Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,6,Mod(1,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, 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("560.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.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: | \(89.8149390953\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 560.1 |
$q$-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 | ||||||||
\(3\) | 12.0000 | 0.769800 | 0.384900 | − | 0.922958i | \(-0.374236\pi\) | ||||
0.384900 | + | 0.922958i | \(0.374236\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −99.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −556.000 | −1.38546 | −0.692729 | − | 0.721198i | \(-0.743592\pi\) | ||||
−0.692729 | + | 0.721198i | \(0.743592\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −354.000 | −0.580958 | −0.290479 | − | 0.956881i | \(-0.593815\pi\) | ||||
−0.290479 | + | 0.956881i | \(0.593815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 300.000 | 0.344265 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 770.000 | 0.646202 | 0.323101 | − | 0.946364i | \(-0.395275\pi\) | ||||
0.323101 | + | 0.946364i | \(0.395275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2684.00 | 1.70568 | 0.852842 | − | 0.522169i | \(-0.174877\pi\) | ||||
0.852842 | + | 0.522169i | \(0.174877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 588.000 | 0.290957 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1528.00 | 0.602287 | 0.301144 | − | 0.953579i | \(-0.402632\pi\) | ||||
0.301144 | + | 0.953579i | \(0.402632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4104.00 | −1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2418.00 | −0.533902 | −0.266951 | − | 0.963710i | \(-0.586016\pi\) | ||||
−0.266951 | + | 0.963710i | \(0.586016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7840.00 | −1.46525 | −0.732625 | − | 0.680632i | \(-0.761705\pi\) | ||||
−0.732625 | + | 0.680632i | \(0.761705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6672.00 | −1.06653 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −314.000 | −0.0377073 | −0.0188536 | − | 0.999822i | \(-0.506002\pi\) | ||||
−0.0188536 | + | 0.999822i | \(0.506002\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4248.00 | −0.447222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17878.0 | −1.66096 | −0.830480 | − | 0.557048i | \(-0.811934\pi\) | ||||
−0.830480 | + | 0.557048i | \(0.811934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16476.0 | −1.35888 | −0.679439 | − | 0.733732i | \(-0.737777\pi\) | ||||
−0.679439 | + | 0.733732i | \(0.737777\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2475.00 | −0.182198 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5376.00 | −0.354989 | −0.177494 | − | 0.984122i | \(-0.556799\pi\) | ||||
−0.177494 | + | 0.984122i | \(0.556799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9240.00 | 0.497447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1654.00 | 0.0808809 | 0.0404404 | − | 0.999182i | \(-0.487124\pi\) | ||||
0.0404404 | + | 0.999182i | \(0.487124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13900.0 | −0.619595 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 32208.0 | 1.31304 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 29492.0 | 1.10300 | 0.551498 | − | 0.834176i | \(-0.314056\pi\) | ||||
0.551498 | + | 0.834176i | \(0.314056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27630.0 | 0.950728 | 0.475364 | − | 0.879789i | \(-0.342316\pi\) | ||||
0.475364 | + | 0.879789i | \(0.342316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4851.00 | −0.153986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8850.00 | −0.259812 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −57716.0 | −1.57076 | −0.785379 | − | 0.619015i | \(-0.787532\pi\) | ||||
−0.785379 | + | 0.619015i | \(0.787532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18336.0 | 0.463641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −70648.0 | −1.66324 | −0.831618 | − | 0.555348i | \(-0.812585\pi\) | ||||
−0.831618 | + | 0.555348i | \(0.812585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 74202.0 | 1.62970 | 0.814851 | − | 0.579670i | \(-0.196818\pi\) | ||||
0.814851 | + | 0.579670i | \(0.196818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7500.00 | 0.153960 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27244.0 | −0.523654 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −74336.0 | −1.34008 | −0.670041 | − | 0.742324i | \(-0.733724\pi\) | ||||
−0.670041 | + | 0.742324i | \(0.733724\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −25191.0 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −44068.0 | −0.702147 | −0.351074 | − | 0.936348i | \(-0.614183\pi\) | ||||
−0.351074 | + | 0.936348i | \(0.614183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19250.0 | 0.288990 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −29016.0 | −0.410998 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 129306. | 1.73039 | 0.865194 | − | 0.501437i | \(-0.167195\pi\) | ||||
0.865194 | + | 0.501437i | \(0.167195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17346.0 | −0.219582 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −94080.0 | −1.12795 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 67100.0 | 0.762805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −137646. | −1.48537 | −0.742684 | − | 0.669642i | \(-0.766448\pi\) | ||||
−0.742684 | + | 0.669642i | \(0.766448\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 55044.0 | 0.564445 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52086.0 | 0.508063 | 0.254032 | − | 0.967196i | \(-0.418243\pi\) | ||||
0.254032 | + | 0.967196i | \(0.418243\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −128216. | −1.19083 | −0.595414 | − | 0.803419i | \(-0.703012\pi\) | ||||
−0.595414 | + | 0.803419i | \(0.703012\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14700.0 | 0.130120 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −113340. | −0.957026 | −0.478513 | − | 0.878080i | \(-0.658824\pi\) | ||||
−0.478513 | + | 0.878080i | \(0.658824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −138946. | −1.12016 | −0.560080 | − | 0.828439i | \(-0.689229\pi\) | ||||
−0.560080 | + | 0.828439i | \(0.689229\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3768.00 | −0.0290271 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −28046.0 | −0.206621 | −0.103311 | − | 0.994649i | \(-0.532944\pi\) | ||||
−0.103311 | + | 0.994649i | \(0.532944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 38200.0 | 0.269351 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 35046.0 | 0.236687 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 37730.0 | 0.244241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 148085. | 0.919491 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −214536. | −1.27861 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26704.0 | 0.146915 | 0.0734576 | − | 0.997298i | \(-0.476597\pi\) | ||||
0.0734576 | + | 0.997298i | \(0.476597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −197712. | −1.04607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7028.00 | −0.0357811 | −0.0178905 | − | 0.999840i | \(-0.505695\pi\) | ||||
−0.0178905 | + | 0.999840i | \(0.505695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 131516. | 0.644688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −102600. | −0.484521 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 140202. | 0.638194 | 0.319097 | − | 0.947722i | \(-0.396620\pi\) | ||||
0.319097 | + | 0.947722i | \(0.396620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 95876.0 | 0.420894 | 0.210447 | − | 0.977605i | \(-0.432508\pi\) | ||||
0.210447 | + | 0.977605i | \(0.432508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −64512.0 | −0.273270 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 196824. | 0.804893 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −60450.0 | −0.238768 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 28812.0 | 0.109971 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −347002. | −1.28046 | −0.640230 | − | 0.768183i | \(-0.721161\pi\) | ||||
−0.640230 | + | 0.768183i | \(0.721161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 270328. | 0.964825 | 0.482413 | − | 0.875944i | \(-0.339761\pi\) | ||||
0.482413 | + | 0.875944i | \(0.339761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −76230.0 | −0.263268 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −196000. | −0.655280 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −151186. | −0.489511 | −0.244755 | − | 0.969585i | \(-0.578708\pi\) | ||||
−0.244755 | + | 0.969585i | \(0.578708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19848.0 | 0.0622621 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 74872.0 | 0.227643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −588148. | −1.73387 | −0.866937 | − | 0.498417i | \(-0.833915\pi\) | ||||
−0.866937 | + | 0.498417i | \(0.833915\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −166800. | −0.476965 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −61912.0 | −0.171784 | −0.0858922 | − | 0.996304i | \(-0.527374\pi\) | ||||
−0.0858922 | + | 0.996304i | \(0.527374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −245977. | −0.662488 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −265716. | −0.694908 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4862.00 | 0.0123509 | 0.00617547 | − | 0.999981i | \(-0.498034\pi\) | ||||
0.00617547 | + | 0.999981i | \(0.498034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30625.0 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 353904. | 0.849087 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17964.0 | 0.0419054 | 0.0209527 | − | 0.999780i | \(-0.493330\pi\) | ||||
0.0209527 | + | 0.999780i | \(0.493330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 228422. | 0.518253 | 0.259126 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259126 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 331560. | 0.731871 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7850.00 | −0.0168632 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −428120. | −0.895285 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −201096. | −0.409495 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 357840. | 0.709750 | 0.354875 | − | 0.934914i | \(-0.384523\pi\) | ||||
0.354875 | + | 0.934914i | \(0.384523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −494174. | −0.954963 | −0.477482 | − | 0.878642i | \(-0.658450\pi\) | ||||
−0.477482 | + | 0.878642i | \(0.658450\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −106200. | −0.200004 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 595302. | 1.09288 | 0.546439 | − | 0.837499i | \(-0.315983\pi\) | ||||
0.546439 | + | 0.837499i | \(0.315983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 261208. | 0.467578 | 0.233789 | − | 0.972287i | \(-0.424888\pi\) | ||||
0.233789 | + | 0.972287i | \(0.424888\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −692592. | −1.20917 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −118482. | −0.201796 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −446950. | −0.742804 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −151272. | −0.245376 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.49230e6 | −2.36315 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −788564. | −1.21936 | −0.609678 | − | 0.792649i | \(-0.708701\pi\) | ||||
−0.609678 | + | 0.792649i | \(0.708701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −847776. | −1.28036 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −411900. | −0.607709 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −384160. | −0.553813 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 890424. | 1.25455 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −272580. | −0.375416 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.35842e6 | 1.82924 | 0.914620 | − | 0.404315i | \(-0.132490\pi\) | ||||
0.914620 | + | 0.404315i | \(0.132490\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −61875.0 | −0.0814815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 461068. | 0.593882 | 0.296941 | − | 0.954896i | \(-0.404033\pi\) | ||||
0.296941 | + | 0.954896i | \(0.404033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.25509e6 | 1.58157 | 0.790783 | − | 0.612096i | \(-0.209673\pi\) | ||||
0.790783 | + | 0.612096i | \(0.209673\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −326928. | −0.403109 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 503914. | 0.608088 | 0.304044 | − | 0.952658i | \(-0.401663\pi\) | ||||
0.304044 | + | 0.952658i | \(0.401663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −134400. | −0.158756 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −892032. | −1.03160 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.50902e6 | −1.70884 | −0.854420 | − | 0.519583i | \(-0.826087\pi\) | ||||
−0.854420 | + | 0.519583i | \(0.826087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −63022.0 | −0.0698956 | −0.0349478 | − | 0.999389i | \(-0.511126\pi\) | ||||
−0.0349478 | + | 0.999389i | \(0.511126\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 694980. | 0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −950136. | −0.990931 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −528816. | −0.540513 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 964820. | 0.966634 | 0.483317 | − | 0.875445i | \(-0.339432\pi\) | ||||
0.483317 | + | 0.875445i | \(0.339432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −849568. | −0.834443 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 231000. | 0.222465 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −495150. | −0.467632 | −0.233816 | − | 0.972281i | \(-0.575121\pi\) | ||||
−0.233816 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15386.0 | −0.0142520 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 239382. | 0.217516 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.18092e6 | −1.94424 | −0.972121 | − | 0.234479i | \(-0.924661\pi\) | ||||
−0.972121 | + | 0.234479i | \(0.924661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41350.0 | 0.0361710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.55167e6 | 1.33205 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −473346. | −0.398839 | −0.199420 | − | 0.979914i | \(-0.563906\pi\) | ||||
−0.199420 | + | 0.979914i | \(0.563906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.19234e6 | 1.81336 | 0.906680 | − | 0.421820i | \(-0.138609\pi\) | ||||
0.906680 | + | 0.421820i | \(0.138609\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −208152. | −0.169034 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −347500. | −0.277091 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 388502. | 0.304224 | 0.152112 | − | 0.988363i | \(-0.451393\pi\) | ||||
0.152112 | + | 0.988363i | \(0.451393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 776160. | 0.596954 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −75462.0 | −0.0570115 | −0.0285058 | − | 0.999594i | \(-0.509075\pi\) | ||||
−0.0285058 | + | 0.999594i | \(0.509075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.17272e6 | −1.61264 | −0.806319 | − | 0.591481i | \(-0.798543\pi\) | ||||
−0.806319 | + | 0.591481i | \(0.798543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 805200. | 0.587208 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −876022. | −0.627784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −826957. | −0.582423 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.65175e6 | −1.14344 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 142902. | 0.0972454 | 0.0486227 | − | 0.998817i | \(-0.484517\pi\) | ||||
0.0486227 | + | 0.998817i | \(0.484517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 737300. | 0.493275 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.28182e6 | 1.50104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −540912. | −0.349904 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −807324. | −0.513608 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 625032. | 0.391107 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 690750. | 0.425178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.05277e6 | −0.637512 | −0.318756 | − | 0.947837i | \(-0.603265\pi\) | ||||
−0.318756 | + | 0.947837i | \(0.603265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.53859e6 | −0.916700 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.11214e6 | 1.82456 | 0.912279 | − | 0.409570i | \(-0.134321\pi\) | ||||
0.912279 | + | 0.409570i | \(0.134321\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.95676e6 | −1.12895 | −0.564477 | − | 0.825449i | \(-0.690922\pi\) | ||||
−0.564477 | + | 0.825449i | \(0.690922\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −121275. | −0.0688644 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.74800e6 | 1.53592 | 0.767959 | − | 0.640499i | \(-0.221272\pi\) | ||||
0.767959 | + | 0.640499i | \(0.221272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.34441e6 | 0.739698 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.36008e6 | −0.736719 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.06668e6 | 1.10222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −221250. | −0.116192 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.66735e6 | −0.862299 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −263424. | −0.134173 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.23019e6 | −1.11885 | −0.559425 | − | 0.828881i | \(-0.688978\pi\) | ||||
−0.559425 | + | 0.828881i | \(0.688978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31086.0 | 0.0153622 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.44290e6 | −0.702464 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.13439e6 | 1.50341 | 0.751706 | − | 0.659499i | \(-0.229231\pi\) | ||||
0.751706 | + | 0.659499i | \(0.229231\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −336552. | −0.159057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.35904e6 | 2.03004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 458400. | 0.207347 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.43003e6 | −1.08340 | −0.541698 | − | 0.840573i | \(-0.682219\pi\) | ||||
−0.541698 | + | 0.840573i | \(0.682219\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46062e6 | 1.52086 | 0.760432 | − | 0.649417i | \(-0.224987\pi\) | ||||
0.760432 | + | 0.649417i | \(0.224987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45282e6 | 0.629423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.25627e6 | −0.536595 | −0.268297 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268297 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.76620e6 | −0.743822 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 452760. | 0.188017 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −878712. | −0.359841 | −0.179920 | − | 0.983681i | \(-0.557584\pi\) | ||||
−0.179920 | + | 0.983681i | \(0.557584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.72776e6 | 1.90936 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.77702e6 | 0.707825 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.85505e6 | 0.728825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −234880. | −0.0910292 | −0.0455146 | − | 0.998964i | \(-0.514493\pi\) | ||||
−0.0455146 | + | 0.998964i | \(0.514493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.76992e6 | 0.676688 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 81046.0 | 0.0305701 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 97430.0 | 0.0362594 | 0.0181297 | − | 0.999836i | \(-0.494229\pi\) | ||||
0.0181297 | + | 0.999836i | \(0.494229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 187500. | 0.0688530 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 855972. | 0.310175 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.99722e6 | 0.714213 | 0.357107 | − | 0.934064i | \(-0.383763\pi\) | ||||
0.357107 | + | 0.934064i | \(0.383763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 320448. | 0.113095 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −119664. | −0.0416837 | −0.0208419 | − | 0.999783i | \(-0.506635\pi\) | ||||
−0.0208419 | + | 0.999783i | \(0.506635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −681100. | −0.234185 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.63112e6 | 0.553617 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 327670. | 0.109790 | 0.0548950 | − | 0.998492i | \(-0.482518\pi\) | ||||
0.0548950 | + | 0.998492i | \(0.482518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.17656e6 | 0.389199 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −84336.0 | −0.0275443 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.85840e6 | −0.599303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.46653e6 | 1.42231 | 0.711154 | − | 0.703036i | \(-0.248173\pi\) | ||||
0.711154 | + | 0.703036i | \(0.248173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.57819e6 | 0.496281 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.83249e6 | −0.569091 | −0.284545 | − | 0.958663i | \(-0.591843\pi\) | ||||
−0.284545 | + | 0.958663i | \(0.591843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.77536e6 | 0.851249 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −629775. | −0.190787 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 174584. | 0.0522418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.59393e6 | −1.65352 | −0.826758 | − | 0.562558i | \(-0.809817\pi\) | ||||
−0.826758 | + | 0.562558i | \(0.809817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.68242e6 | 0.491282 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.44511e6 | 0.416894 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.10170e6 | −0.314010 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.15051e6 | 0.324004 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −562772. | −0.156602 | −0.0783010 | − | 0.996930i | \(-0.524950\pi\) | ||||
−0.0783010 | + | 0.996930i | \(0.524950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 679158. | 0.186752 | 0.0933761 | − | 0.995631i | \(-0.470234\pi\) | ||||
0.0933761 | + | 0.995631i | \(0.470234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 532224. | 0.144625 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 481250. | 0.129240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.35387e6 | 0.359341 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.36189e6 | 0.619607 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.89466e6 | −1.52850 | −0.764250 | − | 0.644920i | \(-0.776891\pi\) | ||||
−0.764250 | + | 0.644920i | \(0.776891\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.64499e6 | −0.421642 | −0.210821 | − | 0.977525i | \(-0.567614\pi\) | ||||
−0.210821 | + | 0.977525i | \(0.567614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −725400. | −0.183804 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.10115e6 | 1.02731 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.20138e6 | 1.04047 | 0.520237 | − | 0.854022i | \(-0.325844\pi\) | ||||
0.520237 | + | 0.854022i | \(0.325844\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −237699. | −0.0582011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 565684. | 0.136951 | 0.0684754 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684754 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.23265e6 | 0.773853 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.16402e6 | −0.985699 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 648386. | 0.151781 | 0.0758906 | − | 0.997116i | \(-0.475820\pi\) | ||||
0.0758906 | + | 0.997116i | \(0.475820\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.94017e6 | 2.30119 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.24394e6 | 0.742723 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −433650. | −0.0981999 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.74713e6 | −0.391322 | −0.195661 | − | 0.980672i | \(-0.562685\pi\) | ||||
−0.195661 | + | 0.980672i | \(0.562685\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.16008e6 | −0.700110 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −317378. | −0.0695544 | −0.0347772 | − | 0.999395i | \(-0.511072\pi\) | ||||
−0.0347772 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.84678e6 | 1.26755 | 0.633774 | − | 0.773518i | \(-0.281505\pi\) | ||||
0.633774 | + | 0.773518i | \(0.281505\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.35200e6 | −0.504435 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.67257e6 | 0.779252 | 0.389626 | − | 0.920973i | \(-0.372604\pi\) | ||||
0.389626 | + | 0.920973i | \(0.372604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.82808e6 | −0.593691 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.81423e6 | −0.376826 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.16066e6 | 1.88267 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.67750e6 | 0.341137 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −163746. | −0.0329515 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.66333e6 | 0.331237 | 0.165619 | − | 0.986190i | \(-0.447038\pi\) | ||||
0.165619 | + | 0.986190i | \(0.447038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 111156. | 0.0219064 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 898464. | 0.175240 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.44115e6 | −0.664277 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.34505e6 | −0.830180 | −0.415090 | − | 0.909780i | \(-0.636250\pi\) | ||||
−0.415090 | + | 0.909780i | \(0.636250\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.05778e6 | −1.33474 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.65016e6 | 1.24488 | 0.622442 | − | 0.782666i | \(-0.286141\pi\) | ||||
0.622442 | + | 0.782666i | \(0.286141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.86186e6 | −0.345008 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.37610e6 | 0.252428 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.46175e6 | −0.628644 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −742996. | −0.133578 | −0.0667890 | − | 0.997767i | \(-0.521275\pi\) | ||||
−0.0667890 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −742944. | −0.132240 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.57126e6 | 0.981823 | 0.490911 | − | 0.871209i | \(-0.336664\pi\) | ||||
0.490911 | + | 0.871209i | \(0.336664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.30215e6 | 0.227213 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.95172e6 | −0.509983 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.91247e6 | −1.01152 | −0.505760 | − | 0.862674i | \(-0.668788\pi\) | ||||
−0.505760 | + | 0.862674i | \(0.668788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.63590e6 | 0.615970 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.10151e7 | −1.84798 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.20540e6 | −0.532555 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.98906e6 | 0.491822 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 58344.0 | 0.00950775 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.34065e6 | 1.02339 | 0.511693 | − | 0.859168i | \(-0.329019\pi\) | ||||
0.511693 | + | 0.859168i | \(0.329019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −118300. | −0.0189117 | −0.00945585 | − | 0.999955i | \(-0.503010\pi\) | ||||
−0.00945585 | + | 0.999955i | \(0.503010\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 367500. | 0.0581914 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.03680e6 | −0.946848 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.10156e6 | −0.637250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.91971e6 | −0.449369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.32881e6 | 0.964949 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.83350e6 | −0.427995 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 215568. | 0.0322588 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.33496e6 | −0.197922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.36248e6 | 0.787721 | 0.393860 | − | 0.919170i | \(-0.371139\pi\) | ||||
0.393860 | + | 0.919170i | \(0.371139\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.74106e6 | 0.398951 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.47365e6 | −0.500950 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 579116. | 0.0827556 | 0.0413778 | − | 0.999144i | \(-0.486825\pi\) | ||||
0.0413778 | + | 0.999144i | \(0.486825\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.73537e6 | −0.387334 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.48991e6 | −0.910667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.64246e6 | −0.506503 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −94200.0 | −0.0129813 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.61880e6 | 0.903943 | 0.451972 | − | 0.892032i | \(-0.350721\pi\) | ||||
0.451972 | + | 0.892032i | \(0.350721\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.83250e6 | 0.789452 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.13744e6 | −0.689191 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.65907e6 | 0.353556 | 0.176778 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176778 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −701150. | −0.0924038 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.23436e6 | −0.161244 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.12650e7 | −1.45865 | −0.729324 | − | 0.684169i | \(-0.760165\pi\) | ||||
−0.729324 | + | 0.684169i | \(0.760165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.05242e6 | 0.520145 | 0.260072 | − | 0.965589i | \(-0.416254\pi\) | ||||
0.260072 | + | 0.965589i | \(0.416254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.29408e6 | 0.546366 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 955000. | 0.120457 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.07566e6 | −0.634678 | −0.317339 | − | 0.948312i | \(-0.602789\pi\) | ||||
−0.317339 | + | 0.948312i | \(0.602789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.93009e6 | −0.735131 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.15933e6 | −0.265387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −919624. | −0.112057 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 876150. | 0.105849 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.07079e6 | 1.08655 | 0.543275 | − | 0.839555i | \(-0.317184\pi\) | ||||
0.543275 | + | 0.839555i | \(0.317184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.10426e7 | −2.49925 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.14362e6 | 0.841298 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.47793e7 | 1.72590 | 0.862951 | − | 0.505288i | \(-0.168614\pi\) | ||||
0.862951 | + | 0.505288i | \(0.168614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 943250. | 0.109228 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.13450e6 | 0.359941 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.06212e6 | −1.03196 | −0.515980 | − | 0.856601i | \(-0.672572\pi\) | ||||
−0.515980 | + | 0.856601i | \(0.672572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.65482e6 | −0.299812 | −0.149906 | − | 0.988700i | \(-0.547897\pi\) | ||||
−0.149906 | + | 0.988700i | \(0.547897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.71388e6 | 0.639938 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.70212e6 | 0.411209 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.52930e7 | −1.68470 | −0.842349 | − | 0.538932i | \(-0.818828\pi\) | ||||
−0.842349 | + | 0.538932i | \(0.818828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.42178e6 | −0.155343 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.90310e6 | 0.206234 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49070e7 | 1.60228 | 0.801139 | − | 0.598479i | \(-0.204228\pi\) | ||||
0.801139 | + | 0.598479i | \(0.204228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.36340e6 | −0.571811 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.12030e6 | 0.541480 | 0.270740 | − | 0.962653i | \(-0.412732\pi\) | ||||
0.270740 | + | 0.962653i | \(0.412732\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.83140e6 | 0.506811 | 0.253405 | − | 0.967360i | \(-0.418449\pi\) | ||||
0.253405 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.27091e6 | −0.652532 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.33599e6 | 0.654025 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.79076e7 | −1.81915 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −241780. | −0.0243665 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.78212e6 | −0.578114 | −0.289057 | − | 0.957312i | \(-0.593342\pi\) | ||||
−0.289057 | + | 0.957312i | \(0.593342\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.46277e6 | −0.938661 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 667600. | 0.0657025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −849954. | −0.0829940 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.99415e6 | 0.677615 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.65691e7 | −1.59277 | −0.796386 | − | 0.604789i | \(-0.793257\pi\) | ||||
−0.796386 | + | 0.604789i | \(0.793257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.28491e6 | 0.885626 | 0.442813 | − | 0.896614i | \(-0.353981\pi\) | ||||
0.442813 | + | 0.896614i | \(0.353981\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.94280e6 | −0.467815 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.31505e7 | 1.23504 | 0.617519 | − | 0.786556i | \(-0.288138\pi\) | ||||
0.617519 | + | 0.786556i | \(0.288138\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.63976e7 | −1.52815 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.60992e6 | −0.426325 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.28207e6 | −0.576527 | −0.288263 | − | 0.957551i | \(-0.593078\pi\) | ||||
−0.288263 | + | 0.957551i | \(0.593078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −175700. | −0.0160018 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.34600e6 | −0.663953 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.16007e7 | 1.93756 | 0.968779 | − | 0.247927i | \(-0.0797492\pi\) | ||||
0.968779 | + | 0.247927i | \(0.0797492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.79235e6 | −0.515645 | −0.257823 | − | 0.966192i | \(-0.583005\pi\) | ||||
−0.257823 | + | 0.966192i | \(0.583005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.27096e6 | −0.288996 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.28790e6 | 0.288313 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.69470e6 | −0.321562 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.63010e7 | 1.40815 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.53623e7 | −1.31719 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.45071e7 | 1.23465 | 0.617324 | − | 0.786709i | \(-0.288217\pi\) | ||||
0.617324 | + | 0.786709i | \(0.288217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.56500e6 | −0.216685 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.66775e7 | 1.39849 | 0.699243 | − | 0.714884i | \(-0.253520\pi\) | ||||
0.699243 | + | 0.714884i | \(0.253520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.74465e6 | −0.561417 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.53282e6 | 0.457171 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.35555e6 | −0.275240 | −0.137620 | − | 0.990485i | \(-0.543945\pi\) | ||||
−0.137620 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.50505e6 | 0.285409 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.50611e7 | 1.21749 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −585516. | −0.0469884 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −80036.0 | −0.00637662 | −0.00318831 | − | 0.999995i | \(-0.501015\pi\) | ||||
−0.00318831 | + | 0.999995i | \(0.501015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.69716e6 | 0.213340 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.39690e6 | 0.188230 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.37661e7 | −1.07332 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.04697e6 | 0.468107 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.26403e7 | 0.971544 | 0.485772 | − | 0.874086i | \(-0.338539\pi\) | ||||
0.485772 | + | 0.874086i | \(0.338539\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −842776. | −0.0643167 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.61280e6 | −0.122210 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.55221e6 | 0.192030 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.03203e7 | 0.771043 | 0.385521 | − | 0.922699i | \(-0.374022\pi\) | ||||
0.385521 | + | 0.922699i | \(0.374022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.35926e6 | 0.545959 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.19795e7 | −0.882502 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.92060e6 | 0.359959 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.81083e7 | −1.31547 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.32330e7 | −0.954630 | −0.477315 | − | 0.878732i | \(-0.658390\pi\) | ||||
−0.477315 | + | 0.878732i | \(0.658390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.28258e6 | −0.450091 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −756264. | −0.0538056 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.51125e6 | −0.106780 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.89447e6 | −0.132939 | −0.0664695 | − | 0.997788i | \(-0.521173\pi\) | ||||
−0.0664695 | + | 0.997788i | \(0.521173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.44612e7 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.26865e7 | −0.878110 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.25023e6 | −0.223436 | −0.111718 | − | 0.993740i | \(-0.535635\pi\) | ||||
−0.111718 | + | 0.993740i | \(0.535635\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 720300. | 0.0491807 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.20901e7 | 2.17622 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.56366e7 | −1.72683 | −0.863415 | − | 0.504495i | \(-0.831679\pi\) | ||||
−0.863415 | + | 0.504495i | \(0.831679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.14016e7 | −0.762819 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.10332e7 | 0.733209 | 0.366605 | − | 0.930377i | \(-0.380520\pi\) | ||||
0.366605 | + | 0.930377i | \(0.380520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.67505e6 | −0.572640 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.36273e6 | 0.286060 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.55366e6 | −0.361722 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.75977e7 | −1.13856 | −0.569279 | − | 0.822144i | \(-0.692778\pi\) | ||||
−0.569279 | + | 0.822144i | \(0.692778\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.15778e7 | 0.744115 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.75820e6 | 0.431483 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.25444e6 | −0.586963 | −0.293481 | − | 0.955965i | \(-0.594814\pi\) | ||||
−0.293481 | + | 0.955965i | \(0.594814\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.01948e7 | −0.642355 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.36640e7 | 0.855293 | 0.427647 | − | 0.903946i | \(-0.359343\pi\) | ||||
0.427647 | + | 0.903946i | \(0.359343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.80835e6 | −0.423380 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.90575e6 | −0.117737 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.04402e7 | −0.640795 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.98498e7 | −1.82023 | −0.910114 | − | 0.414357i | \(-0.864006\pi\) | ||||
−0.910114 | + | 0.414357i | \(0.864006\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.94180e6 | −0.359983 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.32878e7 | 1.40178 | 0.700891 | − | 0.713269i | \(-0.252786\pi\) | ||||
0.700891 | + | 0.713269i | \(0.252786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.90000e6 | −0.293050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −184632. | −0.0109712 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.79846e7 | −2.83307 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.92803e7 | 2.30434 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.92347e6 | 0.578441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.77965e6 | −0.218916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.01691e7 | 0.585259 | 0.292629 | − | 0.956226i | \(-0.405470\pi\) | ||||
0.292629 | + | 0.956226i | \(0.405470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.61710e7 | −1.49668 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.37425e6 | −0.0780955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.78102e6 | −0.552333 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 496200. | 0.0278445 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.43192e6 | 0.135614 | 0.0678068 | − | 0.997698i | \(-0.478400\pi\) | ||||
0.0678068 | + | 0.997698i | \(0.478400\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.13952e6 | −0.229395 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.28013e7 | −0.704973 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.12563e7 | −2.25788 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.87180e6 | 0.101805 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.68015e6 | −0.307027 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.41960e7 | 0.762595 | 0.381298 | − | 0.924452i | \(-0.375477\pi\) | ||||
0.381298 | + | 0.924452i | \(0.375477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.75548e6 | −0.0937227 | −0.0468613 | − | 0.998901i | \(-0.514922\pi\) | ||||
−0.0468613 | + | 0.998901i | \(0.514922\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.63080e7 | 1.39592 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.47037e7 | −0.775412 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.42216e7 | −2.31782 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.71725e6 | 0.0894592 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.69715e7 | 0.878742 | 0.439371 | − | 0.898306i | \(-0.355201\pi\) | ||||
0.439371 | + | 0.898306i | \(0.355201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.85241e6 | 0.455577 | 0.227789 | − | 0.973711i | \(-0.426851\pi\) | ||||
0.227789 | + | 0.973711i | \(0.426851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.17000e6 | −0.213305 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.48418e7 | −1.26304 | −0.631522 | − | 0.775358i | \(-0.717570\pi\) | ||||
−0.631522 | + | 0.775358i | \(0.717570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.55691e6 | 0.179757 | 0.0898787 | − | 0.995953i | \(-0.471352\pi\) | ||||
0.0898787 | + | 0.995953i | \(0.471352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.66202e6 | 0.234192 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.84877e6 | 0.0923146 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.54780e6 | −0.0768243 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.21754e7 | 1.58749 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.51401e7 | −1.23300 | −0.616499 | − | 0.787356i | \(-0.711449\pi\) | ||||
−0.616499 | + | 0.787356i | \(0.711449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.46644e7 | −0.714949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −905544. | −0.0438875 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.14942e6 | −0.296273 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.25616e6 | 0.347535 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.60726e7 | −1.24141 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −479792. | −0.0227106 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.01242e7 | −0.476419 | −0.238209 | − | 0.971214i | \(-0.576560\pi\) | ||||
−0.238209 | + | 0.971214i | \(0.576560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.64290e6 | −0.310772 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.05522e7 | −0.490784 | −0.245392 | − | 0.969424i | \(-0.578917\pi\) | ||||
−0.245392 | + | 0.969424i | \(0.578917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.37758e7 | −1.56179 | −0.780894 | − | 0.624663i | \(-0.785236\pi\) | ||||
−0.780894 | + | 0.624663i | \(0.785236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.05123e7 | −0.483268 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.12652e7 | 1.42901 | 0.714503 | − | 0.699633i | \(-0.246653\pi\) | ||||
0.714503 | + | 0.699633i | \(0.246653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 121550. | 0.00552350 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.92348e6 | −0.448349 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.13308e7 | 1.85663 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04315e7 | 0.912545 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.36270e7 | 0.605150 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.89921e7 | −1.27286 | −0.636430 | − | 0.771334i | \(-0.719590\pi\) | ||||
−0.636430 | + | 0.771334i | \(0.719590\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.71482e6 | 0.0748596 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.43211e6 | −0.279199 | −0.139599 | − | 0.990208i | \(-0.544581\pi\) | ||||
−0.139599 | + | 0.990208i | \(0.544581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.41164e7 | 1.04090 | 0.520452 | − | 0.853891i | \(-0.325764\pi\) | ||||
0.520452 | + | 0.853891i | \(0.325764\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.84760e6 | 0.379723 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.16359e6 | −0.177688 | −0.0888442 | − | 0.996046i | \(-0.528317\pi\) | ||||
−0.0888442 | + | 0.996046i | \(0.528317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.30850e6 | 0.0555288 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.40062e7 | 0.591052 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.44292e7 | −0.605499 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 449100. | 0.0187407 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.49094e6 | −0.269356 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.89571e7 | 0.782300 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.27358e6 | 0.0522654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.68789e6 | −0.395375 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.71055e6 | 0.231770 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.18248e7 | 1.68817 | 0.844083 | − | 0.536212i | \(-0.180145\pi\) | ||||
0.844083 | + | 0.536212i | \(0.180145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.15651e6 | −0.206989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.96323e6 | 0.118296 | 0.0591480 | − | 0.998249i | \(-0.481162\pi\) | ||||
0.0591480 | + | 0.998249i | \(0.481162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.45018e7 | 0.972795 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.28900e6 | 0.327303 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −344372. | −0.0135240 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.22355e7 | −0.868476 | −0.434238 | − | 0.900798i | \(-0.642982\pi\) | ||||
−0.434238 | + | 0.900798i | \(0.642982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.26333e7 | −0.490757 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.50094e7 | 0.966271 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −196250. | −0.00754146 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.26934e7 | 0.485152 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.65046e6 | −0.366867 | −0.183434 | − | 0.983032i | \(-0.558721\pi\) | ||||
−0.183434 | + | 0.983032i | \(0.558721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.44428e6 | 0.243669 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.73456e7 | 1.40455 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.07030e7 | −0.400384 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.45116e7 | −1.65624 | −0.828122 | − | 0.560548i | \(-0.810590\pi\) | ||||
−0.828122 | + | 0.560548i | \(0.810590\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.34811e7 | −0.869069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.08983e7 | 0.401223 | 0.200612 | − | 0.979671i | \(-0.435707\pi\) | ||||
0.200612 | + | 0.979671i | \(0.435707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.73176e7 | −1.00038 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.02740e6 | −0.183132 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.37370e7 | 0.497757 | 0.248879 | − | 0.968535i | \(-0.419938\pi\) | ||||
0.248879 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.62675e7 | −0.946789 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.29760e7 | 1.18235 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.78867e7 | −0.994639 | −0.497319 | − | 0.867568i | \(-0.665682\pi\) | ||||
−0.497319 | + | 0.867568i | \(0.665682\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.94600e6 | 0.317410 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.61329e7 | 0.569420 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.86990e6 | 0.241215 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.28364e7 | 1.14696 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.12207e7 | 0.389900 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.23543e7 | −0.427073 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.36444e6 | −0.253264 | −0.126632 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126632 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.48002e7 | 0.848487 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.71508e6 | 0.296635 | 0.148318 | − | 0.988940i | \(-0.452614\pi\) | ||||
0.148318 | + | 0.988940i | \(0.452614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.69792e6 | 0.159083 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.65500e6 | −0.0894444 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.60032e7 | −0.536377 | −0.268188 | − | 0.963366i | \(-0.586425\pi\) | ||||
−0.268188 | + | 0.963366i | \(0.586425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.18941e7 | −2.39738 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.37557e7 | 0.456361 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.81746e7 | 1.26006 | 0.630030 | − | 0.776571i | \(-0.283043\pi\) | ||||
0.630030 | + | 0.776571i | \(0.283043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.48826e7 | 0.488750 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.16109e6 | −0.103287 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.51753e7 | −0.818435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.76979e7 | 1.21936 | 0.609681 | − | 0.792647i | \(-0.291298\pi\) | ||||
0.609681 | + | 0.792647i | \(0.291298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.67623e7 | −0.861290 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.53020e6 | 0.209107 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.40251e7 | 1.40269 | 0.701347 | − | 0.712820i | \(-0.252582\pi\) | ||||
0.701347 | + | 0.712820i | \(0.252582\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.28866e6 | 0.0408529 |
(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 | 560.6.a.g.1.1 | 1 | ||
4.3 | odd | 2 | 280.6.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
560.6.a.g.1.1 | 1 | 1.1 | even | 1 | trivial |