Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 25872x^{2} - 1407374x - 6356280 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-121.221\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | −171.600 | −1.32365 | −0.661824 | − | 0.749659i | \(-0.730218\pi\) | ||||
−0.661824 | + | 0.749659i | \(0.730218\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 409.367 | 1.02007 | 0.510036 | − | 0.860153i | \(-0.329632\pi\) | ||||
0.510036 | + | 0.860153i | \(0.329632\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −730.649 | −1.19909 | −0.599543 | − | 0.800343i | \(-0.704651\pi\) | ||||
−0.599543 | + | 0.800343i | \(0.704651\pi\) | |||||||
\(14\) | 686.401 | 0.935961 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 248.437 | 0.208494 | 0.104247 | − | 0.994551i | \(-0.466757\pi\) | ||||
0.104247 | + | 0.994551i | \(0.466757\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 1544.40 | 0.764209 | ||||||||
\(22\) | −1637.47 | −0.721300 | ||||||||
\(23\) | 1713.53 | 0.675416 | 0.337708 | − | 0.941251i | \(-0.390348\pi\) | ||||
0.337708 | + | 0.941251i | \(0.390348\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2922.59 | 0.847882 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −2745.60 | −0.661824 | ||||||||
\(29\) | −935.716 | −0.206609 | −0.103305 | − | 0.994650i | \(-0.532942\pi\) | ||||
−0.103305 | + | 0.994650i | \(0.532942\pi\) | |||||||
\(30\) | 900.000 | 0.182574 | ||||||||
\(31\) | 396.792 | 0.0741582 | 0.0370791 | − | 0.999312i | \(-0.488195\pi\) | ||||
0.0370791 | + | 0.999312i | \(0.488195\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −3684.30 | −0.588939 | ||||||||
\(34\) | −993.748 | −0.147428 | ||||||||
\(35\) | −4290.01 | −0.591954 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −495.885 | −0.0595494 | −0.0297747 | − | 0.999557i | \(-0.509479\pi\) | ||||
−0.0297747 | + | 0.999557i | \(0.509479\pi\) | |||||||
\(38\) | −1444.00 | −0.162221 | ||||||||
\(39\) | 6575.84 | 0.692293 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | 17125.9 | 1.59109 | 0.795543 | − | 0.605897i | \(-0.207186\pi\) | ||||
0.795543 | + | 0.605897i | \(0.207186\pi\) | |||||||
\(42\) | −6177.61 | −0.540377 | ||||||||
\(43\) | −22082.9 | −1.82131 | −0.910656 | − | 0.413165i | \(-0.864423\pi\) | ||||
−0.910656 | + | 0.413165i | \(0.864423\pi\) | |||||||
\(44\) | 6549.87 | 0.510036 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | −6854.11 | −0.477591 | ||||||||
\(47\) | 11811.6 | 0.779944 | 0.389972 | − | 0.920827i | \(-0.372485\pi\) | ||||
0.389972 | + | 0.920827i | \(0.372485\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 12639.6 | 0.752046 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −2235.93 | −0.120374 | ||||||||
\(52\) | −11690.4 | −0.599543 | ||||||||
\(53\) | 6642.10 | 0.324800 | 0.162400 | − | 0.986725i | \(-0.448077\pi\) | ||||
0.162400 | + | 0.986725i | \(0.448077\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 10234.2 | 0.456190 | ||||||||
\(56\) | 10982.4 | 0.467981 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | 3742.87 | 0.146095 | ||||||||
\(59\) | 606.503 | 0.0226831 | 0.0113416 | − | 0.999936i | \(-0.496390\pi\) | ||||
0.0113416 | + | 0.999936i | \(0.496390\pi\) | |||||||
\(60\) | −3600.00 | −0.129099 | ||||||||
\(61\) | −33867.0 | −1.16534 | −0.582669 | − | 0.812710i | \(-0.697992\pi\) | ||||
−0.582669 | + | 0.812710i | \(0.697992\pi\) | |||||||
\(62\) | −1587.17 | −0.0524377 | ||||||||
\(63\) | −13899.6 | −0.441216 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −18266.2 | −0.536247 | ||||||||
\(66\) | 14737.2 | 0.416443 | ||||||||
\(67\) | 4109.20 | 0.111833 | 0.0559165 | − | 0.998435i | \(-0.482192\pi\) | ||||
0.0559165 | + | 0.998435i | \(0.482192\pi\) | |||||||
\(68\) | 3974.99 | 0.104247 | ||||||||
\(69\) | −15421.8 | −0.389952 | ||||||||
\(70\) | 17160.0 | 0.418575 | ||||||||
\(71\) | 39645.6 | 0.933360 | 0.466680 | − | 0.884426i | \(-0.345450\pi\) | ||||
0.466680 | + | 0.884426i | \(0.345450\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 40536.8 | 0.890311 | 0.445156 | − | 0.895453i | \(-0.353148\pi\) | ||||
0.445156 | + | 0.895453i | \(0.353148\pi\) | |||||||
\(74\) | 1983.54 | 0.0421078 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 5776.00 | 0.114708 | ||||||||
\(77\) | −70247.4 | −1.35022 | ||||||||
\(78\) | −26303.4 | −0.489525 | ||||||||
\(79\) | 62602.2 | 1.12855 | 0.564276 | − | 0.825586i | \(-0.309155\pi\) | ||||
0.564276 | + | 0.825586i | \(0.309155\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −68503.6 | −1.12507 | ||||||||
\(83\) | −31307.4 | −0.498829 | −0.249415 | − | 0.968397i | \(-0.580238\pi\) | ||||
−0.249415 | + | 0.968397i | \(0.580238\pi\) | |||||||
\(84\) | 24710.4 | 0.382105 | ||||||||
\(85\) | 6210.93 | 0.0932415 | ||||||||
\(86\) | 88331.5 | 1.28786 | ||||||||
\(87\) | 8421.45 | 0.119286 | ||||||||
\(88\) | −26199.5 | −0.360650 | ||||||||
\(89\) | 84209.3 | 1.12690 | 0.563449 | − | 0.826151i | \(-0.309474\pi\) | ||||
0.563449 | + | 0.826151i | \(0.309474\pi\) | |||||||
\(90\) | −8100.00 | −0.105409 | ||||||||
\(91\) | 125380. | 1.58717 | ||||||||
\(92\) | 27416.4 | 0.337708 | ||||||||
\(93\) | −3571.13 | −0.0428152 | ||||||||
\(94\) | −47246.3 | −0.551504 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 17525.0 | 0.189117 | 0.0945583 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945583 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(98\) | −50558.6 | −0.531777 | ||||||||
\(99\) | 33158.7 | 0.340024 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 4156.11 | 0.0405400 | 0.0202700 | − | 0.999795i | \(-0.493547\pi\) | ||||
0.0202700 | + | 0.999795i | \(0.493547\pi\) | |||||||
\(102\) | 8943.73 | 0.0851174 | ||||||||
\(103\) | 12638.4 | 0.117381 | 0.0586906 | − | 0.998276i | \(-0.481307\pi\) | ||||
0.0586906 | + | 0.998276i | \(0.481307\pi\) | |||||||
\(104\) | 46761.5 | 0.423941 | ||||||||
\(105\) | 38610.1 | 0.341765 | ||||||||
\(106\) | −26568.4 | −0.229668 | ||||||||
\(107\) | −80915.4 | −0.683238 | −0.341619 | − | 0.939839i | \(-0.610975\pi\) | ||||
−0.341619 | + | 0.939839i | \(0.610975\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 31453.7 | 0.253574 | 0.126787 | − | 0.991930i | \(-0.459533\pi\) | ||||
0.126787 | + | 0.991930i | \(0.459533\pi\) | |||||||
\(110\) | −40936.7 | −0.322575 | ||||||||
\(111\) | 4462.97 | 0.0343808 | ||||||||
\(112\) | −43929.7 | −0.330912 | ||||||||
\(113\) | −73882.1 | −0.544306 | −0.272153 | − | 0.962254i | \(-0.587736\pi\) | ||||
−0.272153 | + | 0.962254i | \(0.587736\pi\) | |||||||
\(114\) | 12996.0 | 0.0936586 | ||||||||
\(115\) | 42838.2 | 0.302055 | ||||||||
\(116\) | −14971.5 | −0.103305 | ||||||||
\(117\) | −59182.5 | −0.399695 | ||||||||
\(118\) | −2426.01 | −0.0160394 | ||||||||
\(119\) | −42631.9 | −0.275973 | ||||||||
\(120\) | 14400.0 | 0.0912871 | ||||||||
\(121\) | 6530.00 | 0.0405462 | ||||||||
\(122\) | 135468. | 0.824018 | ||||||||
\(123\) | −154133. | −0.918614 | ||||||||
\(124\) | 6348.68 | 0.0370791 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 55598.5 | 0.311987 | ||||||||
\(127\) | 197930. | 1.08894 | 0.544469 | − | 0.838781i | \(-0.316731\pi\) | ||||
0.544469 | + | 0.838781i | \(0.316731\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 198746. | 1.05154 | ||||||||
\(130\) | 73064.9 | 0.379184 | ||||||||
\(131\) | −296740. | −1.51077 | −0.755383 | − | 0.655283i | \(-0.772549\pi\) | ||||
−0.755383 | + | 0.655283i | \(0.772549\pi\) | |||||||
\(132\) | −58948.8 | −0.294469 | ||||||||
\(133\) | −61947.7 | −0.303666 | ||||||||
\(134\) | −16436.8 | −0.0790779 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | −15900.0 | −0.0737138 | ||||||||
\(137\) | −103798. | −0.472486 | −0.236243 | − | 0.971694i | \(-0.575916\pi\) | ||||
−0.236243 | + | 0.971694i | \(0.575916\pi\) | |||||||
\(138\) | 61687.0 | 0.275738 | ||||||||
\(139\) | −208201. | −0.914001 | −0.457000 | − | 0.889466i | \(-0.651076\pi\) | ||||
−0.457000 | + | 0.889466i | \(0.651076\pi\) | |||||||
\(140\) | −68640.1 | −0.295977 | ||||||||
\(141\) | −106304. | −0.450301 | ||||||||
\(142\) | −158582. | −0.659985 | ||||||||
\(143\) | −299103. | −1.22315 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −23392.9 | −0.0923984 | ||||||||
\(146\) | −162147. | −0.629545 | ||||||||
\(147\) | −113757. | −0.434194 | ||||||||
\(148\) | −7934.17 | −0.0297747 | ||||||||
\(149\) | −502065. | −1.85265 | −0.926327 | − | 0.376721i | \(-0.877051\pi\) | ||||
−0.926327 | + | 0.376721i | \(0.877051\pi\) | |||||||
\(150\) | 22500.0 | 0.0816497 | ||||||||
\(151\) | −367258. | −1.31078 | −0.655389 | − | 0.755292i | \(-0.727495\pi\) | ||||
−0.655389 | + | 0.755292i | \(0.727495\pi\) | |||||||
\(152\) | −23104.0 | −0.0811107 | ||||||||
\(153\) | 20123.4 | 0.0694981 | ||||||||
\(154\) | 280990. | 0.954747 | ||||||||
\(155\) | 9919.80 | 0.0331645 | ||||||||
\(156\) | 105213. | 0.346146 | ||||||||
\(157\) | 154312. | 0.499632 | 0.249816 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249816 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(158\) | −250409. | −0.798007 | ||||||||
\(159\) | −59778.9 | −0.187523 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −294042. | −0.894014 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −463772. | −1.36721 | −0.683606 | − | 0.729852i | \(-0.739589\pi\) | ||||
−0.683606 | + | 0.729852i | \(0.739589\pi\) | |||||||
\(164\) | 274014. | 0.795543 | ||||||||
\(165\) | −92107.5 | −0.263381 | ||||||||
\(166\) | 125230. | 0.352726 | ||||||||
\(167\) | −540213. | −1.49891 | −0.749453 | − | 0.662058i | \(-0.769683\pi\) | ||||
−0.749453 | + | 0.662058i | \(0.769683\pi\) | |||||||
\(168\) | −98841.7 | −0.270189 | ||||||||
\(169\) | 162555. | 0.437807 | ||||||||
\(170\) | −24843.7 | −0.0659317 | ||||||||
\(171\) | 29241.0 | 0.0764719 | ||||||||
\(172\) | −353326. | −0.910656 | ||||||||
\(173\) | −381768. | −0.969804 | −0.484902 | − | 0.874569i | \(-0.661145\pi\) | ||||
−0.484902 | + | 0.874569i | \(0.661145\pi\) | |||||||
\(174\) | −33685.8 | −0.0843478 | ||||||||
\(175\) | −107250. | −0.264730 | ||||||||
\(176\) | 104798. | 0.255018 | ||||||||
\(177\) | −5458.53 | −0.0130961 | ||||||||
\(178\) | −336837. | −0.796838 | ||||||||
\(179\) | 197548. | 0.460828 | 0.230414 | − | 0.973093i | \(-0.425992\pi\) | ||||
0.230414 | + | 0.973093i | \(0.425992\pi\) | |||||||
\(180\) | 32400.0 | 0.0745356 | ||||||||
\(181\) | −641241. | −1.45487 | −0.727436 | − | 0.686176i | \(-0.759288\pi\) | ||||
−0.727436 | + | 0.686176i | \(0.759288\pi\) | |||||||
\(182\) | −501518. | −1.12230 | ||||||||
\(183\) | 304803. | 0.672808 | ||||||||
\(184\) | −109666. | −0.238796 | ||||||||
\(185\) | −12397.1 | −0.0266313 | ||||||||
\(186\) | 14284.5 | 0.0302749 | ||||||||
\(187\) | 101702. | 0.212679 | ||||||||
\(188\) | 188985. | 0.389972 | ||||||||
\(189\) | 125097. | 0.254736 | ||||||||
\(190\) | −36100.0 | −0.0725476 | ||||||||
\(191\) | −25116.2 | −0.0498162 | −0.0249081 | − | 0.999690i | \(-0.507929\pi\) | ||||
−0.0249081 | + | 0.999690i | \(0.507929\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −53912.4 | −0.104183 | −0.0520913 | − | 0.998642i | \(-0.516589\pi\) | ||||
−0.0520913 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(194\) | −70100.2 | −0.133726 | ||||||||
\(195\) | 164396. | 0.309603 | ||||||||
\(196\) | 202234. | 0.376023 | ||||||||
\(197\) | 483800. | 0.888179 | 0.444090 | − | 0.895982i | \(-0.353527\pi\) | ||||
0.444090 | + | 0.895982i | \(0.353527\pi\) | |||||||
\(198\) | −132635. | −0.240433 | ||||||||
\(199\) | −808124. | −1.44659 | −0.723295 | − | 0.690540i | \(-0.757373\pi\) | ||||
−0.723295 | + | 0.690540i | \(0.757373\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −36982.8 | −0.0645668 | ||||||||
\(202\) | −16624.4 | −0.0286661 | ||||||||
\(203\) | 160569. | 0.273478 | ||||||||
\(204\) | −35774.9 | −0.0601871 | ||||||||
\(205\) | 428147. | 0.711555 | ||||||||
\(206\) | −50553.6 | −0.0830011 | ||||||||
\(207\) | 138796. | 0.225139 | ||||||||
\(208\) | −187046. | −0.299771 | ||||||||
\(209\) | 147781. | 0.234020 | ||||||||
\(210\) | −154440. | −0.241664 | ||||||||
\(211\) | −28301.7 | −0.0437629 | −0.0218814 | − | 0.999761i | \(-0.506966\pi\) | ||||
−0.0218814 | + | 0.999761i | \(0.506966\pi\) | |||||||
\(212\) | 106274. | 0.162400 | ||||||||
\(213\) | −356811. | −0.538876 | ||||||||
\(214\) | 323662. | 0.483122 | ||||||||
\(215\) | −552072. | −0.814516 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −68089.6 | −0.0981594 | ||||||||
\(218\) | −125815. | −0.179304 | ||||||||
\(219\) | −364831. | −0.514022 | ||||||||
\(220\) | 163747. | 0.228095 | ||||||||
\(221\) | −181520. | −0.250002 | ||||||||
\(222\) | −17851.9 | −0.0243109 | ||||||||
\(223\) | 1.24055e6 | 1.67052 | 0.835260 | − | 0.549855i | \(-0.185317\pi\) | ||||
0.835260 | + | 0.549855i | \(0.185317\pi\) | |||||||
\(224\) | 175719. | 0.233990 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 295528. | 0.384882 | ||||||||
\(227\) | −1.09798e6 | −1.41427 | −0.707134 | − | 0.707080i | \(-0.750012\pi\) | ||||
−0.707134 | + | 0.707080i | \(0.750012\pi\) | |||||||
\(228\) | −51984.0 | −0.0662266 | ||||||||
\(229\) | 971661. | 1.22441 | 0.612204 | − | 0.790700i | \(-0.290283\pi\) | ||||
0.612204 | + | 0.790700i | \(0.290283\pi\) | |||||||
\(230\) | −171353. | −0.213585 | ||||||||
\(231\) | 632227. | 0.779548 | ||||||||
\(232\) | 59885.9 | 0.0730473 | ||||||||
\(233\) | 84185.8 | 0.101590 | 0.0507948 | − | 0.998709i | \(-0.483825\pi\) | ||||
0.0507948 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(234\) | 236730. | 0.282627 | ||||||||
\(235\) | 295290. | 0.348802 | ||||||||
\(236\) | 9704.05 | 0.0113416 | ||||||||
\(237\) | −563420. | −0.651570 | ||||||||
\(238\) | 170527. | 0.195143 | ||||||||
\(239\) | −1.37097e6 | −1.55251 | −0.776253 | − | 0.630422i | \(-0.782882\pi\) | ||||
−0.776253 | + | 0.630422i | \(0.782882\pi\) | |||||||
\(240\) | −57600.0 | −0.0645497 | ||||||||
\(241\) | 936952. | 1.03914 | 0.519571 | − | 0.854427i | \(-0.326092\pi\) | ||||
0.519571 | + | 0.854427i | \(0.326092\pi\) | |||||||
\(242\) | −26120.0 | −0.0286705 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −541872. | −0.582669 | ||||||||
\(245\) | 315991. | 0.336325 | ||||||||
\(246\) | 616532. | 0.649558 | ||||||||
\(247\) | −263764. | −0.275089 | ||||||||
\(248\) | −25394.7 | −0.0262189 | ||||||||
\(249\) | 281767. | 0.287999 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −1.30701e6 | −1.30946 | −0.654732 | − | 0.755861i | \(-0.727218\pi\) | ||||
−0.654732 | + | 0.755861i | \(0.727218\pi\) | |||||||
\(252\) | −222394. | −0.220608 | ||||||||
\(253\) | 701461. | 0.688973 | ||||||||
\(254\) | −791722. | −0.769996 | ||||||||
\(255\) | −55898.3 | −0.0538330 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −996635. | −0.941246 | −0.470623 | − | 0.882334i | \(-0.655971\pi\) | ||||
−0.470623 | + | 0.882334i | \(0.655971\pi\) | |||||||
\(258\) | −794983. | −0.743548 | ||||||||
\(259\) | 85094.1 | 0.0788224 | ||||||||
\(260\) | −292259. | −0.268124 | ||||||||
\(261\) | −75793.0 | −0.0688697 | ||||||||
\(262\) | 1.18696e6 | 1.06827 | ||||||||
\(263\) | −380225. | −0.338962 | −0.169481 | − | 0.985533i | \(-0.554209\pi\) | ||||
−0.169481 | + | 0.985533i | \(0.554209\pi\) | |||||||
\(264\) | 235795. | 0.208221 | ||||||||
\(265\) | 166053. | 0.145255 | ||||||||
\(266\) | 247791. | 0.214724 | ||||||||
\(267\) | −757884. | −0.650615 | ||||||||
\(268\) | 65747.2 | 0.0559165 | ||||||||
\(269\) | 693730. | 0.584534 | 0.292267 | − | 0.956337i | \(-0.405590\pi\) | ||||
0.292267 | + | 0.956337i | \(0.405590\pi\) | |||||||
\(270\) | 72900.0 | 0.0608581 | ||||||||
\(271\) | −2.05362e6 | −1.69862 | −0.849311 | − | 0.527892i | \(-0.822983\pi\) | ||||
−0.849311 | + | 0.527892i | \(0.822983\pi\) | |||||||
\(272\) | 63599.9 | 0.0521236 | ||||||||
\(273\) | −1.12842e6 | −0.916352 | ||||||||
\(274\) | 415193. | 0.334098 | ||||||||
\(275\) | 255854. | 0.204014 | ||||||||
\(276\) | −246748. | −0.194976 | ||||||||
\(277\) | −191006. | −0.149571 | −0.0747855 | − | 0.997200i | \(-0.523827\pi\) | ||||
−0.0747855 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(278\) | 832806. | 0.646296 | ||||||||
\(279\) | 32140.2 | 0.0247194 | ||||||||
\(280\) | 274560. | 0.209287 | ||||||||
\(281\) | 771836. | 0.583121 | 0.291561 | − | 0.956552i | \(-0.405825\pi\) | ||||
0.291561 | + | 0.956552i | \(0.405825\pi\) | |||||||
\(282\) | 425217. | 0.318411 | ||||||||
\(283\) | −442073. | −0.328117 | −0.164058 | − | 0.986451i | \(-0.552459\pi\) | ||||
−0.164058 | + | 0.986451i | \(0.552459\pi\) | |||||||
\(284\) | 634330. | 0.466680 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | 1.19641e6 | 0.864900 | ||||||||
\(287\) | −2.93881e6 | −2.10604 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.35814e6 | −0.956530 | ||||||||
\(290\) | 93571.6 | 0.0653355 | ||||||||
\(291\) | −157725. | −0.109187 | ||||||||
\(292\) | 648588. | 0.445156 | ||||||||
\(293\) | 882501. | 0.600546 | 0.300273 | − | 0.953853i | \(-0.402922\pi\) | ||||
0.300273 | + | 0.953853i | \(0.402922\pi\) | |||||||
\(294\) | 455027. | 0.307022 | ||||||||
\(295\) | 15162.6 | 0.0101442 | ||||||||
\(296\) | 31736.7 | 0.0210539 | ||||||||
\(297\) | −298428. | −0.196313 | ||||||||
\(298\) | 2.00826e6 | 1.31002 | ||||||||
\(299\) | −1.25199e6 | −0.809882 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | 3.78943e6 | 2.41078 | ||||||||
\(302\) | 1.46903e6 | 0.926860 | ||||||||
\(303\) | −37405.0 | −0.0234058 | ||||||||
\(304\) | 92416.0 | 0.0573539 | ||||||||
\(305\) | −846674. | −0.521155 | ||||||||
\(306\) | −80493.6 | −0.0491426 | ||||||||
\(307\) | −2.40614e6 | −1.45705 | −0.728527 | − | 0.685017i | \(-0.759795\pi\) | ||||
−0.728527 | + | 0.685017i | \(0.759795\pi\) | |||||||
\(308\) | −1.12396e6 | −0.675108 | ||||||||
\(309\) | −113746. | −0.0677701 | ||||||||
\(310\) | −39679.2 | −0.0234509 | ||||||||
\(311\) | 671897. | 0.393914 | 0.196957 | − | 0.980412i | \(-0.436894\pi\) | ||||
0.196957 | + | 0.980412i | \(0.436894\pi\) | |||||||
\(312\) | −420854. | −0.244762 | ||||||||
\(313\) | −2.60623e6 | −1.50367 | −0.751833 | − | 0.659353i | \(-0.770830\pi\) | ||||
−0.751833 | + | 0.659353i | \(0.770830\pi\) | |||||||
\(314\) | −617248. | −0.353293 | ||||||||
\(315\) | −347491. | −0.197318 | ||||||||
\(316\) | 1.00164e6 | 0.564276 | ||||||||
\(317\) | 1.80892e6 | 1.01104 | 0.505522 | − | 0.862814i | \(-0.331300\pi\) | ||||
0.505522 | + | 0.862814i | \(0.331300\pi\) | |||||||
\(318\) | 239116. | 0.132599 | ||||||||
\(319\) | −383051. | −0.210756 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 728239. | 0.394468 | ||||||||
\(322\) | 1.17617e6 | 0.632163 | ||||||||
\(323\) | 89685.8 | 0.0478319 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −456655. | −0.239817 | ||||||||
\(326\) | 1.85509e6 | 0.966764 | ||||||||
\(327\) | −283083. | −0.146401 | ||||||||
\(328\) | −1.09606e6 | −0.562534 | ||||||||
\(329\) | −2.02687e6 | −1.03237 | ||||||||
\(330\) | 368430. | 0.186239 | ||||||||
\(331\) | −1.77150e6 | −0.888735 | −0.444367 | − | 0.895845i | \(-0.646571\pi\) | ||||
−0.444367 | + | 0.895845i | \(0.646571\pi\) | |||||||
\(332\) | −500919. | −0.249415 | ||||||||
\(333\) | −40166.7 | −0.0198498 | ||||||||
\(334\) | 2.16085e6 | 1.05989 | ||||||||
\(335\) | 102730. | 0.0500132 | ||||||||
\(336\) | 395367. | 0.191052 | ||||||||
\(337\) | 1.77477e6 | 0.851271 | 0.425636 | − | 0.904895i | \(-0.360051\pi\) | ||||
0.425636 | + | 0.904895i | \(0.360051\pi\) | |||||||
\(338\) | −650218. | −0.309576 | ||||||||
\(339\) | 664939. | 0.314255 | ||||||||
\(340\) | 99374.8 | 0.0466207 | ||||||||
\(341\) | 162433. | 0.0756466 | ||||||||
\(342\) | −116964. | −0.0540738 | ||||||||
\(343\) | 715119. | 0.328203 | ||||||||
\(344\) | 1.41330e6 | 0.643931 | ||||||||
\(345\) | −385544. | −0.174392 | ||||||||
\(346\) | 1.52707e6 | 0.685755 | ||||||||
\(347\) | −2.21658e6 | −0.988235 | −0.494117 | − | 0.869395i | \(-0.664509\pi\) | ||||
−0.494117 | + | 0.869395i | \(0.664509\pi\) | |||||||
\(348\) | 134743. | 0.0596429 | ||||||||
\(349\) | 2.44678e6 | 1.07531 | 0.537653 | − | 0.843166i | \(-0.319311\pi\) | ||||
0.537653 | + | 0.843166i | \(0.319311\pi\) | |||||||
\(350\) | 429001. | 0.187192 | ||||||||
\(351\) | 532643. | 0.230764 | ||||||||
\(352\) | −419191. | −0.180325 | ||||||||
\(353\) | 637853. | 0.272448 | 0.136224 | − | 0.990678i | \(-0.456503\pi\) | ||||
0.136224 | + | 0.990678i | \(0.456503\pi\) | |||||||
\(354\) | 21834.1 | 0.00926035 | ||||||||
\(355\) | 991141. | 0.417411 | ||||||||
\(356\) | 1.34735e6 | 0.563449 | ||||||||
\(357\) | 383687. | 0.159333 | ||||||||
\(358\) | −790191. | −0.325855 | ||||||||
\(359\) | 3.99786e6 | 1.63716 | 0.818580 | − | 0.574392i | \(-0.194761\pi\) | ||||
0.818580 | + | 0.574392i | \(0.194761\pi\) | |||||||
\(360\) | −129600. | −0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 2.56496e6 | 1.02875 | ||||||||
\(363\) | −58770.0 | −0.0234093 | ||||||||
\(364\) | 2.00607e6 | 0.793584 | ||||||||
\(365\) | 1.01342e6 | 0.398159 | ||||||||
\(366\) | −1.21921e6 | −0.475747 | ||||||||
\(367\) | 2.49330e6 | 0.966294 | 0.483147 | − | 0.875539i | \(-0.339494\pi\) | ||||
0.483147 | + | 0.875539i | \(0.339494\pi\) | |||||||
\(368\) | 438663. | 0.168854 | ||||||||
\(369\) | 1.38720e6 | 0.530362 | ||||||||
\(370\) | 49588.5 | 0.0188312 | ||||||||
\(371\) | −1.13979e6 | −0.429921 | ||||||||
\(372\) | −57138.1 | −0.0214076 | ||||||||
\(373\) | −3.44698e6 | −1.28282 | −0.641411 | − | 0.767197i | \(-0.721651\pi\) | ||||
−0.641411 | + | 0.767197i | \(0.721651\pi\) | |||||||
\(374\) | −406807. | −0.150387 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | −755941. | −0.275752 | ||||||||
\(377\) | 683680. | 0.247742 | ||||||||
\(378\) | −500386. | −0.180126 | ||||||||
\(379\) | 1.53562e6 | 0.549143 | 0.274572 | − | 0.961567i | \(-0.411464\pi\) | ||||
0.274572 | + | 0.961567i | \(0.411464\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | −1.78137e6 | −0.628699 | ||||||||
\(382\) | 100465. | 0.0352254 | ||||||||
\(383\) | −3.26271e6 | −1.13653 | −0.568267 | − | 0.822844i | \(-0.692386\pi\) | ||||
−0.568267 | + | 0.822844i | \(0.692386\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −1.75619e6 | −0.603835 | ||||||||
\(386\) | 215650. | 0.0736683 | ||||||||
\(387\) | −1.78871e6 | −0.607104 | ||||||||
\(388\) | 280401. | 0.0945583 | ||||||||
\(389\) | −2.17490e6 | −0.728728 | −0.364364 | − | 0.931257i | \(-0.618714\pi\) | ||||
−0.364364 | + | 0.931257i | \(0.618714\pi\) | |||||||
\(390\) | −657584. | −0.218922 | ||||||||
\(391\) | 425704. | 0.140820 | ||||||||
\(392\) | −808937. | −0.265889 | ||||||||
\(393\) | 2.67066e6 | 0.872242 | ||||||||
\(394\) | −1.93520e6 | −0.628038 | ||||||||
\(395\) | 1.56506e6 | 0.504704 | ||||||||
\(396\) | 530539. | 0.170012 | ||||||||
\(397\) | 4.42115e6 | 1.40786 | 0.703930 | − | 0.710270i | \(-0.251427\pi\) | ||||
0.703930 | + | 0.710270i | \(0.251427\pi\) | |||||||
\(398\) | 3.23250e6 | 1.02289 | ||||||||
\(399\) | 557529. | 0.175322 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −761947. | −0.236627 | −0.118313 | − | 0.992976i | \(-0.537749\pi\) | ||||
−0.118313 | + | 0.992976i | \(0.537749\pi\) | |||||||
\(402\) | 147931. | 0.0456556 | ||||||||
\(403\) | −289916. | −0.0889220 | ||||||||
\(404\) | 66497.7 | 0.0202700 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | −642277. | −0.193378 | ||||||||
\(407\) | −202999. | −0.0607446 | ||||||||
\(408\) | 143100. | 0.0425587 | ||||||||
\(409\) | −2.47581e6 | −0.731829 | −0.365915 | − | 0.930648i | \(-0.619244\pi\) | ||||
−0.365915 | + | 0.930648i | \(0.619244\pi\) | |||||||
\(410\) | −1.71259e6 | −0.503146 | ||||||||
\(411\) | 934185. | 0.272790 | ||||||||
\(412\) | 202214. | 0.0586906 | ||||||||
\(413\) | −104076. | −0.0300245 | ||||||||
\(414\) | −555183. | −0.159197 | ||||||||
\(415\) | −782685. | −0.223083 | ||||||||
\(416\) | 748184. | 0.211970 | ||||||||
\(417\) | 1.87381e6 | 0.527699 | ||||||||
\(418\) | −591125. | −0.165477 | ||||||||
\(419\) | 3.00254e6 | 0.835514 | 0.417757 | − | 0.908559i | \(-0.362816\pi\) | ||||
0.417757 | + | 0.908559i | \(0.362816\pi\) | |||||||
\(420\) | 617761. | 0.170882 | ||||||||
\(421\) | −999018. | −0.274706 | −0.137353 | − | 0.990522i | \(-0.543859\pi\) | ||||
−0.137353 | + | 0.990522i | \(0.543859\pi\) | |||||||
\(422\) | 113207. | 0.0309450 | ||||||||
\(423\) | 956738. | 0.259981 | ||||||||
\(424\) | −425094. | −0.114834 | ||||||||
\(425\) | 155273. | 0.0416989 | ||||||||
\(426\) | 1.42724e6 | 0.381043 | ||||||||
\(427\) | 5.81158e6 | 1.54250 | ||||||||
\(428\) | −1.29465e6 | −0.341619 | ||||||||
\(429\) | 2.69193e6 | 0.706188 | ||||||||
\(430\) | 2.20829e6 | 0.575950 | ||||||||
\(431\) | 2.42741e6 | 0.629433 | 0.314717 | − | 0.949186i | \(-0.398091\pi\) | ||||
0.314717 | + | 0.949186i | \(0.398091\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −1.03044e6 | −0.264120 | −0.132060 | − | 0.991242i | \(-0.542159\pi\) | ||||
−0.132060 | + | 0.991242i | \(0.542159\pi\) | |||||||
\(434\) | 272359. | 0.0694091 | ||||||||
\(435\) | 210536. | 0.0533462 | ||||||||
\(436\) | 503259. | 0.126787 | ||||||||
\(437\) | 618584. | 0.154951 | ||||||||
\(438\) | 1.45932e6 | 0.363468 | ||||||||
\(439\) | −1.35893e6 | −0.336540 | −0.168270 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168270 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(440\) | −654987. | −0.161287 | ||||||||
\(441\) | 1.02381e6 | 0.250682 | ||||||||
\(442\) | 726081. | 0.176778 | ||||||||
\(443\) | 1.54725e6 | 0.374586 | 0.187293 | − | 0.982304i | \(-0.440029\pi\) | ||||
0.187293 | + | 0.982304i | \(0.440029\pi\) | |||||||
\(444\) | 71407.5 | 0.0171904 | ||||||||
\(445\) | 2.10523e6 | 0.503965 | ||||||||
\(446\) | −4.96220e6 | −1.18124 | ||||||||
\(447\) | 4.51858e6 | 1.06963 | ||||||||
\(448\) | −702875. | −0.165456 | ||||||||
\(449\) | −1.84939e6 | −0.432924 | −0.216462 | − | 0.976291i | \(-0.569452\pi\) | ||||
−0.216462 | + | 0.976291i | \(0.569452\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | 7.01077e6 | 1.62302 | ||||||||
\(452\) | −1.18211e6 | −0.272153 | ||||||||
\(453\) | 3.30532e6 | 0.756778 | ||||||||
\(454\) | 4.39194e6 | 1.00004 | ||||||||
\(455\) | 3.13449e6 | 0.709803 | ||||||||
\(456\) | 207936. | 0.0468293 | ||||||||
\(457\) | −2.80271e6 | −0.627751 | −0.313876 | − | 0.949464i | \(-0.601628\pi\) | ||||
−0.313876 | + | 0.949464i | \(0.601628\pi\) | |||||||
\(458\) | −3.88665e6 | −0.865787 | ||||||||
\(459\) | −181111. | −0.0401247 | ||||||||
\(460\) | 685411. | 0.151028 | ||||||||
\(461\) | 7.18545e6 | 1.57471 | 0.787357 | − | 0.616497i | \(-0.211449\pi\) | ||||
0.787357 | + | 0.616497i | \(0.211449\pi\) | |||||||
\(462\) | −2.52891e6 | −0.551224 | ||||||||
\(463\) | −2.63573e6 | −0.571411 | −0.285706 | − | 0.958317i | \(-0.592228\pi\) | ||||
−0.285706 | + | 0.958317i | \(0.592228\pi\) | |||||||
\(464\) | −239543. | −0.0516523 | ||||||||
\(465\) | −89278.2 | −0.0191476 | ||||||||
\(466\) | −336743. | −0.0718346 | ||||||||
\(467\) | −8.54094e6 | −1.81223 | −0.906115 | − | 0.423031i | \(-0.860966\pi\) | ||||
−0.906115 | + | 0.423031i | \(0.860966\pi\) | |||||||
\(468\) | −946921. | −0.199848 | ||||||||
\(469\) | −705139. | −0.148028 | ||||||||
\(470\) | −1.18116e6 | −0.246640 | ||||||||
\(471\) | −1.38881e6 | −0.288463 | ||||||||
\(472\) | −38816.2 | −0.00801970 | ||||||||
\(473\) | −9.03999e6 | −1.85787 | ||||||||
\(474\) | 2.25368e6 | 0.460730 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −682110. | −0.137987 | ||||||||
\(477\) | 538010. | 0.108267 | ||||||||
\(478\) | 5.48388e6 | 1.09779 | ||||||||
\(479\) | 2.83289e6 | 0.564145 | 0.282072 | − | 0.959393i | \(-0.408978\pi\) | ||||
0.282072 | + | 0.959393i | \(0.408978\pi\) | |||||||
\(480\) | 230400. | 0.0456435 | ||||||||
\(481\) | 362318. | 0.0714048 | ||||||||
\(482\) | −3.74781e6 | −0.734784 | ||||||||
\(483\) | 2.64638e6 | 0.516159 | ||||||||
\(484\) | 104480. | 0.0202731 | ||||||||
\(485\) | 438126. | 0.0845755 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 8.31365e6 | 1.58843 | 0.794217 | − | 0.607634i | \(-0.207881\pi\) | ||||
0.794217 | + | 0.607634i | \(0.207881\pi\) | |||||||
\(488\) | 2.16749e6 | 0.412009 | ||||||||
\(489\) | 4.17395e6 | 0.789360 | ||||||||
\(490\) | −1.26396e6 | −0.237818 | ||||||||
\(491\) | −5.74720e6 | −1.07585 | −0.537926 | − | 0.842992i | \(-0.680792\pi\) | ||||
−0.537926 | + | 0.842992i | \(0.680792\pi\) | |||||||
\(492\) | −2.46613e6 | −0.459307 | ||||||||
\(493\) | −232467. | −0.0430768 | ||||||||
\(494\) | 1.05506e6 | 0.194517 | ||||||||
\(495\) | 828967. | 0.152063 | ||||||||
\(496\) | 101579. | 0.0185395 | ||||||||
\(497\) | −6.80320e6 | −1.23544 | ||||||||
\(498\) | −1.12707e6 | −0.203646 | ||||||||
\(499\) | −1.91364e6 | −0.344040 | −0.172020 | − | 0.985093i | \(-0.555029\pi\) | ||||
−0.172020 | + | 0.985093i | \(0.555029\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 4.86192e6 | 0.865393 | ||||||||
\(502\) | 5.22802e6 | 0.925930 | ||||||||
\(503\) | −5.35043e6 | −0.942906 | −0.471453 | − | 0.881891i | \(-0.656270\pi\) | ||||
−0.471453 | + | 0.881891i | \(0.656270\pi\) | |||||||
\(504\) | 889576. | 0.155994 | ||||||||
\(505\) | 103903. | 0.0181300 | ||||||||
\(506\) | −2.80584e6 | −0.487178 | ||||||||
\(507\) | −1.46299e6 | −0.252768 | ||||||||
\(508\) | 3.16689e6 | 0.544469 | ||||||||
\(509\) | −1.51272e6 | −0.258801 | −0.129400 | − | 0.991592i | \(-0.541305\pi\) | ||||
−0.129400 | + | 0.991592i | \(0.541305\pi\) | |||||||
\(510\) | 223593. | 0.0380657 | ||||||||
\(511\) | −6.95612e6 | −1.17846 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | 3.98654e6 | 0.665562 | ||||||||
\(515\) | 315960. | 0.0524945 | ||||||||
\(516\) | 3.17993e6 | 0.525768 | ||||||||
\(517\) | 4.83527e6 | 0.795599 | ||||||||
\(518\) | −340376. | −0.0557359 | ||||||||
\(519\) | 3.43591e6 | 0.559916 | ||||||||
\(520\) | 1.16904e6 | 0.189592 | ||||||||
\(521\) | 3.46529e6 | 0.559300 | 0.279650 | − | 0.960102i | \(-0.409782\pi\) | ||||
0.279650 | + | 0.960102i | \(0.409782\pi\) | |||||||
\(522\) | 303172. | 0.0486982 | ||||||||
\(523\) | −1.12493e7 | −1.79833 | −0.899165 | − | 0.437609i | \(-0.855825\pi\) | ||||
−0.899165 | + | 0.437609i | \(0.855825\pi\) | |||||||
\(524\) | −4.74784e6 | −0.755383 | ||||||||
\(525\) | 965251. | 0.152842 | ||||||||
\(526\) | 1.52090e6 | 0.239683 | ||||||||
\(527\) | 98577.9 | 0.0154615 | ||||||||
\(528\) | −943181. | −0.147235 | ||||||||
\(529\) | −3.50017e6 | −0.543813 | ||||||||
\(530\) | −664210. | −0.102711 | ||||||||
\(531\) | 49126.8 | 0.00756105 | ||||||||
\(532\) | −991163. | −0.151833 | ||||||||
\(533\) | −1.25130e7 | −1.90785 | ||||||||
\(534\) | 3.03153e6 | 0.460055 | ||||||||
\(535\) | −2.02289e6 | −0.305553 | ||||||||
\(536\) | −262989. | −0.0395389 | ||||||||
\(537\) | −1.77793e6 | −0.266059 | ||||||||
\(538\) | −2.77492e6 | −0.413328 | ||||||||
\(539\) | 5.17425e6 | 0.767141 | ||||||||
\(540\) | −291600. | −0.0430331 | ||||||||
\(541\) | −2.89954e6 | −0.425928 | −0.212964 | − | 0.977060i | \(-0.568312\pi\) | ||||
−0.212964 | + | 0.977060i | \(0.568312\pi\) | |||||||
\(542\) | 8.21448e6 | 1.20111 | ||||||||
\(543\) | 5.77116e6 | 0.839970 | ||||||||
\(544\) | −254400. | −0.0368569 | ||||||||
\(545\) | 786342. | 0.113402 | ||||||||
\(546\) | 4.51366e6 | 0.647959 | ||||||||
\(547\) | 5.58514e6 | 0.798116 | 0.399058 | − | 0.916926i | \(-0.369337\pi\) | ||||
0.399058 | + | 0.916926i | \(0.369337\pi\) | |||||||
\(548\) | −1.66077e6 | −0.236243 | ||||||||
\(549\) | −2.74322e6 | −0.388446 | ||||||||
\(550\) | −1.02342e6 | −0.144260 | ||||||||
\(551\) | −337794. | −0.0473994 | ||||||||
\(552\) | 986992. | 0.137869 | ||||||||
\(553\) | −1.07426e7 | −1.49381 | ||||||||
\(554\) | 764024. | 0.105763 | ||||||||
\(555\) | 111574. | 0.0153756 | ||||||||
\(556\) | −3.33122e6 | −0.457000 | ||||||||
\(557\) | 8.64348e6 | 1.18046 | 0.590229 | − | 0.807236i | \(-0.299037\pi\) | ||||
0.590229 | + | 0.807236i | \(0.299037\pi\) | |||||||
\(558\) | −128561. | −0.0174792 | ||||||||
\(559\) | 1.61348e7 | 2.18391 | ||||||||
\(560\) | −1.09824e6 | −0.147988 | ||||||||
\(561\) | −915317. | −0.122790 | ||||||||
\(562\) | −3.08734e6 | −0.412329 | ||||||||
\(563\) | −6.25367e6 | −0.831503 | −0.415751 | − | 0.909478i | \(-0.636481\pi\) | ||||
−0.415751 | + | 0.909478i | \(0.636481\pi\) | |||||||
\(564\) | −1.70087e6 | −0.225150 | ||||||||
\(565\) | −1.84705e6 | −0.243421 | ||||||||
\(566\) | 1.76829e6 | 0.232014 | ||||||||
\(567\) | −1.12587e6 | −0.147072 | ||||||||
\(568\) | −2.53732e6 | −0.329993 | ||||||||
\(569\) | 4.27118e6 | 0.553054 | 0.276527 | − | 0.961006i | \(-0.410816\pi\) | ||||
0.276527 | + | 0.961006i | \(0.410816\pi\) | |||||||
\(570\) | 324900. | 0.0418854 | ||||||||
\(571\) | 5.52096e6 | 0.708638 | 0.354319 | − | 0.935125i | \(-0.384713\pi\) | ||||
0.354319 | + | 0.935125i | \(0.384713\pi\) | |||||||
\(572\) | −4.78565e6 | −0.611577 | ||||||||
\(573\) | 226046. | 0.0287614 | ||||||||
\(574\) | 1.17552e7 | 1.48919 | ||||||||
\(575\) | 1.07095e6 | 0.135083 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 9.36372e6 | 1.17087 | 0.585435 | − | 0.810719i | \(-0.300924\pi\) | ||||
0.585435 | + | 0.810719i | \(0.300924\pi\) | |||||||
\(578\) | 5.43254e6 | 0.676369 | ||||||||
\(579\) | 485212. | 0.0601499 | ||||||||
\(580\) | −374287. | −0.0461992 | ||||||||
\(581\) | 5.37236e6 | 0.660275 | ||||||||
\(582\) | 630901. | 0.0772065 | ||||||||
\(583\) | 2.71905e6 | 0.331319 | ||||||||
\(584\) | −2.59435e6 | −0.314773 | ||||||||
\(585\) | −1.47956e6 | −0.178749 | ||||||||
\(586\) | −3.53000e6 | −0.424650 | ||||||||
\(587\) | −884221. | −0.105917 | −0.0529585 | − | 0.998597i | \(-0.516865\pi\) | ||||
−0.0529585 | + | 0.998597i | \(0.516865\pi\) | |||||||
\(588\) | −1.82011e6 | −0.217097 | ||||||||
\(589\) | 143242. | 0.0170130 | ||||||||
\(590\) | −60650.3 | −0.00717304 | ||||||||
\(591\) | −4.35420e6 | −0.512791 | ||||||||
\(592\) | −126947. | −0.0148873 | ||||||||
\(593\) | 511432. | 0.0597243 | 0.0298621 | − | 0.999554i | \(-0.490493\pi\) | ||||
0.0298621 | + | 0.999554i | \(0.490493\pi\) | |||||||
\(594\) | 1.19371e6 | 0.138814 | ||||||||
\(595\) | −1.06580e6 | −0.123419 | ||||||||
\(596\) | −8.03304e6 | −0.926327 | ||||||||
\(597\) | 7.27311e6 | 0.835189 | ||||||||
\(598\) | 5.00795e6 | 0.572673 | ||||||||
\(599\) | −703758. | −0.0801412 | −0.0400706 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400706 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(600\) | 360000. | 0.0408248 | ||||||||
\(601\) | 709095. | 0.0800790 | 0.0400395 | − | 0.999198i | \(-0.487252\pi\) | ||||
0.0400395 | + | 0.999198i | \(0.487252\pi\) | |||||||
\(602\) | −1.51577e7 | −1.70468 | ||||||||
\(603\) | 332845. | 0.0372777 | ||||||||
\(604\) | −5.87613e6 | −0.655389 | ||||||||
\(605\) | 163250. | 0.0181328 | ||||||||
\(606\) | 149620. | 0.0165504 | ||||||||
\(607\) | 2.68774e6 | 0.296084 | 0.148042 | − | 0.988981i | \(-0.452703\pi\) | ||||
0.148042 | + | 0.988981i | \(0.452703\pi\) | |||||||
\(608\) | −369664. | −0.0405554 | ||||||||
\(609\) | −1.44512e6 | −0.157892 | ||||||||
\(610\) | 3.38670e6 | 0.368512 | ||||||||
\(611\) | −8.63012e6 | −0.935220 | ||||||||
\(612\) | 321974. | 0.0347490 | ||||||||
\(613\) | −411753. | −0.0442574 | −0.0221287 | − | 0.999755i | \(-0.507044\pi\) | ||||
−0.0221287 | + | 0.999755i | \(0.507044\pi\) | |||||||
\(614\) | 9.62458e6 | 1.03029 | ||||||||
\(615\) | −3.85333e6 | −0.410817 | ||||||||
\(616\) | 4.49583e6 | 0.477374 | ||||||||
\(617\) | 1.67449e6 | 0.177080 | 0.0885402 | − | 0.996073i | \(-0.471780\pi\) | ||||
0.0885402 | + | 0.996073i | \(0.471780\pi\) | |||||||
\(618\) | 454982. | 0.0479207 | ||||||||
\(619\) | −5.59624e6 | −0.587043 | −0.293521 | − | 0.955953i | \(-0.594827\pi\) | ||||
−0.293521 | + | 0.955953i | \(0.594827\pi\) | |||||||
\(620\) | 158717. | 0.0165823 | ||||||||
\(621\) | −1.24916e6 | −0.129984 | ||||||||
\(622\) | −2.68759e6 | −0.278539 | ||||||||
\(623\) | −1.44503e7 | −1.49162 | ||||||||
\(624\) | 1.68341e6 | 0.173073 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.04249e7 | 1.06325 | ||||||||
\(627\) | −1.33003e6 | −0.135112 | ||||||||
\(628\) | 2.46899e6 | 0.249816 | ||||||||
\(629\) | −123196. | −0.0124157 | ||||||||
\(630\) | 1.38996e6 | 0.139525 | ||||||||
\(631\) | 8.26101e6 | 0.825961 | 0.412980 | − | 0.910740i | \(-0.364488\pi\) | ||||
0.412980 | + | 0.910740i | \(0.364488\pi\) | |||||||
\(632\) | −4.00654e6 | −0.399004 | ||||||||
\(633\) | 254715. | 0.0252665 | ||||||||
\(634\) | −7.23566e6 | −0.714916 | ||||||||
\(635\) | 4.94826e6 | 0.486988 | ||||||||
\(636\) | −956463. | −0.0937616 | ||||||||
\(637\) | −9.23514e6 | −0.901768 | ||||||||
\(638\) | 1.53220e6 | 0.149027 | ||||||||
\(639\) | 3.21130e6 | 0.311120 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −9.91722e6 | −0.953333 | −0.476667 | − | 0.879084i | \(-0.658155\pi\) | ||||
−0.476667 | + | 0.879084i | \(0.658155\pi\) | |||||||
\(642\) | −2.91296e6 | −0.278931 | ||||||||
\(643\) | −1.85918e7 | −1.77334 | −0.886672 | − | 0.462398i | \(-0.846989\pi\) | ||||
−0.886672 | + | 0.462398i | \(0.846989\pi\) | |||||||
\(644\) | −4.70467e6 | −0.447007 | ||||||||
\(645\) | 4.96865e6 | 0.470261 | ||||||||
\(646\) | −358743. | −0.0338222 | ||||||||
\(647\) | 1.58431e7 | 1.48792 | 0.743961 | − | 0.668223i | \(-0.232945\pi\) | ||||
0.743961 | + | 0.668223i | \(0.232945\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 248282. | 0.0231384 | ||||||||
\(650\) | 1.82662e6 | 0.169576 | ||||||||
\(651\) | 612807. | 0.0566723 | ||||||||
\(652\) | −7.42035e6 | −0.683606 | ||||||||
\(653\) | −1.30198e7 | −1.19487 | −0.597435 | − | 0.801918i | \(-0.703813\pi\) | ||||
−0.597435 | + | 0.801918i | \(0.703813\pi\) | |||||||
\(654\) | 1.13233e6 | 0.103521 | ||||||||
\(655\) | −7.41849e6 | −0.675635 | ||||||||
\(656\) | 4.38423e6 | 0.397771 | ||||||||
\(657\) | 3.28348e6 | 0.296770 | ||||||||
\(658\) | 8.10748e6 | 0.729997 | ||||||||
\(659\) | 4.47538e6 | 0.401436 | 0.200718 | − | 0.979649i | \(-0.435672\pi\) | ||||
0.200718 | + | 0.979649i | \(0.435672\pi\) | |||||||
\(660\) | −1.47372e6 | −0.131691 | ||||||||
\(661\) | 406289. | 0.0361686 | 0.0180843 | − | 0.999836i | \(-0.494243\pi\) | ||||
0.0180843 | + | 0.999836i | \(0.494243\pi\) | |||||||
\(662\) | 7.08601e6 | 0.628430 | ||||||||
\(663\) | 1.63368e6 | 0.144339 | ||||||||
\(664\) | 2.00367e6 | 0.176363 | ||||||||
\(665\) | −1.54869e6 | −0.135804 | ||||||||
\(666\) | 160667. | 0.0140359 | ||||||||
\(667\) | −1.60338e6 | −0.139547 | ||||||||
\(668\) | −8.64342e6 | −0.749453 | ||||||||
\(669\) | −1.11649e7 | −0.964476 | ||||||||
\(670\) | −410920. | −0.0353647 | ||||||||
\(671\) | −1.38640e7 | −1.18873 | ||||||||
\(672\) | −1.58147e6 | −0.135094 | ||||||||
\(673\) | −1.64638e7 | −1.40118 | −0.700588 | − | 0.713566i | \(-0.747079\pi\) | ||||
−0.700588 | + | 0.713566i | \(0.747079\pi\) | |||||||
\(674\) | −7.09909e6 | −0.601940 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 2.60087e6 | 0.218903 | ||||||||
\(677\) | 1.62449e7 | 1.36222 | 0.681108 | − | 0.732183i | \(-0.261498\pi\) | ||||
0.681108 | + | 0.732183i | \(0.261498\pi\) | |||||||
\(678\) | −2.65976e6 | −0.222212 | ||||||||
\(679\) | −3.00730e6 | −0.250324 | ||||||||
\(680\) | −397499. | −0.0329658 | ||||||||
\(681\) | 9.88186e6 | 0.816528 | ||||||||
\(682\) | −649734. | −0.0534902 | ||||||||
\(683\) | −1.69563e7 | −1.39084 | −0.695422 | − | 0.718601i | \(-0.744783\pi\) | ||||
−0.695422 | + | 0.718601i | \(0.744783\pi\) | |||||||
\(684\) | 467856. | 0.0382360 | ||||||||
\(685\) | −2.59496e6 | −0.211302 | ||||||||
\(686\) | −2.86048e6 | −0.232075 | ||||||||
\(687\) | −8.74495e6 | −0.706912 | ||||||||
\(688\) | −5.65322e6 | −0.455328 | ||||||||
\(689\) | −4.85304e6 | −0.389463 | ||||||||
\(690\) | 1.54218e6 | 0.123314 | ||||||||
\(691\) | 4.86180e6 | 0.387348 | 0.193674 | − | 0.981066i | \(-0.437960\pi\) | ||||
0.193674 | + | 0.981066i | \(0.437960\pi\) | |||||||
\(692\) | −6.10828e6 | −0.484902 | ||||||||
\(693\) | −5.69004e6 | −0.450072 | ||||||||
\(694\) | 8.86633e6 | 0.698787 | ||||||||
\(695\) | −5.20503e6 | −0.408754 | ||||||||
\(696\) | −538973. | −0.0421739 | ||||||||
\(697\) | 4.25471e6 | 0.331732 | ||||||||
\(698\) | −9.78714e6 | −0.760356 | ||||||||
\(699\) | −757672. | −0.0586527 | ||||||||
\(700\) | −1.71600e6 | −0.132365 | ||||||||
\(701\) | 3.68475e6 | 0.283213 | 0.141606 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141606 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(702\) | −2.13057e6 | −0.163175 | ||||||||
\(703\) | −179015. | −0.0136616 | ||||||||
\(704\) | 1.67677e6 | 0.127509 | ||||||||
\(705\) | −2.65761e6 | −0.201381 | ||||||||
\(706\) | −2.55141e6 | −0.192650 | ||||||||
\(707\) | −713189. | −0.0536607 | ||||||||
\(708\) | −87336.5 | −0.00654806 | ||||||||
\(709\) | −1.23146e7 | −0.920036 | −0.460018 | − | 0.887910i | \(-0.652157\pi\) | ||||
−0.460018 | + | 0.887910i | \(0.652157\pi\) | |||||||
\(710\) | −3.96456e6 | −0.295154 | ||||||||
\(711\) | 5.07078e6 | 0.376184 | ||||||||
\(712\) | −5.38939e6 | −0.398419 | ||||||||
\(713\) | 679914. | 0.0500876 | ||||||||
\(714\) | −1.53475e6 | −0.112666 | ||||||||
\(715\) | −7.47758e6 | −0.547011 | ||||||||
\(716\) | 3.16076e6 | 0.230414 | ||||||||
\(717\) | 1.23387e7 | 0.896340 | ||||||||
\(718\) | −1.59914e7 | −1.15765 | ||||||||
\(719\) | −3.56575e6 | −0.257234 | −0.128617 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128617 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(720\) | 518400. | 0.0372678 | ||||||||
\(721\) | −2.16875e6 | −0.155372 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | −8.43257e6 | −0.599949 | ||||||||
\(724\) | −1.02598e7 | −0.727436 | ||||||||
\(725\) | −584823. | −0.0413218 | ||||||||
\(726\) | 235080. | 0.0165529 | ||||||||
\(727\) | −3.60456e6 | −0.252939 | −0.126469 | − | 0.991970i | \(-0.540365\pi\) | ||||
−0.126469 | + | 0.991970i | \(0.540365\pi\) | |||||||
\(728\) | −8.02429e6 | −0.561149 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −4.05368e6 | −0.281541 | ||||||||
\(731\) | −5.48620e6 | −0.379733 | ||||||||
\(732\) | 4.87684e6 | 0.336404 | ||||||||
\(733\) | 4.02534e6 | 0.276721 | 0.138361 | − | 0.990382i | \(-0.455817\pi\) | ||||
0.138361 | + | 0.990382i | \(0.455817\pi\) | |||||||
\(734\) | −9.97320e6 | −0.683273 | ||||||||
\(735\) | −2.84392e6 | −0.194178 | ||||||||
\(736\) | −1.75465e6 | −0.119398 | ||||||||
\(737\) | 1.68217e6 | 0.114078 | ||||||||
\(738\) | −5.54879e6 | −0.375023 | ||||||||
\(739\) | −1.64929e7 | −1.11093 | −0.555463 | − | 0.831542i | \(-0.687459\pi\) | ||||
−0.555463 | + | 0.831542i | \(0.687459\pi\) | |||||||
\(740\) | −198354. | −0.0133156 | ||||||||
\(741\) | 2.37388e6 | 0.158823 | ||||||||
\(742\) | 4.55914e6 | 0.304000 | ||||||||
\(743\) | −1.78193e7 | −1.18419 | −0.592093 | − | 0.805870i | \(-0.701698\pi\) | ||||
−0.592093 | + | 0.805870i | \(0.701698\pi\) | |||||||
\(744\) | 228552. | 0.0151375 | ||||||||
\(745\) | −1.25516e7 | −0.828532 | ||||||||
\(746\) | 1.37879e7 | 0.907092 | ||||||||
\(747\) | −2.53590e6 | −0.166276 | ||||||||
\(748\) | 1.62723e6 | 0.106340 | ||||||||
\(749\) | 1.38851e7 | 0.904367 | ||||||||
\(750\) | 562500. | 0.0365148 | ||||||||
\(751\) | −1.50688e7 | −0.974941 | −0.487471 | − | 0.873139i | \(-0.662080\pi\) | ||||
−0.487471 | + | 0.873139i | \(0.662080\pi\) | |||||||
\(752\) | 3.02377e6 | 0.194986 | ||||||||
\(753\) | 1.17631e7 | 0.756019 | ||||||||
\(754\) | −2.73472e6 | −0.175180 | ||||||||
\(755\) | −9.18145e6 | −0.586197 | ||||||||
\(756\) | 2.00155e6 | 0.127368 | ||||||||
\(757\) | 1.62784e7 | 1.03246 | 0.516228 | − | 0.856451i | \(-0.327336\pi\) | ||||
0.516228 | + | 0.856451i | \(0.327336\pi\) | |||||||
\(758\) | −6.14248e6 | −0.388303 | ||||||||
\(759\) | −6.31315e6 | −0.397779 | ||||||||
\(760\) | −577600. | −0.0362738 | ||||||||
\(761\) | 4.51093e6 | 0.282361 | 0.141180 | − | 0.989984i | \(-0.454910\pi\) | ||||
0.141180 | + | 0.989984i | \(0.454910\pi\) | |||||||
\(762\) | 7.12550e6 | 0.444557 | ||||||||
\(763\) | −5.39746e6 | −0.335644 | ||||||||
\(764\) | −401859. | −0.0249081 | ||||||||
\(765\) | 503085. | 0.0310805 | ||||||||
\(766\) | 1.30509e7 | 0.803650 | ||||||||
\(767\) | −443141. | −0.0271990 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 9.47467e6 | 0.577761 | 0.288881 | − | 0.957365i | \(-0.406717\pi\) | ||||
0.288881 | + | 0.957365i | \(0.406717\pi\) | |||||||
\(770\) | 7.02474e6 | 0.426976 | ||||||||
\(771\) | 8.96971e6 | 0.543429 | ||||||||
\(772\) | −862598. | −0.0520913 | ||||||||
\(773\) | −2.83231e6 | −0.170487 | −0.0852436 | − | 0.996360i | \(-0.527167\pi\) | ||||
−0.0852436 | + | 0.996360i | \(0.527167\pi\) | |||||||
\(774\) | 7.15485e6 | 0.429287 | ||||||||
\(775\) | 247995. | 0.0148316 | ||||||||
\(776\) | −1.12160e6 | −0.0668628 | ||||||||
\(777\) | −765847. | −0.0455082 | ||||||||
\(778\) | 8.69961e6 | 0.515289 | ||||||||
\(779\) | 6.18245e6 | 0.365020 | ||||||||
\(780\) | 2.63034e6 | 0.154801 | ||||||||
\(781\) | 1.62296e7 | 0.952094 | ||||||||
\(782\) | −1.70282e6 | −0.0995751 | ||||||||
\(783\) | 682137. | 0.0397619 | ||||||||
\(784\) | 3.23575e6 | 0.188012 | ||||||||
\(785\) | 3.85780e6 | 0.223442 | ||||||||
\(786\) | −1.06826e7 | −0.616768 | ||||||||
\(787\) | 7.88470e6 | 0.453783 | 0.226892 | − | 0.973920i | \(-0.427144\pi\) | ||||
0.226892 | + | 0.973920i | \(0.427144\pi\) | |||||||
\(788\) | 7.74081e6 | 0.444090 | ||||||||
\(789\) | 3.42203e6 | 0.195700 | ||||||||
\(790\) | −6.26022e6 | −0.356880 | ||||||||
\(791\) | 1.26782e7 | 0.720470 | ||||||||
\(792\) | −2.12216e6 | −0.120217 | ||||||||
\(793\) | 2.47449e7 | 1.39734 | ||||||||
\(794\) | −1.76846e7 | −0.995507 | ||||||||
\(795\) | −1.49447e6 | −0.0838630 | ||||||||
\(796\) | −1.29300e7 | −0.723295 | ||||||||
\(797\) | 2.80785e7 | 1.56577 | 0.782884 | − | 0.622168i | \(-0.213748\pi\) | ||||
0.782884 | + | 0.622168i | \(0.213748\pi\) | |||||||
\(798\) | −2.23012e6 | −0.123971 | ||||||||
\(799\) | 2.93444e6 | 0.162614 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 6.82095e6 | 0.375633 | ||||||||
\(802\) | 3.04779e6 | 0.167320 | ||||||||
\(803\) | 1.65944e7 | 0.908181 | ||||||||
\(804\) | −591724. | −0.0322834 | ||||||||
\(805\) | −7.35105e6 | −0.399815 | ||||||||
\(806\) | 1.15966e6 | 0.0628773 | ||||||||
\(807\) | −6.24357e6 | −0.337481 | ||||||||
\(808\) | −265991. | −0.0143330 | ||||||||
\(809\) | −6.92130e6 | −0.371806 | −0.185903 | − | 0.982568i | \(-0.559521\pi\) | ||||
−0.185903 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(810\) | −656100. | −0.0351364 | ||||||||
\(811\) | 1.34048e6 | 0.0715661 | 0.0357831 | − | 0.999360i | \(-0.488607\pi\) | ||||
0.0357831 | + | 0.999360i | \(0.488607\pi\) | |||||||
\(812\) | 2.56911e6 | 0.136739 | ||||||||
\(813\) | 1.84826e7 | 0.980700 | ||||||||
\(814\) | 811996. | 0.0429529 | ||||||||
\(815\) | −1.15943e7 | −0.611435 | ||||||||
\(816\) | −572399. | −0.0300936 | ||||||||
\(817\) | −7.97192e6 | −0.417838 | ||||||||
\(818\) | 9.90326e6 | 0.517481 | ||||||||
\(819\) | 1.01557e7 | 0.529056 | ||||||||
\(820\) | 6.85036e6 | 0.355778 | ||||||||
\(821\) | −1.10064e7 | −0.569883 | −0.284942 | − | 0.958545i | \(-0.591974\pi\) | ||||
−0.284942 | + | 0.958545i | \(0.591974\pi\) | |||||||
\(822\) | −3.73674e6 | −0.192892 | ||||||||
\(823\) | 2.42966e7 | 1.25039 | 0.625195 | − | 0.780468i | \(-0.285019\pi\) | ||||
0.625195 | + | 0.780468i | \(0.285019\pi\) | |||||||
\(824\) | −808857. | −0.0415006 | ||||||||
\(825\) | −2.30269e6 | −0.117788 | ||||||||
\(826\) | 416304. | 0.0212305 | ||||||||
\(827\) | 2.55224e7 | 1.29765 | 0.648826 | − | 0.760937i | \(-0.275260\pi\) | ||||
0.648826 | + | 0.760937i | \(0.275260\pi\) | |||||||
\(828\) | 2.22073e6 | 0.112569 | ||||||||
\(829\) | 1.78840e7 | 0.903814 | 0.451907 | − | 0.892065i | \(-0.350744\pi\) | ||||
0.451907 | + | 0.892065i | \(0.350744\pi\) | |||||||
\(830\) | 3.13074e6 | 0.157744 | ||||||||
\(831\) | 1.71905e6 | 0.0863549 | ||||||||
\(832\) | −2.99274e6 | −0.149886 | ||||||||
\(833\) | 3.14016e6 | 0.156797 | ||||||||
\(834\) | −7.49525e6 | −0.373139 | ||||||||
\(835\) | −1.35053e7 | −0.670331 | ||||||||
\(836\) | 2.36450e6 | 0.117010 | ||||||||
\(837\) | −289262. | −0.0142717 | ||||||||
\(838\) | −1.20102e7 | −0.590798 | ||||||||
\(839\) | −3.35619e7 | −1.64605 | −0.823023 | − | 0.568008i | \(-0.807714\pi\) | ||||
−0.823023 | + | 0.568008i | \(0.807714\pi\) | |||||||
\(840\) | −2.47104e6 | −0.120832 | ||||||||
\(841\) | −1.96356e7 | −0.957313 | ||||||||
\(842\) | 3.99607e6 | 0.194246 | ||||||||
\(843\) | −6.94652e6 | −0.336665 | ||||||||
\(844\) | −452826. | −0.0218814 | ||||||||
\(845\) | 4.06386e6 | 0.195793 | ||||||||
\(846\) | −3.82695e6 | −0.183835 | ||||||||
\(847\) | −1.12055e6 | −0.0536689 | ||||||||
\(848\) | 1.70038e6 | 0.0812000 | ||||||||
\(849\) | 3.97866e6 | 0.189438 | ||||||||
\(850\) | −621093. | −0.0294855 | ||||||||
\(851\) | −849714. | −0.0402206 | ||||||||
\(852\) | −5.70897e6 | −0.269438 | ||||||||
\(853\) | 1.75136e7 | 0.824142 | 0.412071 | − | 0.911152i | \(-0.364805\pi\) | ||||
0.412071 | + | 0.911152i | \(0.364805\pi\) | |||||||
\(854\) | −2.32463e7 | −1.09071 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | 5.17859e6 | 0.241561 | ||||||||
\(857\) | 1.91536e7 | 0.890840 | 0.445420 | − | 0.895322i | \(-0.353054\pi\) | ||||
0.445420 | + | 0.895322i | \(0.353054\pi\) | |||||||
\(858\) | −1.07677e7 | −0.499350 | ||||||||
\(859\) | 3.02413e7 | 1.39836 | 0.699178 | − | 0.714948i | \(-0.253549\pi\) | ||||
0.699178 | + | 0.714948i | \(0.253549\pi\) | |||||||
\(860\) | −8.83315e6 | −0.407258 | ||||||||
\(861\) | 2.64493e7 | 1.21592 | ||||||||
\(862\) | −9.70963e6 | −0.445076 | ||||||||
\(863\) | −1.44389e7 | −0.659946 | −0.329973 | − | 0.943990i | \(-0.607040\pi\) | ||||
−0.329973 | + | 0.943990i | \(0.607040\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | −9.54419e6 | −0.433709 | ||||||||
\(866\) | 4.12174e6 | 0.186761 | ||||||||
\(867\) | 1.22232e7 | 0.552253 | ||||||||
\(868\) | −1.08943e6 | −0.0490797 | ||||||||
\(869\) | 2.56273e7 | 1.15120 | ||||||||
\(870\) | −842145. | −0.0377215 | ||||||||
\(871\) | −3.00238e6 | −0.134097 | ||||||||
\(872\) | −2.01304e6 | −0.0896521 | ||||||||
\(873\) | 1.41953e6 | 0.0630389 | ||||||||
\(874\) | −2.47433e6 | −0.109567 | ||||||||
\(875\) | −2.68125e6 | −0.118391 | ||||||||
\(876\) | −5.83729e6 | −0.257011 | ||||||||
\(877\) | −1.70799e7 | −0.749870 | −0.374935 | − | 0.927051i | \(-0.622335\pi\) | ||||
−0.374935 | + | 0.927051i | \(0.622335\pi\) | |||||||
\(878\) | 5.43574e6 | 0.237970 | ||||||||
\(879\) | −7.94251e6 | −0.346725 | ||||||||
\(880\) | 2.61995e6 | 0.114047 | ||||||||
\(881\) | 2.02133e7 | 0.877400 | 0.438700 | − | 0.898634i | \(-0.355439\pi\) | ||||
0.438700 | + | 0.898634i | \(0.355439\pi\) | |||||||
\(882\) | −4.09525e6 | −0.177259 | ||||||||
\(883\) | 2.66270e7 | 1.14926 | 0.574632 | − | 0.818412i | \(-0.305145\pi\) | ||||
0.574632 | + | 0.818412i | \(0.305145\pi\) | |||||||
\(884\) | −2.90432e6 | −0.125001 | ||||||||
\(885\) | −136463. | −0.00585676 | ||||||||
\(886\) | −6.18901e6 | −0.264872 | ||||||||
\(887\) | 1.77998e7 | 0.759638 | 0.379819 | − | 0.925061i | \(-0.375986\pi\) | ||||
0.379819 | + | 0.925061i | \(0.375986\pi\) | |||||||
\(888\) | −285630. | −0.0121555 | ||||||||
\(889\) | −3.39649e7 | −1.44137 | ||||||||
\(890\) | −8.42093e6 | −0.356357 | ||||||||
\(891\) | 2.68585e6 | 0.113341 | ||||||||
\(892\) | 1.98488e7 | 0.835260 | ||||||||
\(893\) | 4.26398e6 | 0.178931 | ||||||||
\(894\) | −1.80743e7 | −0.756343 | ||||||||
\(895\) | 4.93869e6 | 0.206089 | ||||||||
\(896\) | 2.81150e6 | 0.116995 | ||||||||
\(897\) | 1.12679e7 | 0.467586 | ||||||||
\(898\) | 7.39754e6 | 0.306123 | ||||||||
\(899\) | −371285. | −0.0153217 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | 1.65014e6 | 0.0677189 | ||||||||
\(902\) | −2.80431e7 | −1.14765 | ||||||||
\(903\) | −3.41048e7 | −1.39186 | ||||||||
\(904\) | 4.72845e6 | 0.192441 | ||||||||
\(905\) | −1.60310e7 | −0.650638 | ||||||||
\(906\) | −1.32213e7 | −0.535123 | ||||||||
\(907\) | −4.04476e7 | −1.63258 | −0.816289 | − | 0.577643i | \(-0.803973\pi\) | ||||
−0.816289 | + | 0.577643i | \(0.803973\pi\) | |||||||
\(908\) | −1.75678e7 | −0.707134 | ||||||||
\(909\) | 336645. | 0.0135133 | ||||||||
\(910\) | −1.25380e7 | −0.501907 | ||||||||
\(911\) | −8.24751e6 | −0.329251 | −0.164626 | − | 0.986356i | \(-0.552642\pi\) | ||||
−0.164626 | + | 0.986356i | \(0.552642\pi\) | |||||||
\(912\) | −831744. | −0.0331133 | ||||||||
\(913\) | −1.28162e7 | −0.508842 | ||||||||
\(914\) | 1.12108e7 | 0.443887 | ||||||||
\(915\) | 7.62007e6 | 0.300889 | ||||||||
\(916\) | 1.55466e7 | 0.612204 | ||||||||
\(917\) | 5.09206e7 | 1.99972 | ||||||||
\(918\) | 724442. | 0.0283725 | ||||||||
\(919\) | −1.96298e7 | −0.766704 | −0.383352 | − | 0.923602i | \(-0.625230\pi\) | ||||
−0.383352 | + | 0.923602i | \(0.625230\pi\) | |||||||
\(920\) | −2.74164e6 | −0.106793 | ||||||||
\(921\) | 2.16553e7 | 0.841231 | ||||||||
\(922\) | −2.87418e7 | −1.11349 | ||||||||
\(923\) | −2.89670e7 | −1.11918 | ||||||||
\(924\) | 1.01156e7 | 0.389774 | ||||||||
\(925\) | −309928. | −0.0119099 | ||||||||
\(926\) | 1.05429e7 | 0.404049 | ||||||||
\(927\) | 1.02371e6 | 0.0391271 | ||||||||
\(928\) | 958174. | 0.0365237 | ||||||||
\(929\) | −2.47430e6 | −0.0940619 | −0.0470310 | − | 0.998893i | \(-0.514976\pi\) | ||||
−0.0470310 | + | 0.998893i | \(0.514976\pi\) | |||||||
\(930\) | 357113. | 0.0135394 | ||||||||
\(931\) | 4.56291e6 | 0.172531 | ||||||||
\(932\) | 1.34697e6 | 0.0507948 | ||||||||
\(933\) | −6.04707e6 | −0.227426 | ||||||||
\(934\) | 3.41638e7 | 1.28144 | ||||||||
\(935\) | 2.54255e6 | 0.0951130 | ||||||||
\(936\) | 3.78768e6 | 0.141314 | ||||||||
\(937\) | −1.99378e7 | −0.741872 | −0.370936 | − | 0.928658i | \(-0.620963\pi\) | ||||
−0.370936 | + | 0.928658i | \(0.620963\pi\) | |||||||
\(938\) | 2.82056e6 | 0.104671 | ||||||||
\(939\) | 2.34561e7 | 0.868142 | ||||||||
\(940\) | 4.72463e6 | 0.174401 | ||||||||
\(941\) | −2.44027e6 | −0.0898387 | −0.0449193 | − | 0.998991i | \(-0.514303\pi\) | ||||
−0.0449193 | + | 0.998991i | \(0.514303\pi\) | |||||||
\(942\) | 5.55523e6 | 0.203974 | ||||||||
\(943\) | 2.93457e7 | 1.07465 | ||||||||
\(944\) | 155265. | 0.00567078 | ||||||||
\(945\) | 3.12741e6 | 0.113922 | ||||||||
\(946\) | 3.61600e7 | 1.31371 | ||||||||
\(947\) | −2.17049e7 | −0.786471 | −0.393236 | − | 0.919438i | \(-0.628644\pi\) | ||||
−0.393236 | + | 0.919438i | \(0.628644\pi\) | |||||||
\(948\) | −9.01472e6 | −0.325785 | ||||||||
\(949\) | −2.96181e7 | −1.06756 | ||||||||
\(950\) | −902500. | −0.0324443 | ||||||||
\(951\) | −1.62802e7 | −0.583727 | ||||||||
\(952\) | 2.72844e6 | 0.0975713 | ||||||||
\(953\) | −1.92314e7 | −0.685928 | −0.342964 | − | 0.939349i | \(-0.611431\pi\) | ||||
−0.342964 | + | 0.939349i | \(0.611431\pi\) | |||||||
\(954\) | −2.15204e6 | −0.0765561 | ||||||||
\(955\) | −627905. | −0.0222785 | ||||||||
\(956\) | −2.19355e7 | −0.776253 | ||||||||
\(957\) | 3.44746e6 | 0.121680 | ||||||||
\(958\) | −1.13316e7 | −0.398911 | ||||||||
\(959\) | 1.78118e7 | 0.625405 | ||||||||
\(960\) | −921600. | −0.0322749 | ||||||||
\(961\) | −2.84717e7 | −0.994501 | ||||||||
\(962\) | −1.44927e6 | −0.0504908 | ||||||||
\(963\) | −6.55415e6 | −0.227746 | ||||||||
\(964\) | 1.49912e7 | 0.519571 | ||||||||
\(965\) | −1.34781e6 | −0.0465919 | ||||||||
\(966\) | −1.05855e7 | −0.364980 | ||||||||
\(967\) | −4.40745e7 | −1.51573 | −0.757865 | − | 0.652412i | \(-0.773757\pi\) | ||||
−0.757865 | + | 0.652412i | \(0.773757\pi\) | |||||||
\(968\) | −417920. | −0.0143352 | ||||||||
\(969\) | −807172. | −0.0276157 | ||||||||
\(970\) | −1.75250e6 | −0.0598039 | ||||||||
\(971\) | 4.69411e7 | 1.59773 | 0.798867 | − | 0.601507i | \(-0.205433\pi\) | ||||
0.798867 | + | 0.601507i | \(0.205433\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 3.57274e7 | 1.20982 | ||||||||
\(974\) | −3.32546e7 | −1.12319 | ||||||||
\(975\) | 4.10990e6 | 0.138459 | ||||||||
\(976\) | −8.66995e6 | −0.291334 | ||||||||
\(977\) | −2.26994e7 | −0.760812 | −0.380406 | − | 0.924820i | \(-0.624216\pi\) | ||||
−0.380406 | + | 0.924820i | \(0.624216\pi\) | |||||||
\(978\) | −1.66958e7 | −0.558162 | ||||||||
\(979\) | 3.44725e7 | 1.14952 | ||||||||
\(980\) | 5.05586e6 | 0.168163 | ||||||||
\(981\) | 2.54775e6 | 0.0845248 | ||||||||
\(982\) | 2.29888e7 | 0.760743 | ||||||||
\(983\) | 8.94734e6 | 0.295332 | 0.147666 | − | 0.989037i | \(-0.452824\pi\) | ||||
0.147666 | + | 0.989037i | \(0.452824\pi\) | |||||||
\(984\) | 9.86452e6 | 0.324779 | ||||||||
\(985\) | 1.20950e7 | 0.397206 | ||||||||
\(986\) | 929867. | 0.0304599 | ||||||||
\(987\) | 1.82418e7 | 0.596040 | ||||||||
\(988\) | −4.22023e6 | −0.137545 | ||||||||
\(989\) | −3.78396e7 | −1.23014 | ||||||||
\(990\) | −3.31587e6 | −0.107525 | ||||||||
\(991\) | −4.83394e6 | −0.156357 | −0.0781785 | − | 0.996939i | \(-0.524910\pi\) | ||||
−0.0781785 | + | 0.996939i | \(0.524910\pi\) | |||||||
\(992\) | −406315. | −0.0131094 | ||||||||
\(993\) | 1.59435e7 | 0.513111 | ||||||||
\(994\) | 2.72128e7 | 0.873589 | ||||||||
\(995\) | −2.02031e7 | −0.646934 | ||||||||
\(996\) | 4.50827e6 | 0.144000 | ||||||||
\(997\) | 7.01989e6 | 0.223662 | 0.111831 | − | 0.993727i | \(-0.464328\pi\) | ||||
0.111831 | + | 0.993727i | \(0.464328\pi\) | |||||||
\(998\) | 7.65456e6 | 0.243273 | ||||||||
\(999\) | 361501. | 0.0114603 |
(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 | 570.6.a.j.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.j.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |