0.796100 | ||||||||
\(845\) | −1.79856e7 | −0.866530 | ||||||||
\(846\) | 516096. | 0.0247916 | ||||||||
\(847\) | 146410. | 0.00701233 | ||||||||
\(848\) | 7.64467e6 | 0.365064 | ||||||||
\(849\) | −3.35071e7 | −1.59539 | ||||||||
\(850\) | 7.58442e6 | 0.360060 | ||||||||
\(851\) | 4.47417e7 | 2.11782 | ||||||||
\(852\) | 7.44552e6 | 0.351395 | ||||||||
\(853\) | 2.71291e7 | 1.27662 | 0.638311 | − | 0.769779i | \(-0.279633\pi\) | ||||
0.638311 | + | 0.769779i | \(0.279633\pi\) | |||||||
\(854\) | 679200. | 0.0318679 | ||||||||
\(855\) | −131328. | −0.00614387 | ||||||||
\(856\) | −6.27034e6 | −0.292487 | ||||||||
\(857\) | −2.84232e7 | −1.32197 | −0.660984 | − | 0.750400i | \(-0.729861\pi\) | ||||
−0.660984 | + | 0.750400i | \(0.729861\pi\) | |||||||
\(858\) | 8.33448e6 | 0.386510 | ||||||||
\(859\) | 2.65922e7 | 1.22962 | 0.614810 | − | 0.788675i | \(-0.289233\pi\) | ||||
0.614810 | + | 0.788675i | \(0.289233\pi\) | |||||||
\(860\) | −1.22390e6 | −0.0564289 | ||||||||
\(861\) | 229200. | 0.0105368 | ||||||||
\(862\) | 2.73814e6 | 0.125512 | ||||||||
\(863\) | −2.22500e7 | −1.01696 | −0.508479 | − | 0.861074i | \(-0.669792\pi\) | ||||
−0.508479 | + | 0.861074i | \(0.669792\pi\) | |||||||
\(864\) | −2.00448e7 | −0.913519 | ||||||||
\(865\) | 7.33943e6 | 0.333520 | ||||||||
\(866\) | 1.69036e7 | 0.765923 | ||||||||
\(867\) | 1.42389e7 | 0.643323 | ||||||||
\(868\) | 1.03088e6 | 0.0464418 | ||||||||
\(869\) | −7.88170e6 | −0.354055 | ||||||||
\(870\) | 6.18336e6 | 0.276966 | ||||||||
\(871\) | −3.44389e7 | −1.53817 | ||||||||
\(872\) | −3.56041e7 | −1.58566 | ||||||||
\(873\) | −1.20429e6 | −0.0534805 | ||||||||
\(874\) | 5.69702e6 | 0.252272 | ||||||||
\(875\) | 1.11891e6 | 0.0494055 | ||||||||
\(876\) | 461760. | 0.0203309 | ||||||||
\(877\) | 2.83428e7 | 1.24435 | 0.622176 | − | 0.782877i | \(-0.286249\pi\) | ||||
0.622176 | + | 0.782877i | \(0.286249\pi\) | |||||||
\(878\) | 8.36739e6 | 0.366314 | ||||||||
\(879\) | 2.29662e7 | 1.00258 | ||||||||
\(880\) | −588544. | −0.0256196 | ||||||||
\(881\) | 3.66445e7 | 1.59063 | 0.795315 | − | 0.606196i | \(-0.207305\pi\) | ||||
0.795315 | + | 0.606196i | \(0.207305\pi\) | |||||||
\(882\) | −1.20290e6 | −0.0520666 | ||||||||
\(883\) | 1.68772e7 | 0.728447 | 0.364223 | − | 0.931312i | \(-0.381334\pi\) | ||||
0.364223 | + | 0.931312i | \(0.381334\pi\) | |||||||
\(884\) | 1.26004e7 | 0.542320 | ||||||||
\(885\) | −1.84138e6 | −0.0790290 | ||||||||
\(886\) | −6.25137e6 | −0.267541 | ||||||||
\(887\) | 2.73941e6 | 0.116909 | 0.0584544 | − | 0.998290i | \(-0.481383\pi\) | ||||
0.0584544 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(888\) | −3.47414e7 | −1.47848 | ||||||||
\(889\) | −781840. | −0.0331790 | ||||||||
\(890\) | 1.32354e6 | 0.0560095 | ||||||||
\(891\) | 6.57647e6 | 0.277523 | ||||||||
\(892\) | −7.38050e6 | −0.310580 | ||||||||
\(893\) | −2.75251e6 | −0.115505 | ||||||||
\(894\) | 4.36020e6 | 0.182458 | ||||||||
\(895\) | −1.03565e7 | −0.432171 | ||||||||
\(896\) | 491520. | 0.0204537 | ||||||||
\(897\) | 6.38690e7 | 2.65038 | ||||||||
\(898\) | 1.20180e7 | 0.497325 | ||||||||
\(899\) | 3.49468e7 | 1.44214 | ||||||||
\(900\) | −796032. | −0.0327585 | ||||||||
\(901\) | −2.04853e7 | −0.840681 | ||||||||
\(902\) | −739552. | −0.0302658 | ||||||||
\(903\) | 603900. | 0.0246460 | ||||||||
\(904\) | 1.39870e7 | 0.569251 | ||||||||
\(905\) | 5.31022e6 | 0.215522 | ||||||||
\(906\) | −1.81849e7 | −0.736022 | ||||||||
\(907\) | −3.13286e7 | −1.26451 | −0.632255 | − | 0.774760i | \(-0.717871\pi\) | ||||
−0.632255 | + | 0.774760i | \(0.717871\pi\) | |||||||
\(908\) | 1.36891e7 | 0.551012 | ||||||||
\(909\) | −1.74114e6 | −0.0698914 | ||||||||
\(910\) | −872480. | −0.0349263 | ||||||||
\(911\) | −2.49762e7 | −0.997081 | −0.498541 | − | 0.866866i | \(-0.666131\pi\) | ||||
−0.498541 | + | 0.866866i | \(0.666131\pi\) | |||||||
\(912\) | −1.47456e6 | −0.0587050 | ||||||||
\(913\) | 1.24284e7 | 0.493444 | ||||||||
\(914\) | 9.78206e6 | 0.387316 | ||||||||
\(915\) | −4.83930e6 | −0.191086 | ||||||||
\(916\) | 1.06529e7 | 0.419497 | ||||||||
\(917\) | −4620.00 | −0.000181434 0 | ||||||||
\(918\) | −1.07428e7 | −0.420736 | ||||||||
\(919\) | −1.10613e7 | −0.432032 | −0.216016 | − | 0.976390i | \(-0.569306\pi\) | ||||
−0.216016 | + | 0.976390i | \(0.569306\pi\) | |||||||
\(920\) | −1.35304e7 | −0.527038 | ||||||||
\(921\) | 1.71402e7 | 0.665835 | ||||||||
\(922\) | −3.11641e7 | −1.20734 | ||||||||
\(923\) | −3.56144e7 | −1.37601 | ||||||||
\(924\) | −290400. | −0.0111897 | ||||||||
\(925\) | −3.33421e7 | −1.28127 | ||||||||
\(926\) | 4.20784e6 | 0.161262 | ||||||||
\(927\) | 1.72267e6 | 0.0658420 | ||||||||
\(928\) | 2.77709e7 | 1.05857 | ||||||||
\(929\) | −2.01739e7 | −0.766919 | −0.383460 | − | 0.923558i | \(-0.625267\pi\) | ||||
−0.383460 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(930\) | 7.34502e6 | 0.278475 | ||||||||
\(931\) | 6.41549e6 | 0.242580 | ||||||||
\(932\) | −1.93494e7 | −0.729671 | ||||||||
\(933\) | −8.80434e6 | −0.331126 | ||||||||
\(934\) | −1.58801e7 | −0.595645 | ||||||||
\(935\) | 1.57711e6 | 0.0589976 | ||||||||
\(936\) | 3.96749e6 | 0.148022 | ||||||||
\(937\) | 9.10734e6 | 0.338877 | 0.169439 | − | 0.985541i | \(-0.445805\pi\) | ||||
0.169439 | + | 0.985541i | \(0.445805\pi\) | |||||||
\(938\) | −1.19996e6 | −0.0445307 | ||||||||
\(939\) | 3.50785e6 | 0.129831 | ||||||||
\(940\) | 2.17907e6 | 0.0804363 | ||||||||
\(941\) | −3.67709e7 | −1.35372 | −0.676861 | − | 0.736110i | \(-0.736660\pi\) | ||||
−0.676861 | + | 0.736110i | \(0.736660\pi\) | |||||||
\(942\) | −3.19792e7 | −1.17420 | ||||||||
\(943\) | −5.66735e6 | −0.207540 | ||||||||
\(944\) | 1.65402e6 | 0.0604101 | ||||||||
\(945\) | −743850. | −0.0270960 | ||||||||
\(946\) | −1.94858e6 | −0.0707932 | ||||||||
\(947\) | −4.95743e7 | −1.79631 | −0.898156 | − | 0.439677i | \(-0.855093\pi\) | ||||
−0.898156 | + | 0.439677i | \(0.855093\pi\) | |||||||
\(948\) | 1.56331e7 | 0.564969 | ||||||||
\(949\) | −2.20875e6 | −0.0796125 | ||||||||
\(950\) | −4.24550e6 | −0.152623 | ||||||||
\(951\) | 1.40325e7 | 0.503136 | ||||||||
\(952\) | 1.31712e6 | 0.0471013 | ||||||||
\(953\) | 3.53787e7 | 1.26186 | 0.630928 | − | 0.775841i | \(-0.282674\pi\) | ||||
0.630928 | + | 0.775841i | \(0.282674\pi\) | |||||||
\(954\) | −2.15006e6 | −0.0764857 | ||||||||
\(955\) | 8.44430e6 | 0.299609 | ||||||||
\(956\) | 9.14371e6 | 0.323577 | ||||||||
\(957\) | −9.84456e6 | −0.347469 | ||||||||
\(958\) | 3.41563e7 | 1.20242 | ||||||||
\(959\) | 2.96233e6 | 0.104013 | ||||||||
\(960\) | 8.17152e6 | 0.286170 | ||||||||
\(961\) | 1.28831e7 | 0.449999 | ||||||||
\(962\) | 5.53933e7 | 1.92983 | ||||||||
\(963\) | 587844. | 0.0204266 | ||||||||
\(964\) | 4.27328e6 | 0.148105 | ||||||||
\(965\) | 351044. | 0.0121351 | ||||||||
\(966\) | 2.22540e6 | 0.0767300 | ||||||||
\(967\) | 2.78059e7 | 0.956248 | 0.478124 | − | 0.878292i | \(-0.341317\pi\) | ||||
0.478124 | + | 0.878292i | \(0.341317\pi\) | |||||||
\(968\) | 2.81107e6 | 0.0964237 | ||||||||
\(969\) | 3.95136e6 | 0.135188 | ||||||||
\(970\) | 5.08478e6 | 0.173517 | ||||||||
\(971\) | 1.56835e7 | 0.533821 | 0.266910 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266910 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(972\) | 2.17728e6 | 0.0739177 | ||||||||
\(973\) | −3.99818e6 | −0.135388 | ||||||||
\(974\) | 7.45947e6 | 0.251948 | ||||||||
\(975\) | −4.75961e7 | −1.60347 | ||||||||
\(976\) | 4.34688e6 | 0.146067 | ||||||||
\(977\) | 2.01140e7 | 0.674157 | 0.337079 | − | 0.941476i | \(-0.390561\pi\) | ||||
0.337079 | + | 0.941476i | \(0.390561\pi\) | |||||||
\(978\) | 1.69246e7 | 0.565810 | ||||||||
\(979\) | −2.10722e6 | −0.0702671 | ||||||||
\(980\) | −5.07893e6 | −0.168930 | ||||||||
\(981\) | 3.33788e6 | 0.110739 | ||||||||
\(982\) | −2.06291e7 | −0.682655 | ||||||||
\(983\) | −2.09269e7 | −0.690750 | −0.345375 | − | 0.938465i | \(-0.612248\pi\) | ||||
−0.345375 | + | 0.938465i | \(0.612248\pi\) | |||||||
\(984\) | 4.40064e6 | 0.144887 | ||||||||
\(985\) | −5.13346e6 | −0.168585 | ||||||||
\(986\) | 1.48835e7 | 0.487541 | ||||||||
\(987\) | −1.07520e6 | −0.0351315 | ||||||||
\(988\) | −7.05331e6 | −0.229880 | ||||||||
\(989\) | −1.49324e7 | −0.485445 | ||||||||
\(990\) | 165528. | 0.00536764 | ||||||||
\(991\) | −3.18663e7 | −1.03074 | −0.515368 | − | 0.856969i | \(-0.672345\pi\) | ||||
−0.515368 | + | 0.856969i | \(0.672345\pi\) | |||||||
\(992\) | 3.29882e7 | 1.06434 | ||||||||
\(993\) | 1.58735e7 | 0.510856 | ||||||||
\(994\) | −1.24092e6 | −0.0398362 | ||||||||
\(995\) | −823080. | −0.0263563 | ||||||||
\(996\) | −2.46514e7 | −0.787395 | ||||||||
\(997\) | 1.38913e6 | 0.0442595 | 0.0221297 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221297 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(998\) | −1.81336e7 | −0.576313 | ||||||||
\(999\) | 4.72266e7 | 1.49718 |
(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 | 11.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 99.6.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 176.6.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 275.6.b.a.199.1 | 2 | |||
5.3 | odd | 4 | 275.6.b.a.199.2 | 2 | |||
5.4 | even | 2 | 275.6.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 539.6.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 704.6.a.c.1.1 | 1 | |||
8.5 | even | 2 | 704.6.a.h.1.1 | 1 | |||
11.10 | odd | 2 | 121.6.a.b.1.1 | 1 | |||
33.32 | even | 2 | 1089.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
99.6.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
121.6.a.b.1.1 | 1 | 11.10 | odd | 2 | |||
176.6.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
275.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
275.6.b.a.199.1 | 2 | 5.2 | odd | 4 | |||
275.6.b.a.199.2 | 2 | 5.3 | odd | 4 | |||
539.6.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
704.6.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
704.6.a.h.1.1 | 1 | 8.5 | even | 2 | |||
1089.6.a.c.1.1 | 1 | 33.32 | even | 2 |