Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{505}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 126 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-10.7361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-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 | ||||||||
\(5\) | 106.417 | 1.90364 | 0.951819 | − | 0.306660i | \(-0.0992114\pi\) | ||||
0.951819 | + | 0.306660i | \(0.0992114\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 250.083 | 0.623164 | 0.311582 | − | 0.950219i | \(-0.399141\pi\) | ||||
0.311582 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −300.500 | −0.493158 | −0.246579 | − | 0.969123i | \(-0.579306\pi\) | ||||
−0.246579 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −957.750 | −1.09907 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2021.92 | 1.69684 | 0.848420 | − | 0.529324i | \(-0.177554\pi\) | ||||
0.848420 | + | 0.529324i | \(0.177554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2251.00 | 1.43051 | 0.715255 | − | 0.698863i | \(-0.246310\pi\) | ||||
0.715255 | + | 0.698863i | \(0.246310\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3092.75 | −1.21906 | −0.609530 | − | 0.792763i | \(-0.708642\pi\) | ||||
−0.609530 | + | 0.792763i | \(0.708642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8199.50 | 2.62384 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6603.66 | −1.45811 | −0.729054 | − | 0.684456i | \(-0.760040\pi\) | ||||
−0.729054 | + | 0.684456i | \(0.760040\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −833.002 | −0.155683 | −0.0778416 | − | 0.996966i | \(-0.524803\pi\) | ||||
−0.0778416 | + | 0.996966i | \(0.524803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2250.75 | −0.359784 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5214.41 | −0.719508 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8954.50 | 1.07532 | 0.537659 | − | 0.843162i | \(-0.319309\pi\) | ||||
0.537659 | + | 0.843162i | \(0.319309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2704.50 | 0.284725 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7206.58 | −0.669530 | −0.334765 | − | 0.942302i | \(-0.608657\pi\) | ||||
−0.334765 | + | 0.942302i | \(0.608657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14446.0 | −1.19145 | −0.595726 | − | 0.803188i | \(-0.703135\pi\) | ||||
−0.595726 | + | 0.803188i | \(0.703135\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8619.75 | 0.634546 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17968.2 | 1.18648 | 0.593238 | − | 0.805027i | \(-0.297849\pi\) | ||||
0.593238 | + | 0.805027i | \(0.297849\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18197.2 | −0.979671 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15810.5 | −0.773136 | −0.386568 | − | 0.922261i | \(-0.626340\pi\) | ||||
−0.386568 | + | 0.922261i | \(0.626340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26613.0 | 1.18628 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20259.0 | −0.825906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26710.5 | 0.998969 | 0.499485 | − | 0.866323i | \(-0.333523\pi\) | ||||
0.499485 | + | 0.866323i | \(0.333523\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26799.0 | −0.922133 | −0.461067 | − | 0.887365i | \(-0.652533\pi\) | ||||
−0.461067 | + | 0.887365i | \(0.652533\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −31978.2 | −0.938794 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44494.5 | 1.21093 | 0.605465 | − | 0.795872i | \(-0.292987\pi\) | ||||
0.605465 | + | 0.795872i | \(0.292987\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 27834.7 | 0.703825 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 20414.1 | 0.480600 | 0.240300 | − | 0.970699i | \(-0.422754\pi\) | ||||
0.240300 | + | 0.970699i | \(0.422754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38742.5 | 0.850904 | 0.425452 | − | 0.904981i | \(-0.360115\pi\) | ||||
0.425452 | + | 0.904981i | \(0.360115\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −73795.5 | −1.51487 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12254.1 | −0.235534 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 67211.5 | 1.21165 | 0.605823 | − | 0.795600i | \(-0.292844\pi\) | ||||
0.605823 | + | 0.795600i | \(0.292844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 35850.7 | 0.571218 | 0.285609 | − | 0.958346i | \(-0.407804\pi\) | ||||
0.285609 | + | 0.958346i | \(0.407804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 215165. | 3.23017 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 59433.0 | 0.841839 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 106267. | 1.42208 | 0.711041 | − | 0.703150i | \(-0.248224\pi\) | ||||
0.711041 | + | 0.703150i | \(0.248224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14724.5 | 0.186396 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7497.02 | 0.0898837 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 239544. | 2.72318 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 98133.5 | 1.05898 | 0.529490 | − | 0.848316i | \(-0.322383\pi\) | ||||
0.529490 | + | 0.848316i | \(0.322383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20256.7 | 0.207721 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50480.7 | −0.492404 | −0.246202 | − | 0.969219i | \(-0.579183\pi\) | ||||
−0.246202 | + | 0.969219i | \(0.579183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14246.0 | 0.132312 | 0.0661561 | − | 0.997809i | \(-0.478926\pi\) | ||||
0.0661561 | + | 0.997809i | \(0.478926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 46929.7 | 0.415408 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −39457.9 | −0.333176 | −0.166588 | − | 0.986027i | \(-0.553275\pi\) | ||||
−0.166588 | + | 0.986027i | \(0.553275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14194.0 | 0.114430 | 0.0572148 | − | 0.998362i | \(-0.481778\pi\) | ||||
0.0572148 | + | 0.998362i | \(0.481778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −80590.5 | −0.620835 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −114936. | −0.846761 | −0.423380 | − | 0.905952i | \(-0.639157\pi\) | ||||
−0.423380 | + | 0.905952i | \(0.639157\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −329120. | −2.32065 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −24340.5 | −0.164386 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −99073.9 | −0.641345 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −98509.5 | −0.611666 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 64859.2 | 0.386553 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 540011. | 3.09120 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −194998. | −1.07281 | −0.536404 | − | 0.843961i | \(-0.680218\pi\) | ||||
−0.536404 | + | 0.843961i | \(0.680218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 130014. | 0.687885 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 200981. | 1.02324 | 0.511619 | − | 0.859212i | \(-0.329046\pi\) | ||||
0.511619 | + | 0.859212i | \(0.329046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −110299. | −0.540682 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −77577.7 | −0.366355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 60872.4 | 0.277089 | 0.138544 | − | 0.990356i | \(-0.455758\pi\) | ||||
0.138544 | + | 0.990356i | \(0.455758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 386638. | 1.69733 | 0.848667 | − | 0.528928i | \(-0.177406\pi\) | ||||
0.848667 | + | 0.528928i | \(0.177406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −161713. | −0.685012 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −75149.9 | −0.307318 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −702739. | −2.77571 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −152878. | −0.564132 | −0.282066 | − | 0.959395i | \(-0.591020\pi\) | ||||
−0.282066 | + | 0.959395i | \(0.591020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 134322. | 0.479408 | 0.239704 | − | 0.970846i | \(-0.422950\pi\) | ||||
0.239704 | + | 0.970846i | \(0.422950\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 163775. | 0.565613 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −88645.2 | −0.296364 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 80730.0 | 0.261388 | 0.130694 | − | 0.991423i | \(-0.458279\pi\) | ||||
0.130694 | + | 0.991423i | \(0.458279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 142295. | 0.446370 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 151545. | 0.460761 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −90972.2 | −0.268188 | −0.134094 | − | 0.990969i | \(-0.542812\pi\) | ||||
−0.134094 | + | 0.990969i | \(0.542812\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −239517. | −0.684899 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 70407.3 | 0.195356 | 0.0976779 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976779 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −280993. | −0.756796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 182331. | 0.476837 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −304829. | −0.774356 | −0.387178 | − | 0.922005i | \(-0.626550\pi\) | ||||
−0.387178 | + | 0.922005i | \(0.626550\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −401775. | −0.991718 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −240395. | −0.576755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 586010. | 1.36701 | 0.683506 | − | 0.729945i | \(-0.260454\pi\) | ||||
0.683506 | + | 0.729945i | \(0.260454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 797296. | 1.80894 | 0.904468 | − | 0.426542i | \(-0.140268\pi\) | ||||
0.904468 | + | 0.426542i | \(0.140268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 241191. | 0.532394 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 952907. | 2.04702 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 505647. | 1.05741 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 150935. | 0.299369 | 0.149684 | − | 0.988734i | \(-0.452174\pi\) | ||||
0.149684 | + | 0.988734i | \(0.452174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −701556. | −1.35572 | −0.677859 | − | 0.735192i | \(-0.737092\pi\) | ||||
−0.677859 | + | 0.735192i | \(0.737092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 287803. | 0.542013 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 605633. | 1.11184 | 0.555922 | − | 0.831234i | \(-0.312365\pi\) | ||||
0.555922 | + | 0.831234i | \(0.312365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −155407. | −0.278188 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −400450. | −0.699131 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 323579. | 0.551113 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −766900. | −1.27454 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −250513. | −0.406353 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 562937. | 0.891443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −305091. | −0.471762 | −0.235881 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235881 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −183727. | −0.277475 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.53729e6 | −2.26809 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40817.1 | 0.0588427 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −348682. | −0.491269 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −607585. | −0.836809 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.35555e6 | −1.82538 | −0.912688 | − | 0.408658i | \(-0.865997\pi\) | ||||
−0.912688 | + | 0.408658i | \(0.865997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 664159. | 0.874613 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −234584. | −0.302157 | −0.151079 | − | 0.988522i | \(-0.548275\pi\) | ||||
−0.151079 | + | 0.988522i | \(0.548275\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.47823e6 | 1.86274 | 0.931369 | − | 0.364076i | \(-0.118615\pi\) | ||||
0.931369 | + | 0.364076i | \(0.118615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 110287. | 0.135986 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 262304. | 0.316531 | 0.158265 | − | 0.987397i | \(-0.449410\pi\) | ||||
0.158265 | + | 0.987397i | \(0.449410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.91211e6 | 2.25862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −604903. | −0.699544 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.62761e6 | −1.84312 | −0.921562 | − | 0.388232i | \(-0.873086\pi\) | ||||
−0.921562 | + | 0.388232i | \(0.873086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.25026e6 | −1.38662 | −0.693310 | − | 0.720639i | \(-0.743849\pi\) | ||||
−0.693310 | + | 0.720639i | \(0.743849\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 255506. | 0.271948 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −676424. | −0.705467 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −322656. | −0.329793 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −193945. | −0.194310 | −0.0971549 | − | 0.995269i | \(-0.530974\pi\) | ||||
−0.0971549 | + | 0.995269i | \(0.530974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −773444. | −0.759675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.93649e6 | −1.86494 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −254093. | −0.239972 | −0.119986 | − | 0.992776i | \(-0.538285\pi\) | ||||
−0.119986 | + | 0.992776i | \(0.538285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −438770. | −0.406432 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −534897. | −0.486036 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 746211. | 0.665230 | 0.332615 | − | 0.943063i | \(-0.392069\pi\) | ||||
0.332615 | + | 0.943063i | \(0.392069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.68250e6 | −1.47177 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −956406. | −0.821040 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.87146e6 | −1.57689 | −0.788444 | − | 0.615107i | \(-0.789113\pi\) | ||||
−0.788444 | + | 0.615107i | \(0.789113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −98046.4 | −0.0810977 | −0.0405488 | − | 0.999178i | \(-0.512911\pi\) | ||||
−0.0405488 | + | 0.999178i | \(0.512911\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −132520. | −0.107616 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.05056e6 | 1.63508 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.57273e6 | 1.23156 | 0.615781 | − | 0.787918i | \(-0.288841\pi\) | ||||
0.615781 | + | 0.787918i | \(0.288841\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −67473.2 | −0.0518944 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.88960e6 | 1.42759 | 0.713797 | − | 0.700352i | \(-0.246974\pi\) | ||||
0.713797 | + | 0.700352i | \(0.246974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.94676e6 | −1.44493 | −0.722464 | − | 0.691409i | \(-0.756990\pi\) | ||||
−0.722464 | + | 0.691409i | \(0.756990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.15589e6 | −1.57223 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 353123. | 0.253058 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.66829e6 | 1.87926 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −883202. | −0.611403 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 238275. | 0.162147 | 0.0810735 | − | 0.996708i | \(-0.474165\pi\) | ||||
0.0810735 | + | 0.996708i | \(0.474165\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.84244e6 | 1.90168 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −182311. | −0.119928 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 929370. | 0.601189 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 707854. | 0.450326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 454326. | 0.284290 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.85186e6 | −1.75541 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.70996e6 | −1.03547 | −0.517737 | − | 0.855540i | \(-0.673225\pi\) | ||||
−0.517737 | + | 0.855540i | \(0.673225\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −128214. | −0.0763905 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −301648. | −0.176848 | −0.0884240 | − | 0.996083i | \(-0.528183\pi\) | ||||
−0.0884240 | + | 0.996083i | \(0.528183\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −399739. | −0.230630 | −0.115315 | − | 0.993329i | \(-0.536788\pi\) | ||||
−0.115315 | + | 0.993329i | \(0.536788\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −422368. | −0.239836 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −479312. | −0.267899 | −0.133949 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133949 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.65146e6 | −0.908641 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 355121. | 0.192359 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.55133e6 | 2.42735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.46395e6 | −1.29397 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −127746. | −0.0660660 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −880440. | −0.448446 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −52366.6 | −0.0262715 | −0.0131357 | − | 0.999914i | \(-0.504181\pi\) | ||||
−0.0131357 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 725314. | 0.358439 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.73495e6 | 2.30517 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.31382e6 | −1.10983 | −0.554913 | − | 0.831909i | \(-0.687248\pi\) | ||||
−0.554913 | + | 0.831909i | \(0.687248\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.03443e6 | 0.488878 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −208320. | −0.0970162 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.96208e6 | 1.33983 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.82303e6 | −1.70445 | −0.852225 | − | 0.523175i | \(-0.824747\pi\) | ||||
−0.852225 | + | 0.523175i | \(0.824747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.19867e6 | −1.40574 | −0.702872 | − | 0.711316i | \(-0.748099\pi\) | ||||
−0.702872 | + | 0.711316i | \(0.748099\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 219064. | 0.0949082 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.47712e6 | 0.630927 | 0.315464 | − | 0.948938i | \(-0.397840\pi\) | ||||
0.315464 | + | 0.948938i | \(0.397840\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.17240e6 | 0.914890 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 891665. | 0.370281 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.12162e6 | 0.459315 | 0.229657 | − | 0.973272i | \(-0.426239\pi\) | ||||
0.229657 | + | 0.973272i | \(0.426239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.59089e6 | 1.04636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 886585. | 0.353146 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.12285e6 | 1.61981 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.40681e6 | −0.932774 | −0.466387 | − | 0.884581i | \(-0.654445\pi\) | ||||
−0.466387 | + | 0.884581i | \(0.654445\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −583733. | −0.223177 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 774715. | 0.292218 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.38495e6 | 0.515421 | 0.257711 | − | 0.966222i | \(-0.417032\pi\) | ||||
0.257711 | + | 0.966222i | \(0.417032\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.86010e6 | −1.78471 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.98440e6 | 0.719077 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.35789e6 | −0.843190 | −0.421595 | − | 0.906784i | \(-0.638530\pi\) | ||||
−0.421595 | + | 0.906784i | \(0.638530\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.75499e6 | 0.619386 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.67412e6 | −1.27984 | −0.639922 | − | 0.768440i | \(-0.721033\pi\) | ||||
−0.639922 | + | 0.768440i | \(0.721033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.30404e6 | −0.448371 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.17013e6 | −0.397150 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 123837. | 0.0414932 | 0.0207466 | − | 0.999785i | \(-0.493396\pi\) | ||||
0.0207466 | + | 0.999785i | \(0.493396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.25328e6 | −2.06855 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.80883e6 | −0.590767 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.15242e6 | 2.30653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.66109e6 | −0.528954 | −0.264477 | − | 0.964392i | \(-0.585199\pi\) | ||||
−0.264477 | + | 0.964392i | \(0.585199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 992690. | 0.312163 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −291011. | −0.0903750 | −0.0451875 | − | 0.998979i | \(-0.514389\pi\) | ||||
−0.0451875 | + | 0.998979i | \(0.514389\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 250317. | 0.0767763 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 698199. | 0.211515 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.23937e6 | 0.670100 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.64280e6 | 0.485597 | 0.242798 | − | 0.970077i | \(-0.421935\pi\) | ||||
0.242798 | + | 0.970077i | \(0.421935\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −547851. | −0.159977 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.30881e6 | −0.377575 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.81511e6 | 1.08739 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.47974e6 | −0.979956 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.89016e6 | −1.36078 | −0.680391 | − | 0.732850i | \(-0.738190\pi\) | ||||
−0.680391 | + | 0.732850i | \(0.738190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.91443e6 | 1.07637 | 0.538187 | − | 0.842825i | \(-0.319109\pi\) | ||||
0.538187 | + | 0.842825i | \(0.319109\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.45542e6 | 0.395492 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.65787e7 | 4.45223 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.31315e6 | 0.348534 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 676349. | 0.177430 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 461156. | 0.119579 | 0.0597895 | − | 0.998211i | \(-0.480957\pi\) | ||||
0.0597895 | + | 0.998211i | \(0.480957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.23092e6 | −1.85342 | −0.926711 | − | 0.375776i | \(-0.877376\pi\) | ||||
−0.926711 | + | 0.375776i | \(0.877376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.32465e6 | 1.60256 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.96177e6 | −1.74388 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −243865. | −0.0603932 | −0.0301966 | − | 0.999544i | \(-0.509613\pi\) | ||||
−0.0301966 | + | 0.999544i | \(0.509613\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.58521e6 | 1.83636 | 0.918181 | − | 0.396162i | \(-0.129658\pi\) | ||||
0.918181 | + | 0.396162i | \(0.129658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.13086e7 | 2.70713 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.37591e6 | 0.325702 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −117953. | −0.0276118 | −0.0138059 | − | 0.999905i | \(-0.504395\pi\) | ||||
−0.0138059 | + | 0.999905i | \(0.504395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.80224e6 | −0.417227 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.20890e6 | −0.276786 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.56693e6 | 0.354831 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.31220e6 | 0.965848 | 0.482924 | − | 0.875662i | \(-0.339575\pi\) | ||||
0.482924 | + | 0.875662i | \(0.339575\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.47398e6 | −0.326557 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.82503e6 | 0.399960 | 0.199980 | − | 0.979800i | \(-0.435912\pi\) | ||||
0.199980 | + | 0.979800i | \(0.435912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.94213e6 | −1.07143 | −0.535713 | − | 0.844400i | \(-0.679957\pi\) | ||||
−0.535713 | + | 0.844400i | \(0.679957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 797807. | 0.171106 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.24041e6 | −1.74846 | −0.874232 | − | 0.485508i | \(-0.838635\pi\) | ||||
−0.874232 | + | 0.485508i | \(0.838635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.18023e6 | −0.457689 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −726570. | −0.150912 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.61270e6 | −0.742470 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.84571e7 | 3.75343 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.28065e6 | −0.257712 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.06615e6 | −0.212315 | −0.106158 | − | 0.994349i | \(-0.533855\pi\) | ||||
−0.106158 | + | 0.994349i | \(0.533855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.69082e6 | −0.530301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.36390e6 | −0.266021 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.04430e7 | 2.01592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.25993e6 | −0.431790 | −0.215895 | − | 0.976417i | \(-0.569267\pi\) | ||||
−0.215895 | + | 0.976417i | \(0.569267\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 818750. | 0.154839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.15916e6 | 0.591382 | 0.295691 | − | 0.955284i | \(-0.404450\pi\) | ||||
0.295691 | + | 0.955284i | \(0.404450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.33520e7 | −2.47418 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.15565e6 | 0.395426 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.00029e6 | −0.181650 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.40623e6 | 1.33151 | 0.665757 | − | 0.746168i | \(-0.268109\pi\) | ||||
0.665757 | + | 0.746168i | \(0.268109\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −633666. | −0.112789 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.82580e6 | 0.321761 | 0.160881 | − | 0.986974i | \(-0.448567\pi\) | ||||
0.160881 | + | 0.986974i | \(0.448567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.37198e6 | −0.937359 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.52894e6 | 0.436936 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.68759e6 | −0.459800 | −0.229900 | − | 0.973214i | \(-0.573840\pi\) | ||||
−0.229900 | + | 0.973214i | \(0.573840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.89838e6 | −0.321611 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.64098e6 | −0.275302 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.51601e6 | 0.251875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.49353e6 | 0.739370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.74346e6 | 0.447075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.27987e6 | 0.852174 | 0.426087 | − | 0.904682i | \(-0.359892\pi\) | ||||
0.426087 | + | 0.904682i | \(0.359892\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.39485e6 | 1.34202 | 0.671010 | − | 0.741449i | \(-0.265861\pi\) | ||||
0.671010 | + | 0.741449i | \(0.265861\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.61598e6 | 0.572569 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.68426e6 | −0.264169 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.12875e6 | 0.486107 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.16355e6 | 0.332990 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.16558e6 | 0.330184 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.19897e6 | −0.634247 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.27409e6 | −0.789245 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 600449. | 0.0890235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.11826e6 | 0.898741 | 0.449370 | − | 0.893346i | \(-0.351648\pi\) | ||||
0.449370 | + | 0.893346i | \(0.351648\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.17566e6 | −1.04439 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.51048e6 | 0.217833 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.59301e6 | 0.799241 | 0.399620 | − | 0.916681i | \(-0.369142\pi\) | ||||
0.399620 | + | 0.916681i | \(0.369142\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.17072e6 | −0.307378 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.48648e7 | −2.08584 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.29336e6 | −0.457959 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.57617e6 | −1.18185 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.52668e6 | 0.345074 | 0.172537 | − | 0.985003i | \(-0.444804\pi\) | ||||
0.172537 | + | 0.985003i | \(0.444804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.34102e6 | 0.587573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.55082e6 | −0.610496 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.32508e6 | 0.708036 | 0.354018 | − | 0.935239i | \(-0.384815\pi\) | ||||
0.354018 | + | 0.935239i | \(0.384815\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.22311e7 | −1.61193 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.05147e6 | −1.17203 | −0.586015 | − | 0.810300i | \(-0.699304\pi\) | ||||
−0.586015 | + | 0.810300i | \(0.699304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.41867e6 | −0.823863 | −0.411932 | − | 0.911215i | \(-0.635146\pi\) | ||||
−0.411932 | + | 0.911215i | \(0.635146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.35842e6 | −0.172841 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.53590e7 | −3.19862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.40363e7 | 1.75515 | 0.877574 | − | 0.479442i | \(-0.159161\pi\) | ||||
0.877574 | + | 0.479442i | \(0.159161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.31401e6 | 0.782724 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.75668e6 | −0.215900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.95394e6 | −0.481791 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.59023e6 | −0.312931 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.39012e7 | 1.66516 | 0.832579 | − | 0.553906i | \(-0.186863\pi\) | ||||
0.832579 | + | 0.553906i | \(0.186863\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.87509e6 | −0.222706 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.45070e6 | −0.641924 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.17354e7 | −1.37045 | −0.685224 | − | 0.728332i | \(-0.740296\pi\) | ||||
−0.685224 | + | 0.728332i | \(0.740296\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.05431e7 | −1.22089 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.39867e6 | 0.160612 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.01682e6 | −0.229668 | −0.114834 | − | 0.993385i | \(-0.536634\pi\) | ||||
−0.114834 | + | 0.993385i | \(0.536634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.72242e6 | 0.420378 | 0.210189 | − | 0.977661i | \(-0.432592\pi\) | ||||
0.210189 | + | 0.977661i | \(0.432592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.60405e6 | 0.403644 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.04830e7 | −1.16439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.18076e6 | −0.680879 | −0.340440 | − | 0.940266i | \(-0.610576\pi\) | ||||
−0.340440 | + | 0.940266i | \(0.610576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.91221e6 | −0.318185 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.39943e6 | −0.585120 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.43775e6 | −0.262022 | −0.131011 | − | 0.991381i | \(-0.541822\pi\) | ||||
−0.131011 | + | 0.991381i | \(0.541822\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.90210e6 | 0.735857 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.19168e7 | −1.26022 | −0.630109 | − | 0.776506i | \(-0.716990\pi\) | ||||
−0.630109 | + | 0.776506i | \(0.716990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.61238e6 | −1.00833 | −0.504167 | − | 0.863606i | \(-0.668200\pi\) | ||||
−0.504167 | + | 0.863606i | \(0.668200\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.25461e6 | 0.234608 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.20710e6 | −0.537497 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.18427e7 | 3.26069 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.06643e6 | −0.514675 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.81052e7 | 1.82464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.44826e6 | 0.444750 | 0.222375 | − | 0.974961i | \(-0.428619\pi\) | ||||
0.222375 | + | 0.974961i | \(0.428619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.74582e6 | 0.272372 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.07511e7 | −2.04224 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −721500. | −0.0704511 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.65354e6 | 0.160200 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.20161e6 | −0.788414 | −0.394207 | − | 0.919022i | \(-0.628981\pi\) | ||||
−0.394207 | + | 0.919022i | \(0.628981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.38379e7 | −1.31990 | −0.659952 | − | 0.751308i | \(-0.729423\pi\) | ||||
−0.659952 | + | 0.751308i | \(0.729423\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38356e7 | 1.30948 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.57496e6 | 0.335746 | 0.167873 | − | 0.985809i | \(-0.446310\pi\) | ||||
0.167873 | + | 0.985809i | \(0.446310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.67985e6 | 0.622522 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −367354. | −0.0339729 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.08055e7 | −1.90939 | −0.954695 | − | 0.297587i | \(-0.903818\pi\) | ||||
−0.954695 | + | 0.297587i | \(0.903818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.13877e7 | 1.94787 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.13814e6 | 0.283635 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.34521e6 | −0.389760 | −0.194880 | − | 0.980827i | \(-0.562432\pi\) | ||||
−0.194880 | + | 0.980827i | \(0.562432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.59984e6 | −0.320464 | −0.160232 | − | 0.987079i | \(-0.551224\pi\) | ||||
−0.160232 | + | 0.987079i | \(0.551224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.46827e6 | 0.483132 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.17376e7 | −1.02926 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.04235e7 | 1.77752 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.21999e7 | 1.05388 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.70197e6 | −0.574641 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.35130e7 | −1.15005 | −0.575023 | − | 0.818137i | \(-0.695007\pi\) | ||||
−0.575023 | + | 0.818137i | \(0.695007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.97743e6 | −0.504958 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.06427e6 | 0.592373 | 0.296187 | − | 0.955130i | \(-0.404285\pi\) | ||||
0.296187 | + | 0.955130i | \(0.404285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.80854e6 | −0.400257 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.11125e6 | 0.174451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.75676e7 | 1.44099 | 0.720494 | − | 0.693461i | \(-0.243915\pi\) | ||||
0.720494 | + | 0.693461i | \(0.243915\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.47783e6 | 0.527477 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.33040e7 | −1.07545 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.75105e6 | 0.381278 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 617820. | 0.0492229 | 0.0246114 | − | 0.999697i | \(-0.492165\pi\) | ||||
0.0246114 | + | 0.999697i | \(0.492165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −992580. | −0.0785113 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.11447e7 | 3.23111 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.45711e7 | −1.13608 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.36074e6 | −0.182749 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.54273e7 | 1.18576 | 0.592879 | − | 0.805292i | \(-0.297991\pi\) | ||||
0.592879 | + | 0.805292i | \(0.297991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.01566e7 | 1.53825 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.72090e7 | −1.30402 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.47355e6 | 0.186111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.42780e7 | −1.81383 | −0.906917 | − | 0.421309i | \(-0.861571\pi\) | ||||
−0.906917 | + | 0.421309i | \(0.861571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.44413e6 | 0.403882 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.57627e6 | 0.189787 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.99720e6 | −0.585023 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.46485e7 | 1.06413 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.00425e6 | 0.577429 | 0.288714 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288714 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −698054. | −0.0500093 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.12523e7 | 0.800566 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.41467e7 | −3.82584 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.03222e7 | −1.42605 | −0.713025 | − | 0.701139i | \(-0.752675\pi\) | ||||
−0.713025 | + | 0.701139i | \(0.752675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.92086e7 | −2.02170 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.77940e6 | 0.466049 | 0.233024 | − | 0.972471i | \(-0.425138\pi\) | ||||
0.233024 | + | 0.972471i | \(0.425138\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.29956e6 | −0.157009 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.11273e7 | 0.754609 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.62382e7 | −1.09377 | −0.546887 | − | 0.837207i | \(-0.684187\pi\) | ||||
−0.546887 | + | 0.837207i | \(0.684187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.08782e6 | 0.407302 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.34767e6 | 0.156014 | 0.0780072 | − | 0.996953i | \(-0.475144\pi\) | ||||
0.0780072 | + | 0.996953i | \(0.475144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.62688e7 | −1.07390 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.90390e6 | 0.190406 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.93343e6 | 0.125929 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.15068e7 | −1.39147 | −0.695737 | − | 0.718296i | \(-0.744922\pi\) | ||||
−0.695737 | + | 0.718296i | \(0.744922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.74551e6 | 0.112185 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.42941e7 | 0.912619 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.88736e6 | −0.309981 | −0.154990 | − | 0.987916i | \(-0.549535\pi\) | ||||
−0.154990 | + | 0.987916i | \(0.549535\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.96100e6 | 0.438598 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.09272e7 | −0.683988 | −0.341994 | − | 0.939702i | \(-0.611102\pi\) | ||||
−0.341994 | + | 0.939702i | \(0.611102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −695506. | −0.0432503 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.74284e7 | 1.07672 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.02650e6 | −0.492649 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.31780e6 | 0.507216 | 0.253608 | − | 0.967307i | \(-0.418383\pi\) | ||||
0.253608 | + | 0.967307i | \(0.418383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.28684e6 | 0.138548 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.78229e7 | −1.67476 | −0.837381 | − | 0.546620i | \(-0.815914\pi\) | ||||
−0.837381 | + | 0.546620i | \(0.815914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.83020e6 | −0.408488 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.94893e6 | 0.234654 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.62220e7 | −0.957769 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.10522e6 | 0.299493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.81407e6 | 0.280613 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.59101e6 | 0.497588 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.14847e7 | −1.81202 | −0.906009 | − | 0.423258i | \(-0.860886\pi\) | ||||
−0.906009 | + | 0.423258i | \(0.860886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.71590e6 | −0.384071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.63187e6 | 0.320046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.05309e6 | 0.454757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.51425e7 | 0.849728 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.29354e6 | 0.518245 | 0.259123 | − | 0.965844i | \(-0.416567\pi\) | ||||
0.259123 | + | 0.965844i | \(0.416567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.63301e7 | 2.01326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.60766e6 | 0.474028 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.68884e6 | 0.530253 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.61269e7 | 0.877123 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.68432e7 | 0.910417 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.36908e7 | −0.735459 | −0.367730 | − | 0.929933i | \(-0.619865\pi\) | ||||
−0.367730 | + | 0.929933i | \(0.619865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.83843e6 | −0.418482 | −0.209241 | − | 0.977864i | \(-0.567099\pi\) | ||||
−0.209241 | + | 0.977864i | \(0.567099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 882418. | 0.0468218 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.68096e6 | −0.510534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.25179e7 | −1.70438 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.19268e6 | 0.0621320 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.77295e7 | −1.43577 | −0.717883 | − | 0.696164i | \(-0.754889\pi\) | ||||
−0.717883 | + | 0.696164i | \(0.754889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.04827e6 | 0.105411 | 0.0527057 | − | 0.998610i | \(-0.483215\pi\) | ||||
0.0527057 | + | 0.998610i | \(0.483215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.84550e7 | −0.944015 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.35186e7 | −1.19577 | −0.597884 | − | 0.801582i | \(-0.703992\pi\) | ||||
−0.597884 | + | 0.801582i | \(0.703992\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.93665e7 | 0.978734 | 0.489367 | − | 0.872078i | \(-0.337228\pi\) | ||||
0.489367 | + | 0.872078i | \(0.337228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41546e7 | −0.711042 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.85462e6 | 0.242406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.49250e6 | 0.371887 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 607258. | 0.0299612 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.84417e7 | −0.904473 | −0.452236 | − | 0.891898i | \(-0.649374\pi\) | ||||
−0.452236 | + | 0.891898i | \(0.649374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.30972e7 | 1.12608 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.70064e7 | −0.824222 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.99023e7 | −1.44067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.82696e6 | 0.231188 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.75208e7 | 0.834229 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.76940e7 | −1.31088 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.91827e7 | 0.902689 | 0.451345 | − | 0.892350i | \(-0.350945\pi\) | ||||
0.451345 | + | 0.892350i | \(0.350945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.94030e7 | 0.907725 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.65637e7 | 1.23548 | 0.617741 | − | 0.786381i | \(-0.288048\pi\) | ||||
0.617741 | + | 0.786381i | \(0.288048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.68342e7 | 0.778410 | 0.389205 | − | 0.921151i | \(-0.372750\pi\) | ||||
0.389205 | + | 0.921151i | \(0.372750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.17810e6 | −0.146103 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.26732e6 | 0.195042 | 0.0975210 | − | 0.995233i | \(-0.468909\pi\) | ||||
0.0975210 | + | 0.995233i | \(0.468909\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.24389e7 | −1.47409 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.40146e7 | −1.08499 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.68084e7 | 0.755054 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.33706e7 | −0.597180 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.94881e6 | 0.352994 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.64605e7 | −1.16836 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.58174e7 | 1.13348 | 0.566739 | − | 0.823897i | \(-0.308205\pi\) | ||||
0.566739 | + | 0.823897i | \(0.308205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.14447e6 | −0.0936156 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.99398e7 | 1.29960 | 0.649799 | − | 0.760106i | \(-0.274853\pi\) | ||||
0.649799 | + | 0.760106i | \(0.274853\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.46525e6 | 0.192727 | 0.0963637 | − | 0.995346i | \(-0.469279\pi\) | ||||
0.0963637 | + | 0.995346i | \(0.469279\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.55820e7 | −1.09793 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.89113e7 | −1.23384 | −0.616919 | − | 0.787027i | \(-0.711619\pi\) | ||||
−0.616919 | + | 0.787027i | \(0.711619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.55492e6 | 0.405483 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.64080e6 | 0.0692405 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.04463e7 | 1.69727 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.23612e7 | 2.60230 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.36433e6 | −0.347096 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.50086e6 | 0.227003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.19675e7 | −1.31189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.37068e6 | −0.259996 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.48456e7 | 3.44356 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.38019e6 | 0.297885 | 0.148943 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148943 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.08893e6 | −0.164135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.25542e7 | 1.69882 | 0.849409 | − | 0.527736i | \(-0.176959\pi\) | ||||
0.849409 | + | 0.527736i | \(0.176959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.96565e6 | 0.355963 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.56667e7 | 1.01349 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.84807e6 | −0.386748 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.88119e7 | 1.12534 | 0.562669 | − | 0.826682i | \(-0.309775\pi\) | ||||
0.562669 | + | 0.826682i | \(0.309775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.53896e7 | 0.597831 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.13443e6 | −0.237012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.34224e7 | 2.82146 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.15393e6 | 0.0441041 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.82043e7 | 1.83251 | 0.916255 | − | 0.400595i | \(-0.131196\pi\) | ||||
0.916255 | + | 0.400595i | \(0.131196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.40465e6 | 0.204359 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.71484e6 | 0.102103 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.38092e7 | 2.01293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.04317e7 | −0.760247 | −0.380123 | − | 0.924936i | \(-0.624118\pi\) | ||||
−0.380123 | + | 0.924936i | \(0.624118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.59765e6 | 0.133154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.62728e7 | −0.967237 | −0.483618 | − | 0.875279i | \(-0.660678\pi\) | ||||
−0.483618 | + | 0.875279i | \(0.660678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.22882e7 | 0.816197 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.80131e6 | 0.138469 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.94399e7 | 1.06675 | 0.533373 | − | 0.845880i | \(-0.320924\pi\) | ||||
0.533373 | + | 0.845880i | \(0.320924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.16421e7 | −0.419630 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.31381e6 | 0.154671 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.07999e7 | −1.09854 | −0.549272 | − | 0.835644i | \(-0.685095\pi\) | ||||
−0.549272 | + | 0.835644i | \(0.685095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.60620e7 | 0.569890 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.48632e7 | 0.524604 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.98275e6 | −0.104730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.79353e7 | −0.975763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.19609e6 | −0.111059 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.46573e7 | −2.58080 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.02028e7 | −1.03868 | −0.519338 | − | 0.854569i | \(-0.673822\pi\) | ||||
−0.519338 | + | 0.854569i | \(0.673822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.09620e7 | −1.40143 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.75051e6 | −0.0936192 | −0.0468096 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468096 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.89452e7 | −0.641532 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.21755e7 | 0.747071 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.71690e7 | 0.575452 | 0.287726 | − | 0.957713i | \(-0.407101\pi\) | ||||
0.287726 | + | 0.957713i | \(0.407101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.65757e7 | 0.886191 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.14971e6 | 0.0381432 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.13066e7 | −1.69352 | −0.846758 | − | 0.531979i | \(-0.821449\pi\) | ||||
−0.846758 | + | 0.531979i | \(0.821449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.44494e7 | 2.11655 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.92396e6 | 0.258910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.46778e7 | 1.45245 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.39045e7 | −0.773207 | −0.386603 | − | 0.922246i | \(-0.626352\pi\) | ||||
−0.386603 | + | 0.922246i | \(0.626352\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 471300. | 0.0151678 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.65379e7 | −0.529570 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.08351e6 | 0.257550 | 0.128775 | − | 0.991674i | \(-0.458895\pi\) | ||||
0.128775 | + | 0.991674i | \(0.458895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.52783e6 | −0.206945 |
(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 | 336.6.a.u.1.2 | 2 | ||
3.2 | odd | 2 | 1008.6.a.bf.1.1 | 2 | |||
4.3 | odd | 2 | 84.6.a.d.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 252.6.a.e.1.1 | 2 | |||
28.3 | even | 6 | 588.6.i.n.373.2 | 4 | |||
28.11 | odd | 6 | 588.6.i.h.373.1 | 4 | |||
28.19 | even | 6 | 588.6.i.n.361.2 | 4 | |||
28.23 | odd | 6 | 588.6.i.h.361.1 | 4 | |||
28.27 | even | 2 | 588.6.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
252.6.a.e.1.1 | 2 | 12.11 | even | 2 | |||
336.6.a.u.1.2 | 2 | 1.1 | even | 1 | trivial | ||
588.6.a.g.1.1 | 2 | 28.27 | even | 2 | |||
588.6.i.h.361.1 | 4 | 28.23 | odd | 6 | |||
588.6.i.h.373.1 | 4 | 28.11 | odd | 6 | |||
588.6.i.n.361.2 | 4 | 28.19 | even | 6 | |||
588.6.i.n.373.2 | 4 | 28.3 | even | 6 | |||
1008.6.a.bf.1.1 | 2 | 3.2 | odd | 2 |