Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,6,Mod(1,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("240.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.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: | \(38.4921167551\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 240.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.0000 | 0.123417 | 0.0617085 | − | 0.998094i | \(-0.480345\pi\) | ||||
0.0617085 | + | 0.998094i | \(0.480345\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 564.000 | 1.40539 | 0.702696 | − | 0.711490i | \(-0.251979\pi\) | ||||
0.702696 | + | 0.711490i | \(0.251979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −370.000 | −0.607216 | −0.303608 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303608 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1086.00 | −0.911397 | −0.455698 | − | 0.890134i | \(-0.650610\pi\) | ||||
−0.455698 | + | 0.890134i | \(0.650610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2860.00 | 1.81753 | 0.908766 | − | 0.417306i | \(-0.137026\pi\) | ||||
0.908766 | + | 0.417306i | \(0.137026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 144.000 | 0.0712548 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1584.00 | −0.624361 | −0.312180 | − | 0.950023i | \(-0.601059\pi\) | ||||
−0.312180 | + | 0.950023i | \(0.601059\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1134.00 | 0.250391 | 0.125195 | − | 0.992132i | \(-0.460044\pi\) | ||||
0.125195 | + | 0.992132i | \(0.460044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6016.00 | 1.12436 | 0.562178 | − | 0.827016i | \(-0.309964\pi\) | ||||
0.562178 | + | 0.827016i | \(0.309964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5076.00 | 0.811403 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 400.000 | 0.0551937 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −538.000 | −0.0646068 | −0.0323034 | − | 0.999478i | \(-0.510284\pi\) | ||||
−0.0323034 | + | 0.999478i | \(0.510284\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3330.00 | −0.350576 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11370.0 | 1.05633 | 0.528166 | − | 0.849141i | \(-0.322880\pi\) | ||||
0.528166 | + | 0.849141i | \(0.322880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5444.00 | −0.449001 | −0.224500 | − | 0.974474i | \(-0.572075\pi\) | ||||
−0.224500 | + | 0.974474i | \(0.572075\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10296.0 | −0.679867 | −0.339933 | − | 0.940449i | \(-0.610405\pi\) | ||||
−0.339933 | + | 0.940449i | \(0.610405\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16551.0 | −0.984768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9774.00 | −0.526195 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 34758.0 | 1.69967 | 0.849836 | − | 0.527047i | \(-0.176701\pi\) | ||||
0.849836 | + | 0.527047i | \(0.176701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14100.0 | 0.628510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 25740.0 | 1.04935 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26196.0 | 0.979727 | 0.489863 | − | 0.871799i | \(-0.337047\pi\) | ||||
0.489863 | + | 0.871799i | \(0.337047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9422.00 | 0.324204 | 0.162102 | − | 0.986774i | \(-0.448173\pi\) | ||||
0.162102 | + | 0.986774i | \(0.448173\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1296.00 | 0.0411390 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9250.00 | −0.271555 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 51124.0 | 1.39135 | 0.695677 | − | 0.718354i | \(-0.255104\pi\) | ||||
0.695677 | + | 0.718354i | \(0.255104\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14256.0 | −0.360475 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14520.0 | −0.341838 | −0.170919 | − | 0.985285i | \(-0.554674\pi\) | ||||
−0.170919 | + | 0.985285i | \(0.554674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −22678.0 | −0.498078 | −0.249039 | − | 0.968493i | \(-0.580115\pi\) | ||||
−0.249039 | + | 0.968493i | \(0.580115\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9024.00 | 0.173449 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 97312.0 | 1.75428 | 0.877140 | − | 0.480236i | \(-0.159449\pi\) | ||||
0.877140 | + | 0.480236i | \(0.159449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7956.00 | 0.126765 | 0.0633825 | − | 0.997989i | \(-0.479811\pi\) | ||||
0.0633825 | + | 0.997989i | \(0.479811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27150.0 | −0.407589 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10206.0 | 0.144563 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −47910.0 | −0.641137 | −0.320569 | − | 0.947225i | \(-0.603874\pi\) | ||||
−0.320569 | + | 0.947225i | \(0.603874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5920.00 | −0.0749408 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 54144.0 | 0.649147 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 71500.0 | 0.812825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140738. | 1.51874 | 0.759368 | − | 0.650662i | \(-0.225508\pi\) | ||||
0.759368 | + | 0.650662i | \(0.225508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 45684.0 | 0.468464 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 85398.0 | 0.832999 | 0.416499 | − | 0.909136i | \(-0.363257\pi\) | ||||
0.416499 | + | 0.909136i | \(0.363257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −198656. | −1.84505 | −0.922526 | − | 0.385935i | \(-0.873879\pi\) | ||||
−0.922526 | + | 0.385935i | \(0.873879\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3600.00 | 0.0318661 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 116268. | 0.981750 | 0.490875 | − | 0.871230i | \(-0.336677\pi\) | ||||
0.490875 | + | 0.871230i | \(0.336677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −146722. | −1.18285 | −0.591424 | − | 0.806361i | \(-0.701434\pi\) | ||||
−0.591424 | + | 0.806361i | \(0.701434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4842.00 | −0.0373007 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 210882. | 1.55361 | 0.776807 | − | 0.629738i | \(-0.216838\pi\) | ||||
0.776807 | + | 0.629738i | \(0.216838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39600.0 | −0.279223 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −29970.0 | −0.202405 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17376.0 | −0.112482 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 157045. | 0.975126 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 102330. | 0.609874 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −244424. | −1.34473 | −0.672364 | − | 0.740221i | \(-0.734721\pi\) | ||||
−0.672364 | + | 0.740221i | \(0.734721\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −48996.0 | −0.259231 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 145308. | 0.739795 | 0.369897 | − | 0.929073i | \(-0.379393\pi\) | ||||
0.369897 | + | 0.929073i | \(0.379393\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45760.0 | 0.224314 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −125478. | −0.571171 | −0.285586 | − | 0.958353i | \(-0.592188\pi\) | ||||
−0.285586 | + | 0.958353i | \(0.592188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −251756. | −1.10520 | −0.552602 | − | 0.833445i | \(-0.686365\pi\) | ||||
−0.552602 | + | 0.833445i | \(0.686365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −92664.0 | −0.392521 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −208680. | −0.853377 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28350.0 | 0.111978 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −148959. | −0.568556 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −167322. | −0.617430 | −0.308715 | − | 0.951155i | \(-0.599899\pi\) | ||||
−0.308715 | + | 0.951155i | \(0.599899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −68120.0 | −0.243126 | −0.121563 | − | 0.992584i | \(-0.538791\pi\) | ||||
−0.121563 | + | 0.992584i | \(0.538791\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −87966.0 | −0.303799 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 150400. | 0.502827 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −361762. | −1.17132 | −0.585658 | − | 0.810559i | \(-0.699164\pi\) | ||||
−0.585658 | + | 0.810559i | \(0.699164\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 312822. | 0.981306 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25344.0 | −0.0770567 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −121820. | −0.359128 | −0.179564 | − | 0.983746i | \(-0.557469\pi\) | ||||
−0.179564 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 126900. | 0.362871 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 409008. | 1.13486 | 0.567428 | − | 0.823423i | \(-0.307939\pi\) | ||||
0.567428 | + | 0.823423i | \(0.307939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −234393. | −0.631288 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 231660. | 0.605844 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −729954. | −1.85430 | −0.927151 | − | 0.374689i | \(-0.877749\pi\) | ||||
−0.927151 | + | 0.374689i | \(0.877749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10000.0 | 0.0246834 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 235764. | 0.565645 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −704484. | −1.64338 | −0.821691 | − | 0.569933i | \(-0.806969\pi\) | ||||
−0.821691 | + | 0.569933i | \(0.806969\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −405850. | −0.920808 | −0.460404 | − | 0.887709i | \(-0.652295\pi\) | ||||
−0.460404 | + | 0.887709i | \(0.652295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 84798.0 | 0.187179 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13450.0 | −0.0288930 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −612504. | −1.28087 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11664.0 | 0.0237516 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −183024. | −0.363015 | −0.181508 | − | 0.983390i | \(-0.558098\pi\) | ||||
−0.181508 | + | 0.983390i | \(0.558098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −853054. | −1.64848 | −0.824239 | − | 0.566242i | \(-0.808397\pi\) | ||||
−0.824239 | + | 0.566242i | \(0.808397\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −83250.0 | −0.156783 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −476394. | −0.874582 | −0.437291 | − | 0.899320i | \(-0.644062\pi\) | ||||
−0.437291 | + | 0.899320i | \(0.644062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −470648. | −0.842488 | −0.421244 | − | 0.906947i | \(-0.638406\pi\) | ||||
−0.421244 | + | 0.906947i | \(0.638406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 460116. | 0.803299 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18144.0 | 0.0309025 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 284250. | 0.472406 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −128304. | −0.208120 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.61304e6 | 2.55434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14140.0 | 0.0218647 | 0.0109323 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109323 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −130680. | −0.197360 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −136100. | −0.200799 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 96256.0 | 0.138765 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −204102. | −0.287566 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 401820. | 0.553415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.08052e6 | 1.45503 | 0.727513 | − | 0.686094i | \(-0.240676\pi\) | ||||
0.727513 | + | 0.686094i | \(0.240676\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 340500. | 0.438584 | 0.219292 | − | 0.975659i | \(-0.429625\pi\) | ||||
0.219292 | + | 0.975659i | \(0.429625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −787594. | −0.992462 | −0.496231 | − | 0.868191i | \(-0.665283\pi\) | ||||
−0.496231 | + | 0.868191i | \(0.665283\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 81216.0 | 0.100141 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.51881e6 | 1.83279 | 0.916397 | − | 0.400271i | \(-0.131084\pi\) | ||||
0.916397 | + | 0.400271i | \(0.131084\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −257400. | −0.304046 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 875808. | 1.01283 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.18181e6 | −1.33830 | −0.669148 | − | 0.743129i | \(-0.733341\pi\) | ||||
−0.669148 | + | 0.743129i | \(0.733341\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −523342. | −0.580421 | −0.290210 | − | 0.956963i | \(-0.593725\pi\) | ||||
−0.290210 | + | 0.956963i | \(0.593725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −413775. | −0.440402 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.05820e6 | −1.10363 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 71604.0 | 0.0731878 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.27741e6 | 1.27981 | 0.639907 | − | 0.768453i | \(-0.278973\pi\) | ||||
0.639907 | + | 0.768453i | \(0.278973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −893376. | −0.877471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −244350. | −0.235322 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.93112e6 | −1.82379 | −0.911897 | − | 0.410418i | \(-0.865383\pi\) | ||||
−0.911897 | + | 0.410418i | \(0.865383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8608.00 | −0.00797357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 91854.0 | 0.0834635 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 822336. | 0.733094 | 0.366547 | − | 0.930399i | \(-0.380540\pi\) | ||||
0.366547 | + | 0.930399i | \(0.380540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 868950. | 0.760116 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −431190. | −0.370161 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.59181e6 | 1.34125 | 0.670625 | − | 0.741797i | \(-0.266026\pi\) | ||||
0.670625 | + | 0.741797i | \(0.266026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.21106e6 | 1.00171 | 0.500854 | − | 0.865532i | \(-0.333019\pi\) | ||||
0.500854 | + | 0.865532i | \(0.333019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −53280.0 | −0.0432671 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 352500. | 0.281078 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.34356e6 | −1.83517 | −0.917587 | − | 0.397536i | \(-0.869865\pi\) | ||||
−0.917587 | + | 0.397536i | \(0.869865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 487296. | 0.374785 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.86211e6 | 1.40682 | 0.703410 | − | 0.710784i | \(-0.251660\pi\) | ||||
0.703410 | + | 0.710784i | \(0.251660\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −108212. | −0.0803173 | −0.0401587 | − | 0.999193i | \(-0.512786\pi\) | ||||
−0.0401587 | + | 0.999193i | \(0.512786\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 643500. | 0.469285 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 181920. | 0.130369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −240461. | −0.169356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.26664e6 | 0.876842 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −959658. | −0.653052 | −0.326526 | − | 0.945188i | \(-0.605878\pi\) | ||||
−0.326526 | + | 0.945188i | \(0.605878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 654900. | 0.438147 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 411156. | 0.270468 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 586080. | 0.379122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −87104.0 | −0.0554143 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 768582. | 0.480932 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 235550. | 0.144988 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.62729e6 | −0.985416 | −0.492708 | − | 0.870195i | \(-0.663993\pi\) | ||||
−0.492708 | + | 0.870195i | \(0.663993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.78790e6 | −1.06524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.84086e6 | 1.66551 | 0.832757 | − | 0.553639i | \(-0.186761\pi\) | ||||
0.832757 | + | 0.553639i | \(0.186761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.61715e6 | 0.933014 | 0.466507 | − | 0.884517i | \(-0.345512\pi\) | ||||
0.466507 | + | 0.884517i | \(0.345512\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 32400.0 | 0.0183979 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.04367e6 | −1.14225 | −0.571126 | − | 0.820863i | \(-0.693493\pi\) | ||||
−0.571126 | + | 0.820863i | \(0.693493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 639576. | 0.351897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.04641e6 | 0.566813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.10596e6 | −1.65649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −231250. | −0.121443 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.32050e6 | −0.682918 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −164736. | −0.0839071 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00425e6 | −0.503817 | −0.251908 | − | 0.967751i | \(-0.581058\pi\) | ||||
−0.251908 | + | 0.967751i | \(0.581058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −43578.0 | −0.0215356 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.27810e6 | 0.622233 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.91960e6 | 1.40039 | 0.700195 | − | 0.713952i | \(-0.253096\pi\) | ||||
0.700195 | + | 0.713952i | \(0.253096\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.89794e6 | 0.896980 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.39302e6 | 1.58016 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −533728. | −0.244954 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −356400. | −0.161209 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.21075e6 | 0.985634 | 0.492817 | − | 0.870133i | \(-0.335967\pi\) | ||||
0.492817 | + | 0.870133i | \(0.335967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 375566. | 0.165053 | 0.0825264 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825264 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −269730. | −0.116859 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.49992e6 | 0.640666 | 0.320333 | − | 0.947305i | \(-0.396205\pi\) | ||||
0.320333 | + | 0.947305i | \(0.396205\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −363000. | −0.152875 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −156384. | −0.0649414 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.49626e6 | −1.02224 | −0.511122 | − | 0.859508i | \(-0.670770\pi\) | ||||
−0.511122 | + | 0.859508i | \(0.670770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.70350e6 | 2.30342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41340e6 | 0.562989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −566950. | −0.222747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.09714e6 | −1.58787 | −0.793937 | − | 0.608000i | \(-0.791972\pi\) | ||||
−0.793937 | + | 0.608000i | \(0.791972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 920970. | 0.352111 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 556128. | 0.209768 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.24213e6 | 0.462271 | 0.231135 | − | 0.972922i | \(-0.425756\pi\) | ||||
0.231135 | + | 0.972922i | \(0.425756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −419580. | −0.152041 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.28413e6 | 0.816814 | 0.408407 | − | 0.912800i | \(-0.366084\pi\) | ||||
0.408407 | + | 0.912800i | \(0.366084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.19982e6 | −0.776379 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 565128. | 0.196857 | 0.0984283 | − | 0.995144i | \(-0.468618\pi\) | ||||
0.0984283 | + | 0.995144i | \(0.468618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 225600. | 0.0775688 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −440964. | −0.149667 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.37367e6 | −1.13039 | −0.565196 | − | 0.824957i | \(-0.691199\pi\) | ||||
−0.565196 | + | 0.824957i | \(0.691199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.72022e6 | 0.569040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.30777e6 | 0.427121 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.43280e6 | 0.784537 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −745138. | −0.237280 | −0.118640 | − | 0.992937i | \(-0.537853\pi\) | ||||
−0.118640 | + | 0.992937i | \(0.537853\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 411840. | 0.129508 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 864786. | 0.268564 | 0.134282 | − | 0.990943i | \(-0.457127\pi\) | ||||
0.134282 | + | 0.990943i | \(0.457127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.22592e6 | −0.682727 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −303432. | −0.0907978 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.70189e6 | −1.68543 | −0.842715 | − | 0.538359i | \(-0.819044\pi\) | ||||
−0.842715 | + | 0.538359i | \(0.819044\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.12930e6 | −0.329766 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 419136. | 0.120915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 198900. | 0.0566911 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.26580e6 | −0.638090 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.91947e6 | 0.812398 | 0.406199 | − | 0.913785i | \(-0.366854\pi\) | ||||
0.406199 | + | 0.913785i | \(0.366854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.08815e6 | 0.299215 | 0.149608 | − | 0.988745i | \(-0.452199\pi\) | ||||
0.149608 | + | 0.988745i | \(0.452199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −833976. | −0.226622 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −678750. | −0.182279 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 150752. | 0.0400123 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.87812e6 | −0.492697 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.64573e6 | −1.20465 | −0.602325 | − | 0.798251i | \(-0.705759\pi\) | ||||
−0.602325 | + | 0.798251i | \(0.705759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −702094. | −0.179960 | −0.0899799 | − | 0.995944i | \(-0.528680\pi\) | ||||
−0.0899799 | + | 0.995944i | \(0.528680\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 255150. | 0.0646506 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.53024e6 | −1.13480 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.63343e6 | 0.404520 | 0.202260 | − | 0.979332i | \(-0.435171\pi\) | ||||
0.202260 | + | 0.979332i | \(0.435171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.34063e6 | −0.328256 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.39500e6 | −1.30612 | −0.653058 | − | 0.757308i | \(-0.726514\pi\) | ||||
−0.653058 | + | 0.757308i | \(0.726514\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.19775e6 | −0.286725 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.50590e6 | −0.356473 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −918462. | −0.215003 | −0.107502 | − | 0.994205i | \(-0.534285\pi\) | ||||
−0.107502 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.41268e6 | 1.48456 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −613080. | −0.140369 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −148000. | −0.0335145 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.55695e6 | −0.348726 | −0.174363 | − | 0.984681i | \(-0.555787\pi\) | ||||
−0.174363 | + | 0.984681i | \(0.555787\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −791694. | −0.175398 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.19299e6 | −1.13806 | −0.569030 | − | 0.822316i | \(-0.692681\pi\) | ||||
−0.569030 | + | 0.822316i | \(0.692681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 665848. | 0.144352 | 0.0721760 | − | 0.997392i | \(-0.477006\pi\) | ||||
0.0721760 | + | 0.997392i | \(0.477006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.35360e6 | 0.290307 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.84073e6 | −1.45148 | −0.725739 | − | 0.687970i | \(-0.758502\pi\) | ||||
−0.725739 | + | 0.687970i | \(0.758502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 817984. | 0.171717 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.25586e6 | −0.676259 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.07042e6 | −0.631022 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.78750e6 | 0.363506 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.81540e6 | 0.566557 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.26214e6 | −0.450486 | −0.225243 | − | 0.974303i | \(-0.572318\pi\) | ||||
−0.225243 | + | 0.974303i | \(0.572318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 199060. | 0.0392303 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −228096. | −0.0444887 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.51845e6 | 0.679199 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.78443e6 | 1.29626 | 0.648128 | − | 0.761531i | \(-0.275552\pi\) | ||||
0.648128 | + | 0.761531i | \(0.275552\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.09638e6 | −0.207343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.75964e6 | 1.26538 | 0.632688 | − | 0.774407i | \(-0.281952\pi\) | ||||
0.632688 | + | 0.774407i | \(0.281952\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.23152e6 | −0.228205 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.14210e6 | 0.209503 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −232320. | −0.0421886 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.73256e6 | −1.56997 | −0.784983 | − | 0.619517i | \(-0.787329\pi\) | ||||
−0.784983 | + | 0.619517i | \(0.787329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.68107e6 | 0.655209 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.75426e6 | −0.837843 | −0.418921 | − | 0.908022i | \(-0.637592\pi\) | ||||
−0.418921 | + | 0.908022i | \(0.637592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.13495e6 | 0.372528 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.10954e6 | −0.364475 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.13074e6 | −0.364532 | −0.182266 | − | 0.983249i | \(-0.558343\pi\) | ||||
−0.182266 | + | 0.983249i | \(0.558343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −362848. | −0.0614713 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.08494e6 | 0.349784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.96640e6 | −0.825132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.80694e6 | −0.955479 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.56959e6 | −1.07058 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.10967e7 | 1.79101 | 0.895507 | − | 0.445048i | \(-0.146813\pi\) | ||||
0.895507 | + | 0.445048i | \(0.146813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −941252. | −0.150471 | −0.0752353 | − | 0.997166i | \(-0.523971\pi\) | ||||
−0.0752353 | + | 0.997166i | \(0.523971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 90000.0 | 0.0142510 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.53338e6 | −1.02473 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.92729e6 | −0.610174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.12188e6 | 0.326576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.20690e6 | −0.641422 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.90670e6 | 0.439052 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.34036e6 | −0.948807 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.33476e6 | −1.38399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.39896e6 | 0.352395 | 0.176197 | − | 0.984355i | \(-0.443620\pi\) | ||||
0.176197 | + | 0.984355i | \(0.443620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.65265e6 | −0.531629 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.66805e6 | −0.528986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55851e6 | −0.222711 | −0.111355 | − | 0.993781i | \(-0.535519\pi\) | ||||
−0.111355 | + | 0.993781i | \(0.535519\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 763182. | 0.108068 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.24324e6 | 0.455093 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.55699e6 | 0.216508 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −121050. | −0.0166814 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.19451e7 | 1.63137 | 0.815685 | − | 0.578496i | \(-0.196360\pi\) | ||||
0.815685 | + | 0.578496i | \(0.196360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.01428e6 | 0.272640 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.51254e6 | −0.739510 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.63906e6 | 1.28163 | 0.640817 | − | 0.767694i | \(-0.278596\pi\) | ||||
0.640817 | + | 0.767694i | \(0.278596\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.27205e6 | 0.694798 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 104976. | 0.0137130 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 830106. | 0.107486 | 0.0537431 | − | 0.998555i | \(-0.482885\pi\) | ||||
0.0537431 | + | 0.998555i | \(0.482885\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.32914e6 | 0.427309 | 0.213654 | − | 0.976909i | \(-0.431463\pi\) | ||||
0.213654 | + | 0.976909i | \(0.431463\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.64722e6 | −0.209587 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −990000. | −0.124872 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.40026e6 | 0.550223 | 0.275111 | − | 0.961412i | \(-0.411285\pi\) | ||||
0.275111 | + | 0.961412i | \(0.411285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.67749e6 | −0.951749 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 127296. | 0.0156450 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.96035e7 | 2.38870 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −749250. | −0.0905184 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.25848e6 | 0.869461 | 0.434731 | − | 0.900561i | \(-0.356844\pi\) | ||||
0.434731 | + | 0.900561i | \(0.356844\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.72058e7 | 2.04355 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.28755e6 | −0.504940 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.55171e7 | −1.81206 | −0.906032 | − | 0.423210i | \(-0.860903\pi\) | ||||
−0.906032 | + | 0.423210i | \(0.860903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −434400. | −0.0503034 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.23583e6 | −0.486410 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02670e7 | 1.16917 | 0.584583 | − | 0.811334i | \(-0.301258\pi\) | ||||
0.584583 | + | 0.811334i | \(0.301258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.42362e6 | −1.06422 | −0.532110 | − | 0.846675i | \(-0.678601\pi\) | ||||
−0.532110 | + | 0.846675i | \(0.678601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.14104e6 | 0.463785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.92612e6 | 0.436090 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.67289e6 | 0.845254 | 0.422627 | − | 0.906304i | \(-0.361108\pi\) | ||||
0.422627 | + | 0.906304i | \(0.361108\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 163296. | 0.0178415 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.80952e6 | 0.412826 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.30598e6 | −0.247859 | −0.123929 | − | 0.992291i | \(-0.539550\pi\) | ||||
−0.123929 | + | 0.992291i | \(0.539550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.55825e6 | 0.272744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −505254. | −0.0534314 | −0.0267157 | − | 0.999643i | \(-0.508505\pi\) | ||||
−0.0267157 | + | 0.999643i | \(0.508505\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.61380e6 | −0.483986 | −0.241993 | − | 0.970278i | \(-0.577801\pi\) | ||||
−0.241993 | + | 0.970278i | \(0.577801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.15474e6 | −0.120158 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −766560. | −0.0791272 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.45174e7 | 1.47475 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 584268. | 0.0588824 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.77327e6 | −0.477247 | −0.238623 | − | 0.971112i | \(-0.576696\pi\) | ||||
−0.238623 | + | 0.971112i | \(0.576696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 127260. | 0.0126236 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.11060e6 | −0.601381 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.12387e6 | 0.597967 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.17612e6 | −0.113946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.09254e7 | −1.05025 | −0.525125 | − | 0.851025i | \(-0.675981\pi\) | ||||
−0.525125 | + | 0.851025i | \(0.675981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.13952e6 | −0.108691 | −0.0543454 | − | 0.998522i | \(-0.517307\pi\) | ||||
−0.0543454 | + | 0.998522i | \(0.517307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.22490e6 | −0.115931 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.10955e6 | −0.479868 | −0.239934 | − | 0.970789i | \(-0.577126\pi\) | ||||
−0.239934 | + | 0.970789i | \(0.577126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.47745e7 | 1.37690 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 866304. | 0.0801157 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.81591e6 | −0.717293 | −0.358646 | − | 0.933474i | \(-0.616762\pi\) | ||||
−0.358646 | + | 0.933474i | \(0.616762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.63270e6 | 0.330846 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.83692e6 | −0.166026 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.05905e7 | 0.949954 | 0.474977 | − | 0.879998i | \(-0.342456\pi\) | ||||
0.474977 | + | 0.879998i | \(0.342456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.67092e6 | 0.415814 | 0.207907 | − | 0.978149i | \(-0.433335\pi\) | ||||
0.207907 | + | 0.978149i | \(0.433335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.61638e6 | 0.319514 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.14400e6 | 0.100316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.79626e6 | −0.156334 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.72468e6 | 0.840059 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.31401e6 | 0.455634 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.07728e7 | 1.76790 | 0.883948 | − | 0.467585i | \(-0.154876\pi\) | ||||
0.883948 | + | 0.467585i | \(0.154876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.67497e7 | 1.40454 | 0.702270 | − | 0.711911i | \(-0.252170\pi\) | ||||
0.702270 | + | 0.711911i | \(0.252170\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.25181e6 | 0.187438 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.06450e6 | 0.253216 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.41700e6 | −0.362306 | −0.181153 | − | 0.983455i | \(-0.557983\pi\) | ||||
−0.181153 | + | 0.983455i | \(0.557983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.13695e6 | −0.255435 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.08835e6 | −0.572998 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.28605e7 | −1.03207 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.86481e7 | −1.48573 | −0.742863 | − | 0.669443i | \(-0.766533\pi\) | ||||
−0.742863 | + | 0.669443i | \(0.766533\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 730944. | 0.0578164 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.29390e6 | −0.494263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.23478e7 | −0.962739 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.36693e7 | 1.05816 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.28389e6 | 0.559845 | 0.279923 | − | 0.960023i | \(-0.409691\pi\) | ||||
0.279923 | + | 0.960023i | \(0.409691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.53868e6 | −0.117425 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.31660e6 | −0.175541 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.36637e6 | 0.102806 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.82063e7 | 1.36021 | 0.680105 | − | 0.733115i | \(-0.261934\pi\) | ||||
0.680105 | + | 0.733115i | \(0.261934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.88227e6 | 0.584760 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.52934e6 | −0.702003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.21700e6 | −0.381642 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.06363e7 | −0.772666 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.46901e6 | −0.466676 | −0.233338 | − | 0.972396i | \(-0.574965\pi\) | ||||
−0.233338 | + | 0.972396i | \(0.574965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.17850e6 | −0.227711 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.71008e6 | −0.335106 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 708750. | 0.0500781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.39991e7 | 0.982343 | 0.491172 | − | 0.871063i | \(-0.336569\pi\) | ||||
0.491172 | + | 0.871063i | \(0.336569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.91218e6 | 0.409218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.51019e7 | 1.72562 | 0.862811 | − | 0.505526i | \(-0.168702\pi\) | ||||
0.862811 | + | 0.505526i | \(0.168702\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.72398e6 | −0.254266 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.88339e7 | 1.95540 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.73514e6 | −0.655739 | −0.327870 | − | 0.944723i | \(-0.606331\pi\) | ||||
−0.327870 | + | 0.944723i | \(0.606331\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.52380e6 | −0.637184 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.03370e6 | −0.201604 | −0.100802 | − | 0.994906i | \(-0.532141\pi\) | ||||
−0.100802 | + | 0.994906i | \(0.532141\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.18305e6 | −0.276123 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 644436. | 0.0422550 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.86029e6 | 0.121165 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.07557e6 | 0.393086 | 0.196543 | − | 0.980495i | \(-0.437029\pi\) | ||||
0.196543 | + | 0.980495i | \(0.437029\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.14967e7 | 0.738901 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.70300e6 | −0.108729 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.82103e6 | −0.305774 | −0.152887 | − | 0.988244i | \(-0.548857\pi\) | ||||
−0.152887 | + | 0.988244i | \(0.548857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.04038e6 | −0.506608 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.82748e6 | 0.364770 | 0.182385 | − | 0.983227i | \(-0.441618\pi\) | ||||
0.182385 | + | 0.983227i | \(0.441618\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.34755e6 | −0.145984 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.19915e6 | −0.135863 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.69252e6 | −0.594906 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.71546e7 | −1.65587 | −0.827936 | − | 0.560822i | \(-0.810485\pi\) | ||||
−0.827936 | + | 0.560822i | \(0.810485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.73801e7 | −1.05297 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6678.00 | 0.000401974 0 | 0.000200987 | − | 1.00000i | \(-0.499936\pi\) | ||||
0.000200987 | 1.00000i | \(0.499936\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.76000e6 | 0.224871 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −77472.0 | −0.00460354 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.25182e7 | 1.91992 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.18928e6 | −0.480417 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 826686. | 0.0481877 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.04405e6 | −0.523828 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.44352e7 | −0.830781 | −0.415391 | − | 0.909643i | \(-0.636355\pi\) | ||||
−0.415391 | + | 0.909643i | \(0.636355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.40102e6 | 0.423252 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.37411e6 | 0.191742 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.48614e6 | −0.196862 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.82055e6 | 0.438853 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.90792e6 | −0.106393 | −0.0531967 | − | 0.998584i | \(-0.516941\pi\) | ||||
−0.0531967 | + | 0.998584i | \(0.516941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.11815e7 | 0.619629 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.88071e6 | −0.213712 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.27904e7 | −0.699995 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −633600. | −0.0344608 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.43263e7 | 0.774371 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.48543e7 | −1.87234 | −0.936171 | − | 0.351546i | \(-0.885656\pi\) | ||||
−0.936171 | + | 0.351546i | \(0.885656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.41263e7 | −0.754182 | −0.377091 | − | 0.926176i | \(-0.623076\pi\) | ||||
−0.377091 | + | 0.926176i | \(0.623076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.08995e7 | 0.578336 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.04550e6 | −0.160607 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.55698e7 | −0.816073 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −479520. | −0.0249803 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.78858e7 | 0.926082 | 0.463041 | − | 0.886337i | \(-0.346758\pi\) | ||||
0.463041 | + | 0.886337i | \(0.346758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.73695e7 | 0.893897 | 0.446948 | − | 0.894560i | \(-0.352511\pi\) | ||||
0.446948 | + | 0.894560i | \(0.352511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.17250e6 | 0.162281 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.84745e7 | 0.939310 | 0.469655 | − | 0.882850i | \(-0.344378\pi\) | ||||
0.469655 | + | 0.882850i | \(0.344378\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.02647e7 | −1.52950 | −0.764750 | − | 0.644327i | \(-0.777138\pi\) | ||||
−0.764750 | + | 0.644327i | \(0.777138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.10921e7 | −1.05954 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.79744e7 | 0.897515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02252e7 | 0.507523 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.38566e6 | 0.216382 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.10237e7 | 1.03111 | 0.515555 | − | 0.856856i | \(-0.327586\pi\) | ||||
0.515555 | + | 0.856856i | \(0.327586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.92252e7 | −0.937305 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.67590e7 | 0.812228 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.85982e6 | −0.282321 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.51272e6 | 0.120347 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −973908. | −0.0463712 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 852192. | 0.0403379 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.60690e7 | −1.22674 | −0.613369 | − | 0.789796i | \(-0.710186\pi\) | ||||
−0.613369 | + | 0.789796i | \(0.710186\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.79150e6 | 0.270942 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 489738. | 0.0227778 | 0.0113889 | − | 0.999935i | \(-0.496375\pi\) | ||||
0.0113889 | + | 0.999935i | \(0.496375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.17067e7 | 1.00371 | 0.501857 | − | 0.864951i | \(-0.332650\pi\) | ||||
0.501857 | + | 0.864951i | \(0.332650\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.63728e6 | 0.0752688 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.91038e7 | −1.33022 | −0.665108 | − | 0.746747i | \(-0.731615\pi\) | ||||
−0.665108 | + | 0.746747i | \(0.731615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.82488e7 | −0.829269 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.16415e6 | −0.0977776 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.48840e7 | 2.46545 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.89159e7 | −0.844853 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.13998e7 | 0.506245 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 250000. | 0.0110387 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.11648e7 | 0.929215 | 0.464607 | − | 0.885517i | \(-0.346195\pi\) | ||||
0.464607 | + | 0.885517i | \(0.346195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.63692e6 | −0.377039 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.60651e6 | −0.416990 | −0.208495 | − | 0.978023i | \(-0.566857\pi\) | ||||
−0.208495 | + | 0.978023i | \(0.566857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.58825e7 | −1.11713 | −0.558566 | − | 0.829460i | \(-0.688648\pi\) | ||||
−0.558566 | + | 0.829460i | \(0.688648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.89410e6 | 0.252964 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.43249e7 | −1.03811 | −0.519053 | − | 0.854742i | \(-0.673715\pi\) | ||||
−0.519053 | + | 0.854742i | \(0.673715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.91078e6 | −0.165962 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.70040e6 | 0.156155 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.94466e7 | −1.23568 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.76121e7 | −0.734943 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.27472e6 | 0.218886 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.82214e6 | 0.281528 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.77472e7 | −1.54908 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −783936. | −0.0319935 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.01462e7 | −0.411798 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.87371e6 | 0.317805 | 0.158903 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158903 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.91724e6 | 0.277666 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.74478e7 | −1.89418 | −0.947088 | − | 0.320975i | \(-0.895990\pi\) | ||||
−0.947088 | + | 0.320975i | \(0.895990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.48718e6 | 0.178155 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.11995e6 | 0.0837091 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.32493e6 | 0.0913032 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −605288. | −0.0236414 | −0.0118207 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118207 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.46456e7 | −0.568930 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.37240e6 | 0.207570 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −336250. | −0.0129214 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.60911e7 | −0.615017 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.52438e6 | −0.362074 | −0.181037 | − | 0.983476i | \(-0.557945\pi\) | ||||
−0.181037 | + | 0.983476i | \(0.557945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.73359e7 | −1.78985 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.55677e7 | 0.961585 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.53126e7 | −0.572822 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.15708e6 | −0.340728 | −0.170364 | − | 0.985381i | \(-0.554494\pi\) | ||||
−0.170364 | + | 0.985381i | \(0.554494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.45543e7 | 0.538676 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.46291e6 | 0.0906723 | 0.0453361 | − | 0.998972i | \(-0.485564\pi\) | ||||
0.0453361 | + | 0.998972i | \(0.485564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.80101e7 | −0.659533 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 291600. | 0.0106220 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.13961e6 | −0.294937 | −0.147468 | − | 0.989067i | \(-0.547112\pi\) | ||||
−0.147468 | + | 0.989067i | \(0.547112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.39086e6 | 0.302441 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.83930e7 | −0.659479 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.65014e7 | 0.588557 | 0.294278 | − | 0.955720i | \(-0.404921\pi\) | ||||
0.294278 | + | 0.955720i | \(0.404921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.57560e6 | −0.162345 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.75618e6 | 0.203168 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00765e6 | −0.0704922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.56310e6 | 0.264175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.41771e6 | 0.327250 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.13264e7 | −0.737222 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.72505e7 | 0.937148 | 0.468574 | − | 0.883424i | \(-0.344768\pi\) | ||||
0.468574 | + | 0.883424i | \(0.344768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.79536e7 | −0.956377 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.77172e7 | 0.603040 | 0.301520 | − | 0.953460i | \(-0.402506\pi\) | ||||
0.301520 | + | 0.953460i | \(0.402506\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.02810e6 | −0.136401 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.08125e6 | −0.0701153 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.57062e7 | 0.861591 | 0.430795 | − | 0.902450i | \(-0.358233\pi\) | ||||
0.430795 | + | 0.902450i | \(0.358233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.70212e7 | −0.901049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.18845e7 | −0.394283 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.05067e6 | −0.133704 | −0.0668518 | − | 0.997763i | \(-0.521295\pi\) | ||||
−0.0668518 | + | 0.997763i | \(0.521295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.19098e7 | −0.391125 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.48262e6 | −0.0484438 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.62330e6 | 0.280338 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.71299e6 | 0.0554078 | 0.0277039 | − | 0.999616i | \(-0.491180\pi\) | ||||
0.0277039 | + | 0.999616i | \(0.491180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.03827e6 | −0.290879 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.17662e7 | −0.376772 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.09874e7 | 0.668683 | 0.334341 | − | 0.942452i | \(-0.391486\pi\) | ||||
0.334341 | + | 0.942452i | \(0.391486\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −392202. | −0.0124336 |
(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 | 240.6.a.m.1.1 | 1 | ||
3.2 | odd | 2 | 720.6.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 60.6.a.b.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 960.6.a.r.1.1 | 1 | |||
8.5 | even | 2 | 960.6.a.c.1.1 | 1 | |||
12.11 | even | 2 | 180.6.a.a.1.1 | 1 | |||
20.3 | even | 4 | 300.6.d.a.49.1 | 2 | |||
20.7 | even | 4 | 300.6.d.a.49.2 | 2 | |||
20.19 | odd | 2 | 300.6.a.e.1.1 | 1 | |||
60.23 | odd | 4 | 900.6.d.i.649.2 | 2 | |||
60.47 | odd | 4 | 900.6.d.i.649.1 | 2 | |||
60.59 | even | 2 | 900.6.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
180.6.a.a.1.1 | 1 | 12.11 | even | 2 | |||
240.6.a.m.1.1 | 1 | 1.1 | even | 1 | trivial | ||
300.6.a.e.1.1 | 1 | 20.19 | odd | 2 | |||
300.6.d.a.49.1 | 2 | 20.3 | even | 4 | |||
300.6.d.a.49.2 | 2 | 20.7 | even | 4 | |||
720.6.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
900.6.a.g.1.1 | 1 | 60.59 | even | 2 | |||
900.6.d.i.649.1 | 2 | 60.47 | odd | 4 | |||
900.6.d.i.649.2 | 2 | 60.23 | odd | 4 | |||
960.6.a.c.1.1 | 1 | 8.5 | even | 2 | |||
960.6.a.r.1.1 | 1 | 8.3 | odd | 2 |