Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,6,Mod(1,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, 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("7.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(1.12268673869\) |
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 | \(\chi\) | \(=\) | 7.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.0000 | −1.76777 | −0.883883 | − | 0.467707i | \(-0.845080\pi\) | ||||
−0.883883 | + | 0.467707i | \(0.845080\pi\) | |||||||
\(3\) | −14.0000 | −0.898100 | −0.449050 | − | 0.893507i | \(-0.648238\pi\) | ||||
−0.449050 | + | 0.893507i | \(0.648238\pi\) | |||||||
\(4\) | 68.0000 | 2.12500 | ||||||||
\(5\) | −56.0000 | −1.00176 | −0.500879 | − | 0.865517i | \(-0.666990\pi\) | ||||
−0.500879 | + | 0.865517i | \(0.666990\pi\) | |||||||
\(6\) | 140.000 | 1.58763 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −360.000 | −1.98874 | ||||||||
\(9\) | −47.0000 | −0.193416 | ||||||||
\(10\) | 560.000 | 1.77088 | ||||||||
\(11\) | 232.000 | 0.578104 | 0.289052 | − | 0.957313i | \(-0.406660\pi\) | ||||
0.289052 | + | 0.957313i | \(0.406660\pi\) | |||||||
\(12\) | −952.000 | −1.90846 | ||||||||
\(13\) | −140.000 | −0.229757 | −0.114879 | − | 0.993380i | \(-0.536648\pi\) | ||||
−0.114879 | + | 0.993380i | \(0.536648\pi\) | |||||||
\(14\) | 490.000 | 0.668153 | ||||||||
\(15\) | 784.000 | 0.899680 | ||||||||
\(16\) | 1424.00 | 1.39062 | ||||||||
\(17\) | −1722.00 | −1.44514 | −0.722572 | − | 0.691296i | \(-0.757040\pi\) | ||||
−0.722572 | + | 0.691296i | \(0.757040\pi\) | |||||||
\(18\) | 470.000 | 0.341914 | ||||||||
\(19\) | −98.0000 | −0.0622791 | −0.0311395 | − | 0.999515i | \(-0.509914\pi\) | ||||
−0.0311395 | + | 0.999515i | \(0.509914\pi\) | |||||||
\(20\) | −3808.00 | −2.12874 | ||||||||
\(21\) | 686.000 | 0.339450 | ||||||||
\(22\) | −2320.00 | −1.02195 | ||||||||
\(23\) | 1824.00 | 0.718961 | 0.359480 | − | 0.933153i | \(-0.382954\pi\) | ||||
0.359480 | + | 0.933153i | \(0.382954\pi\) | |||||||
\(24\) | 5040.00 | 1.78609 | ||||||||
\(25\) | 11.0000 | 0.00352000 | ||||||||
\(26\) | 1400.00 | 0.406158 | ||||||||
\(27\) | 4060.00 | 1.07181 | ||||||||
\(28\) | −3332.00 | −0.803175 | ||||||||
\(29\) | 3418.00 | 0.754705 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(30\) | −7840.00 | −1.59042 | ||||||||
\(31\) | −7644.00 | −1.42862 | −0.714310 | − | 0.699830i | \(-0.753259\pi\) | ||||
−0.714310 | + | 0.699830i | \(0.753259\pi\) | |||||||
\(32\) | −2720.00 | −0.469563 | ||||||||
\(33\) | −3248.00 | −0.519196 | ||||||||
\(34\) | 17220.0 | 2.55468 | ||||||||
\(35\) | 2744.00 | 0.378629 | ||||||||
\(36\) | −3196.00 | −0.411008 | ||||||||
\(37\) | −10398.0 | −1.24866 | −0.624332 | − | 0.781159i | \(-0.714629\pi\) | ||||
−0.624332 | + | 0.781159i | \(0.714629\pi\) | |||||||
\(38\) | 980.000 | 0.110095 | ||||||||
\(39\) | 1960.00 | 0.206345 | ||||||||
\(40\) | 20160.0 | 1.99223 | ||||||||
\(41\) | −17962.0 | −1.66876 | −0.834382 | − | 0.551186i | \(-0.814175\pi\) | ||||
−0.834382 | + | 0.551186i | \(0.814175\pi\) | |||||||
\(42\) | −6860.00 | −0.600069 | ||||||||
\(43\) | 10880.0 | 0.897342 | 0.448671 | − | 0.893697i | \(-0.351898\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351898\pi\) | |||||||
\(44\) | 15776.0 | 1.22847 | ||||||||
\(45\) | 2632.00 | 0.193756 | ||||||||
\(46\) | −18240.0 | −1.27096 | ||||||||
\(47\) | 9324.00 | 0.615684 | 0.307842 | − | 0.951438i | \(-0.400393\pi\) | ||||
0.307842 | + | 0.951438i | \(0.400393\pi\) | |||||||
\(48\) | −19936.0 | −1.24892 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −110.000 | −0.00622254 | ||||||||
\(51\) | 24108.0 | 1.29788 | ||||||||
\(52\) | −9520.00 | −0.488235 | ||||||||
\(53\) | 2262.00 | 0.110612 | 0.0553061 | − | 0.998469i | \(-0.482387\pi\) | ||||
0.0553061 | + | 0.998469i | \(0.482387\pi\) | |||||||
\(54\) | −40600.0 | −1.89471 | ||||||||
\(55\) | −12992.0 | −0.579121 | ||||||||
\(56\) | 17640.0 | 0.751672 | ||||||||
\(57\) | 1372.00 | 0.0559329 | ||||||||
\(58\) | −34180.0 | −1.33414 | ||||||||
\(59\) | −2730.00 | −0.102102 | −0.0510508 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510508 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(60\) | 53312.0 | 1.91182 | ||||||||
\(61\) | 25648.0 | 0.882529 | 0.441264 | − | 0.897377i | \(-0.354530\pi\) | ||||
0.441264 | + | 0.897377i | \(0.354530\pi\) | |||||||
\(62\) | 76440.0 | 2.52547 | ||||||||
\(63\) | 2303.00 | 0.0731042 | ||||||||
\(64\) | −18368.0 | −0.560547 | ||||||||
\(65\) | 7840.00 | 0.230161 | ||||||||
\(66\) | 32480.0 | 0.917817 | ||||||||
\(67\) | −48404.0 | −1.31733 | −0.658664 | − | 0.752437i | \(-0.728878\pi\) | ||||
−0.658664 | + | 0.752437i | \(0.728878\pi\) | |||||||
\(68\) | −117096. | −3.07093 | ||||||||
\(69\) | −25536.0 | −0.645699 | ||||||||
\(70\) | −27440.0 | −0.669328 | ||||||||
\(71\) | −58560.0 | −1.37865 | −0.689327 | − | 0.724450i | \(-0.742094\pi\) | ||||
−0.689327 | + | 0.724450i | \(0.742094\pi\) | |||||||
\(72\) | 16920.0 | 0.384653 | ||||||||
\(73\) | 68082.0 | 1.49529 | 0.747645 | − | 0.664099i | \(-0.231185\pi\) | ||||
0.747645 | + | 0.664099i | \(0.231185\pi\) | |||||||
\(74\) | 103980. | 2.20735 | ||||||||
\(75\) | −154.000 | −0.00316131 | ||||||||
\(76\) | −6664.00 | −0.132343 | ||||||||
\(77\) | −11368.0 | −0.218503 | ||||||||
\(78\) | −19600.0 | −0.364770 | ||||||||
\(79\) | 31784.0 | 0.572982 | 0.286491 | − | 0.958083i | \(-0.407511\pi\) | ||||
0.286491 | + | 0.958083i | \(0.407511\pi\) | |||||||
\(80\) | −79744.0 | −1.39307 | ||||||||
\(81\) | −45419.0 | −0.769175 | ||||||||
\(82\) | 179620. | 2.94999 | ||||||||
\(83\) | −20538.0 | −0.327237 | −0.163619 | − | 0.986524i | \(-0.552317\pi\) | ||||
−0.163619 | + | 0.986524i | \(0.552317\pi\) | |||||||
\(84\) | 46648.0 | 0.721331 | ||||||||
\(85\) | 96432.0 | 1.44768 | ||||||||
\(86\) | −108800. | −1.58629 | ||||||||
\(87\) | −47852.0 | −0.677801 | ||||||||
\(88\) | −83520.0 | −1.14970 | ||||||||
\(89\) | −50582.0 | −0.676894 | −0.338447 | − | 0.940985i | \(-0.609902\pi\) | ||||
−0.338447 | + | 0.940985i | \(0.609902\pi\) | |||||||
\(90\) | −26320.0 | −0.342515 | ||||||||
\(91\) | 6860.00 | 0.0868402 | ||||||||
\(92\) | 124032. | 1.52779 | ||||||||
\(93\) | 107016. | 1.28304 | ||||||||
\(94\) | −93240.0 | −1.08839 | ||||||||
\(95\) | 5488.00 | 0.0623886 | ||||||||
\(96\) | 38080.0 | 0.421715 | ||||||||
\(97\) | −58506.0 | −0.631351 | −0.315676 | − | 0.948867i | \(-0.602231\pi\) | ||||
−0.315676 | + | 0.948867i | \(0.602231\pi\) | |||||||
\(98\) | −24010.0 | −0.252538 | ||||||||
\(99\) | −10904.0 | −0.111814 | ||||||||
\(100\) | 748.000 | 0.00748000 | ||||||||
\(101\) | 38696.0 | 0.377453 | 0.188726 | − | 0.982030i | \(-0.439564\pi\) | ||||
0.188726 | + | 0.982030i | \(0.439564\pi\) | |||||||
\(102\) | −241080. | −2.29436 | ||||||||
\(103\) | 53060.0 | 0.492804 | 0.246402 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246402 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(104\) | 50400.0 | 0.456927 | ||||||||
\(105\) | −38416.0 | −0.340047 | ||||||||
\(106\) | −22620.0 | −0.195537 | ||||||||
\(107\) | −146324. | −1.23554 | −0.617769 | − | 0.786360i | \(-0.711963\pi\) | ||||
−0.617769 | + | 0.786360i | \(0.711963\pi\) | |||||||
\(108\) | 276080. | 2.27759 | ||||||||
\(109\) | 92898.0 | 0.748928 | 0.374464 | − | 0.927241i | \(-0.377827\pi\) | ||||
0.374464 | + | 0.927241i | \(0.377827\pi\) | |||||||
\(110\) | 129920. | 1.02375 | ||||||||
\(111\) | 145572. | 1.12143 | ||||||||
\(112\) | −69776.0 | −0.525607 | ||||||||
\(113\) | −83354.0 | −0.614088 | −0.307044 | − | 0.951695i | \(-0.599340\pi\) | ||||
−0.307044 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(114\) | −13720.0 | −0.0988762 | ||||||||
\(115\) | −102144. | −0.720225 | ||||||||
\(116\) | 232424. | 1.60375 | ||||||||
\(117\) | 6580.00 | 0.0444387 | ||||||||
\(118\) | 27300.0 | 0.180492 | ||||||||
\(119\) | 84378.0 | 0.546213 | ||||||||
\(120\) | −282240. | −1.78923 | ||||||||
\(121\) | −107227. | −0.665795 | ||||||||
\(122\) | −256480. | −1.56011 | ||||||||
\(123\) | 251468. | 1.49872 | ||||||||
\(124\) | −519792. | −3.03582 | ||||||||
\(125\) | 174384. | 0.998232 | ||||||||
\(126\) | −23030.0 | −0.129231 | ||||||||
\(127\) | 60384.0 | 0.332210 | 0.166105 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166105 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(128\) | 270720. | 1.46048 | ||||||||
\(129\) | −152320. | −0.805903 | ||||||||
\(130\) | −78400.0 | −0.406872 | ||||||||
\(131\) | −61586.0 | −0.313548 | −0.156774 | − | 0.987635i | \(-0.550109\pi\) | ||||
−0.156774 | + | 0.987635i | \(0.550109\pi\) | |||||||
\(132\) | −220864. | −1.10329 | ||||||||
\(133\) | 4802.00 | 0.0235393 | ||||||||
\(134\) | 484040. | 2.32873 | ||||||||
\(135\) | −227360. | −1.07369 | ||||||||
\(136\) | 619920. | 2.87401 | ||||||||
\(137\) | −204462. | −0.930703 | −0.465352 | − | 0.885126i | \(-0.654072\pi\) | ||||
−0.465352 | + | 0.885126i | \(0.654072\pi\) | |||||||
\(138\) | 255360. | 1.14145 | ||||||||
\(139\) | −35406.0 | −0.155432 | −0.0777159 | − | 0.996976i | \(-0.524763\pi\) | ||||
−0.0777159 | + | 0.996976i | \(0.524763\pi\) | |||||||
\(140\) | 186592. | 0.804587 | ||||||||
\(141\) | −130536. | −0.552946 | ||||||||
\(142\) | 585600. | 2.43714 | ||||||||
\(143\) | −32480.0 | −0.132824 | ||||||||
\(144\) | −66928.0 | −0.268969 | ||||||||
\(145\) | −191408. | −0.756032 | ||||||||
\(146\) | −680820. | −2.64332 | ||||||||
\(147\) | −33614.0 | −0.128300 | ||||||||
\(148\) | −707064. | −2.65341 | ||||||||
\(149\) | −20226.0 | −0.0746353 | −0.0373177 | − | 0.999303i | \(-0.511881\pi\) | ||||
−0.0373177 | + | 0.999303i | \(0.511881\pi\) | |||||||
\(150\) | 1540.00 | 0.00558847 | ||||||||
\(151\) | 70904.0 | 0.253063 | 0.126531 | − | 0.991963i | \(-0.459616\pi\) | ||||
0.126531 | + | 0.991963i | \(0.459616\pi\) | |||||||
\(152\) | 35280.0 | 0.123857 | ||||||||
\(153\) | 80934.0 | 0.279513 | ||||||||
\(154\) | 113680. | 0.386262 | ||||||||
\(155\) | 428064. | 1.43113 | ||||||||
\(156\) | 133280. | 0.438484 | ||||||||
\(157\) | 293524. | 0.950374 | 0.475187 | − | 0.879885i | \(-0.342380\pi\) | ||||
0.475187 | + | 0.879885i | \(0.342380\pi\) | |||||||
\(158\) | −317840. | −1.01290 | ||||||||
\(159\) | −31668.0 | −0.0993408 | ||||||||
\(160\) | 152320. | 0.470389 | ||||||||
\(161\) | −89376.0 | −0.271742 | ||||||||
\(162\) | 454190. | 1.35972 | ||||||||
\(163\) | 13192.0 | 0.0388903 | 0.0194452 | − | 0.999811i | \(-0.493810\pi\) | ||||
0.0194452 | + | 0.999811i | \(0.493810\pi\) | |||||||
\(164\) | −1.22142e6 | −3.54612 | ||||||||
\(165\) | 181888. | 0.520109 | ||||||||
\(166\) | 205380. | 0.578479 | ||||||||
\(167\) | 493612. | 1.36960 | 0.684801 | − | 0.728730i | \(-0.259889\pi\) | ||||
0.684801 | + | 0.728730i | \(0.259889\pi\) | |||||||
\(168\) | −246960. | −0.675077 | ||||||||
\(169\) | −351693. | −0.947212 | ||||||||
\(170\) | −964320. | −2.55917 | ||||||||
\(171\) | 4606.00 | 0.0120457 | ||||||||
\(172\) | 739840. | 1.90685 | ||||||||
\(173\) | 240716. | 0.611490 | 0.305745 | − | 0.952113i | \(-0.401094\pi\) | ||||
0.305745 | + | 0.952113i | \(0.401094\pi\) | |||||||
\(174\) | 478520. | 1.19819 | ||||||||
\(175\) | −539.000 | −0.00133043 | ||||||||
\(176\) | 330368. | 0.803926 | ||||||||
\(177\) | 38220.0 | 0.0916975 | ||||||||
\(178\) | 505820. | 1.19659 | ||||||||
\(179\) | 294932. | 0.688001 | 0.344001 | − | 0.938969i | \(-0.388218\pi\) | ||||
0.344001 | + | 0.938969i | \(0.388218\pi\) | |||||||
\(180\) | 178976. | 0.411731 | ||||||||
\(181\) | −336980. | −0.764553 | −0.382277 | − | 0.924048i | \(-0.624860\pi\) | ||||
−0.382277 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(182\) | −68600.0 | −0.153513 | ||||||||
\(183\) | −359072. | −0.792600 | ||||||||
\(184\) | −656640. | −1.42982 | ||||||||
\(185\) | 582288. | 1.25086 | ||||||||
\(186\) | −1.07016e6 | −2.26812 | ||||||||
\(187\) | −399504. | −0.835444 | ||||||||
\(188\) | 634032. | 1.30833 | ||||||||
\(189\) | −198940. | −0.405105 | ||||||||
\(190\) | −54880.0 | −0.110288 | ||||||||
\(191\) | 358264. | 0.710591 | 0.355296 | − | 0.934754i | \(-0.384380\pi\) | ||||
0.355296 | + | 0.934754i | \(0.384380\pi\) | |||||||
\(192\) | 257152. | 0.503427 | ||||||||
\(193\) | −989554. | −1.91226 | −0.956128 | − | 0.292948i | \(-0.905364\pi\) | ||||
−0.956128 | + | 0.292948i | \(0.905364\pi\) | |||||||
\(194\) | 585060. | 1.11608 | ||||||||
\(195\) | −109760. | −0.206708 | ||||||||
\(196\) | 163268. | 0.303571 | ||||||||
\(197\) | −990050. | −1.81757 | −0.908786 | − | 0.417263i | \(-0.862989\pi\) | ||||
−0.908786 | + | 0.417263i | \(0.862989\pi\) | |||||||
\(198\) | 109040. | 0.197662 | ||||||||
\(199\) | −840756. | −1.50500 | −0.752501 | − | 0.658591i | \(-0.771153\pi\) | ||||
−0.752501 | + | 0.658591i | \(0.771153\pi\) | |||||||
\(200\) | −3960.00 | −0.00700036 | ||||||||
\(201\) | 677656. | 1.18309 | ||||||||
\(202\) | −386960. | −0.667249 | ||||||||
\(203\) | −167482. | −0.285252 | ||||||||
\(204\) | 1.63934e6 | 2.75800 | ||||||||
\(205\) | 1.00587e6 | 1.67170 | ||||||||
\(206\) | −530600. | −0.871163 | ||||||||
\(207\) | −85728.0 | −0.139058 | ||||||||
\(208\) | −199360. | −0.319506 | ||||||||
\(209\) | −22736.0 | −0.0360038 | ||||||||
\(210\) | 384160. | 0.601124 | ||||||||
\(211\) | 1.15073e6 | 1.77938 | 0.889689 | − | 0.456568i | \(-0.150921\pi\) | ||||
0.889689 | + | 0.456568i | \(0.150921\pi\) | |||||||
\(212\) | 153816. | 0.235051 | ||||||||
\(213\) | 819840. | 1.23817 | ||||||||
\(214\) | 1.46324e6 | 2.18414 | ||||||||
\(215\) | −609280. | −0.898919 | ||||||||
\(216\) | −1.46160e6 | −2.13154 | ||||||||
\(217\) | 374556. | 0.539967 | ||||||||
\(218\) | −928980. | −1.32393 | ||||||||
\(219\) | −953148. | −1.34292 | ||||||||
\(220\) | −883456. | −1.23063 | ||||||||
\(221\) | 241080. | 0.332032 | ||||||||
\(222\) | −1.45572e6 | −1.98242 | ||||||||
\(223\) | −824264. | −1.10995 | −0.554976 | − | 0.831866i | \(-0.687273\pi\) | ||||
−0.554976 | + | 0.831866i | \(0.687273\pi\) | |||||||
\(224\) | 133280. | 0.177478 | ||||||||
\(225\) | −517.000 | −0.000680823 0 | ||||||||
\(226\) | 833540. | 1.08556 | ||||||||
\(227\) | 74382.0 | 0.0958083 | 0.0479042 | − | 0.998852i | \(-0.484746\pi\) | ||||
0.0479042 | + | 0.998852i | \(0.484746\pi\) | |||||||
\(228\) | 93296.0 | 0.118857 | ||||||||
\(229\) | 1.13196e6 | 1.42640 | 0.713199 | − | 0.700961i | \(-0.247245\pi\) | ||||
0.713199 | + | 0.700961i | \(0.247245\pi\) | |||||||
\(230\) | 1.02144e6 | 1.27319 | ||||||||
\(231\) | 159152. | 0.196238 | ||||||||
\(232\) | −1.23048e6 | −1.50091 | ||||||||
\(233\) | −198726. | −0.239809 | −0.119904 | − | 0.992785i | \(-0.538259\pi\) | ||||
−0.119904 | + | 0.992785i | \(0.538259\pi\) | |||||||
\(234\) | −65800.0 | −0.0785572 | ||||||||
\(235\) | −522144. | −0.616766 | ||||||||
\(236\) | −185640. | −0.216966 | ||||||||
\(237\) | −444976. | −0.514595 | ||||||||
\(238\) | −843780. | −0.965577 | ||||||||
\(239\) | 482904. | 0.546847 | 0.273424 | − | 0.961894i | \(-0.411844\pi\) | ||||
0.273424 | + | 0.961894i | \(0.411844\pi\) | |||||||
\(240\) | 1.11642e6 | 1.25112 | ||||||||
\(241\) | 805910. | 0.893807 | 0.446904 | − | 0.894582i | \(-0.352527\pi\) | ||||
0.446904 | + | 0.894582i | \(0.352527\pi\) | |||||||
\(242\) | 1.07227e6 | 1.17697 | ||||||||
\(243\) | −350714. | −0.381011 | ||||||||
\(244\) | 1.74406e6 | 1.87537 | ||||||||
\(245\) | −134456. | −0.143108 | ||||||||
\(246\) | −2.51468e6 | −2.64938 | ||||||||
\(247\) | 13720.0 | 0.0143091 | ||||||||
\(248\) | 2.75184e6 | 2.84115 | ||||||||
\(249\) | 287532. | 0.293892 | ||||||||
\(250\) | −1.74384e6 | −1.76464 | ||||||||
\(251\) | 430738. | 0.431548 | 0.215774 | − | 0.976443i | \(-0.430773\pi\) | ||||
0.215774 | + | 0.976443i | \(0.430773\pi\) | |||||||
\(252\) | 156604. | 0.155347 | ||||||||
\(253\) | 423168. | 0.415634 | ||||||||
\(254\) | −603840. | −0.587270 | ||||||||
\(255\) | −1.35005e6 | −1.30017 | ||||||||
\(256\) | −2.11942e6 | −2.02124 | ||||||||
\(257\) | −1.17691e6 | −1.11150 | −0.555751 | − | 0.831349i | \(-0.687569\pi\) | ||||
−0.555751 | + | 0.831349i | \(0.687569\pi\) | |||||||
\(258\) | 1.52320e6 | 1.42465 | ||||||||
\(259\) | 509502. | 0.471951 | ||||||||
\(260\) | 533120. | 0.489093 | ||||||||
\(261\) | −160646. | −0.145972 | ||||||||
\(262\) | 615860. | 0.554279 | ||||||||
\(263\) | 1.29098e6 | 1.15088 | 0.575438 | − | 0.817845i | \(-0.304831\pi\) | ||||
0.575438 | + | 0.817845i | \(0.304831\pi\) | |||||||
\(264\) | 1.16928e6 | 1.03254 | ||||||||
\(265\) | −126672. | −0.110807 | ||||||||
\(266\) | −48020.0 | −0.0416119 | ||||||||
\(267\) | 708148. | 0.607919 | ||||||||
\(268\) | −3.29147e6 | −2.79932 | ||||||||
\(269\) | −1.27756e6 | −1.07646 | −0.538232 | − | 0.842797i | \(-0.680907\pi\) | ||||
−0.538232 | + | 0.842797i | \(0.680907\pi\) | |||||||
\(270\) | 2.27360e6 | 1.89804 | ||||||||
\(271\) | 1.65054e6 | 1.36522 | 0.682612 | − | 0.730781i | \(-0.260844\pi\) | ||||
0.682612 | + | 0.730781i | \(0.260844\pi\) | |||||||
\(272\) | −2.45213e6 | −2.00965 | ||||||||
\(273\) | −96040.0 | −0.0779912 | ||||||||
\(274\) | 2.04462e6 | 1.64527 | ||||||||
\(275\) | 2552.00 | 0.00203493 | ||||||||
\(276\) | −1.73645e6 | −1.37211 | ||||||||
\(277\) | −1.06409e6 | −0.833257 | −0.416628 | − | 0.909077i | \(-0.636788\pi\) | ||||
−0.416628 | + | 0.909077i | \(0.636788\pi\) | |||||||
\(278\) | 354060. | 0.274767 | ||||||||
\(279\) | 359268. | 0.276317 | ||||||||
\(280\) | −987840. | −0.752994 | ||||||||
\(281\) | −22342.0 | −0.0168794 | −0.00843969 | − | 0.999964i | \(-0.502686\pi\) | ||||
−0.00843969 | + | 0.999964i | \(0.502686\pi\) | |||||||
\(282\) | 1.30536e6 | 0.977479 | ||||||||
\(283\) | −2.49574e6 | −1.85239 | −0.926196 | − | 0.377042i | \(-0.876941\pi\) | ||||
−0.926196 | + | 0.377042i | \(0.876941\pi\) | |||||||
\(284\) | −3.98208e6 | −2.92964 | ||||||||
\(285\) | −76832.0 | −0.0560312 | ||||||||
\(286\) | 324800. | 0.234802 | ||||||||
\(287\) | 880138. | 0.630734 | ||||||||
\(288\) | 127840. | 0.0908208 | ||||||||
\(289\) | 1.54543e6 | 1.08844 | ||||||||
\(290\) | 1.91408e6 | 1.33649 | ||||||||
\(291\) | 819084. | 0.567017 | ||||||||
\(292\) | 4.62958e6 | 3.17749 | ||||||||
\(293\) | −1.93178e6 | −1.31458 | −0.657291 | − | 0.753637i | \(-0.728298\pi\) | ||||
−0.657291 | + | 0.753637i | \(0.728298\pi\) | |||||||
\(294\) | 336140. | 0.226805 | ||||||||
\(295\) | 152880. | 0.102281 | ||||||||
\(296\) | 3.74328e6 | 2.48326 | ||||||||
\(297\) | 941920. | 0.619616 | ||||||||
\(298\) | 202260. | 0.131938 | ||||||||
\(299\) | −255360. | −0.165187 | ||||||||
\(300\) | −10472.0 | −0.00671779 | ||||||||
\(301\) | −533120. | −0.339163 | ||||||||
\(302\) | −709040. | −0.447356 | ||||||||
\(303\) | −541744. | −0.338991 | ||||||||
\(304\) | −139552. | −0.0866068 | ||||||||
\(305\) | −1.43629e6 | −0.884081 | ||||||||
\(306\) | −809340. | −0.494114 | ||||||||
\(307\) | −459074. | −0.277995 | −0.138997 | − | 0.990293i | \(-0.544388\pi\) | ||||
−0.138997 | + | 0.990293i | \(0.544388\pi\) | |||||||
\(308\) | −773024. | −0.464319 | ||||||||
\(309\) | −742840. | −0.442587 | ||||||||
\(310\) | −4.28064e6 | −2.52991 | ||||||||
\(311\) | 667128. | 0.391118 | 0.195559 | − | 0.980692i | \(-0.437348\pi\) | ||||
0.195559 | + | 0.980692i | \(0.437348\pi\) | |||||||
\(312\) | −705600. | −0.410367 | ||||||||
\(313\) | −111034. | −0.0640612 | −0.0320306 | − | 0.999487i | \(-0.510197\pi\) | ||||
−0.0320306 | + | 0.999487i | \(0.510197\pi\) | |||||||
\(314\) | −2.93524e6 | −1.68004 | ||||||||
\(315\) | −128968. | −0.0732328 | ||||||||
\(316\) | 2.16131e6 | 1.21759 | ||||||||
\(317\) | −68778.0 | −0.0384416 | −0.0192208 | − | 0.999815i | \(-0.506119\pi\) | ||||
−0.0192208 | + | 0.999815i | \(0.506119\pi\) | |||||||
\(318\) | 316680. | 0.175611 | ||||||||
\(319\) | 792976. | 0.436298 | ||||||||
\(320\) | 1.02861e6 | 0.561533 | ||||||||
\(321\) | 2.04854e6 | 1.10964 | ||||||||
\(322\) | 893760. | 0.480376 | ||||||||
\(323\) | 168756. | 0.0900022 | ||||||||
\(324\) | −3.08849e6 | −1.63450 | ||||||||
\(325\) | −1540.00 | −0.000808746 0 | ||||||||
\(326\) | −131920. | −0.0687490 | ||||||||
\(327\) | −1.30057e6 | −0.672613 | ||||||||
\(328\) | 6.46632e6 | 3.31874 | ||||||||
\(329\) | −456876. | −0.232707 | ||||||||
\(330\) | −1.81888e6 | −0.919431 | ||||||||
\(331\) | −564448. | −0.283174 | −0.141587 | − | 0.989926i | \(-0.545221\pi\) | ||||
−0.141587 | + | 0.989926i | \(0.545221\pi\) | |||||||
\(332\) | −1.39658e6 | −0.695379 | ||||||||
\(333\) | 488706. | 0.241511 | ||||||||
\(334\) | −4.93612e6 | −2.42114 | ||||||||
\(335\) | 2.71062e6 | 1.31965 | ||||||||
\(336\) | 976864. | 0.472048 | ||||||||
\(337\) | 2.07729e6 | 0.996376 | 0.498188 | − | 0.867069i | \(-0.333999\pi\) | ||||
0.498188 | + | 0.867069i | \(0.333999\pi\) | |||||||
\(338\) | 3.51693e6 | 1.67445 | ||||||||
\(339\) | 1.16696e6 | 0.551512 | ||||||||
\(340\) | 6.55738e6 | 3.07633 | ||||||||
\(341\) | −1.77341e6 | −0.825891 | ||||||||
\(342\) | −46060.0 | −0.0212941 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −3.91680e6 | −1.78458 | ||||||||
\(345\) | 1.43002e6 | 0.646834 | ||||||||
\(346\) | −2.40716e6 | −1.08097 | ||||||||
\(347\) | −53248.0 | −0.0237399 | −0.0118700 | − | 0.999930i | \(-0.503778\pi\) | ||||
−0.0118700 | + | 0.999930i | \(0.503778\pi\) | |||||||
\(348\) | −3.25394e6 | −1.44033 | ||||||||
\(349\) | −2.27200e6 | −0.998494 | −0.499247 | − | 0.866460i | \(-0.666390\pi\) | ||||
−0.499247 | + | 0.866460i | \(0.666390\pi\) | |||||||
\(350\) | 5390.00 | 0.00235190 | ||||||||
\(351\) | −568400. | −0.246256 | ||||||||
\(352\) | −631040. | −0.271456 | ||||||||
\(353\) | 4.00645e6 | 1.71129 | 0.855644 | − | 0.517565i | \(-0.173162\pi\) | ||||
0.855644 | + | 0.517565i | \(0.173162\pi\) | |||||||
\(354\) | −382200. | −0.162100 | ||||||||
\(355\) | 3.27936e6 | 1.38108 | ||||||||
\(356\) | −3.43958e6 | −1.43840 | ||||||||
\(357\) | −1.18129e6 | −0.490554 | ||||||||
\(358\) | −2.94932e6 | −1.21623 | ||||||||
\(359\) | 73784.0 | 0.0302152 | 0.0151076 | − | 0.999886i | \(-0.495191\pi\) | ||||
0.0151076 | + | 0.999886i | \(0.495191\pi\) | |||||||
\(360\) | −947520. | −0.385329 | ||||||||
\(361\) | −2.46650e6 | −0.996121 | ||||||||
\(362\) | 3.36980e6 | 1.35155 | ||||||||
\(363\) | 1.50118e6 | 0.597951 | ||||||||
\(364\) | 466480. | 0.184535 | ||||||||
\(365\) | −3.81259e6 | −1.49792 | ||||||||
\(366\) | 3.59072e6 | 1.40113 | ||||||||
\(367\) | 1.40431e6 | 0.544250 | 0.272125 | − | 0.962262i | \(-0.412274\pi\) | ||||
0.272125 | + | 0.962262i | \(0.412274\pi\) | |||||||
\(368\) | 2.59738e6 | 0.999805 | ||||||||
\(369\) | 844214. | 0.322765 | ||||||||
\(370\) | −5.82288e6 | −2.21123 | ||||||||
\(371\) | −110838. | −0.0418075 | ||||||||
\(372\) | 7.27709e6 | 2.72647 | ||||||||
\(373\) | −1.60323e6 | −0.596657 | −0.298329 | − | 0.954463i | \(-0.596429\pi\) | ||||
−0.298329 | + | 0.954463i | \(0.596429\pi\) | |||||||
\(374\) | 3.99504e6 | 1.47687 | ||||||||
\(375\) | −2.44138e6 | −0.896513 | ||||||||
\(376\) | −3.35664e6 | −1.22443 | ||||||||
\(377\) | −478520. | −0.173399 | ||||||||
\(378\) | 1.98940e6 | 0.716131 | ||||||||
\(379\) | −4.77012e6 | −1.70581 | −0.852906 | − | 0.522064i | \(-0.825162\pi\) | ||||
−0.852906 | + | 0.522064i | \(0.825162\pi\) | |||||||
\(380\) | 373184. | 0.132576 | ||||||||
\(381\) | −845376. | −0.298358 | ||||||||
\(382\) | −3.58264e6 | −1.25616 | ||||||||
\(383\) | −2.23079e6 | −0.777072 | −0.388536 | − | 0.921434i | \(-0.627019\pi\) | ||||
−0.388536 | + | 0.921434i | \(0.627019\pi\) | |||||||
\(384\) | −3.79008e6 | −1.31166 | ||||||||
\(385\) | 636608. | 0.218887 | ||||||||
\(386\) | 9.89554e6 | 3.38042 | ||||||||
\(387\) | −511360. | −0.173560 | ||||||||
\(388\) | −3.97841e6 | −1.34162 | ||||||||
\(389\) | 4.84024e6 | 1.62178 | 0.810892 | − | 0.585196i | \(-0.198982\pi\) | ||||
0.810892 | + | 0.585196i | \(0.198982\pi\) | |||||||
\(390\) | 1.09760e6 | 0.365412 | ||||||||
\(391\) | −3.14093e6 | −1.03900 | ||||||||
\(392\) | −864360. | −0.284105 | ||||||||
\(393\) | 862204. | 0.281597 | ||||||||
\(394\) | 9.90050e6 | 3.21304 | ||||||||
\(395\) | −1.77990e6 | −0.573989 | ||||||||
\(396\) | −741472. | −0.237606 | ||||||||
\(397\) | 995820. | 0.317106 | 0.158553 | − | 0.987350i | \(-0.449317\pi\) | ||||
0.158553 | + | 0.987350i | \(0.449317\pi\) | |||||||
\(398\) | 8.40756e6 | 2.66049 | ||||||||
\(399\) | −67228.0 | −0.0211406 | ||||||||
\(400\) | 15664.0 | 0.00489500 | ||||||||
\(401\) | −3.31605e6 | −1.02982 | −0.514909 | − | 0.857245i | \(-0.672174\pi\) | ||||
−0.514909 | + | 0.857245i | \(0.672174\pi\) | |||||||
\(402\) | −6.77656e6 | −2.09143 | ||||||||
\(403\) | 1.07016e6 | 0.328236 | ||||||||
\(404\) | 2.63133e6 | 0.802087 | ||||||||
\(405\) | 2.54346e6 | 0.770527 | ||||||||
\(406\) | 1.67482e6 | 0.504258 | ||||||||
\(407\) | −2.41234e6 | −0.721858 | ||||||||
\(408\) | −8.67888e6 | −2.58115 | ||||||||
\(409\) | 3.07273e6 | 0.908274 | 0.454137 | − | 0.890932i | \(-0.349948\pi\) | ||||
0.454137 | + | 0.890932i | \(0.349948\pi\) | |||||||
\(410\) | −1.00587e7 | −2.95517 | ||||||||
\(411\) | 2.86247e6 | 0.835865 | ||||||||
\(412\) | 3.60808e6 | 1.04721 | ||||||||
\(413\) | 133770. | 0.0385908 | ||||||||
\(414\) | 857280. | 0.245823 | ||||||||
\(415\) | 1.15013e6 | 0.327813 | ||||||||
\(416\) | 380800. | 0.107886 | ||||||||
\(417\) | 495684. | 0.139593 | ||||||||
\(418\) | 227360. | 0.0636463 | ||||||||
\(419\) | 2.81438e6 | 0.783154 | 0.391577 | − | 0.920145i | \(-0.371930\pi\) | ||||
0.391577 | + | 0.920145i | \(0.371930\pi\) | |||||||
\(420\) | −2.61229e6 | −0.722600 | ||||||||
\(421\) | 3.05802e6 | 0.840883 | 0.420441 | − | 0.907320i | \(-0.361875\pi\) | ||||
0.420441 | + | 0.907320i | \(0.361875\pi\) | |||||||
\(422\) | −1.15073e7 | −3.14552 | ||||||||
\(423\) | −438228. | −0.119083 | ||||||||
\(424\) | −814320. | −0.219979 | ||||||||
\(425\) | −18942.0 | −0.00508690 | ||||||||
\(426\) | −8.19840e6 | −2.18880 | ||||||||
\(427\) | −1.25675e6 | −0.333565 | ||||||||
\(428\) | −9.95003e6 | −2.62552 | ||||||||
\(429\) | 454720. | 0.119289 | ||||||||
\(430\) | 6.09280e6 | 1.58908 | ||||||||
\(431\) | 1.93750e6 | 0.502398 | 0.251199 | − | 0.967936i | \(-0.419175\pi\) | ||||
0.251199 | + | 0.967936i | \(0.419175\pi\) | |||||||
\(432\) | 5.78144e6 | 1.49048 | ||||||||
\(433\) | 3.94790e6 | 1.01192 | 0.505961 | − | 0.862557i | \(-0.331138\pi\) | ||||
0.505961 | + | 0.862557i | \(0.331138\pi\) | |||||||
\(434\) | −3.74556e6 | −0.954536 | ||||||||
\(435\) | 2.67971e6 | 0.678993 | ||||||||
\(436\) | 6.31706e6 | 1.59147 | ||||||||
\(437\) | −178752. | −0.0447762 | ||||||||
\(438\) | 9.53148e6 | 2.37397 | ||||||||
\(439\) | −7.41770e6 | −1.83700 | −0.918498 | − | 0.395426i | \(-0.870597\pi\) | ||||
−0.918498 | + | 0.395426i | \(0.870597\pi\) | |||||||
\(440\) | 4.67712e6 | 1.15172 | ||||||||
\(441\) | −112847. | −0.0276308 | ||||||||
\(442\) | −2.41080e6 | −0.586956 | ||||||||
\(443\) | 1.40269e6 | 0.339589 | 0.169794 | − | 0.985480i | \(-0.445690\pi\) | ||||
0.169794 | + | 0.985480i | \(0.445690\pi\) | |||||||
\(444\) | 9.89890e6 | 2.38303 | ||||||||
\(445\) | 2.83259e6 | 0.678085 | ||||||||
\(446\) | 8.24264e6 | 1.96214 | ||||||||
\(447\) | 283164. | 0.0670300 | ||||||||
\(448\) | 900032. | 0.211867 | ||||||||
\(449\) | −590574. | −0.138248 | −0.0691239 | − | 0.997608i | \(-0.522020\pi\) | ||||
−0.0691239 | + | 0.997608i | \(0.522020\pi\) | |||||||
\(450\) | 5170.00 | 0.00120354 | ||||||||
\(451\) | −4.16718e6 | −0.964720 | ||||||||
\(452\) | −5.66807e6 | −1.30494 | ||||||||
\(453\) | −992656. | −0.227276 | ||||||||
\(454\) | −743820. | −0.169367 | ||||||||
\(455\) | −384160. | −0.0869929 | ||||||||
\(456\) | −493920. | −0.111236 | ||||||||
\(457\) | −2.90484e6 | −0.650627 | −0.325313 | − | 0.945606i | \(-0.605470\pi\) | ||||
−0.325313 | + | 0.945606i | \(0.605470\pi\) | |||||||
\(458\) | −1.13196e7 | −2.52154 | ||||||||
\(459\) | −6.99132e6 | −1.54891 | ||||||||
\(460\) | −6.94579e6 | −1.53048 | ||||||||
\(461\) | −922684. | −0.202209 | −0.101105 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101105 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(462\) | −1.59152e6 | −0.346902 | ||||||||
\(463\) | 7.18235e6 | 1.55709 | 0.778546 | − | 0.627588i | \(-0.215958\pi\) | ||||
0.778546 | + | 0.627588i | \(0.215958\pi\) | |||||||
\(464\) | 4.86723e6 | 1.04951 | ||||||||
\(465\) | −5.99290e6 | −1.28530 | ||||||||
\(466\) | 1.98726e6 | 0.423926 | ||||||||
\(467\) | −612570. | −0.129976 | −0.0649881 | − | 0.997886i | \(-0.520701\pi\) | ||||
−0.0649881 | + | 0.997886i | \(0.520701\pi\) | |||||||
\(468\) | 447440. | 0.0944322 | ||||||||
\(469\) | 2.37180e6 | 0.497904 | ||||||||
\(470\) | 5.22144e6 | 1.09030 | ||||||||
\(471\) | −4.10934e6 | −0.853531 | ||||||||
\(472\) | 982800. | 0.203053 | ||||||||
\(473\) | 2.52416e6 | 0.518757 | ||||||||
\(474\) | 4.44976e6 | 0.909684 | ||||||||
\(475\) | −1078.00 | −0.000219222 0 | ||||||||
\(476\) | 5.73770e6 | 1.16070 | ||||||||
\(477\) | −106314. | −0.0213941 | ||||||||
\(478\) | −4.82904e6 | −0.966699 | ||||||||
\(479\) | 2.60330e6 | 0.518424 | 0.259212 | − | 0.965820i | \(-0.416537\pi\) | ||||
0.259212 | + | 0.965820i | \(0.416537\pi\) | |||||||
\(480\) | −2.13248e6 | −0.422456 | ||||||||
\(481\) | 1.45572e6 | 0.286890 | ||||||||
\(482\) | −8.05910e6 | −1.58004 | ||||||||
\(483\) | 1.25126e6 | 0.244051 | ||||||||
\(484\) | −7.29144e6 | −1.41482 | ||||||||
\(485\) | 3.27634e6 | 0.632461 | ||||||||
\(486\) | 3.50714e6 | 0.673539 | ||||||||
\(487\) | 5.46309e6 | 1.04380 | 0.521898 | − | 0.853008i | \(-0.325224\pi\) | ||||
0.521898 | + | 0.853008i | \(0.325224\pi\) | |||||||
\(488\) | −9.23328e6 | −1.75512 | ||||||||
\(489\) | −184688. | −0.0349274 | ||||||||
\(490\) | 1.34456e6 | 0.252982 | ||||||||
\(491\) | 1.64090e6 | 0.307170 | 0.153585 | − | 0.988135i | \(-0.450918\pi\) | ||||
0.153585 | + | 0.988135i | \(0.450918\pi\) | |||||||
\(492\) | 1.70998e7 | 3.18478 | ||||||||
\(493\) | −5.88580e6 | −1.09066 | ||||||||
\(494\) | −137200. | −0.0252951 | ||||||||
\(495\) | 610624. | 0.112011 | ||||||||
\(496\) | −1.08851e7 | −1.98667 | ||||||||
\(497\) | 2.86944e6 | 0.521082 | ||||||||
\(498\) | −2.87532e6 | −0.519533 | ||||||||
\(499\) | 2.99796e6 | 0.538983 | 0.269491 | − | 0.963003i | \(-0.413144\pi\) | ||||
0.269491 | + | 0.963003i | \(0.413144\pi\) | |||||||
\(500\) | 1.18581e7 | 2.12124 | ||||||||
\(501\) | −6.91057e6 | −1.23004 | ||||||||
\(502\) | −4.30738e6 | −0.762876 | ||||||||
\(503\) | −6.89405e6 | −1.21494 | −0.607469 | − | 0.794343i | \(-0.707815\pi\) | ||||
−0.607469 | + | 0.794343i | \(0.707815\pi\) | |||||||
\(504\) | −829080. | −0.145385 | ||||||||
\(505\) | −2.16698e6 | −0.378117 | ||||||||
\(506\) | −4.23168e6 | −0.734745 | ||||||||
\(507\) | 4.92370e6 | 0.850691 | ||||||||
\(508\) | 4.10611e6 | 0.705946 | ||||||||
\(509\) | 2.30476e6 | 0.394305 | 0.197152 | − | 0.980373i | \(-0.436831\pi\) | ||||
0.197152 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(510\) | 1.35005e7 | 2.29839 | ||||||||
\(511\) | −3.33602e6 | −0.565166 | ||||||||
\(512\) | 1.25312e7 | 2.11260 | ||||||||
\(513\) | −397880. | −0.0667511 | ||||||||
\(514\) | 1.17691e7 | 1.96488 | ||||||||
\(515\) | −2.97136e6 | −0.493671 | ||||||||
\(516\) | −1.03578e7 | −1.71254 | ||||||||
\(517\) | 2.16317e6 | 0.355929 | ||||||||
\(518\) | −5.09502e6 | −0.834299 | ||||||||
\(519\) | −3.37002e6 | −0.549180 | ||||||||
\(520\) | −2.82240e6 | −0.457731 | ||||||||
\(521\) | −1.20960e7 | −1.95231 | −0.976155 | − | 0.217073i | \(-0.930349\pi\) | ||||
−0.976155 | + | 0.217073i | \(0.930349\pi\) | |||||||
\(522\) | 1.60646e6 | 0.258044 | ||||||||
\(523\) | 5.48443e6 | 0.876753 | 0.438377 | − | 0.898791i | \(-0.355554\pi\) | ||||
0.438377 | + | 0.898791i | \(0.355554\pi\) | |||||||
\(524\) | −4.18785e6 | −0.666289 | ||||||||
\(525\) | 7546.00 | 0.00119486 | ||||||||
\(526\) | −1.29098e7 | −2.03448 | ||||||||
\(527\) | 1.31630e7 | 2.06456 | ||||||||
\(528\) | −4.62515e6 | −0.722007 | ||||||||
\(529\) | −3.10937e6 | −0.483095 | ||||||||
\(530\) | 1.26672e6 | 0.195880 | ||||||||
\(531\) | 128310. | 0.0197480 | ||||||||
\(532\) | 326536. | 0.0500210 | ||||||||
\(533\) | 2.51468e6 | 0.383411 | ||||||||
\(534\) | −7.08148e6 | −1.07466 | ||||||||
\(535\) | 8.19414e6 | 1.23771 | ||||||||
\(536\) | 1.74254e7 | 2.61982 | ||||||||
\(537\) | −4.12905e6 | −0.617894 | ||||||||
\(538\) | 1.27756e7 | 1.90294 | ||||||||
\(539\) | 557032. | 0.0825863 | ||||||||
\(540\) | −1.54605e7 | −2.28160 | ||||||||
\(541\) | −6.71799e6 | −0.986839 | −0.493420 | − | 0.869791i | \(-0.664253\pi\) | ||||
−0.493420 | + | 0.869791i | \(0.664253\pi\) | |||||||
\(542\) | −1.65054e7 | −2.41340 | ||||||||
\(543\) | 4.71772e6 | 0.686646 | ||||||||
\(544\) | 4.68384e6 | 0.678586 | ||||||||
\(545\) | −5.20229e6 | −0.750245 | ||||||||
\(546\) | 960400. | 0.137870 | ||||||||
\(547\) | −5.00235e6 | −0.714835 | −0.357418 | − | 0.933945i | \(-0.616343\pi\) | ||||
−0.357418 | + | 0.933945i | \(0.616343\pi\) | |||||||
\(548\) | −1.39034e7 | −1.97774 | ||||||||
\(549\) | −1.20546e6 | −0.170695 | ||||||||
\(550\) | −25520.0 | −0.00359728 | ||||||||
\(551\) | −334964. | −0.0470023 | ||||||||
\(552\) | 9.19296e6 | 1.28413 | ||||||||
\(553\) | −1.55742e6 | −0.216567 | ||||||||
\(554\) | 1.06409e7 | 1.47300 | ||||||||
\(555\) | −8.15203e6 | −1.12340 | ||||||||
\(556\) | −2.40761e6 | −0.330293 | ||||||||
\(557\) | 9.01961e6 | 1.23183 | 0.615913 | − | 0.787814i | \(-0.288787\pi\) | ||||
0.615913 | + | 0.787814i | \(0.288787\pi\) | |||||||
\(558\) | −3.59268e6 | −0.488465 | ||||||||
\(559\) | −1.52320e6 | −0.206171 | ||||||||
\(560\) | 3.90746e6 | 0.526531 | ||||||||
\(561\) | 5.59306e6 | 0.750312 | ||||||||
\(562\) | 223420. | 0.0298388 | ||||||||
\(563\) | 1.24051e7 | 1.64941 | 0.824707 | − | 0.565561i | \(-0.191340\pi\) | ||||
0.824707 | + | 0.565561i | \(0.191340\pi\) | |||||||
\(564\) | −8.87645e6 | −1.17501 | ||||||||
\(565\) | 4.66782e6 | 0.615167 | ||||||||
\(566\) | 2.49574e7 | 3.27460 | ||||||||
\(567\) | 2.22553e6 | 0.290721 | ||||||||
\(568\) | 2.10816e7 | 2.74178 | ||||||||
\(569\) | 6.48804e6 | 0.840103 | 0.420052 | − | 0.907500i | \(-0.362012\pi\) | ||||
0.420052 | + | 0.907500i | \(0.362012\pi\) | |||||||
\(570\) | 768320. | 0.0990501 | ||||||||
\(571\) | −1.02285e7 | −1.31287 | −0.656435 | − | 0.754382i | \(-0.727936\pi\) | ||||
−0.656435 | + | 0.754382i | \(0.727936\pi\) | |||||||
\(572\) | −2.20864e6 | −0.282251 | ||||||||
\(573\) | −5.01570e6 | −0.638182 | ||||||||
\(574\) | −8.80138e6 | −1.11499 | ||||||||
\(575\) | 20064.0 | 0.00253074 | ||||||||
\(576\) | 863296. | 0.108419 | ||||||||
\(577\) | 2.65338e6 | 0.331787 | 0.165894 | − | 0.986144i | \(-0.446949\pi\) | ||||
0.165894 | + | 0.986144i | \(0.446949\pi\) | |||||||
\(578\) | −1.54543e7 | −1.92411 | ||||||||
\(579\) | 1.38538e7 | 1.71740 | ||||||||
\(580\) | −1.30157e7 | −1.60657 | ||||||||
\(581\) | 1.00636e6 | 0.123684 | ||||||||
\(582\) | −8.19084e6 | −1.00235 | ||||||||
\(583\) | 524784. | 0.0639454 | ||||||||
\(584\) | −2.45095e7 | −2.97374 | ||||||||
\(585\) | −368480. | −0.0445168 | ||||||||
\(586\) | 1.93178e7 | 2.32387 | ||||||||
\(587\) | −1.43044e7 | −1.71346 | −0.856729 | − | 0.515766i | \(-0.827507\pi\) | ||||
−0.856729 | + | 0.515766i | \(0.827507\pi\) | |||||||
\(588\) | −2.28575e6 | −0.272638 | ||||||||
\(589\) | 749112. | 0.0889731 | ||||||||
\(590\) | −1.52880e6 | −0.180809 | ||||||||
\(591\) | 1.38607e7 | 1.63236 | ||||||||
\(592\) | −1.48068e7 | −1.73642 | ||||||||
\(593\) | −1.00265e7 | −1.17088 | −0.585442 | − | 0.810714i | \(-0.699079\pi\) | ||||
−0.585442 | + | 0.810714i | \(0.699079\pi\) | |||||||
\(594\) | −9.41920e6 | −1.09534 | ||||||||
\(595\) | −4.72517e6 | −0.547173 | ||||||||
\(596\) | −1.37537e6 | −0.158600 | ||||||||
\(597\) | 1.17706e7 | 1.35164 | ||||||||
\(598\) | 2.55360e6 | 0.292011 | ||||||||
\(599\) | −7.52292e6 | −0.856681 | −0.428341 | − | 0.903617i | \(-0.640902\pi\) | ||||
−0.428341 | + | 0.903617i | \(0.640902\pi\) | |||||||
\(600\) | 55440.0 | 0.00628702 | ||||||||
\(601\) | 3.38625e6 | 0.382413 | 0.191207 | − | 0.981550i | \(-0.438760\pi\) | ||||
0.191207 | + | 0.981550i | \(0.438760\pi\) | |||||||
\(602\) | 5.33120e6 | 0.599562 | ||||||||
\(603\) | 2.27499e6 | 0.254792 | ||||||||
\(604\) | 4.82147e6 | 0.537759 | ||||||||
\(605\) | 6.00471e6 | 0.666966 | ||||||||
\(606\) | 5.41744e6 | 0.599256 | ||||||||
\(607\) | −6.90861e6 | −0.761060 | −0.380530 | − | 0.924769i | \(-0.624258\pi\) | ||||
−0.380530 | + | 0.924769i | \(0.624258\pi\) | |||||||
\(608\) | 266560. | 0.0292439 | ||||||||
\(609\) | 2.34475e6 | 0.256185 | ||||||||
\(610\) | 1.43629e7 | 1.56285 | ||||||||
\(611\) | −1.30536e6 | −0.141458 | ||||||||
\(612\) | 5.50351e6 | 0.593966 | ||||||||
\(613\) | −9.68896e6 | −1.04142 | −0.520710 | − | 0.853734i | \(-0.674333\pi\) | ||||
−0.520710 | + | 0.853734i | \(0.674333\pi\) | |||||||
\(614\) | 4.59074e6 | 0.491430 | ||||||||
\(615\) | −1.40822e7 | −1.50135 | ||||||||
\(616\) | 4.09248e6 | 0.434545 | ||||||||
\(617\) | −7.84742e6 | −0.829877 | −0.414939 | − | 0.909849i | \(-0.636197\pi\) | ||||
−0.414939 | + | 0.909849i | \(0.636197\pi\) | |||||||
\(618\) | 7.42840e6 | 0.782391 | ||||||||
\(619\) | −1.01972e7 | −1.06968 | −0.534840 | − | 0.844953i | \(-0.679628\pi\) | ||||
−0.534840 | + | 0.844953i | \(0.679628\pi\) | |||||||
\(620\) | 2.91084e7 | 3.04115 | ||||||||
\(621\) | 7.40544e6 | 0.770587 | ||||||||
\(622\) | −6.67128e6 | −0.691406 | ||||||||
\(623\) | 2.47852e6 | 0.255842 | ||||||||
\(624\) | 2.79104e6 | 0.286949 | ||||||||
\(625\) | −9.79988e6 | −1.00351 | ||||||||
\(626\) | 1.11034e6 | 0.113245 | ||||||||
\(627\) | 318304. | 0.0323350 | ||||||||
\(628\) | 1.99596e7 | 2.01954 | ||||||||
\(629\) | 1.79054e7 | 1.80450 | ||||||||
\(630\) | 1.28968e6 | 0.129459 | ||||||||
\(631\) | −8.36258e6 | −0.836116 | −0.418058 | − | 0.908420i | \(-0.637289\pi\) | ||||
−0.418058 | + | 0.908420i | \(0.637289\pi\) | |||||||
\(632\) | −1.14422e7 | −1.13951 | ||||||||
\(633\) | −1.61102e7 | −1.59806 | ||||||||
\(634\) | 687780. | 0.0679558 | ||||||||
\(635\) | −3.38150e6 | −0.332794 | ||||||||
\(636\) | −2.15342e6 | −0.211099 | ||||||||
\(637\) | −336140. | −0.0328225 | ||||||||
\(638\) | −7.92976e6 | −0.771273 | ||||||||
\(639\) | 2.75232e6 | 0.266653 | ||||||||
\(640\) | −1.51603e7 | −1.46305 | ||||||||
\(641\) | 1.10283e6 | 0.106014 | 0.0530070 | − | 0.998594i | \(-0.483119\pi\) | ||||
0.0530070 | + | 0.998594i | \(0.483119\pi\) | |||||||
\(642\) | −2.04854e7 | −1.96158 | ||||||||
\(643\) | 1.71354e7 | 1.63443 | 0.817217 | − | 0.576330i | \(-0.195516\pi\) | ||||
0.817217 | + | 0.576330i | \(0.195516\pi\) | |||||||
\(644\) | −6.07757e6 | −0.577451 | ||||||||
\(645\) | 8.52992e6 | 0.807320 | ||||||||
\(646\) | −1.68756e6 | −0.159103 | ||||||||
\(647\) | −54964.0 | −0.00516200 | −0.00258100 | − | 0.999997i | \(-0.500822\pi\) | ||||
−0.00258100 | + | 0.999997i | \(0.500822\pi\) | |||||||
\(648\) | 1.63508e7 | 1.52969 | ||||||||
\(649\) | −633360. | −0.0590254 | ||||||||
\(650\) | 15400.0 | 0.00142968 | ||||||||
\(651\) | −5.24378e6 | −0.484945 | ||||||||
\(652\) | 897056. | 0.0826420 | ||||||||
\(653\) | −485166. | −0.0445254 | −0.0222627 | − | 0.999752i | \(-0.507087\pi\) | ||||
−0.0222627 | + | 0.999752i | \(0.507087\pi\) | |||||||
\(654\) | 1.30057e7 | 1.18902 | ||||||||
\(655\) | 3.44882e6 | 0.314099 | ||||||||
\(656\) | −2.55779e7 | −2.32063 | ||||||||
\(657\) | −3.19985e6 | −0.289212 | ||||||||
\(658\) | 4.56876e6 | 0.411371 | ||||||||
\(659\) | −2.72136e6 | −0.244103 | −0.122051 | − | 0.992524i | \(-0.538947\pi\) | ||||
−0.122051 | + | 0.992524i | \(0.538947\pi\) | |||||||
\(660\) | 1.23684e7 | 1.10523 | ||||||||
\(661\) | −2.14525e6 | −0.190974 | −0.0954869 | − | 0.995431i | \(-0.530441\pi\) | ||||
−0.0954869 | + | 0.995431i | \(0.530441\pi\) | |||||||
\(662\) | 5.64448e6 | 0.500586 | ||||||||
\(663\) | −3.37512e6 | −0.298198 | ||||||||
\(664\) | 7.39368e6 | 0.650789 | ||||||||
\(665\) | −268912. | −0.0235807 | ||||||||
\(666\) | −4.88706e6 | −0.426935 | ||||||||
\(667\) | 6.23443e6 | 0.542603 | ||||||||
\(668\) | 3.35656e7 | 2.91041 | ||||||||
\(669\) | 1.15397e7 | 0.996848 | ||||||||
\(670\) | −2.71062e7 | −2.33283 | ||||||||
\(671\) | 5.95034e6 | 0.510194 | ||||||||
\(672\) | −1.86592e6 | −0.159393 | ||||||||
\(673\) | 2.92796e6 | 0.249188 | 0.124594 | − | 0.992208i | \(-0.460237\pi\) | ||||
0.124594 | + | 0.992208i | \(0.460237\pi\) | |||||||
\(674\) | −2.07729e7 | −1.76136 | ||||||||
\(675\) | 44660.0 | 0.00377276 | ||||||||
\(676\) | −2.39151e7 | −2.01282 | ||||||||
\(677\) | −1.34992e7 | −1.13198 | −0.565988 | − | 0.824414i | \(-0.691505\pi\) | ||||
−0.565988 | + | 0.824414i | \(0.691505\pi\) | |||||||
\(678\) | −1.16696e7 | −0.974945 | ||||||||
\(679\) | 2.86679e6 | 0.238628 | ||||||||
\(680\) | −3.47155e7 | −2.87906 | ||||||||
\(681\) | −1.04135e6 | −0.0860455 | ||||||||
\(682\) | 1.77341e7 | 1.45998 | ||||||||
\(683\) | −5.42972e6 | −0.445375 | −0.222688 | − | 0.974890i | \(-0.571483\pi\) | ||||
−0.222688 | + | 0.974890i | \(0.571483\pi\) | |||||||
\(684\) | 313208. | 0.0255972 | ||||||||
\(685\) | 1.14499e7 | 0.932340 | ||||||||
\(686\) | 1.17649e6 | 0.0954504 | ||||||||
\(687\) | −1.58474e7 | −1.28105 | ||||||||
\(688\) | 1.54931e7 | 1.24787 | ||||||||
\(689\) | −316680. | −0.0254140 | ||||||||
\(690\) | −1.43002e7 | −1.14345 | ||||||||
\(691\) | 2.08280e7 | 1.65940 | 0.829702 | − | 0.558207i | \(-0.188510\pi\) | ||||
0.829702 | + | 0.558207i | \(0.188510\pi\) | |||||||
\(692\) | 1.63687e7 | 1.29942 | ||||||||
\(693\) | 534296. | 0.0422619 | ||||||||
\(694\) | 532480. | 0.0419667 | ||||||||
\(695\) | 1.98274e6 | 0.155705 | ||||||||
\(696\) | 1.72267e7 | 1.34797 | ||||||||
\(697\) | 3.09306e7 | 2.41160 | ||||||||
\(698\) | 2.27200e7 | 1.76510 | ||||||||
\(699\) | 2.78216e6 | 0.215372 | ||||||||
\(700\) | −36652.0 | −0.00282717 | ||||||||
\(701\) | 2.35141e7 | 1.80731 | 0.903655 | − | 0.428261i | \(-0.140874\pi\) | ||||
0.903655 | + | 0.428261i | \(0.140874\pi\) | |||||||
\(702\) | 5.68400e6 | 0.435323 | ||||||||
\(703\) | 1.01900e6 | 0.0777656 | ||||||||
\(704\) | −4.26138e6 | −0.324055 | ||||||||
\(705\) | 7.31002e6 | 0.553918 | ||||||||
\(706\) | −4.00645e7 | −3.02516 | ||||||||
\(707\) | −1.89610e6 | −0.142664 | ||||||||
\(708\) | 2.59896e6 | 0.194857 | ||||||||
\(709\) | −1.95747e7 | −1.46244 | −0.731221 | − | 0.682140i | \(-0.761049\pi\) | ||||
−0.731221 | + | 0.682140i | \(0.761049\pi\) | |||||||
\(710\) | −3.27936e7 | −2.44142 | ||||||||
\(711\) | −1.49385e6 | −0.110824 | ||||||||
\(712\) | 1.82095e7 | 1.34617 | ||||||||
\(713\) | −1.39427e7 | −1.02712 | ||||||||
\(714\) | 1.18129e7 | 0.867185 | ||||||||
\(715\) | 1.81888e6 | 0.133057 | ||||||||
\(716\) | 2.00554e7 | 1.46200 | ||||||||
\(717\) | −6.76066e6 | −0.491124 | ||||||||
\(718\) | −737840. | −0.0534135 | ||||||||
\(719\) | −2.61152e7 | −1.88396 | −0.941978 | − | 0.335674i | \(-0.891036\pi\) | ||||
−0.941978 | + | 0.335674i | \(0.891036\pi\) | |||||||
\(720\) | 3.74797e6 | 0.269442 | ||||||||
\(721\) | −2.59994e6 | −0.186262 | ||||||||
\(722\) | 2.46650e7 | 1.76091 | ||||||||
\(723\) | −1.12827e7 | −0.802729 | ||||||||
\(724\) | −2.29146e7 | −1.62468 | ||||||||
\(725\) | 37598.0 | 0.00265656 | ||||||||
\(726\) | −1.50118e7 | −1.05704 | ||||||||
\(727\) | 1.54126e7 | 1.08154 | 0.540768 | − | 0.841172i | \(-0.318134\pi\) | ||||
0.540768 | + | 0.841172i | \(0.318134\pi\) | |||||||
\(728\) | −2.46960e6 | −0.172702 | ||||||||
\(729\) | 1.59468e7 | 1.11136 | ||||||||
\(730\) | 3.81259e7 | 2.64797 | ||||||||
\(731\) | −1.87354e7 | −1.29679 | ||||||||
\(732\) | −2.44169e7 | −1.68427 | ||||||||
\(733\) | −1.69868e7 | −1.16776 | −0.583878 | − | 0.811841i | \(-0.698465\pi\) | ||||
−0.583878 | + | 0.811841i | \(0.698465\pi\) | |||||||
\(734\) | −1.40431e7 | −0.962107 | ||||||||
\(735\) | 1.88238e6 | 0.128526 | ||||||||
\(736\) | −4.96128e6 | −0.337597 | ||||||||
\(737\) | −1.12297e7 | −0.761554 | ||||||||
\(738\) | −8.44214e6 | −0.570574 | ||||||||
\(739\) | 2.01511e6 | 0.135734 | 0.0678669 | − | 0.997694i | \(-0.478381\pi\) | ||||
0.0678669 | + | 0.997694i | \(0.478381\pi\) | |||||||
\(740\) | 3.95956e7 | 2.65808 | ||||||||
\(741\) | −192080. | −0.0128510 | ||||||||
\(742\) | 1.10838e6 | 0.0739059 | ||||||||
\(743\) | −1.51381e7 | −1.00600 | −0.503001 | − | 0.864286i | \(-0.667771\pi\) | ||||
−0.503001 | + | 0.864286i | \(0.667771\pi\) | |||||||
\(744\) | −3.85258e7 | −2.55164 | ||||||||
\(745\) | 1.13266e6 | 0.0747666 | ||||||||
\(746\) | 1.60323e7 | 1.05475 | ||||||||
\(747\) | 965286. | 0.0632928 | ||||||||
\(748\) | −2.71663e7 | −1.77532 | ||||||||
\(749\) | 7.16988e6 | 0.466989 | ||||||||
\(750\) | 2.44138e7 | 1.58483 | ||||||||
\(751\) | 7.21401e6 | 0.466742 | 0.233371 | − | 0.972388i | \(-0.425024\pi\) | ||||
0.233371 | + | 0.972388i | \(0.425024\pi\) | |||||||
\(752\) | 1.32774e7 | 0.856185 | ||||||||
\(753\) | −6.03033e6 | −0.387573 | ||||||||
\(754\) | 4.78520e6 | 0.306529 | ||||||||
\(755\) | −3.97062e6 | −0.253508 | ||||||||
\(756\) | −1.35279e7 | −0.860848 | ||||||||
\(757\) | −1.09697e7 | −0.695755 | −0.347877 | − | 0.937540i | \(-0.613097\pi\) | ||||
−0.347877 | + | 0.937540i | \(0.613097\pi\) | |||||||
\(758\) | 4.77012e7 | 3.01548 | ||||||||
\(759\) | −5.92435e6 | −0.373281 | ||||||||
\(760\) | −1.97568e6 | −0.124075 | ||||||||
\(761\) | 1.92442e7 | 1.20459 | 0.602293 | − | 0.798275i | \(-0.294254\pi\) | ||||
0.602293 | + | 0.798275i | \(0.294254\pi\) | |||||||
\(762\) | 8.45376e6 | 0.527427 | ||||||||
\(763\) | −4.55200e6 | −0.283068 | ||||||||
\(764\) | 2.43620e7 | 1.51001 | ||||||||
\(765\) | −4.53230e6 | −0.280005 | ||||||||
\(766\) | 2.23079e7 | 1.37368 | ||||||||
\(767\) | 382200. | 0.0234586 | ||||||||
\(768\) | 2.96719e7 | 1.81528 | ||||||||
\(769\) | 8.21185e6 | 0.500755 | 0.250378 | − | 0.968148i | \(-0.419445\pi\) | ||||
0.250378 | + | 0.968148i | \(0.419445\pi\) | |||||||
\(770\) | −6.36608e6 | −0.386941 | ||||||||
\(771\) | 1.64767e7 | 0.998241 | ||||||||
\(772\) | −6.72897e7 | −4.06355 | ||||||||
\(773\) | 1.86187e7 | 1.12073 | 0.560363 | − | 0.828247i | \(-0.310662\pi\) | ||||
0.560363 | + | 0.828247i | \(0.310662\pi\) | |||||||
\(774\) | 5.11360e6 | 0.306813 | ||||||||
\(775\) | −84084.0 | −0.00502874 | ||||||||
\(776\) | 2.10622e7 | 1.25559 | ||||||||
\(777\) | −7.13303e6 | −0.423859 | ||||||||
\(778\) | −4.84024e7 | −2.86694 | ||||||||
\(779\) | 1.76028e6 | 0.103929 | ||||||||
\(780\) | −7.46368e6 | −0.439255 | ||||||||
\(781\) | −1.35859e7 | −0.797006 | ||||||||
\(782\) | 3.14093e7 | 1.83671 | ||||||||
\(783\) | 1.38771e7 | 0.808898 | ||||||||
\(784\) | 3.41902e6 | 0.198661 | ||||||||
\(785\) | −1.64373e7 | −0.952045 | ||||||||
\(786\) | −8.62204e6 | −0.497799 | ||||||||
\(787\) | 2.62501e7 | 1.51075 | 0.755377 | − | 0.655291i | \(-0.227454\pi\) | ||||
0.755377 | + | 0.655291i | \(0.227454\pi\) | |||||||
\(788\) | −6.73234e7 | −3.86234 | ||||||||
\(789\) | −1.80737e7 | −1.03360 | ||||||||
\(790\) | 1.77990e7 | 1.01468 | ||||||||
\(791\) | 4.08435e6 | 0.232103 | ||||||||
\(792\) | 3.92544e6 | 0.222370 | ||||||||
\(793\) | −3.59072e6 | −0.202768 | ||||||||
\(794\) | −9.95820e6 | −0.560570 | ||||||||
\(795\) | 1.77341e6 | 0.0995155 | ||||||||
\(796\) | −5.71714e7 | −3.19813 | ||||||||
\(797\) | −1.00373e7 | −0.559720 | −0.279860 | − | 0.960041i | \(-0.590288\pi\) | ||||
−0.279860 | + | 0.960041i | \(0.590288\pi\) | |||||||
\(798\) | 672280. | 0.0373717 | ||||||||
\(799\) | −1.60559e7 | −0.889751 | ||||||||
\(800\) | −29920.0 | −0.00165286 | ||||||||
\(801\) | 2.37735e6 | 0.130922 | ||||||||
\(802\) | 3.31605e7 | 1.82048 | ||||||||
\(803\) | 1.57950e7 | 0.864433 | ||||||||
\(804\) | 4.60806e7 | 2.51407 | ||||||||
\(805\) | 5.00506e6 | 0.272220 | ||||||||
\(806\) | −1.07016e7 | −0.580245 | ||||||||
\(807\) | 1.78858e7 | 0.966772 | ||||||||
\(808\) | −1.39306e7 | −0.750655 | ||||||||
\(809\) | 1.40884e7 | 0.756816 | 0.378408 | − | 0.925639i | \(-0.376472\pi\) | ||||
0.378408 | + | 0.925639i | \(0.376472\pi\) | |||||||
\(810\) | −2.54346e7 | −1.36211 | ||||||||
\(811\) | 1.81433e7 | 0.968646 | 0.484323 | − | 0.874889i | \(-0.339066\pi\) | ||||
0.484323 | + | 0.874889i | \(0.339066\pi\) | |||||||
\(812\) | −1.13888e7 | −0.606160 | ||||||||
\(813\) | −2.31076e7 | −1.22611 | ||||||||
\(814\) | 2.41234e7 | 1.27608 | ||||||||
\(815\) | −738752. | −0.0389587 | ||||||||
\(816\) | 3.43298e7 | 1.80487 | ||||||||
\(817\) | −1.06624e6 | −0.0558856 | ||||||||
\(818\) | −3.07273e7 | −1.60562 | ||||||||
\(819\) | −322420. | −0.0167962 | ||||||||
\(820\) | 6.83993e7 | 3.55236 | ||||||||
\(821\) | −2.13669e7 | −1.10633 | −0.553164 | − | 0.833072i | \(-0.686580\pi\) | ||||
−0.553164 | + | 0.833072i | \(0.686580\pi\) | |||||||
\(822\) | −2.86247e7 | −1.47761 | ||||||||
\(823\) | 1.78017e7 | 0.916142 | 0.458071 | − | 0.888916i | \(-0.348541\pi\) | ||||
0.458071 | + | 0.888916i | \(0.348541\pi\) | |||||||
\(824\) | −1.91016e7 | −0.980058 | ||||||||
\(825\) | −35728.0 | −0.00182757 | ||||||||
\(826\) | −1.33770e6 | −0.0682195 | ||||||||
\(827\) | 1.62921e7 | 0.828350 | 0.414175 | − | 0.910197i | \(-0.364070\pi\) | ||||
0.414175 | + | 0.910197i | \(0.364070\pi\) | |||||||
\(828\) | −5.82950e6 | −0.295499 | ||||||||
\(829\) | −2.08499e6 | −0.105370 | −0.0526851 | − | 0.998611i | \(-0.516778\pi\) | ||||
−0.0526851 | + | 0.998611i | \(0.516778\pi\) | |||||||
\(830\) | −1.15013e7 | −0.579497 | ||||||||
\(831\) | 1.48973e7 | 0.748348 | ||||||||
\(832\) | 2.57152e6 | 0.128790 | ||||||||
\(833\) | −4.13452e6 | −0.206449 | ||||||||
\(834\) | −4.95684e6 | −0.246769 | ||||||||
\(835\) | −2.76423e7 | −1.37201 | ||||||||
\(836\) | −1.54605e6 | −0.0765081 | ||||||||
\(837\) | −3.10346e7 | −1.53120 | ||||||||
\(838\) | −2.81438e7 | −1.38443 | ||||||||
\(839\) | −2.27850e7 | −1.11749 | −0.558745 | − | 0.829340i | \(-0.688717\pi\) | ||||
−0.558745 | + | 0.829340i | \(0.688717\pi\) | |||||||
\(840\) | 1.38298e7 | 0.676264 | ||||||||
\(841\) | −8.82842e6 | −0.430421 | ||||||||
\(842\) | −3.05802e7 | −1.48648 | ||||||||
\(843\) | 312788. | 0.0151594 | ||||||||
\(844\) | 7.82498e7 | 3.78118 | ||||||||
\(845\) | 1.96948e7 | 0.948877 | ||||||||
\(846\) | 4.38228e6 | 0.210511 | ||||||||
\(847\) | 5.25412e6 | 0.251647 | ||||||||
\(848\) | 3.22109e6 | 0.153820 | ||||||||
\(849\) | 3.49403e7 | 1.66363 | ||||||||
\(850\) | 189420. | 0.00899246 | ||||||||
\(851\) | −1.89660e7 | −0.897740 | ||||||||
\(852\) | 5.57491e7 | 2.63111 | ||||||||
\(853\) | −2.26975e7 | −1.06808 | −0.534042 | − | 0.845458i | \(-0.679328\pi\) | ||||
−0.534042 | + | 0.845458i | \(0.679328\pi\) | |||||||
\(854\) | 1.25675e7 | 0.589664 | ||||||||
\(855\) | −257936. | −0.0120669 | ||||||||
\(856\) | 5.26766e7 | 2.45716 | ||||||||
\(857\) | 2.52900e7 | 1.17624 | 0.588120 | − | 0.808774i | \(-0.299868\pi\) | ||||
0.588120 | + | 0.808774i | \(0.299868\pi\) | |||||||
\(858\) | −4.54720e6 | −0.210875 | ||||||||
\(859\) | −1.03947e7 | −0.480652 | −0.240326 | − | 0.970692i | \(-0.577254\pi\) | ||||
−0.240326 | + | 0.970692i | \(0.577254\pi\) | |||||||
\(860\) | −4.14310e7 | −1.91020 | ||||||||
\(861\) | −1.23219e7 | −0.566462 | ||||||||
\(862\) | −1.93750e7 | −0.888122 | ||||||||
\(863\) | 4.33399e7 | 1.98089 | 0.990447 | − | 0.137892i | \(-0.0440327\pi\) | ||||
0.990447 | + | 0.137892i | \(0.0440327\pi\) | |||||||
\(864\) | −1.10432e7 | −0.503281 | ||||||||
\(865\) | −1.34801e7 | −0.612566 | ||||||||
\(866\) | −3.94790e7 | −1.78884 | ||||||||
\(867\) | −2.16360e7 | −0.977527 | ||||||||
\(868\) | 2.54698e7 | 1.14743 | ||||||||
\(869\) | 7.37389e6 | 0.331243 | ||||||||
\(870\) | −2.67971e7 | −1.20030 | ||||||||
\(871\) | 6.77656e6 | 0.302666 | ||||||||
\(872\) | −3.34433e7 | −1.48942 | ||||||||
\(873\) | 2.74978e6 | 0.122113 | ||||||||
\(874\) | 1.78752e6 | 0.0791539 | ||||||||
\(875\) | −8.54482e6 | −0.377296 | ||||||||
\(876\) | −6.48141e7 | −2.85370 | ||||||||
\(877\) | 3.71659e7 | 1.63172 | 0.815861 | − | 0.578248i | \(-0.196264\pi\) | ||||
0.815861 | + | 0.578248i | \(0.196264\pi\) | |||||||
\(878\) | 7.41770e7 | 3.24738 | ||||||||
\(879\) | 2.70449e7 | 1.18063 | ||||||||
\(880\) | −1.85006e7 | −0.805340 | ||||||||
\(881\) | 9.04785e6 | 0.392740 | 0.196370 | − | 0.980530i | \(-0.437085\pi\) | ||||
0.196370 | + | 0.980530i | \(0.437085\pi\) | |||||||
\(882\) | 1.12847e6 | 0.0488448 | ||||||||
\(883\) | 3.29679e7 | 1.42295 | 0.711474 | − | 0.702712i | \(-0.248028\pi\) | ||||
0.711474 | + | 0.702712i | \(0.248028\pi\) | |||||||
\(884\) | 1.63934e7 | 0.705569 | ||||||||
\(885\) | −2.14032e6 | −0.0918588 | ||||||||
\(886\) | −1.40269e7 | −0.600313 | ||||||||
\(887\) | −1.61099e7 | −0.687517 | −0.343758 | − | 0.939058i | \(-0.611700\pi\) | ||||
−0.343758 | + | 0.939058i | \(0.611700\pi\) | |||||||
\(888\) | −5.24059e7 | −2.23022 | ||||||||
\(889\) | −2.95882e6 | −0.125564 | ||||||||
\(890\) | −2.83259e7 | −1.19870 | ||||||||
\(891\) | −1.05372e7 | −0.444663 | ||||||||
\(892\) | −5.60500e7 | −2.35865 | ||||||||
\(893\) | −913752. | −0.0383442 | ||||||||
\(894\) | −2.83164e6 | −0.118493 | ||||||||
\(895\) | −1.65162e7 | −0.689211 | ||||||||
\(896\) | −1.32653e7 | −0.552009 | ||||||||
\(897\) | 3.57504e6 | 0.148354 | ||||||||
\(898\) | 5.90574e6 | 0.244390 | ||||||||
\(899\) | −2.61272e7 | −1.07819 | ||||||||
\(900\) | −35156.0 | −0.00144675 | ||||||||
\(901\) | −3.89516e6 | −0.159850 | ||||||||
\(902\) | 4.16718e7 | 1.70540 | ||||||||
\(903\) | 7.46368e6 | 0.304603 | ||||||||
\(904\) | 3.00074e7 | 1.22126 | ||||||||
\(905\) | 1.88709e7 | 0.765898 | ||||||||
\(906\) | 9.92656e6 | 0.401771 | ||||||||
\(907\) | −4.47286e7 | −1.80537 | −0.902686 | − | 0.430300i | \(-0.858408\pi\) | ||||
−0.902686 | + | 0.430300i | \(0.858408\pi\) | |||||||
\(908\) | 5.05798e6 | 0.203593 | ||||||||
\(909\) | −1.81871e6 | −0.0730053 | ||||||||
\(910\) | 3.84160e6 | 0.153783 | ||||||||
\(911\) | −6.60518e6 | −0.263687 | −0.131844 | − | 0.991271i | \(-0.542090\pi\) | ||||
−0.131844 | + | 0.991271i | \(0.542090\pi\) | |||||||
\(912\) | 1.95373e6 | 0.0777816 | ||||||||
\(913\) | −4.76482e6 | −0.189177 | ||||||||
\(914\) | 2.90484e7 | 1.15016 | ||||||||
\(915\) | 2.01080e7 | 0.793993 | ||||||||
\(916\) | 7.69730e7 | 3.03110 | ||||||||
\(917\) | 3.01771e6 | 0.118510 | ||||||||
\(918\) | 6.99132e7 | 2.73812 | ||||||||
\(919\) | −3.08930e7 | −1.20662 | −0.603311 | − | 0.797506i | \(-0.706152\pi\) | ||||
−0.603311 | + | 0.797506i | \(0.706152\pi\) | |||||||
\(920\) | 3.67718e7 | 1.43234 | ||||||||
\(921\) | 6.42704e6 | 0.249667 | ||||||||
\(922\) | 9.22684e6 | 0.357459 | ||||||||
\(923\) | 8.19840e6 | 0.316756 | ||||||||
\(924\) | 1.08223e7 | 0.417005 | ||||||||
\(925\) | −114378. | −0.00439530 | ||||||||
\(926\) | −7.18235e7 | −2.75258 | ||||||||
\(927\) | −2.49382e6 | −0.0953160 | ||||||||
\(928\) | −9.29696e6 | −0.354381 | ||||||||
\(929\) | −4.87215e6 | −0.185217 | −0.0926087 | − | 0.995703i | \(-0.529521\pi\) | ||||
−0.0926087 | + | 0.995703i | \(0.529521\pi\) | |||||||
\(930\) | 5.99290e7 | 2.27211 | ||||||||
\(931\) | −235298. | −0.00889701 | ||||||||
\(932\) | −1.35134e7 | −0.509593 | ||||||||
\(933\) | −9.33979e6 | −0.351264 | ||||||||
\(934\) | 6.12570e6 | 0.229767 | ||||||||
\(935\) | 2.23722e7 | 0.836913 | ||||||||
\(936\) | −2.36880e6 | −0.0883769 | ||||||||
\(937\) | −3.25004e7 | −1.20932 | −0.604658 | − | 0.796485i | \(-0.706690\pi\) | ||||
−0.604658 | + | 0.796485i | \(0.706690\pi\) | |||||||
\(938\) | −2.37180e7 | −0.880177 | ||||||||
\(939\) | 1.55448e6 | 0.0575334 | ||||||||
\(940\) | −3.55058e7 | −1.31063 | ||||||||
\(941\) | −2.64040e6 | −0.0972066 | −0.0486033 | − | 0.998818i | \(-0.515477\pi\) | ||||
−0.0486033 | + | 0.998818i | \(0.515477\pi\) | |||||||
\(942\) | 4.10934e7 | 1.50884 | ||||||||
\(943\) | −3.27627e7 | −1.19978 | ||||||||
\(944\) | −3.88752e6 | −0.141985 | ||||||||
\(945\) | 1.11406e7 | 0.405817 | ||||||||
\(946\) | −2.52416e7 | −0.917042 | ||||||||
\(947\) | −4.08179e7 | −1.47903 | −0.739513 | − | 0.673142i | \(-0.764944\pi\) | ||||
−0.739513 | + | 0.673142i | \(0.764944\pi\) | |||||||
\(948\) | −3.02584e7 | −1.09351 | ||||||||
\(949\) | −9.53148e6 | −0.343554 | ||||||||
\(950\) | 10780.0 | 0.000387534 0 | ||||||||
\(951\) | 962892. | 0.0345244 | ||||||||
\(952\) | −3.03761e7 | −1.08627 | ||||||||
\(953\) | −6.71983e6 | −0.239677 | −0.119838 | − | 0.992793i | \(-0.538238\pi\) | ||||
−0.119838 | + | 0.992793i | \(0.538238\pi\) | |||||||
\(954\) | 1.06314e6 | 0.0378198 | ||||||||
\(955\) | −2.00628e7 | −0.711841 | ||||||||
\(956\) | 3.28375e7 | 1.16205 | ||||||||
\(957\) | −1.11017e7 | −0.391840 | ||||||||
\(958\) | −2.60330e7 | −0.916454 | ||||||||
\(959\) | 1.00186e7 | 0.351773 | ||||||||
\(960\) | −1.44005e7 | −0.504313 | ||||||||
\(961\) | 2.98016e7 | 1.04095 | ||||||||
\(962\) | −1.45572e7 | −0.507154 | ||||||||
\(963\) | 6.87723e6 | 0.238972 | ||||||||
\(964\) | 5.48019e7 | 1.89934 | ||||||||
\(965\) | 5.54150e7 | 1.91562 | ||||||||
\(966\) | −1.25126e7 | −0.431426 | ||||||||
\(967\) | −2.78979e6 | −0.0959413 | −0.0479707 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479707 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(968\) | 3.86017e7 | 1.32409 | ||||||||
\(969\) | −2.36258e6 | −0.0808310 | ||||||||
\(970\) | −3.27634e7 | −1.11804 | ||||||||
\(971\) | 3.33594e7 | 1.13545 | 0.567727 | − | 0.823217i | \(-0.307823\pi\) | ||||
0.567727 | + | 0.823217i | \(0.307823\pi\) | |||||||
\(972\) | −2.38486e7 | −0.809648 | ||||||||
\(973\) | 1.73489e6 | 0.0587477 | ||||||||
\(974\) | −5.46309e7 | −1.84519 | ||||||||
\(975\) | 21560.0 | 0.000726335 0 | ||||||||
\(976\) | 3.65228e7 | 1.22727 | ||||||||
\(977\) | −7.60033e6 | −0.254739 | −0.127370 | − | 0.991855i | \(-0.540653\pi\) | ||||
−0.127370 | + | 0.991855i | \(0.540653\pi\) | |||||||
\(978\) | 1.84688e6 | 0.0617435 | ||||||||
\(979\) | −1.17350e7 | −0.391316 | ||||||||
\(980\) | −9.14301e6 | −0.304105 | ||||||||
\(981\) | −4.36621e6 | −0.144854 | ||||||||
\(982\) | −1.64090e7 | −0.543004 | ||||||||
\(983\) | −5.79760e6 | −0.191366 | −0.0956829 | − | 0.995412i | \(-0.530503\pi\) | ||||
−0.0956829 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(984\) | −9.05285e7 | −2.98056 | ||||||||
\(985\) | 5.54428e7 | 1.82077 | ||||||||
\(986\) | 5.88580e7 | 1.92803 | ||||||||
\(987\) | 6.39626e6 | 0.208994 | ||||||||
\(988\) | 932960. | 0.0304068 | ||||||||
\(989\) | 1.98451e7 | 0.645153 | ||||||||
\(990\) | −6.10624e6 | −0.198009 | ||||||||
\(991\) | 1.26825e7 | 0.410224 | 0.205112 | − | 0.978739i | \(-0.434244\pi\) | ||||
0.205112 | + | 0.978739i | \(0.434244\pi\) | |||||||
\(992\) | 2.07917e7 | 0.670827 | ||||||||
\(993\) | 7.90227e6 | 0.254319 | ||||||||
\(994\) | −2.86944e7 | −0.921152 | ||||||||
\(995\) | 4.70823e7 | 1.50765 | ||||||||
\(996\) | 1.95522e7 | 0.624521 | ||||||||
\(997\) | 1.44400e7 | 0.460077 | 0.230039 | − | 0.973182i | \(-0.426115\pi\) | ||||
0.230039 | + | 0.973182i | \(0.426115\pi\) | |||||||
\(998\) | −2.99796e7 | −0.952796 | ||||||||
\(999\) | −4.22159e7 | −1.33833 |
(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 | 7.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 63.6.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 112.6.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 175.6.b.a.99.1 | 2 | |||
5.3 | odd | 4 | 175.6.b.a.99.2 | 2 | |||
5.4 | even | 2 | 175.6.a.b.1.1 | 1 | |||
7.2 | even | 3 | 49.6.c.c.18.1 | 2 | |||
7.3 | odd | 6 | 49.6.c.b.30.1 | 2 | |||
7.4 | even | 3 | 49.6.c.c.30.1 | 2 | |||
7.5 | odd | 6 | 49.6.c.b.18.1 | 2 | |||
7.6 | odd | 2 | 49.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 448.6.a.c.1.1 | 1 | |||
8.5 | even | 2 | 448.6.a.m.1.1 | 1 | |||
11.10 | odd | 2 | 847.6.a.b.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.y.1.1 | 1 | |||
21.20 | even | 2 | 441.6.a.k.1.1 | 1 | |||
28.27 | even | 2 | 784.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
49.6.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
49.6.c.b.18.1 | 2 | 7.5 | odd | 6 | |||
49.6.c.b.30.1 | 2 | 7.3 | odd | 6 | |||
49.6.c.c.18.1 | 2 | 7.2 | even | 3 | |||
49.6.c.c.30.1 | 2 | 7.4 | even | 3 | |||
63.6.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
112.6.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
175.6.a.b.1.1 | 1 | 5.4 | even | 2 | |||
175.6.b.a.99.1 | 2 | 5.2 | odd | 4 | |||
175.6.b.a.99.2 | 2 | 5.3 | odd | 4 | |||
441.6.a.k.1.1 | 1 | 21.20 | even | 2 | |||
448.6.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
448.6.a.m.1.1 | 1 | 8.5 | even | 2 | |||
784.6.a.c.1.1 | 1 | 28.27 | even | 2 | |||
847.6.a.b.1.1 | 1 | 11.10 | odd | 2 | |||
1008.6.a.y.1.1 | 1 | 12.11 | even | 2 |