Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,8,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(4.99816040775\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 | ||||||||
\(3\) | −44.0000 | −0.940867 | −0.470434 | − | 0.882435i | \(-0.655902\pi\) | ||||
−0.470434 | + | 0.882435i | \(0.655902\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 430.000 | 1.53841 | 0.769207 | − | 0.638999i | \(-0.220651\pi\) | ||||
0.769207 | + | 0.638999i | \(0.220651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1224.00 | 1.34877 | 0.674386 | − | 0.738379i | \(-0.264409\pi\) | ||||
0.674386 | + | 0.738379i | \(0.264409\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −251.000 | −0.114769 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3164.00 | 0.716741 | 0.358370 | − | 0.933580i | \(-0.383333\pi\) | ||||
0.358370 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6118.00 | 0.772339 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18920.0 | −1.44744 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16270.0 | −0.803186 | −0.401593 | − | 0.915818i | \(-0.631543\pi\) | ||||
−0.401593 | + | 0.915818i | \(0.631543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5476.00 | 0.183158 | 0.0915790 | − | 0.995798i | \(-0.470809\pi\) | ||||
0.0915790 | + | 0.995798i | \(0.470809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −53856.0 | −1.26901 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1576.00 | −0.0270090 | −0.0135045 | − | 0.999909i | \(-0.504299\pi\) | ||||
−0.0135045 | + | 0.999909i | \(0.504299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 106775. | 1.36672 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 107272. | 1.04885 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 122838. | 0.935276 | 0.467638 | − | 0.883920i | \(-0.345105\pi\) | ||||
0.467638 | + | 0.883920i | \(0.345105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −251360. | −1.51541 | −0.757705 | − | 0.652597i | \(-0.773679\pi\) | ||||
−0.757705 | + | 0.652597i | \(0.773679\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −139216. | −0.674358 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 526320. | 2.07497 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −52338.0 | −0.169868 | −0.0849339 | − | 0.996387i | \(-0.527068\pi\) | ||||
−0.0849339 | + | 0.996387i | \(0.527068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −269192. | −0.726668 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −319398. | −0.723750 | −0.361875 | − | 0.932227i | \(-0.617863\pi\) | ||||
−0.361875 | + | 0.932227i | \(0.617863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −710788. | −1.36333 | −0.681664 | − | 0.731665i | \(-0.738743\pi\) | ||||
−0.681664 | + | 0.731665i | \(0.738743\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −107930. | −0.176562 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −284112. | −0.399160 | −0.199580 | − | 0.979882i | \(-0.563958\pi\) | ||||
−0.199580 | + | 0.979882i | \(0.563958\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 674633. | 0.819184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 715880. | 0.755692 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 296062. | 0.273160 | 0.136580 | − | 0.990629i | \(-0.456389\pi\) | ||||
0.136580 | + | 0.990629i | \(0.456389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.36052e6 | 1.10264 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −240944. | −0.172327 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 897548. | 0.568952 | 0.284476 | − | 0.958683i | \(-0.408180\pi\) | ||||
0.284476 | + | 0.958683i | \(0.408180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −884810. | −0.499109 | −0.249555 | − | 0.968361i | \(-0.580284\pi\) | ||||
−0.249555 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −307224. | −0.154797 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.63074e6 | 1.18818 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.65969e6 | −1.89276 | −0.946380 | − | 0.323057i | \(-0.895290\pi\) | ||||
−0.946380 | + | 0.323057i | \(0.895290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 69344.0 | 0.0254119 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.71079e6 | 0.898860 | 0.449430 | − | 0.893316i | \(-0.351627\pi\) | ||||
0.449430 | + | 0.893316i | \(0.351627\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.67085e6 | −1.70615 | −0.853077 | − | 0.521784i | \(-0.825267\pi\) | ||||
−0.853077 | + | 0.521784i | \(0.825267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.69810e6 | −1.28590 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.87274e6 | 0.966719 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.12418e6 | 1.16931 | 0.584654 | − | 0.811282i | \(-0.301230\pi\) | ||||
0.584654 | + | 0.811282i | \(0.301230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.17103e6 | −0.872059 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.56356e6 | 0.300151 | 0.150076 | − | 0.988675i | \(-0.452048\pi\) | ||||
0.150076 | + | 0.988675i | \(0.452048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.99610e6 | −1.23563 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.40487e6 | −0.879970 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.16057e7 | 1.74504 | 0.872520 | − | 0.488579i | \(-0.162484\pi\) | ||||
0.872520 | + | 0.488579i | \(0.162484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.48843e6 | 1.04171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.10598e7 | 1.42580 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.35468e6 | 0.281773 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.09316e7 | 1.21614 | 0.608070 | − | 0.793884i | \(-0.291944\pi\) | ||||
0.608070 | + | 0.793884i | \(0.291944\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −794164. | −0.0822597 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.47908e7 | −1.42846 | −0.714230 | − | 0.699911i | \(-0.753223\pi\) | ||||
−0.714230 | + | 0.699911i | \(0.753223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.76105e6 | −0.789998 | −0.394999 | − | 0.918682i | \(-0.629255\pi\) | ||||
−0.394999 | + | 0.918682i | \(0.629255\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.31581e7 | −1.95227 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.29510e6 | 0.338946 | 0.169473 | − | 0.985535i | \(-0.445794\pi\) | ||||
0.169473 | + | 0.985535i | \(0.445794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.74465e6 | 0.276961 | 0.138480 | − | 0.990365i | \(-0.455778\pi\) | ||||
0.138480 | + | 0.990365i | \(0.455778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.30287e6 | 0.159823 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.90760e6 | 0.254763 | 0.127381 | − | 0.991854i | \(-0.459343\pi\) | ||||
0.127381 | + | 0.991854i | \(0.459343\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −677680. | −0.0415511 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.53562e6 | −0.0886406 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.99145e7 | −1.08331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47628e6 | −0.486283 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.40535e7 | 0.680953 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.23195e7 | 0.564167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.23320e7 | −1.83382 | −0.916909 | − | 0.399097i | \(-0.869324\pi\) | ||||
−0.916909 | + | 0.399097i | \(0.869324\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.12747e7 | 1.28271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.72098e7 | 1.05749 | 0.528745 | − | 0.848781i | \(-0.322663\pi\) | ||||
0.528745 | + | 0.848781i | \(0.322663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.70262e6 | 0.247038 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.61270e7 | 1.61357 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.01235e7 | −1.66540 | −0.832702 | − | 0.553721i | \(-0.813207\pi\) | ||||
−0.832702 | + | 0.553721i | \(0.813207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.22073e7 | 0.385539 | 0.192770 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192770 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.25009e7 | 0.375557 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.93574e7 | 0.553567 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.28203e7 | 1.43884 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.96839e7 | −0.770743 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.66478e7 | −1.15526 | −0.577629 | − | 0.816299i | \(-0.696022\pi\) | ||||
−0.577629 | + | 0.816299i | \(0.696022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.04359e7 | 0.719395 | 0.359697 | − | 0.933069i | \(-0.382880\pi\) | ||||
0.359697 | + | 0.933069i | \(0.382880\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.08377e6 | 0.0921810 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.08085e8 | −2.33133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.24060e6 | 0.128700 | 0.0643498 | − | 0.997927i | \(-0.479503\pi\) | ||||
0.0643498 | + | 0.997927i | \(0.479503\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.30267e7 | −0.257007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.92902e6 | −0.0364290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.74060e6 | 0.0495665 | 0.0247833 | − | 0.999693i | \(-0.492110\pi\) | ||||
0.0247833 | + | 0.999693i | \(0.492110\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.98629e7 | −1.03744 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.27680e7 | −0.710578 | −0.355289 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355289 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.53186e7 | −0.403493 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.37448e6 | −0.0210209 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.21411e7 | 1.05931 | 0.529653 | − | 0.848214i | \(-0.322322\pi\) | ||||
0.529653 | + | 0.848214i | \(0.322322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.30693e8 | 1.84339 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.94921e7 | −0.535308 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.21119e7 | 0.939769 | 0.469885 | − | 0.882728i | \(-0.344296\pi\) | ||||
0.469885 | + | 0.882728i | \(0.344296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.44881e7 | 0.181608 | 0.0908041 | − | 0.995869i | \(-0.471056\pi\) | ||||
0.0908041 | + | 0.995869i | \(0.471056\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.89316e7 | 0.469595 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.25053e7 | −0.261327 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.14783e7 | −0.575676 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.31301e8 | 1.41466 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.10503e8 | −1.14751 | −0.573755 | − | 0.819027i | \(-0.694514\pi\) | ||||
−0.573755 | + | 0.819027i | \(0.694514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.43354e6 | 0.0343788 | 0.0171894 | − | 0.999852i | \(-0.494528\pi\) | ||||
0.0171894 | + | 0.999852i | \(0.494528\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.15753e8 | −1.11792 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.77557e7 | −0.351844 | −0.175922 | − | 0.984404i | \(-0.556291\pi\) | ||||
−0.175922 | + | 0.984404i | \(0.556291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.37979e8 | 1.24116 | 0.620580 | − | 0.784143i | \(-0.286897\pi\) | ||||
0.620580 | + | 0.784143i | \(0.286897\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.05026e8 | 1.78084 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.50354e8 | 1.26147 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.37341e8 | −1.11343 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 395576. | 0.00309980 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.73261e7 | 0.131277 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.05441e8 | −0.772720 | −0.386360 | − | 0.922348i | \(-0.626268\pi\) | ||||
−0.386360 | + | 0.922348i | \(0.626268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.19275e8 | −0.845708 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.05639e8 | −2.09736 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.07665e8 | −2.04394 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.49518e8 | 1.60527 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.95399e7 | −0.620332 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.32420e8 | −0.799625 | −0.399812 | − | 0.916597i | \(-0.630925\pi\) | ||||
−0.399812 | + | 0.916597i | \(0.630925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.68005e7 | −0.156857 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.23501e8 | 1.26820 | 0.634102 | − | 0.773249i | \(-0.281370\pi\) | ||||
0.634102 | + | 0.773249i | \(0.281370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.58523e8 | 1.97284 | 0.986422 | − | 0.164228i | \(-0.0525132\pi\) | ||||
0.986422 | + | 0.164228i | \(0.0525132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.70400e8 | −0.909554 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.05337e8 | 1.06346 | 0.531731 | − | 0.846913i | \(-0.321542\pi\) | ||||
0.531731 | + | 0.846913i | \(0.321542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.22168e8 | −0.614074 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.25464e8 | −1.10016 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.27881e8 | 0.605917 | 0.302959 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302959 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.13448e8 | 0.982275 | 0.491138 | − | 0.871082i | \(-0.336581\pi\) | ||||
0.491138 | + | 0.871082i | \(0.336581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.10785e7 | −0.228358 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.90092e8 | 1.26024 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.35022e7 | 0.141460 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.87965e7 | −0.282402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.81046e8 | 1.12181 | 0.560906 | − | 0.827880i | \(-0.310453\pi\) | ||||
0.560906 | + | 0.827880i | \(0.310453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.98646e6 | −0.0193585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.07828e8 | 1.16257 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.11663e8 | −1.51278 | −0.756389 | − | 0.654122i | \(-0.773038\pi\) | ||||
−0.756389 | + | 0.654122i | \(0.773038\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.40617e7 | −0.229113 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.08323e7 | −0.107341 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.01818e8 | 0.345127 | 0.172563 | − | 0.984998i | \(-0.444795\pi\) | ||||
0.172563 | + | 0.984998i | \(0.444795\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.27307e8 | 0.420233 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.10650e8 | −1.64185 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.30511e6 | −0.0166173 | −0.00830867 | − | 0.999965i | \(-0.502645\pi\) | ||||
−0.00830867 | + | 0.999965i | \(0.502645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.51186e8 | −0.766660 | −0.383330 | − | 0.923611i | \(-0.625223\pi\) | ||||
−0.383330 | + | 0.923611i | \(0.625223\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.29491e8 | −0.980109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.37836e8 | 0.979584 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.19651e8 | −0.338251 | −0.169125 | − | 0.985595i | \(-0.554094\pi\) | ||||
−0.169125 | + | 0.985595i | \(0.554094\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.30914e7 | 0.173922 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.21696e8 | 1.67150 | 0.835749 | − | 0.549111i | \(-0.185034\pi\) | ||||
0.835749 | + | 0.549111i | \(0.185034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.41726e8 | −0.896243 | −0.448122 | − | 0.893973i | \(-0.647907\pi\) | ||||
−0.448122 | + | 0.893973i | \(0.647907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.03606e8 | −0.265111 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.90943e8 | −0.976173 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.45626e8 | −0.354892 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.80991e8 | −1.14423 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.71317e6 | 0.00862398 | 0.00431199 | − | 0.999991i | \(-0.498627\pi\) | ||||
0.00431199 | + | 0.999991i | \(0.498627\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.85946e8 | 0.875284 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.39409e8 | 0.751753 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.64197e6 | −0.0208601 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.70005e8 | −1.83882 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.50797e8 | 1.34399 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.80468e8 | −0.767837 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.23276e7 | 0.0637659 | 0.0318830 | − | 0.999492i | \(-0.489850\pi\) | ||||
0.0318830 | + | 0.999492i | \(0.489850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.85486e8 | 0.743283 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.26997e8 | 1.55899 | 0.779494 | − | 0.626410i | \(-0.215476\pi\) | ||||
0.779494 | + | 0.626410i | \(0.215476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.53027e8 | 0.650732 | 0.325366 | − | 0.945588i | \(-0.394513\pi\) | ||||
0.325366 | + | 0.945588i | \(0.394513\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.32106e8 | −0.238142 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.30187e8 | 1.64007 | 0.820036 | − | 0.572312i | \(-0.193953\pi\) | ||||
0.820036 | + | 0.572312i | \(0.193953\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.88659e8 | 0.670350 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.88984e8 | −0.318903 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.90945e7 | −0.147110 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.53249e8 | 1.05557 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.64764e8 | −0.260583 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.47753e8 | −0.538376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.21754e8 | 0.487670 | 0.243835 | − | 0.969817i | \(-0.421594\pi\) | ||||
0.243835 | + | 0.969817i | \(0.421594\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.31368e7 | 0.0194956 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00367e9 | −2.91185 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.47705e8 | −0.352558 | −0.176279 | − | 0.984340i | \(-0.556406\pi\) | ||||
−0.176279 | + | 0.984340i | \(0.556406\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.71934e8 | −0.239698 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.95303e8 | −1.08616 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.82266e8 | −0.243880 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.98179e7 | 0.0390940 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.23076e8 | 0.286615 | 0.143308 | − | 0.989678i | \(-0.454226\pi\) | ||||
0.143308 | + | 0.989678i | \(0.454226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.57087e8 | −0.701510 | −0.350755 | − | 0.936467i | \(-0.614075\pi\) | ||||
−0.350755 | + | 0.936467i | \(0.614075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.56290e8 | 0.810067 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.64509e8 | 0.683061 | 0.341530 | − | 0.939871i | \(-0.389055\pi\) | ||||
0.341530 | + | 0.939871i | \(0.389055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.16564e9 | 1.38282 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.76237e8 | 1.01926 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.66005e9 | −1.89361 | −0.946803 | − | 0.321813i | \(-0.895708\pi\) | ||||
−0.946803 | + | 0.321813i | \(0.895708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.63885e8 | −0.966453 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.16956e8 | 0.457527 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.43847e9 | −2.62477 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00412e8 | 0.739643 | 0.369822 | − | 0.929103i | \(-0.379419\pi\) | ||||
0.369822 | + | 0.929103i | \(0.379419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.01689e7 | 0.0830642 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.62380e8 | 0.368430 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33445e8 | 0.432467 | 0.216233 | − | 0.976342i | \(-0.430623\pi\) | ||||
0.216233 | + | 0.976342i | \(0.430623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.42058e8 | −0.530807 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.51523e8 | 0.722350 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.38421e9 | −1.30606 | −0.653032 | − | 0.757330i | \(-0.726504\pi\) | ||||
−0.653032 | + | 0.757330i | \(0.726504\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.86261e9 | 1.72538 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.70821e8 | 0.428213 | 0.214107 | − | 0.976810i | \(-0.431316\pi\) | ||||
0.214107 | + | 0.976810i | \(0.431316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.66528e9 | 1.48722 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.78408e8 | 0.156468 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.52817e7 | 0.0131628 | 0.00658140 | − | 0.999978i | \(-0.497905\pi\) | ||||
0.00658140 | + | 0.999978i | \(0.497905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.56415e7 | 0.0216933 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.19723e9 | −0.994957 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.20340e9 | 1.79888 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.02601e9 | 0.822969 | 0.411485 | − | 0.911417i | \(-0.365010\pi\) | ||||
0.411485 | + | 0.911417i | \(0.365010\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.94915e8 | −0.232430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.18349e8 | −0.169101 | −0.0845504 | − | 0.996419i | \(-0.526945\pi\) | ||||
−0.0845504 | + | 0.996419i | \(0.526945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.53782e9 | −1.17041 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.79354e9 | −1.34159 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.65597e8 | −0.121751 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50779e8 | 0.542601 | 0.271300 | − | 0.962495i | \(-0.412546\pi\) | ||||
0.271300 | + | 0.962495i | \(0.412546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.20544e9 | 1.56692 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.09860e9 | 0.767386 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.72329e8 | 0.461757 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.37122e8 | −0.362741 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.38283e8 | −0.158250 | −0.0791251 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791251 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.23640e9 | −0.807552 | −0.403776 | − | 0.914858i | \(-0.632303\pi\) | ||||
−0.403776 | + | 0.914858i | \(0.632303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.13121e7 | 0.0458112 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.73723e9 | −1.09773 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.08301e9 | −0.673184 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.51723e8 | −0.520833 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.24030e9 | −1.34783 | −0.673915 | − | 0.738809i | \(-0.735389\pi\) | ||||
−0.673915 | + | 0.738809i | \(0.735389\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.19040e9 | −0.704670 | −0.352335 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352335 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.32409e9 | −1.35376 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.63018e6 | −0.00494692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.38822e9 | 0.783127 | 0.391564 | − | 0.920151i | \(-0.371934\pi\) | ||||
0.391564 | + | 0.920151i | \(0.371934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.69333e8 | −0.0940170 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.85788e9 | −1.56182 | −0.780911 | − | 0.624642i | \(-0.785245\pi\) | ||||
−0.780911 | + | 0.624642i | \(0.785245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.99044e9 | 2.68460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.05250e9 | 1.08694 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.96866e7 | 0.0154774 | 0.00773870 | − | 0.999970i | \(-0.497537\pi\) | ||||
0.00773870 | + | 0.999970i | \(0.497537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.01058e9 | −0.518741 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.33918e9 | −0.676855 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.22003e9 | 1.60258 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.83015e9 | 0.896974 | 0.448487 | − | 0.893789i | \(-0.351963\pi\) | ||||
0.448487 | + | 0.893789i | \(0.351963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.74532e9 | −0.842422 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.13408e8 | −0.386683 | −0.193342 | − | 0.981132i | \(-0.561933\pi\) | ||||
−0.193342 | + | 0.981132i | \(0.561933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.01303e9 | 0.474337 | 0.237168 | − | 0.971469i | \(-0.423781\pi\) | ||||
0.237168 | + | 0.971469i | \(0.423781\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.75573e9 | 2.19347 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.80251e9 | 1.72767 | 0.863837 | − | 0.503771i | \(-0.168055\pi\) | ||||
0.863837 | + | 0.503771i | \(0.168055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.70346e9 | −2.55290 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.74586e8 | −0.121089 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.24893e9 | −0.977153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.84700e8 | 0.250326 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.43116e7 | −0.0313503 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.67385e8 | 0.360610 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.20204e8 | −0.131195 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.48771e7 | 0.0342748 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.70060e9 | 1.87093 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.30043e9 | −0.510195 | −0.255098 | − | 0.966915i | \(-0.582108\pi\) | ||||
−0.255098 | + | 0.966915i | \(0.582108\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.20586e8 | −0.0466355 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.88652e9 | −0.719244 | −0.359622 | − | 0.933098i | \(-0.617094\pi\) | ||||
−0.359622 | + | 0.933098i | \(0.617094\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.99857e9 | −0.751201 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.41491e8 | −0.126550 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.31801e9 | 1.21236 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.81787e9 | 1.37553 | 0.687763 | − | 0.725935i | \(-0.258593\pi\) | ||||
0.687763 | + | 0.725935i | \(0.258593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.88179e9 | 0.668559 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.47974e8 | 0.156951 | 0.0784757 | − | 0.996916i | \(-0.474995\pi\) | ||||
0.0784757 | + | 0.996916i | \(0.474995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.36006e9 | −2.19756 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.11402e9 | 0.379633 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.50519e9 | 1.51426 | 0.757131 | − | 0.653263i | \(-0.226600\pi\) | ||||
0.757131 | + | 0.653263i | \(0.226600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.94113e9 | −2.30121 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.87421e8 | 0.192105 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.76725e9 | −1.21534 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.98930e8 | −0.286094 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.17421e9 | −0.996666 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.27301e8 | 0.132374 | 0.0661868 | − | 0.997807i | \(-0.478917\pi\) | ||||
0.0661868 | + | 0.997807i | \(0.478917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.14705e8 | −0.249026 | −0.124513 | − | 0.992218i | \(-0.539737\pi\) | ||||
−0.124513 | + | 0.992218i | \(0.539737\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.75047e9 | −1.73439 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.08963e9 | 1.21716 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.40234e9 | −0.999271 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.25285e8 | −0.0652981 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.95408e9 | −0.558980 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.84689e9 | 0.521439 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.17292e9 | −0.884198 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.13454e9 | 0.587142 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.17489e9 | 1.40511 | 0.702556 | − | 0.711629i | \(-0.252042\pi\) | ||||
0.702556 | + | 0.711629i | \(0.252042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.37475e8 | −0.170869 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.61020e9 | 0.426080 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.45830e9 | 1.68718 | 0.843592 | − | 0.536984i | \(-0.180436\pi\) | ||||
0.843592 | + | 0.536984i | \(0.180436\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.22087e8 | 0.0572823 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.72661e8 | 0.171303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.27199e9 | 1.57713 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.90235e8 | 0.245874 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.83562e9 | −1.18566 | −0.592829 | − | 0.805328i | \(-0.701989\pi\) | ||||
−0.592829 | + | 0.805328i | \(0.701989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.34860e9 | −1.05295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.26504e9 | 0.541635 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.16508e9 | −0.275154 | −0.137577 | − | 0.990491i | \(-0.543931\pi\) | ||||
−0.137577 | + | 0.990491i | \(0.543931\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.68027e9 | 0.391931 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.10534e9 | −1.17621 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.79201e9 | 0.635367 | 0.317683 | − | 0.948197i | \(-0.397095\pi\) | ||||
0.317683 | + | 0.948197i | \(0.397095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.14069e9 | 1.60514 | 0.802572 | − | 0.596555i | \(-0.203464\pi\) | ||||
0.802572 | + | 0.596555i | \(0.203464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.86212e9 | 1.07965 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.68277e8 | −0.0369138 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.44897e7 | 0.00964148 | 0.00482074 | − | 0.999988i | \(-0.498466\pi\) | ||||
0.00482074 | + | 0.999988i | \(0.498466\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.51076e8 | −0.0323459 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.91379e9 | 0.404835 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.36740e8 | 0.195785 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.60316e8 | −0.136366 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.21422e8 | 0.0859972 | 0.0429986 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429986 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.37645e9 | −0.277559 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.66125e9 | 0.331039 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.60547e9 | −0.906948 | −0.453474 | − | 0.891270i | \(-0.649815\pi\) | ||||
−0.453474 | + | 0.891270i | \(0.649815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.56323e9 | −1.66659 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.07109e9 | −1.16777 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.96438e8 | 0.113389 | 0.0566946 | − | 0.998392i | \(-0.481944\pi\) | ||||
0.0566946 | + | 0.998392i | \(0.481944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.18925e9 | 0.411372 | 0.205686 | − | 0.978618i | \(-0.434058\pi\) | ||||
0.205686 | + | 0.978618i | \(0.434058\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.16958e9 | 0.217230 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.07480e9 | −0.748105 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.88184e8 | −0.179340 | −0.0896701 | − | 0.995972i | \(-0.528581\pi\) | ||||
−0.0896701 | + | 0.995972i | \(0.528581\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.61556e9 | −1.18688 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.73820e9 | −0.308287 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.18993e8 | 0.0559332 | 0.0279666 | − | 0.999609i | \(-0.491097\pi\) | ||||
0.0279666 | + | 0.999609i | \(0.491097\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.04301e9 | 1.04759 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.83798e9 | 0.657816 | 0.328908 | − | 0.944362i | \(-0.393319\pi\) | ||||
0.328908 | + | 0.944362i | \(0.393319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.96834e9 | −0.503032 | −0.251516 | − | 0.967853i | \(-0.580929\pi\) | ||||
−0.251516 | + | 0.967853i | \(0.580929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.69061e8 | −0.0283284 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.42053e10 | 2.35366 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.04441e9 | −0.498796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.62347e8 | −0.123514 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.51539e8 | 0.136436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.10788e9 | −1.28471 | −0.642354 | − | 0.766408i | \(-0.722042\pi\) | ||||
−0.642354 | + | 0.766408i | \(0.722042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.63941e9 | 0.727026 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.82028e10 | −2.82117 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.12740e9 | 0.632687 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.80409e8 | −0.103161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.10357e10 | −1.65499 | −0.827495 | − | 0.561473i | \(-0.810235\pi\) | ||||
−0.827495 | + | 0.561473i | \(0.810235\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.76532e9 | −1.00358 | −0.501788 | − | 0.864991i | \(-0.667324\pi\) | ||||
−0.501788 | + | 0.864991i | \(0.667324\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.34481e10 | 1.97334 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.76242e9 | −0.981606 | −0.490803 | − | 0.871271i | \(-0.663297\pi\) | ||||
−0.490803 | + | 0.871271i | \(0.663297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.83984e9 | 0.407791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.35372e10 | 1.92308 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.17211e9 | −1.28906 | −0.644530 | − | 0.764579i | \(-0.722947\pi\) | ||||
−0.644530 | + | 0.764579i | \(0.722947\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.17002e10 | 1.62686 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.42338e9 | 0.195814 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.62299e9 | 0.765364 | 0.382682 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382682 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.39966e9 | 0.457857 | 0.228928 | − | 0.973443i | \(-0.426478\pi\) | ||||
0.228928 | + | 0.973443i | \(0.426478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.37975e9 | 0.583650 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.88213e9 | 0.380047 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.93593e8 | −0.0252609 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.82647e9 | 0.752340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.79954e9 | −0.357732 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.14073e10 | 1.44254 | 0.721271 | − | 0.692653i | \(-0.243558\pi\) | ||||
0.721271 | + | 0.692653i | \(0.243558\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.14540e10 | 1.43348 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.10086e9 | 0.384080 | 0.192040 | − | 0.981387i | \(-0.438490\pi\) | ||||
0.192040 | + | 0.981387i | \(0.438490\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.33803e10 | 1.64029 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.83405e9 | −1.19321 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.43067e9 | −0.772296 | −0.386148 | − | 0.922437i | \(-0.626195\pi\) | ||||
−0.386148 | + | 0.922437i | \(0.626195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.15531e10 | −2.56208 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.57750e10 | −1.85618 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.81131e9 | 0.210972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.53885e9 | 0.523326 | 0.261663 | − | 0.965159i | \(-0.415729\pi\) | ||||
0.261663 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.72057e8 | −0.110949 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.24915e9 | 0.593119 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.19661e9 | 0.581306 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.03484e9 | −1.00058 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.84396e9 | −0.860047 | −0.430024 | − | 0.902818i | \(-0.641495\pi\) | ||||
−0.430024 | + | 0.902818i | \(0.641495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.86603e8 | −0.0311126 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.37540e9 | 0.577762 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.81040e10 | −1.92666 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.05387e9 | 0.427177 | 0.213588 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213588 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.28617e9 | −0.134201 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.96143e8 | 0.0409297 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.32366e9 | 0.851615 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.62676e9 | −0.570087 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.84938e9 | −0.787561 | −0.393780 | − | 0.919205i | \(-0.628833\pi\) | ||||
−0.393780 | + | 0.919205i | \(0.628833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.07235e10 | −1.06553 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.39173e9 | −0.924190 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.31160e10 | 1.27826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.44318e9 | −0.621913 | −0.310957 | − | 0.950424i | \(-0.600649\pi\) | ||||
−0.310957 | + | 0.950424i | \(0.600649\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.13695e10 | 1.08691 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.15645e10 | 1.09501 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.48714e9 | 0.889757 | 0.444879 | − | 0.895591i | \(-0.353247\pi\) | ||||
0.444879 | + | 0.895591i | \(0.353247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.27641e10 | −1.18572 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.47433e10 | −1.35662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.07907e10 | 1.89502 | 0.947508 | − | 0.319733i | \(-0.103593\pi\) | ||||
0.947508 | + | 0.319733i | \(0.103593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.47410e9 | −0.133095 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.87068e9 | 0.525083 | 0.262541 | − | 0.964921i | \(-0.415439\pi\) | ||||
0.262541 | + | 0.964921i | \(0.415439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00585e10 | −1.77727 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.92453e8 | −0.0344481 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.25720e9 | 0.457160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.08413e9 | −0.610305 | −0.305152 | − | 0.952304i | \(-0.598707\pi\) | ||||
−0.305152 | + | 0.952304i | \(0.598707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.23660e10 | −1.05548 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.30874e10 | 1.10673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.12028e10 | −0.938622 | −0.469311 | − | 0.883033i | \(-0.655498\pi\) | ||||
−0.469311 | + | 0.883033i | \(0.655498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.19404e8 | 0.0182137 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.08007e10 | 1.71093 | 0.855465 | − | 0.517861i | \(-0.173272\pi\) | ||||
0.855465 | + | 0.517861i | \(0.173272\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.58345e9 | 0.373557 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.75602e9 | 0.141813 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.49120e9 | 0.439424 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94604e10 | 1.54315 | 0.771576 | − | 0.636137i | \(-0.219469\pi\) | ||||
0.771576 | + | 0.636137i | \(0.219469\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.81132e10 | 1.42332 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.81342e7 | 0.00141211 | 0.000706057 | − | 1.00000i | \(-0.499775\pi\) | ||||
0.000706057 | 1.00000i | \(0.499775\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.68390e10 | −2.07114 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.81872e9 | 0.215565 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.74902e9 | −0.132561 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.57695e9 | 0.644249 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.31771e10 | 0.980964 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.68346e9 | 0.197993 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.48980e9 | −0.255205 | −0.127603 | − | 0.991825i | \(-0.540728\pi\) | ||||
−0.127603 | + | 0.991825i | \(0.540728\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.47998e9 | −0.324718 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.78290e9 | 0.343617 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.41327e9 | −0.385481 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.60149e9 | −0.395384 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.60101e9 | 0.671758 | 0.335879 | − | 0.941905i | \(-0.390967\pi\) | ||||
0.335879 | + | 0.941905i | \(0.390967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.62250e9 | 0.320600 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.91302e9 | −0.200277 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.79426e10 | −1.22287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.29480e8 | −0.0560429 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.33425e8 | 0.0156347 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.28054e10 | 0.850305 | 0.425152 | − | 0.905122i | \(-0.360221\pi\) | ||||
0.425152 | + | 0.905122i | \(0.360221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.41860e10 | −0.933871 | −0.466936 | − | 0.884291i | \(-0.654642\pi\) | ||||
−0.466936 | + | 0.884291i | \(0.654642\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.10522e10 | 0.721325 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.17846e9 | 0.0762539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.89228e9 | −0.249704 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.87960e9 | −0.119556 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.88610e10 | −1.18950 | −0.594749 | − | 0.803912i | \(-0.702749\pi\) | ||||
−0.594749 | + | 0.803912i | \(0.702749\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.98216e9 | 0.499138 | 0.249569 | − | 0.968357i | \(-0.419711\pi\) | ||||
0.249569 | + | 0.968357i | \(0.419711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.48648e10 | −0.921658 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.69379e10 | 1.04134 | 0.520668 | − | 0.853759i | \(-0.325683\pi\) | ||||
0.520668 | + | 0.853759i | \(0.325683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.93636e10 | −1.18044 | −0.590221 | − | 0.807242i | \(-0.700960\pi\) | ||||
−0.590221 | + | 0.807242i | \(0.700960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.26466e9 | 0.318249 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.09763e10 | −0.657957 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.83903e10 | −1.09316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.69639e10 | −1.58944 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.16289e9 | 0.535631 | 0.267815 | − | 0.963470i | \(-0.413698\pi\) | ||||
0.267815 | + | 0.963470i | \(0.413698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.16070e9 | −0.125259 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.73546e10 | −1.57266 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.08870e10 | −0.620740 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.15990e10 | −0.655884 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.50360e10 | 0.843246 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.24847e7 | 0.00458796 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.16335e10 | 1.19345 | 0.596727 | − | 0.802445i | \(-0.296468\pi\) | ||||
0.596727 | + | 0.802445i | \(0.296468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.91025e8 | −0.0323388 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.34574e10 | −0.730345 | −0.365172 | − | 0.930940i | \(-0.618990\pi\) | ||||
−0.365172 | + | 0.930940i | \(0.618990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.10347e10 | 1.13230 | 0.566148 | − | 0.824304i | \(-0.308433\pi\) | ||||
0.566148 | + | 0.824304i | \(0.308433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.72015e10 | 0.918449 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.15666e10 | 1.67182 | 0.835912 | − | 0.548863i | \(-0.184939\pi\) | ||||
0.835912 | + | 0.548863i | \(0.184939\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.10207e10 | 1.62965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.40753e9 | 0.333906 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.62129e10 | 0.838091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.85080e10 | −1.46185 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.74384e9 | −0.139575 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.50791e10 | 0.760933 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.09323e10 | 1.54851 | 0.774254 | − | 0.632875i | \(-0.218125\pi\) | ||||
0.774254 | + | 0.632875i | \(0.218125\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.63379e8 | −0.00811402 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.59947e10 | 1.28077 | 0.640383 | − | 0.768056i | \(-0.278776\pi\) | ||||
0.640383 | + | 0.768056i | \(0.278776\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.77295e10 | −1.35544 | −0.677718 | − | 0.735322i | \(-0.737031\pi\) | ||||
−0.677718 | + | 0.735322i | \(0.737031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.69816e10 | −0.823526 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.18068e9 | 0.297374 | 0.148687 | − | 0.988884i | \(-0.452495\pi\) | ||||
0.148687 | + | 0.988884i | \(0.452495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.18144e10 | −2.47340 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.31971e10 | −0.625040 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.55580e9 | −0.0731093 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.10081e10 | 1.44575 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.24247e8 | 0.0196266 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.08766e10 | −1.41733 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.81693e9 | −0.219398 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.82802e10 | 1.73008 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.22987e9 | 0.279389 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.47637e9 | 0.421713 | 0.210856 | − | 0.977517i | \(-0.432375\pi\) | ||||
0.210856 | + | 0.977517i | \(0.432375\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.71250e9 | 0.163943 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.63833e10 | −1.15615 | −0.578075 | − | 0.815983i | \(-0.696196\pi\) | ||||
−0.578075 | + | 0.815983i | \(0.696196\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.94709e9 | 0.215131 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.67406e10 | 0.722433 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.33048e10 | 1.42631 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34537e10 | 0.996797 | 0.498398 | − | 0.866948i | \(-0.333922\pi\) | ||||
0.498398 | + | 0.866948i | \(0.333922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.42241e9 | −0.0599952 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.65846e10 | 0.694224 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.58839e9 | −0.232162 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.19902e9 | 0.0906673 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.04287e10 | −1.65438 | −0.827189 | − | 0.561924i | \(-0.810061\pi\) | ||||
−0.827189 | + | 0.561924i | \(0.810061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.69429e9 | 0.150040 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.63879e10 | −1.46680 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.21357e10 | −0.885629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.09610e10 | −0.435273 | −0.217636 | − | 0.976030i | \(-0.569835\pi\) | ||||
−0.217636 | + | 0.976030i | \(0.569835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.55332e10 | −0.612252 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.87938e9 | −0.0735276 | −0.0367638 | − | 0.999324i | \(-0.511705\pi\) | ||||
−0.0367638 | + | 0.999324i | \(0.511705\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.03371e8 | 0.0195478 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.64594e10 | 2.17633 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.97695e10 | 0.756435 | 0.378218 | − | 0.925717i | \(-0.376537\pi\) | ||||
0.378218 | + | 0.925717i | \(0.376537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.46943e10 | −1.31773 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.09282e10 | −1.54309 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.81049e9 | 0.105186 | 0.0525929 | − | 0.998616i | \(-0.483251\pi\) | ||||
0.0525929 | + | 0.998616i | \(0.483251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.75162e10 | −1.76535 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.71010e10 | −0.630711 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.13512e10 | −2.24625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.56692e10 | 1.29647 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.07807e9 | −0.0389005 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.47642e9 | 0.0528889 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.06586e10 | 0.734697 | 0.367348 | − | 0.930083i | \(-0.380266\pi\) | ||||
0.367348 | + | 0.930083i | \(0.380266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.92016e9 | 0.138411 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.53900e10 | 1.59108 | 0.795542 | − | 0.605899i | \(-0.207186\pi\) | ||||
0.795542 | + | 0.605899i | \(0.207186\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.49418e10 | 0.520004 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.87430e10 | −0.993152 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.14529e10 | −0.735960 | −0.367980 | − | 0.929834i | \(-0.619950\pi\) | ||||
−0.367980 | + | 0.929834i | \(0.619950\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.67204e10 | 1.25074 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.39906e8 | −0.0317865 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.89213e10 | −1.30692 | −0.653462 | − | 0.756960i | \(-0.726684\pi\) | ||||
−0.653462 | + | 0.756960i | \(0.726684\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.62349e10 | −0.541282 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.53011e10 | 0.506540 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.12020e9 | 0.0368222 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.27057e10 | 1.06749 | 0.533747 | − | 0.845644i | \(-0.320784\pi\) | ||||
0.533747 | + | 0.845644i | \(0.320784\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.41572e10 | −0.458833 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.93311e10 | 1.90942 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.21065e9 | −0.294345 | −0.147173 | − | 0.989111i | \(-0.547017\pi\) | ||||
−0.147173 | + | 0.989111i | \(0.547017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.61440e9 | −0.178166 |
(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 | 16.8.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 144.8.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 8.8.a.b.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 400.8.c.f.49.2 | 2 | |||
5.3 | odd | 4 | 400.8.c.f.49.1 | 2 | |||
5.4 | even | 2 | 400.8.a.p.1.1 | 1 | |||
8.3 | odd | 2 | 64.8.a.b.1.1 | 1 | |||
8.5 | even | 2 | 64.8.a.f.1.1 | 1 | |||
12.11 | even | 2 | 72.8.a.a.1.1 | 1 | |||
16.3 | odd | 4 | 256.8.b.g.129.2 | 2 | |||
16.5 | even | 4 | 256.8.b.a.129.2 | 2 | |||
16.11 | odd | 4 | 256.8.b.g.129.1 | 2 | |||
16.13 | even | 4 | 256.8.b.a.129.1 | 2 | |||
20.3 | even | 4 | 200.8.c.c.49.2 | 2 | |||
20.7 | even | 4 | 200.8.c.c.49.1 | 2 | |||
20.19 | odd | 2 | 200.8.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 576.8.a.z.1.1 | 1 | |||
24.11 | even | 2 | 576.8.a.y.1.1 | 1 | |||
28.27 | even | 2 | 392.8.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
16.8.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
64.8.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
64.8.a.f.1.1 | 1 | 8.5 | even | 2 | |||
72.8.a.a.1.1 | 1 | 12.11 | even | 2 | |||
144.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
200.8.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
200.8.c.c.49.1 | 2 | 20.7 | even | 4 | |||
200.8.c.c.49.2 | 2 | 20.3 | even | 4 | |||
256.8.b.a.129.1 | 2 | 16.13 | even | 4 | |||
256.8.b.a.129.2 | 2 | 16.5 | even | 4 | |||
256.8.b.g.129.1 | 2 | 16.11 | odd | 4 | |||
256.8.b.g.129.2 | 2 | 16.3 | odd | 4 | |||
392.8.a.b.1.1 | 1 | 28.27 | even | 2 | |||
400.8.a.p.1.1 | 1 | 5.4 | even | 2 | |||
400.8.c.f.49.1 | 2 | 5.3 | odd | 4 | |||
400.8.c.f.49.2 | 2 | 5.2 | odd | 4 | |||
576.8.a.y.1.1 | 1 | 24.11 | even | 2 | |||
576.8.a.z.1.1 | 1 | 24.5 | odd | 2 |