Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,6,Mod(1,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.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: | \(3.84921167551\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 24.1 |
$q$-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 | ||||||||
\(5\) | 38.0000 | 0.679765 | 0.339882 | − | 0.940468i | \(-0.389613\pi\) | ||||
0.339882 | + | 0.940468i | \(0.389613\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 120.000 | 0.925627 | 0.462814 | − | 0.886456i | \(-0.346840\pi\) | ||||
0.462814 | + | 0.886456i | \(0.346840\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 524.000 | 1.30572 | 0.652859 | − | 0.757479i | \(-0.273569\pi\) | ||||
0.652859 | + | 0.757479i | \(0.273569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −962.000 | −1.57876 | −0.789381 | − | 0.613904i | \(-0.789598\pi\) | ||||
−0.789381 | + | 0.613904i | \(0.789598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 342.000 | 0.392462 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1358.00 | −1.13967 | −0.569833 | − | 0.821761i | \(-0.692992\pi\) | ||||
−0.569833 | + | 0.821761i | \(0.692992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2284.00 | −1.45148 | −0.725742 | − | 0.687967i | \(-0.758503\pi\) | ||||
−0.725742 | + | 0.687967i | \(0.758503\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1080.00 | 0.534411 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2552.00 | 1.00591 | 0.502957 | − | 0.864311i | \(-0.332245\pi\) | ||||
0.502957 | + | 0.864311i | \(0.332245\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1681.00 | −0.537920 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3966.00 | 0.875705 | 0.437852 | − | 0.899047i | \(-0.355739\pi\) | ||||
0.437852 | + | 0.899047i | \(0.355739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2992.00 | −0.559187 | −0.279594 | − | 0.960118i | \(-0.590200\pi\) | ||||
−0.279594 | + | 0.960118i | \(0.590200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4716.00 | 0.753857 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4560.00 | 0.629209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13206.0 | 1.58587 | 0.792934 | − | 0.609308i | \(-0.208553\pi\) | ||||
0.792934 | + | 0.609308i | \(0.208553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8658.00 | −0.911499 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15126.0 | −1.40529 | −0.702643 | − | 0.711543i | \(-0.747997\pi\) | ||||
−0.702643 | + | 0.711543i | \(0.747997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7316.00 | −0.603396 | −0.301698 | − | 0.953404i | \(-0.597553\pi\) | ||||
−0.301698 | + | 0.953404i | \(0.597553\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3078.00 | 0.226588 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6960.00 | −0.459584 | −0.229792 | − | 0.973240i | \(-0.573805\pi\) | ||||
−0.229792 | + | 0.973240i | \(0.573805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2407.00 | −0.143214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12222.0 | −0.657986 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −17482.0 | −0.854873 | −0.427436 | − | 0.904045i | \(-0.640583\pi\) | ||||
−0.427436 | + | 0.904045i | \(0.640583\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19912.0 | 0.887581 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20556.0 | −0.838014 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 33884.0 | 1.26726 | 0.633628 | − | 0.773638i | \(-0.281565\pi\) | ||||
0.633628 | + | 0.773638i | \(0.281565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39118.0 | 1.34602 | 0.673011 | − | 0.739633i | \(-0.265001\pi\) | ||||
0.673011 | + | 0.739633i | \(0.265001\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9720.00 | 0.308542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −36556.0 | −1.07319 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 32996.0 | 0.897996 | 0.448998 | − | 0.893533i | \(-0.351781\pi\) | ||||
0.448998 | + | 0.893533i | \(0.351781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22968.0 | 0.580765 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14248.0 | 0.335435 | 0.167717 | − | 0.985835i | \(-0.446360\pi\) | ||||
0.167717 | + | 0.985835i | \(0.446360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −35990.0 | −0.790451 | −0.395225 | − | 0.918584i | \(-0.629333\pi\) | ||||
−0.395225 | + | 0.918584i | \(0.629333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15129.0 | −0.310568 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 62880.0 | 1.20861 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29888.0 | −0.538802 | −0.269401 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269401 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −51884.0 | −0.826682 | −0.413341 | − | 0.910576i | \(-0.635638\pi\) | ||||
−0.413341 | + | 0.910576i | \(0.635638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −51604.0 | −0.774704 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 35694.0 | 0.505588 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30714.0 | 0.411018 | 0.205509 | − | 0.978655i | \(-0.434115\pi\) | ||||
0.205509 | + | 0.978655i | \(0.434115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −115440. | −1.46135 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26928.0 | −0.322847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −86792.0 | −0.986667 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −48478.0 | −0.523137 | −0.261568 | − | 0.965185i | \(-0.584240\pi\) | ||||
−0.261568 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 42444.0 | 0.435240 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 93222.0 | 0.909316 | 0.454658 | − | 0.890666i | \(-0.349761\pi\) | ||||
0.454658 | + | 0.890666i | \(0.349761\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2296.00 | 0.0213245 | 0.0106622 | − | 0.999943i | \(-0.496606\pi\) | ||||
0.0106622 | + | 0.999943i | \(0.496606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 41040.0 | 0.363274 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 38988.0 | 0.329209 | 0.164604 | − | 0.986360i | \(-0.447365\pi\) | ||||
0.164604 | + | 0.986360i | \(0.447365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6238.00 | 0.0502897 | 0.0251449 | − | 0.999684i | \(-0.491995\pi\) | ||||
0.0251449 | + | 0.999684i | \(0.491995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 118854. | 0.915601 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 213618. | 1.57377 | 0.786886 | − | 0.617099i | \(-0.211692\pi\) | ||||
0.786886 | + | 0.617099i | \(0.211692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 96976.0 | 0.683785 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −77922.0 | −0.526254 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −162960. | −1.05491 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 113525. | 0.704901 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −136134. | −0.811342 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −182628. | −1.04542 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 205072. | 1.12823 | 0.564114 | − | 0.825697i | \(-0.309218\pi\) | ||||
0.564114 | + | 0.825697i | \(0.309218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −65844.0 | −0.348371 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 350116. | 1.78252 | 0.891259 | − | 0.453495i | \(-0.149823\pi\) | ||||
0.891259 | + | 0.453495i | \(0.149823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −274080. | −1.34353 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27702.0 | 0.130821 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −234486. | −1.06737 | −0.533686 | − | 0.845683i | \(-0.679193\pi\) | ||||
−0.533686 | + | 0.845683i | \(0.679193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16428.0 | 0.0721187 | 0.0360593 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360593 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −62640.0 | −0.265341 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −504088. | −2.06142 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 150708. | 0.595273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21663.0 | −0.0826847 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −92426.0 | −0.341058 | −0.170529 | − | 0.985353i | \(-0.554548\pi\) | ||||
−0.170529 | + | 0.985353i | \(0.554548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 350984. | 1.25269 | 0.626347 | − | 0.779544i | \(-0.284549\pi\) | ||||
0.626347 | + | 0.779544i | \(0.284549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −109998. | −0.379889 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −113696. | −0.380116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 46318.0 | 0.149969 | 0.0749844 | − | 0.997185i | \(-0.476109\pi\) | ||||
0.0749844 | + | 0.997185i | \(0.476109\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −157338. | −0.493561 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 306240. | 0.931102 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −394908. | −1.16420 | −0.582099 | − | 0.813118i | \(-0.697768\pi\) | ||||
−0.582099 | + | 0.813118i | \(0.697768\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 179208. | 0.512445 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 514344. | 1.42713 | 0.713563 | − | 0.700591i | \(-0.247080\pi\) | ||||
0.713563 | + | 0.700591i | \(0.247080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 554151. | 1.49249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −185004. | −0.483828 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −497874. | −1.26475 | −0.632374 | − | 0.774663i | \(-0.717920\pi\) | ||||
−0.632374 | + | 0.774663i | \(0.717920\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −201720. | −0.497913 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 304956. | 0.731651 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 711252. | 1.65917 | 0.829585 | − | 0.558380i | \(-0.188577\pi\) | ||||
0.829585 | + | 0.558380i | \(0.188577\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 471366. | 1.06945 | 0.534727 | − | 0.845025i | \(-0.320415\pi\) | ||||
0.534727 | + | 0.845025i | \(0.320415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 352062. | 0.777126 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 501828. | 1.07802 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −711592. | −1.48808 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 87480.0 | 0.178137 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −646080. | −1.28145 | −0.640727 | − | 0.767769i | \(-0.721367\pi\) | ||||
−0.640727 | + | 0.767769i | \(0.721367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −826558. | −1.59728 | −0.798638 | − | 0.601811i | \(-0.794446\pi\) | ||||
−0.798638 | + | 0.601811i | \(0.794446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −329004. | −0.619605 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −126138. | −0.231569 | −0.115784 | − | 0.993274i | \(-0.536938\pi\) | ||||
−0.115784 | + | 0.993274i | \(0.536938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −119144. | −0.213275 | −0.106637 | − | 0.994298i | \(-0.534008\pi\) | ||||
−0.106637 | + | 0.994298i | \(0.534008\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 296964. | 0.518458 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 475920. | 0.810576 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −574788. | −0.955263 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 206712. | 0.335305 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.19682e6 | −1.89523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 341620. | 0.528247 | 0.264124 | − | 0.964489i | \(-0.414917\pi\) | ||||
0.264124 | + | 0.964489i | \(0.414917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 128232. | 0.193663 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −278008. | −0.410167 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −359040. | −0.517599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −323910. | −0.456367 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.30640e6 | 1.79926 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −523088. | −0.704389 | −0.352195 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352195 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −136161. | −0.179307 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.03261e6 | 1.33006 | 0.665032 | − | 0.746815i | \(-0.268418\pi\) | ||||
0.665032 | + | 0.746815i | \(0.268418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 50422.0 | 0.0635377 | 0.0317688 | − | 0.999495i | \(-0.489886\pi\) | ||||
0.0317688 | + | 0.999495i | \(0.489886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 565920. | 0.697791 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −991030. | −1.19591 | −0.597953 | − | 0.801531i | \(-0.704019\pi\) | ||||
−0.597953 | + | 0.801531i | \(0.704019\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −264480. | −0.312409 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −268992. | −0.311077 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 514864. | 0.583039 | 0.291520 | − | 0.956565i | \(-0.405839\pi\) | ||||
0.291520 | + | 0.956565i | \(0.405839\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 480498. | 0.532904 | 0.266452 | − | 0.963848i | \(-0.414149\pi\) | ||||
0.266452 | + | 0.963848i | \(0.414149\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −91466.0 | −0.0973519 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.19721e6 | 2.29155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −466956. | −0.477285 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −768260. | −0.769704 | −0.384852 | − | 0.922978i | \(-0.625748\pi\) | ||||
−0.384852 | + | 0.922978i | \(0.625748\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.33725e6 | 1.31344 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −464436. | −0.447276 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 316162. | 0.298591 | 0.149296 | − | 0.988793i | \(-0.452299\pi\) | ||||
0.149296 | + | 0.988793i | \(0.452299\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.58472e6 | 1.46792 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 321246. | 0.291902 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.33017e6 | −1.18582 | −0.592908 | − | 0.805270i | \(-0.702020\pi\) | ||||
−0.592908 | + | 0.805270i | \(0.702020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −664316. | −0.581112 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 276426. | 0.237302 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 812590. | 0.684685 | 0.342342 | − | 0.939575i | \(-0.388780\pi\) | ||||
0.342342 | + | 0.939575i | \(0.388780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.99235e6 | −1.64795 | −0.823973 | − | 0.566629i | \(-0.808247\pi\) | ||||
−0.823973 | + | 0.566629i | \(0.808247\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.03896e6 | −0.843708 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −880844. | −0.702372 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 356134. | 0.278878 | 0.139439 | − | 0.990231i | \(-0.455470\pi\) | ||||
0.139439 | + | 0.990231i | \(0.455470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −242352. | −0.186396 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 644986. | 0.487287 | 0.243643 | − | 0.969865i | \(-0.421657\pi\) | ||||
0.243643 | + | 0.969865i | \(0.421657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −677188. | −0.502624 | −0.251312 | − | 0.967906i | \(-0.580862\pi\) | ||||
−0.251312 | + | 0.967906i | \(0.580862\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −781128. | −0.569653 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.81512e6 | −1.30077 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 424307. | 0.298838 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −436302. | −0.302033 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 414822. | 0.282288 | 0.141144 | − | 0.989989i | \(-0.454922\pi\) | ||||
0.141144 | + | 0.989989i | \(0.454922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.28759e6 | 0.861436 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 381996. | 0.251286 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.45502e6 | −1.58810 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −877920. | −0.558520 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 838998. | 0.524994 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.48648e6 | 0.914978 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −362028. | −0.219228 | −0.109614 | − | 0.993974i | \(-0.534961\pi\) | ||||
−0.109614 | + | 0.993974i | \(0.534961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20664.0 | 0.0123117 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.54342e6 | 0.904861 | 0.452431 | − | 0.891800i | \(-0.350557\pi\) | ||||
0.452431 | + | 0.891800i | \(0.350557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.54225e6 | −0.889801 | −0.444900 | − | 0.895580i | \(-0.646761\pi\) | ||||
−0.444900 | + | 0.895580i | \(0.646761\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 369360. | 0.209736 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33246.0 | 0.0185819 | 0.00929097 | − | 0.999957i | \(-0.497043\pi\) | ||||
0.00929097 | + | 0.999957i | \(0.497043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.07818e6 | 1.14342 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 350892. | 0.190069 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.10167e6 | 1.65421 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.61712e6 | 0.849248 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 56142.0 | 0.0290348 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −835200. | −0.425403 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.60738e6 | −0.806396 | −0.403198 | − | 0.915113i | \(-0.632101\pi\) | ||||
−0.403198 | + | 0.915113i | \(0.632101\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06969e6 | 0.528623 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.25385e6 | 0.610426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.44958e6 | −0.695293 | −0.347647 | − | 0.937626i | \(-0.613019\pi\) | ||||
−0.347647 | + | 0.937626i | \(0.613019\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.92256e6 | 0.908618 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.56781e6 | −0.730141 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.30568e6 | −1.05819 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 872784. | 0.394784 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 474588. | 0.211589 | 0.105794 | − | 0.994388i | \(-0.466261\pi\) | ||||
0.105794 | + | 0.994388i | \(0.466261\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.98869e6 | −1.31346 | −0.656731 | − | 0.754125i | \(-0.728061\pi\) | ||||
−0.656731 | + | 0.754125i | \(0.728061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −701298. | −0.303833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.26480e6 | 1.39451 | 0.697253 | − | 0.716826i | \(-0.254406\pi\) | ||||
0.697253 | + | 0.716826i | \(0.254406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 541424. | 0.228017 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.46664e6 | −0.609050 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.92430e6 | 0.788017 | 0.394009 | − | 0.919107i | \(-0.371088\pi\) | ||||
0.394009 | + | 0.919107i | \(0.371088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.74056e6 | 1.10680 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.02172e6 | 0.406975 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.36762e6 | −0.537320 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50013e6 | −0.581384 | −0.290692 | − | 0.956817i | \(-0.593886\pi\) | ||||
−0.290692 | + | 0.956817i | \(0.593886\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.22521e6 | −0.468428 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.09784e6 | −0.791293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.70185e6 | −1.74983 | −0.874917 | − | 0.484273i | \(-0.839084\pi\) | ||||
−0.874917 | + | 0.484273i | \(0.839084\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.64365e6 | −0.603576 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.81529e6 | −1.38253 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.51526e6 | 0.541863 | 0.270931 | − | 0.962599i | \(-0.412668\pi\) | ||||
0.270931 | + | 0.962599i | \(0.412668\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.84565e6 | 0.651383 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 155520. | 0.0541738 | 0.0270869 | − | 0.999633i | \(-0.491377\pi\) | ||||
0.0270869 | + | 0.999633i | \(0.491377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.38944e6 | 0.821569 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −592596. | −0.201132 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.05084e6 | −1.02222 | −0.511112 | − | 0.859514i | \(-0.670766\pi\) | ||||
−0.511112 | + | 0.859514i | \(0.670766\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.46562e6 | −1.14641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.15104e6 | 1.02914 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.13574e6 | −0.366258 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 196574. | 0.0625965 | 0.0312982 | − | 0.999510i | \(-0.490036\pi\) | ||||
0.0312982 | + | 0.999510i | \(0.490036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.46672e6 | −0.775689 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −752910. | −0.233820 | −0.116910 | − | 0.993142i | \(-0.537299\pi\) | ||||
−0.116910 | + | 0.993142i | \(0.537299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.87830e6 | 0.882824 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 249318. | 0.0755294 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.91994e6 | 2.07070 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.61695e6 | 1.66032 | 0.830162 | − | 0.557523i | \(-0.188248\pi\) | ||||
0.830162 | + | 0.557523i | \(0.188248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.11037e6 | −0.616247 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.06608e6 | 1.17301 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.97159e6 | −0.561949 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 147852. | 0.0416377 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.35267e6 | −1.76775 | −0.883876 | − | 0.467722i | \(-0.845075\pi\) | ||||
−0.883876 | + | 0.467722i | \(0.845075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.80991e6 | 1.59759 | 0.798793 | − | 0.601606i | \(-0.205472\pi\) | ||||
0.798793 | + | 0.601606i | \(0.205472\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −563760. | −0.153195 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.28280e6 | 0.613049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.69416e6 | 1.24591 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.53679e6 | −1.19016 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.31099e6 | 0.339944 | 0.169972 | − | 0.985449i | \(-0.445632\pi\) | ||||
0.169972 | + | 0.985449i | \(0.445632\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.76127e6 | 0.964083 | 0.482041 | − | 0.876148i | \(-0.339895\pi\) | ||||
0.482041 | + | 0.876148i | \(0.339895\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.35637e6 | 0.343681 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.82877e6 | −1.46007 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.00116e6 | 0.247937 | 0.123969 | − | 0.992286i | \(-0.460438\pi\) | ||||
0.123969 | + | 0.992286i | \(0.460438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −194967. | −0.0477380 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.01542e6 | 0.972124 | 0.486062 | − | 0.873924i | \(-0.338433\pi\) | ||||
0.486062 | + | 0.873924i | \(0.338433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.16713e6 | 0.279396 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −831834. | −0.196910 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 322466. | 0.0754863 | 0.0377431 | − | 0.999287i | \(-0.487983\pi\) | ||||
0.0377431 | + | 0.999287i | \(0.487983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.92602e6 | −1.83491 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.15886e6 | 0.723243 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.38672e6 | −0.993371 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.64994e6 | −1.48945 | −0.744727 | − | 0.667369i | \(-0.767421\pi\) | ||||
−0.744727 | + | 0.667369i | \(0.767421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −989982. | −0.219329 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.17793e6 | 0.258148 | 0.129074 | − | 0.991635i | \(-0.458800\pi\) | ||||
0.129074 | + | 0.991635i | \(0.458800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.85949e6 | 1.27030 | 0.635151 | − | 0.772388i | \(-0.280938\pi\) | ||||
0.635151 | + | 0.772388i | \(0.280938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.02326e6 | −0.219460 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.28056e6 | −0.908255 | −0.454128 | − | 0.890937i | \(-0.650049\pi\) | ||||
−0.454128 | + | 0.890937i | \(0.650049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.95952e6 | 0.831209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 416862. | 0.0865845 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.83358e6 | −0.787866 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.83940e6 | 0.780782 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41604e6 | −0.284958 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.75622e6 | 1.14630 | 0.573151 | − | 0.819450i | \(-0.305721\pi\) | ||||
0.573151 | + | 0.819450i | \(0.305721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27042e7 | −2.50371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.75616e6 | 0.537572 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.84216e6 | −0.355610 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.63127e6 | −1.07593 | −0.537965 | − | 0.842967i | \(-0.680807\pi\) | ||||
−0.537965 | + | 0.842967i | \(0.680807\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.55417e6 | −0.672150 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.46885e6 | −0.649355 | −0.324677 | − | 0.945825i | \(-0.605256\pi\) | ||||
−0.324677 | + | 0.945825i | \(0.605256\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.38583e6 | −0.998011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.61287e6 | 0.295860 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.70976e6 | 0.310488 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.98837e6 | 1.07661 | 0.538304 | − | 0.842751i | \(-0.319065\pi\) | ||||
0.538304 | + | 0.842751i | \(0.319065\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.62910e6 | 0.823952 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.13058e6 | 0.551703 | 0.275852 | − | 0.961200i | \(-0.411040\pi\) | ||||
0.275852 | + | 0.961200i | \(0.411040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.54244e6 | 0.618121 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.98736e6 | 0.861689 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.11965e6 | 0.533717 | 0.266858 | − | 0.963736i | \(-0.414014\pi\) | ||||
0.266858 | + | 0.963736i | \(0.414014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.31880e6 | −0.731663 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.66504e6 | −0.279338 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 87248.0 | 0.0144956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.64704e6 | −0.600087 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.48087e6 | −0.730203 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.34939e6 | 0.701994 | 0.350997 | − | 0.936377i | \(-0.385843\pi\) | ||||
0.350997 | + | 0.936377i | \(0.385843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.08524e6 | −0.333350 | −0.166675 | − | 0.986012i | \(-0.553303\pi\) | ||||
−0.166675 | + | 0.986012i | \(0.553303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.81548e6 | −0.287470 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.06314e6 | 0.637287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 76361.0 | 0.0118640 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.74460e6 | 0.422419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.45512e7 | 2.21861 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.48154e6 | 0.223785 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.40127e6 | 0.957922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.26127e6 | −0.186997 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.16722e6 | −0.318353 | −0.159177 | − | 0.987250i | \(-0.550884\pi\) | ||||
−0.159177 | + | 0.987250i | \(0.550884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.24229e6 | 0.617449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 237044. | 0.0341852 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.02512e6 | −0.146489 | −0.0732444 | − | 0.997314i | \(-0.523335\pi\) | ||||
−0.0732444 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.16856e6 | 0.448674 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.05834e6 | −1.27107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.58656e6 | −0.498730 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.51645e6 | 0.622393 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.08401e6 | 1.24062 | 0.620311 | − | 0.784356i | \(-0.287006\pi\) | ||||
0.620311 | + | 0.784356i | \(0.287006\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.03799e6 | 0.952619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.40433e6 | −0.859145 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.45921e6 | −1.12476 | −0.562379 | − | 0.826880i | \(-0.690114\pi\) | ||||
−0.562379 | + | 0.826880i | \(0.690114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.11748e6 | 1.06979 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 787320. | 0.102847 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.16334e7 | −1.50634 | −0.753172 | − | 0.657824i | \(-0.771477\pi\) | ||||
−0.753172 | + | 0.657824i | \(0.771477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.01840e6 | −0.515779 | −0.257889 | − | 0.966174i | \(-0.583027\pi\) | ||||
−0.257889 | + | 0.966174i | \(0.583027\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.81472e6 | −0.739848 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.28991e6 | −0.541102 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.55296e6 | −0.444274 | −0.222137 | − | 0.975016i | \(-0.571303\pi\) | ||||
−0.222137 | + | 0.975016i | \(0.571303\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.43902e6 | −0.922188 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.22608e6 | −0.765199 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.16057e6 | −1.11622 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.96104e6 | −0.357729 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.29496e6 | 0.754045 | 0.377023 | − | 0.926204i | \(-0.376948\pi\) | ||||
0.377023 | + | 0.926204i | \(0.376948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.83373e6 | 0.811651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.13524e6 | −0.133696 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.01935e6 | 1.05327 | 0.526633 | − | 0.850093i | \(-0.323454\pi\) | ||||
0.526633 | + | 0.850093i | \(0.323454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.19248e6 | −0.717088 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.07230e6 | −0.123134 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.24315e7 | −1.41565 | −0.707826 | − | 0.706387i | \(-0.750324\pi\) | ||||
−0.707826 | + | 0.706387i | \(0.750324\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.74476e6 | 0.535832 | 0.267916 | − | 0.963442i | \(-0.413665\pi\) | ||||
0.267916 | + | 0.963442i | \(0.413665\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.67268e6 | 0.299332 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.31395e6 | 0.479167 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.49784e6 | 0.385326 | 0.192663 | − | 0.981265i | \(-0.438288\pi\) | ||||
0.192663 | + | 0.981265i | \(0.438288\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.28328e6 | 0.467986 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.69552e6 | 0.725573 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −358762. | −0.0385616 | −0.0192808 | − | 0.999814i | \(-0.506138\pi\) | ||||
−0.0192808 | + | 0.999814i | \(0.506138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.17309e6 | −0.551521 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.26388e7 | −1.33658 | −0.668289 | − | 0.743902i | \(-0.732973\pi\) | ||||
−0.668289 | + | 0.743902i | \(0.732973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.06705e7 | 1.11933 | 0.559664 | − | 0.828720i | \(-0.310930\pi\) | ||||
0.559664 | + | 0.828720i | \(0.310930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.86041e6 | 0.193588 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.68568e6 | 0.380450 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.68674e6 | −0.172722 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.07713e7 | −1.09421 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.79337e7 | −1.80736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.32621e7 | 1.32598 | 0.662991 | − | 0.748628i | \(-0.269287\pi\) | ||||
0.662991 | + | 0.748628i | \(0.269287\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.07458e6 | 0.304984 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.79274e6 | 0.766930 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.31553e6 | 0.226101 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.15409e6 | 0.111812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.29879e6 | 0.701626 | 0.350813 | − | 0.936446i | \(-0.385905\pi\) | ||||
0.350813 | + | 0.936446i | \(0.385905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.97747e6 | −0.188618 | −0.0943088 | − | 0.995543i | \(-0.530064\pi\) | ||||
−0.0943088 | + | 0.995543i | \(0.530064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.50207e6 | −0.236810 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −272792. | −0.0256195 | −0.0128098 | − | 0.999918i | \(-0.504078\pi\) | ||||
−0.0128098 | + | 0.999918i | \(0.504078\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.77552e7 | 1.65468 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.23136e6 | −0.298836 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.13845e6 | 0.379799 | 0.189900 | − | 0.981803i | \(-0.439184\pi\) | ||||
0.189900 | + | 0.981803i | \(0.439184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.33044e7 | 1.21169 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.91519e6 | −0.263484 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 445812. | 0.0399888 | 0.0199944 | − | 0.999800i | \(-0.493635\pi\) | ||||
0.0199944 | + | 0.999800i | \(0.493635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.65881e6 | −0.325714 | −0.162857 | − | 0.986650i | \(-0.552071\pi\) | ||||
−0.162857 | + | 0.986650i | \(0.552071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.17576e7 | 1.03880 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.04150e7 | −0.913286 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.01212e7 | 0.880884 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.70779e6 | −0.406679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.04978e7 | 1.75753 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.42444e7 | −1.21229 | −0.606147 | − | 0.795353i | \(-0.707286\pi\) | ||||
−0.606147 | + | 0.795353i | \(0.707286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.22545e6 | −0.103523 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.33128e7 | −1.11634 | −0.558170 | − | 0.829727i | \(-0.688496\pi\) | ||||
−0.558170 | + | 0.829727i | \(0.688496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.81736e6 | −0.484230 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.29351e6 | 0.767913 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.49468e6 | −0.122601 | −0.0613007 | − | 0.998119i | \(-0.519525\pi\) | ||||
−0.0613007 | + | 0.998119i | \(0.519525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.91047e6 | −0.725561 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 453798. | 0.0366835 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.68177e7 | 1.34964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.11320e7 | −0.886910 | −0.443455 | − | 0.896297i | \(-0.646247\pi\) | ||||
−0.443455 | + | 0.896297i | \(0.646247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.09328e6 | 0.402870 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 624264. | 0.0490237 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.05411e7 | 1.60156 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.91927e6 | −0.690457 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.52327e7 | −1.17080 | −0.585398 | − | 0.810746i | \(-0.699062\pi\) | ||||
−0.585398 | + | 0.810746i | \(0.699062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.01625e7 | −2.30186 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.38032e6 | −0.180369 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.11866e7 | 0.841688 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.59921e6 | −0.642455 | −0.321228 | − | 0.947002i | \(-0.604095\pi\) | ||||
−0.321228 | + | 0.947002i | \(0.604095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.42093e6 | −0.179601 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.63558e6 | −0.562495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.91553e7 | −1.40128 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.63378e6 | 0.336618 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.84891e6 | −0.205521 | −0.102761 | − | 0.994706i | \(-0.532768\pi\) | ||||
−0.102761 | + | 0.994706i | \(0.532768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 275520. | 0.0197385 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.32448e6 | 0.307672 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.66685e6 | −0.471059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.11615e6 | −0.569527 | −0.284763 | − | 0.958598i | \(-0.591915\pi\) | ||||
−0.284763 | + | 0.958598i | \(0.591915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.93513e6 | 0.687670 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.14038e7 | −0.783954 | −0.391977 | − | 0.919975i | \(-0.628209\pi\) | ||||
−0.391977 | + | 0.919975i | \(0.628209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −823194. | −0.0562062 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.72899e7 | 1.17253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.28780e6 | −0.154102 | −0.0770509 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770509 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.97749e7 | 1.32303 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.92359e7 | −1.94287 | −0.971437 | − | 0.237296i | \(-0.923739\pi\) | ||||
−0.971437 | + | 0.237296i | \(0.923739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.51219e6 | −0.231839 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.20260e6 | −0.275561 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.67856e6 | 0.304725 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71311e7 | 1.10837 | 0.554186 | − | 0.832393i | \(-0.313030\pi\) | ||||
0.554186 | + | 0.832393i | \(0.313030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.91434e6 | −0.444389 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.33374e7 | 0.851537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.31732e6 | 0.210401 | 0.105200 | − | 0.994451i | \(-0.466452\pi\) | ||||
0.105200 | + | 0.994451i | \(0.466452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.20352e7 | 0.758316 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.28948e7 | 0.807146 | 0.403573 | − | 0.914947i | \(-0.367768\pi\) | ||||
0.403573 | + | 0.914947i | \(0.367768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 748560. | 0.0465495 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.17992e6 | −0.258235 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.25964e7 | −2.00070 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.87622e7 | 1.14411 | 0.572056 | − | 0.820214i | \(-0.306146\pi\) | ||||
0.572056 | + | 0.820214i | \(0.306146\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.84546e6 | 0.172392 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.84442e6 | 0.411991 | 0.205996 | − | 0.978553i | \(-0.433957\pi\) | ||||
0.205996 | + | 0.978553i | \(0.433957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.02955e6 | 0.300798 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.42625e7 | 0.847505 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.45478e7 | 2.03975 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.46595e6 | 0.437983 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.89121e6 | 0.168529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.76008e6 | 0.101943 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.91272e7 | −1.67634 | −0.838170 | − | 0.545409i | \(-0.816374\pi\) | ||||
−0.838170 | + | 0.545409i | \(0.816374\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.19715e7 | −0.684631 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.56342e7 | 1.45673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.76315e7 | −2.12505 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.97884e6 | −0.335505 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.12485e7 | 1.74254 | 0.871272 | − | 0.490800i | \(-0.163295\pi\) | ||||
0.871272 | + | 0.490800i | \(0.163295\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.45168e6 | 0.523772 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.48783e6 | 0.137006 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.88588e7 | −1.03211 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.16371e7 | 0.632930 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.31331e6 | 0.395303 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.27324e7 | −0.683972 | −0.341986 | − | 0.939705i | \(-0.611099\pi\) | ||||
−0.341986 | + | 0.939705i | \(0.611099\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.65194e7 | 1.41583 | 0.707916 | − | 0.706297i | \(-0.249636\pi\) | ||||
0.707916 | + | 0.706297i | \(0.249636\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.79312e7 | −0.951442 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.50065e7 | −0.791381 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.67097e7 | 0.875820 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.35064e6 | −0.487115 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.84134e7 | −1.47118 | −0.735590 | − | 0.677427i | \(-0.763095\pi\) | ||||
−0.735590 | + | 0.677427i | \(0.763095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.21639e7 | 1.65527 | 0.827637 | − | 0.561264i | \(-0.189685\pi\) | ||||
0.827637 | + | 0.561264i | \(0.189685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.92760e6 | −0.405515 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.01436e7 | −1.53261 | −0.766304 | − | 0.642478i | \(-0.777906\pi\) | ||||
−0.766304 | + | 0.642478i | \(0.777906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.01164e7 | −1.01663 | −0.508315 | − | 0.861171i | \(-0.669732\pi\) | ||||
−0.508315 | + | 0.861171i | \(0.669732\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.20521e6 | 0.161010 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.26871e6 | 0.163216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.95451e7 | 0.970110 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.18117e6 | −0.107616 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.20685e7 | −1.08235 | −0.541175 | − | 0.840910i | \(-0.682020\pi\) | ||||
−0.541175 | + | 0.840910i | \(0.682020\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.78199e6 | −0.233141 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.80487e6 | 0.281335 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.10577e7 | 1.01454 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.36230e7 | 0.652476 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.09469e6 | −0.290190 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.37017e7 | 1.59525 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.12740e7 | 0.530524 | 0.265262 | − | 0.964176i | \(-0.414542\pi\) | ||||
0.265262 | + | 0.964176i | \(0.414542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.03015e6 | −0.328889 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.67412e7 | −0.778634 | −0.389317 | − | 0.921104i | \(-0.627289\pi\) | ||||
−0.389317 | + | 0.921104i | \(0.627289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.26435e7 | −1.50943 | −0.754716 | − | 0.656051i | \(-0.772225\pi\) | ||||
−0.754716 | + | 0.656051i | \(0.772225\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.63361e7 | −0.751000 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.54029e7 | −1.16106 | −0.580532 | − | 0.814237i | \(-0.697156\pi\) | ||||
−0.580532 | + | 0.814237i | \(0.697156\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.89192e7 | −0.859731 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.81876e6 | 0.172534 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.56613e7 | −0.703524 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.17422e7 | −1.41772 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.92672e6 | −0.174379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.19154e7 | −0.967673 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.55846e6 | 0.156230 | 0.0781148 | − | 0.996944i | \(-0.475110\pi\) | ||||
0.0781148 | + | 0.996944i | \(0.475110\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.73340e6 | 0.162979 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.10156e7 | −1.78037 | −0.890184 | − | 0.455602i | \(-0.849424\pi\) | ||||
−0.890184 | + | 0.455602i | \(0.849424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.51736e7 | 1.51815 | 0.759075 | − | 0.651004i | \(-0.225652\pi\) | ||||
0.759075 | + | 0.651004i | \(0.225652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.15883e7 | 0.497351 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.33071e7 | 1.84821 | 0.924103 | − | 0.382144i | \(-0.124814\pi\) | ||||
0.924103 | + | 0.382144i | \(0.124814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.46086e7 | 1.04432 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.43796e6 | 0.145080 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.58966e7 | 0.667078 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.70276e7 | 1.12785 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.20952e7 | −0.916890 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.18663e7 | −0.489683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.37406e7 | 0.974269 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.90128e6 | −0.322462 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.79119e7 | 0.726977 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.33192e7 | −0.537599 | −0.268800 | − | 0.963196i | \(-0.586627\pi\) | ||||
−0.268800 | + | 0.963196i | \(0.586627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.55098e6 | 0.303105 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.92578e6 | 0.356328 | 0.178164 | − | 0.984001i | \(-0.442984\pi\) | ||||
0.178164 | + | 0.984001i | \(0.442984\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.71872e7 | −1.07941 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.33784e7 | 0.528263 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.20139e7 | 1.64995 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.13982e7 | 1.61694 | 0.808468 | − | 0.588540i | \(-0.200297\pi\) | ||||
0.808468 | + | 0.588540i | \(0.200297\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.25825e6 | −0.126571 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.37066e7 | −0.529572 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.21993e7 | −0.853070 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 185976. | 0.00710817 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.42481e7 | 1.30196 | 0.650980 | − | 0.759095i | \(-0.274358\pi\) | ||||
0.650980 | + | 0.759095i | \(0.274358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.49759e6 | 0.207873 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.38907e7 | 0.522422 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.70405e7 | −1.01155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.44468e6 | 0.202593 | 0.101296 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101296 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.38802e7 | −0.513727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.54752e7 | 1.30602 | 0.653012 | − | 0.757347i | \(-0.273505\pi\) | ||||
0.653012 | + | 0.757347i | \(0.273505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.86016e7 | −1.41360 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.32424e6 | 0.121091 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.22505e7 | 0.443892 | 0.221946 | − | 0.975059i | \(-0.428759\pi\) | ||||
0.221946 | + | 0.975059i | \(0.428759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.46224e7 | 1.24793 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 299214. | 0.0107283 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.77139e6 | 0.170181 | 0.0850907 | − | 0.996373i | \(-0.472882\pi\) | ||||
0.0850907 | + | 0.996373i | \(0.472882\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.45510e7 | −0.871087 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.87037e7 | 0.660156 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.81383e7 | −0.987988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96771e7 | −0.687309 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.15803e6 | 0.109736 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.14092e7 | −1.08577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.31939e7 | −1.48544 | −0.742722 | − | 0.669600i | \(-0.766466\pi\) | ||||
−0.742722 | + | 0.669600i | \(0.766466\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.79150e7 | 0.955056 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.73630e7 | 0.590984 | 0.295492 | − | 0.955345i | \(-0.404516\pi\) | ||||
0.295492 | + | 0.955345i | \(0.404516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.97136e6 | 0.0667550 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.45541e7 | 0.490313 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.71680e7 | −0.575416 | −0.287708 | − | 0.957718i | \(-0.592893\pi\) | ||||
−0.287708 | + | 0.957718i | \(0.592893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.60941e7 | 0.536674 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 505278. | 0.0167632 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.53993e7 | 1.16845 | 0.584225 | − | 0.811592i | \(-0.301398\pi\) | ||||
0.584225 | + | 0.811592i | \(0.301398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.79324e6 | −0.157412 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.51680e6 | −0.245607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.86704e7 | −0.606965 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.23340e7 | −1.69278 | −0.846389 | − | 0.532566i | \(-0.821228\pi\) | ||||
−0.846389 | + | 0.532566i | \(0.821228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.44664e7 | −0.465573 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.52747e6 | −0.144977 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.21035e6 | −0.229730 | −0.114865 | − | 0.993381i | \(-0.536644\pi\) | ||||
−0.114865 | + | 0.993381i | \(0.536644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.62717e6 | 0.305200 |
(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 | 24.6.a.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 72.6.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 48.6.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 600.6.f.h.49.1 | 2 | |||
5.3 | odd | 4 | 600.6.f.h.49.2 | 2 | |||
5.4 | even | 2 | 600.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 192.6.a.j.1.1 | 1 | |||
8.5 | even | 2 | 192.6.a.b.1.1 | 1 | |||
12.11 | even | 2 | 144.6.a.d.1.1 | 1 | |||
16.3 | odd | 4 | 768.6.d.m.385.1 | 2 | |||
16.5 | even | 4 | 768.6.d.f.385.1 | 2 | |||
16.11 | odd | 4 | 768.6.d.m.385.2 | 2 | |||
16.13 | even | 4 | 768.6.d.f.385.2 | 2 | |||
24.5 | odd | 2 | 576.6.a.bb.1.1 | 1 | |||
24.11 | even | 2 | 576.6.a.ba.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.6.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
48.6.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
72.6.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
144.6.a.d.1.1 | 1 | 12.11 | even | 2 | |||
192.6.a.b.1.1 | 1 | 8.5 | even | 2 | |||
192.6.a.j.1.1 | 1 | 8.3 | odd | 2 | |||
576.6.a.ba.1.1 | 1 | 24.11 | even | 2 | |||
576.6.a.bb.1.1 | 1 | 24.5 | odd | 2 | |||
600.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
600.6.f.h.49.1 | 2 | 5.2 | odd | 4 | |||
600.6.f.h.49.2 | 2 | 5.3 | odd | 4 | |||
768.6.d.f.385.1 | 2 | 16.5 | even | 4 | |||
768.6.d.f.385.2 | 2 | 16.13 | even | 4 | |||
768.6.d.m.385.1 | 2 | 16.3 | odd | 4 | |||
768.6.d.m.385.2 | 2 | 16.11 | odd | 4 |