Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,6,Mod(1,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.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: | \(62.8704573667\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2732674592.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 113x^{2} + 882 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.90430\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.1 |
$q$-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 | ||||||||
\(3\) | −28.9227 | −1.85539 | −0.927695 | − | 0.373339i | \(-0.878213\pi\) | ||||
−0.927695 | + | 0.373339i | \(0.878213\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 63.5336 | 1.13652 | 0.568262 | − | 0.822848i | \(-0.307616\pi\) | ||||
0.568262 | + | 0.822848i | \(0.307616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 593.520 | 2.44247 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −592.520 | −1.47646 | −0.738230 | − | 0.674549i | \(-0.764338\pi\) | ||||
−0.738230 | + | 0.674549i | \(0.764338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −433.359 | −0.711196 | −0.355598 | − | 0.934639i | \(-0.615723\pi\) | ||||
−0.355598 | + | 0.934639i | \(0.615723\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1837.56 | −2.10869 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −32.2049 | −0.0270271 | −0.0135135 | − | 0.999909i | \(-0.504302\pi\) | ||||
−0.0135135 | + | 0.999909i | \(0.504302\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2712.56 | 1.72383 | 0.861917 | − | 0.507049i | \(-0.169264\pi\) | ||||
0.861917 | + | 0.507049i | \(0.169264\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3342.60 | −1.31754 | −0.658772 | − | 0.752343i | \(-0.728924\pi\) | ||||
−0.658772 | + | 0.752343i | \(0.728924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 911.520 | 0.291687 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10138.0 | −2.67635 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8378.33 | 1.84996 | 0.924980 | − | 0.380016i | \(-0.124081\pi\) | ||||
0.924980 | + | 0.380016i | \(0.124081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3301.03 | 0.616944 | 0.308472 | − | 0.951233i | \(-0.400182\pi\) | ||||
0.308472 | + | 0.951233i | \(0.400182\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17137.3 | 2.73941 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −812.959 | −0.0976257 | −0.0488129 | − | 0.998808i | \(-0.515544\pi\) | ||||
−0.0488129 | + | 0.998808i | \(0.515544\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12533.9 | 1.31955 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8718.28 | 0.809974 | 0.404987 | − | 0.914322i | \(-0.367276\pi\) | ||||
0.404987 | + | 0.914322i | \(0.367276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9723.64 | −0.801970 | −0.400985 | − | 0.916085i | \(-0.631332\pi\) | ||||
−0.400985 | + | 0.916085i | \(0.631332\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 37708.5 | 2.77593 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20235.8 | 1.33621 | 0.668106 | − | 0.744066i | \(-0.267105\pi\) | ||||
0.668106 | + | 0.744066i | \(0.267105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 931.451 | 0.0501458 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9249.61 | −0.452308 | −0.226154 | − | 0.974092i | \(-0.572615\pi\) | ||||
−0.226154 | + | 0.974092i | \(0.572615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −37645.0 | −1.67803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −78454.5 | −3.19838 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4039.25 | 0.151067 | 0.0755337 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755337 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10891.2 | −0.374758 | −0.187379 | − | 0.982288i | \(-0.559999\pi\) | ||||
−0.187379 | + | 0.982288i | \(0.559999\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −27532.8 | −0.808291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52765.6 | −1.43603 | −0.718016 | − | 0.696027i | \(-0.754949\pi\) | ||||
−0.718016 | + | 0.696027i | \(0.754949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 96677.0 | 2.44456 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52278.1 | 1.23076 | 0.615380 | − | 0.788230i | \(-0.289002\pi\) | ||||
0.615380 | + | 0.788230i | \(0.289002\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50714.2 | 1.11384 | 0.556919 | − | 0.830567i | \(-0.311983\pi\) | ||||
0.556919 | + | 0.830567i | \(0.311983\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −26363.6 | −0.541192 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −79876.5 | −1.43996 | −0.719981 | − | 0.693993i | \(-0.755850\pi\) | ||||
−0.719981 | + | 0.693993i | \(0.755850\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 148992. | 2.52319 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −46491.8 | −0.740767 | −0.370383 | − | 0.928879i | \(-0.620774\pi\) | ||||
−0.370383 | + | 0.928879i | \(0.620774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2046.09 | −0.0307169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −242324. | −3.43240 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −148975. | −1.99360 | −0.996800 | − | 0.0799329i | \(-0.974529\pi\) | ||||
−0.996800 | + | 0.0799329i | \(0.974529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −95474.7 | −1.14467 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 172339. | 1.95918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 29601.7 | 0.319439 | 0.159719 | − | 0.987162i | \(-0.448941\pi\) | ||||
0.159719 | + | 0.987162i | \(0.448941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −351673. | −3.60621 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −106123. | −1.03515 | −0.517577 | − | 0.855636i | \(-0.673166\pi\) | ||||
−0.517577 | + | 0.855636i | \(0.673166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26722.6 | 0.248190 | 0.124095 | − | 0.992270i | \(-0.460397\pi\) | ||||
0.124095 | + | 0.992270i | \(0.460397\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −108549. | −0.916573 | −0.458287 | − | 0.888804i | \(-0.651537\pi\) | ||||
−0.458287 | + | 0.888804i | \(0.651537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −76781.6 | −0.619000 | −0.309500 | − | 0.950899i | \(-0.600162\pi\) | ||||
−0.309500 | + | 0.950899i | \(0.600162\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23512.9 | 0.181134 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −89821.9 | −0.661738 | −0.330869 | − | 0.943677i | \(-0.607342\pi\) | ||||
−0.330869 | + | 0.943677i | \(0.607342\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −212368. | −1.49742 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −257207. | −1.73708 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190030. | 1.17993 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −252156. | −1.50282 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −140630. | −0.805015 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −48119.5 | −0.264735 | −0.132368 | − | 0.991201i | \(-0.542258\pi\) | ||||
−0.132368 | + | 0.991201i | \(0.542258\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 281234. | 1.48797 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6888.93 | −0.0350730 | −0.0175365 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175365 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −644103. | −3.04173 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 103794. | 0.472467 | 0.236233 | − | 0.971696i | \(-0.424087\pi\) | ||||
0.236233 | + | 0.971696i | \(0.424087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 325743. | 1.43001 | 0.715003 | − | 0.699121i | \(-0.246425\pi\) | ||||
0.715003 | + | 0.699121i | \(0.246425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −585273. | −2.47920 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 256774. | 1.05005 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 532305. | 2.10252 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −109769. | −0.405055 | −0.202528 | − | 0.979277i | \(-0.564916\pi\) | ||||
−0.202528 | + | 0.979277i | \(0.564916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 312238. | 1.11441 | 0.557204 | − | 0.830376i | \(-0.311874\pi\) | ||||
0.557204 | + | 0.830376i | \(0.311874\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19114.2 | −0.0660129 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 209727. | 0.701171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −120613. | −0.390520 | −0.195260 | − | 0.980751i | \(-0.562555\pi\) | ||||
−0.195260 | + | 0.980751i | \(0.562555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 267523. | 0.839207 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −176764. | −0.521104 | −0.260552 | − | 0.965460i | \(-0.583905\pi\) | ||||
−0.260552 | + | 0.965460i | \(0.583905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.08879e6 | 3.11340 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −487840. | −1.35359 | −0.676794 | − | 0.736172i | \(-0.736631\pi\) | ||||
−0.676794 | + | 0.736172i | \(0.736631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −183493. | −0.494201 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60996e6 | 4.21042 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 77727.6 | 0.197451 | 0.0987257 | − | 0.995115i | \(-0.468523\pi\) | ||||
0.0987257 | + | 0.995115i | \(0.468523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −116826. | −0.280289 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −307721. | −0.717834 | −0.358917 | − | 0.933369i | \(-0.616854\pi\) | ||||
−0.358917 | + | 0.933369i | \(0.616854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −210791. | −0.478251 | −0.239126 | − | 0.970989i | \(-0.576861\pi\) | ||||
−0.239126 | + | 0.970989i | \(0.576861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 315002. | 0.695322 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −51650.2 | −0.110954 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19082.0 | 0.0399044 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 593394. | 1.17695 | 0.588477 | − | 0.808514i | \(-0.299728\pi\) | ||||
0.588477 | + | 0.808514i | \(0.299728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −369858. | −0.714729 | −0.357365 | − | 0.933965i | \(-0.616325\pi\) | ||||
−0.357365 | + | 0.933965i | \(0.616325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 796323. | 1.49969 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −458329. | −0.841419 | −0.420709 | − | 0.907196i | \(-0.638219\pi\) | ||||
−0.420709 | + | 0.907196i | \(0.638219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −444199. | −0.795142 | −0.397571 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397571 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52612e6 | 2.66440 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 553904. | 0.920555 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.98390e6 | −3.21806 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.60725e6 | −2.54517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −327421. | −0.506291 | −0.253146 | − | 0.967428i | \(-0.581465\pi\) | ||||
−0.253146 | + | 0.967428i | \(0.581465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.51202e6 | −2.28354 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −617778. | −0.911458 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.46679e6 | −2.06660 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13956.3 | 0.0192215 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −449149. | −0.604823 | −0.302411 | − | 0.953177i | \(-0.597792\pi\) | ||||
−0.302411 | + | 0.953177i | \(0.597792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 541006. | 0.712436 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −36225.2 | −0.0466602 | −0.0233301 | − | 0.999728i | \(-0.507427\pi\) | ||||
−0.0233301 | + | 0.999728i | \(0.507427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −807858. | −1.01800 | −0.508998 | − | 0.860768i | \(-0.669984\pi\) | ||||
−0.508998 | + | 0.860768i | \(0.669984\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.21525e6 | 1.46648 | 0.733242 | − | 0.679968i | \(-0.238006\pi\) | ||||
0.733242 | + | 0.679968i | \(0.238006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.28565e6 | 1.51864 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.31024e6 | 2.67169 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −203963. | −0.230970 | −0.115485 | − | 0.993309i | \(-0.536842\pi\) | ||||
−0.115485 | + | 0.993309i | \(0.536842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −650170. | −0.721082 | −0.360541 | − | 0.932743i | \(-0.617408\pi\) | ||||
−0.360541 | + | 0.932743i | \(0.617408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.84572e6 | −2.00516 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17551e6 | −1.22598 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.34467e6 | 1.37441 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 69444.4 | 0.0695750 | 0.0347875 | − | 0.999395i | \(-0.488925\pi\) | ||||
0.0347875 | + | 0.999395i | \(0.488925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.98056e6 | 1.94530 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 59178.4 | 0.0569919 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −332991. | −0.314485 | −0.157242 | − | 0.987560i | \(-0.550260\pi\) | ||||
−0.157242 | + | 0.987560i | \(0.550260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.97271e6 | 4.51847 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −896118. | −0.798870 | −0.399435 | − | 0.916762i | \(-0.630794\pi\) | ||||
−0.399435 | + | 0.916762i | \(0.630794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −587661. | −0.514058 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.30875e6 | 3.69891 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.70580e6 | −1.43730 | −0.718652 | − | 0.695370i | \(-0.755240\pi\) | ||||
−0.718652 | + | 0.695370i | \(0.755240\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 69736.1 | 0.0576812 | 0.0288406 | − | 0.999584i | \(-0.490818\pi\) | ||||
0.0288406 | + | 0.999584i | \(0.490818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −540095. | −0.430663 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −559541. | −0.438160 | −0.219080 | − | 0.975707i | \(-0.570305\pi\) | ||||
−0.219080 | + | 0.975707i | \(0.570305\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.95923e6 | 1.50687 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −837805. | −0.632961 | −0.316481 | − | 0.948599i | \(-0.602501\pi\) | ||||
−0.316481 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.83538e6 | −1.36226 | −0.681131 | − | 0.732162i | \(-0.738512\pi\) | ||||
−0.681131 | + | 0.732162i | \(0.738512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.98450e6 | −3.63504 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41882e6 | −0.999270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −856161. | −0.592684 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −245011. | −0.166731 | −0.0833655 | − | 0.996519i | \(-0.526567\pi\) | ||||
−0.0833655 | + | 0.996519i | \(0.526567\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 256628. | 0.171692 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.00696e6 | 3.95152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.44855e6 | 0.937032 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.06935e6 | 1.92062 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −691957. | −0.425922 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 396561. | 0.240140 | 0.120070 | − | 0.992765i | \(-0.461688\pi\) | ||||
0.120070 | + | 0.992765i | \(0.461688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −772888. | −0.460490 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.14081e6 | −1.25509 | −0.627547 | − | 0.778579i | \(-0.715941\pi\) | ||||
−0.627547 | + | 0.778579i | \(0.715941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.24441e6 | 1.87187 | 0.935934 | − | 0.352175i | \(-0.114558\pi\) | ||||
0.935934 | + | 0.352175i | \(0.114558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.63757e6 | −1.47420 | −0.737100 | − | 0.675784i | \(-0.763805\pi\) | ||||
−0.737100 | + | 0.675784i | \(0.763805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.96433e6 | −2.73139 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.13953e6 | 1.70060 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −87357.7 | −0.0465902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −395015. | −0.207446 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.22073e6 | 1.14849 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.83433e6 | 0.920251 | 0.460126 | − | 0.887854i | \(-0.347804\pi\) | ||||
0.460126 | + | 0.887854i | \(0.347804\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −482508. | −0.238448 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.35239e6 | −1.63208 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 433695. | 0.208022 | 0.104011 | − | 0.994576i | \(-0.466832\pi\) | ||||
0.104011 | + | 0.994576i | \(0.466832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.59789e6 | 1.22778 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.95593e6 | −0.910893 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.14224e6 | 2.77830 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −703899. | −0.313825 | −0.156912 | − | 0.987613i | \(-0.550154\pi\) | ||||
−0.156912 | + | 0.987613i | \(0.550154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.26554e6 | −0.995653 | −0.497826 | − | 0.867277i | \(-0.665868\pi\) | ||||
−0.497826 | + | 0.867277i | \(0.665868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.39338e6 | 1.90341 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.84527e6 | 1.64244 | 0.821220 | − | 0.570611i | \(-0.193294\pi\) | ||||
0.821220 | + | 0.570611i | \(0.193294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.32142e6 | 1.39879 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −263792. | −0.108025 | −0.0540126 | − | 0.998540i | \(-0.517201\pi\) | ||||
−0.0540126 | + | 0.998540i | \(0.517201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.88189e6 | 1.97160 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.49616e6 | −2.18924 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.22205e6 | 1.26590 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.09852e6 | −1.20085 | −0.600426 | − | 0.799680i | \(-0.705002\pi\) | ||||
−0.600426 | + | 0.799680i | \(0.705002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.17448e6 | 1.97834 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −460228. | −0.171278 | −0.0856388 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856388 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.06740e6 | 1.49362 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.63082e6 | −1.31568 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −951319. | −0.340195 | −0.170098 | − | 0.985427i | \(-0.554408\pi\) | ||||
−0.170098 | + | 0.985427i | \(0.554408\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.39174e6 | 0.491187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.35711e6 | 1.16942 | 0.584708 | − | 0.811244i | \(-0.301209\pi\) | ||||
0.584708 | + | 0.811244i | \(0.301209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.77118e6 | −1.95879 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.31496e6 | 1.11072 | 0.555359 | − | 0.831611i | \(-0.312581\pi\) | ||||
0.555359 | + | 0.831611i | \(0.312581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 107648. | 0.0356094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 199246. | 0.0650741 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.07484e6 | −1.63655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00849e6 | 0.639576 | 0.319788 | − | 0.947489i | \(-0.396388\pi\) | ||||
0.319788 | + | 0.947489i | \(0.396388\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.76149e6 | 0.857595 | 0.428797 | − | 0.903401i | \(-0.358937\pi\) | ||||
0.428797 | + | 0.903401i | \(0.358937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.43053e6 | −0.438768 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.46601e6 | 2.86767 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 481695. | 0.144140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.93620e6 | 0.867916 | 0.433958 | − | 0.900933i | \(-0.357117\pi\) | ||||
0.433958 | + | 0.900933i | \(0.357117\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00200e6 | −0.876610 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.95380e6 | −0.841899 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.42135e6 | −2.65322 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −355495. | −0.0989233 | −0.0494617 | − | 0.998776i | \(-0.515751\pi\) | ||||
−0.0494617 | + | 0.998776i | \(0.515751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.22340e6 | −1.16133 | −0.580666 | − | 0.814142i | \(-0.697208\pi\) | ||||
−0.580666 | + | 0.814142i | \(0.697208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.20104e7 | 3.26366 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29355.4 | −0.00788344 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.42659e6 | −1.94826 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.75307e6 | 1.49179 | 0.745893 | − | 0.666066i | \(-0.232023\pi\) | ||||
0.745893 | + | 0.666066i | \(0.232023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.17411e6 | −1.58254 | −0.791269 | − | 0.611468i | \(-0.790579\pi\) | ||||
−0.791269 | + | 0.611468i | \(0.790579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.53957e7 | −3.90100 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.06701e6 | −2.27123 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.07395e6 | −1.50422 | −0.752108 | − | 0.659040i | \(-0.770963\pi\) | ||||
−0.752108 | + | 0.659040i | \(0.770963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.98673e6 | 0.965177 | 0.482589 | − | 0.875847i | \(-0.339697\pi\) | ||||
0.482589 | + | 0.875847i | \(0.339697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.46492e6 | −2.26577 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.17481e6 | 0.751535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.65019e6 | 0.854475 | 0.427238 | − | 0.904139i | \(-0.359487\pi\) | ||||
0.427238 | + | 0.904139i | \(0.359487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.16576e6 | −1.19589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.03077e6 | −2.06766 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −654800. | −0.146662 | −0.0733311 | − | 0.997308i | \(-0.523363\pi\) | ||||
−0.0733311 | + | 0.997308i | \(0.523363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 326493. | 0.0723338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.72912e6 | 1.25555 | 0.627777 | − | 0.778393i | \(-0.283965\pi\) | ||||
0.627777 | + | 0.778393i | \(0.283965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.03283e6 | 1.30788 | 0.653941 | − | 0.756545i | \(-0.273114\pi\) | ||||
0.653941 | + | 0.756545i | \(0.273114\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.06585e6 | −1.30095 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.23056e6 | 0.685465 | 0.342732 | − | 0.939433i | \(-0.388648\pi\) | ||||
0.342732 | + | 0.939433i | \(0.388648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.48844e6 | 0.724567 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.76146e6 | 1.18408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.47255e6 | 0.502819 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.48984e6 | −1.10475 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.22571e6 | 0.841513 | 0.420756 | − | 0.907174i | \(-0.361765\pi\) | ||||
0.420756 | + | 0.907174i | \(0.361765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 352303. | 0.0694310 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.88070e6 | 0.363050 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.71427e6 | 0.709662 | 0.354831 | − | 0.934930i | \(-0.384538\pi\) | ||||
0.354831 | + | 0.934930i | \(0.384538\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.11248e6 | 0.966851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.98790e6 | −1.30811 | −0.654053 | − | 0.756449i | \(-0.726933\pi\) | ||||
−0.654053 | + | 0.756449i | \(0.726933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −269823. | −0.0499990 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.23431e7 | −4.09854 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −366427. | −0.0658773 | −0.0329387 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329387 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.41096e7 | 2.51143 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.94067e6 | 1.75185 | 0.875923 | − | 0.482452i | \(-0.160254\pi\) | ||||
0.875923 | + | 0.482452i | \(0.160254\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.74237e6 | −1.17648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.30711e6 | 0.916935 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.23471e6 | 0.382320 | 0.191160 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191160 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.74999e7 | −4.61358 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.69778e6 | 0.282074 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.19901e7 | −1.97286 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.24809e6 | −0.366349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.40325e6 | −1.51769 | −0.758846 | − | 0.651271i | \(-0.774236\pi\) | ||||
−0.758846 | + | 0.651271i | \(0.774236\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.59427e6 | −1.21404 | −0.607018 | − | 0.794688i | \(-0.707634\pi\) | ||||
−0.607018 | + | 0.794688i | \(0.707634\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −106309. | −0.0166742 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.73665e6 | 0.735922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.39738e6 | 0.368978 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.77814e6 | −0.576050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.89652e6 | −1.04171 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.90010e6 | 1.33186 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.38619e6 | −1.23189 | −0.615945 | − | 0.787789i | \(-0.711226\pi\) | ||||
−0.615945 | + | 0.787789i | \(0.711226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.09664e6 | 0.887342 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.87821e6 | −0.703509 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.66890e6 | 0.810084 | 0.405042 | − | 0.914298i | \(-0.367257\pi\) | ||||
0.405042 | + | 0.914298i | \(0.367257\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.46415e6 | −0.915336 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.27267e7 | 3.18902 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.49386e6 | 0.205863 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.27409e6 | −0.993438 | −0.496719 | − | 0.867911i | \(-0.665462\pi\) | ||||
−0.496719 | + | 0.867911i | \(0.665462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.21383e6 | 0.570357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −551904. | −0.0740382 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.69351e6 | −0.225173 | −0.112586 | − | 0.993642i | \(-0.535914\pi\) | ||||
−0.112586 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.70671e6 | −0.752081 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 868712. | 0.112485 | 0.0562426 | − | 0.998417i | \(-0.482088\pi\) | ||||
0.0562426 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.85740e6 | −0.366759 | −0.183380 | − | 0.983042i | \(-0.558704\pi\) | ||||
−0.183380 | + | 0.983042i | \(0.558704\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.71625e7 | −2.18371 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.04685e6 | −0.384310 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 764271. | 0.0955670 | 0.0477835 | − | 0.998858i | \(-0.484784\pi\) | ||||
0.0477835 | + | 0.998858i | \(0.484784\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.06973e7 | 1.32610 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.48059e6 | 0.667814 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.63413e7 | −1.97423 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.53684e6 | 0.423663 | 0.211832 | − | 0.977306i | \(-0.432057\pi\) | ||||
0.211832 | + | 0.977306i | \(0.432057\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.95425e6 | 1.06351 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.32561e7 | 1.56116 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.39698e7 | −1.63137 | −0.815686 | − | 0.578495i | \(-0.803640\pi\) | ||||
−0.815686 | + | 0.578495i | \(0.803640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.28474e7 | 1.47530 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.65719e6 | −0.871972 | −0.435986 | − | 0.899954i | \(-0.643600\pi\) | ||||
−0.435986 | + | 0.899954i | \(0.643600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.93011e6 | −0.669694 | −0.334847 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334847 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.13175e7 | −3.50747 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.20733e7 | 1.34102 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.71203e6 | 0.849565 | 0.424783 | − | 0.905295i | \(-0.360350\pi\) | ||||
0.424783 | + | 0.905295i | \(0.360350\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.76936e6 | −0.950309 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.64407e7 | −1.76713 | −0.883564 | − | 0.468311i | \(-0.844863\pi\) | ||||
−0.883564 | + | 0.468311i | \(0.844863\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.60204e7 | −1.70799 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.11040e7 | −1.17427 | −0.587133 | − | 0.809491i | \(-0.699743\pi\) | ||||
−0.587133 | + | 0.809491i | \(0.699743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.44209e6 | 0.885571 | 0.442785 | − | 0.896628i | \(-0.353990\pi\) | ||||
0.442785 | + | 0.896628i | \(0.353990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.38873e7 | 3.52620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.17833e7 | −1.20661 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.64859e7 | 4.72229 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26181.2 | 0.00263854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.47137e6 | −0.347078 | −0.173539 | − | 0.984827i | \(-0.555520\pi\) | ||||
−0.173539 | + | 0.984827i | \(0.555520\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.46988e6 | 0.939367 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.05721e6 | −0.300878 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.10281e7 | 3.00610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.34206e6 | −0.705786 | −0.352893 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352893 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.28361e6 | −0.122435 | −0.0612177 | − | 0.998124i | \(-0.519498\pi\) | ||||
−0.0612177 | + | 0.998124i | \(0.519498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.78678e7 | 1.69111 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.09922e6 | −0.291066 | −0.145533 | − | 0.989353i | \(-0.546490\pi\) | ||||
−0.145533 | + | 0.989353i | \(0.546490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.39334e6 | −0.223045 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.46219e6 | −0.225964 | −0.112982 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112982 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −437678. | −0.0398613 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.00999e7 | 2.72052 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.60217e6 | 0.592206 | 0.296103 | − | 0.955156i | \(-0.404313\pi\) | ||||
0.296103 | + | 0.955156i | \(0.404313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.79222e7 | 1.59547 | 0.797733 | − | 0.603011i | \(-0.206032\pi\) | ||||
0.797733 | + | 0.603011i | \(0.206032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −403652. | −0.0356635 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.80054e7 | −2.43740 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.29906e7 | 1.12218 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.45326e6 | 0.553315 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.90502e7 | 1.62130 | 0.810648 | − | 0.585534i | \(-0.199115\pi\) | ||||
0.810648 | + | 0.585534i | \(0.199115\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.24098e6 | −0.780654 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.09514e6 | 0.678817 | 0.339408 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339408 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.04773e6 | 0.0865728 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.69330e6 | 0.631046 | 0.315523 | − | 0.948918i | \(-0.397820\pi\) | ||||
0.315523 | + | 0.948918i | \(0.397820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.59441e6 | 0.536970 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.33654e7 | 1.88878 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00840e6 | 0.321679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.64579e7 | 1.31123 | 0.655616 | − | 0.755094i | \(-0.272409\pi\) | ||||
0.655616 | + | 0.755094i | \(0.272409\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.06956e7 | 1.62524 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −280771. | −0.0218912 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.51484e7 | −2.72090 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.18690e6 | 0.244948 | 0.122474 | − | 0.992472i | \(-0.460917\pi\) | ||||
0.122474 | + | 0.992472i | \(0.460917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.20520e6 | −0.168291 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.71845e7 | −2.81767 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.60785e7 | −1.20124 | −0.600621 | − | 0.799534i | \(-0.705080\pi\) | ||||
−0.600621 | + | 0.799534i | \(0.705080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.74083e7 | −3.51707 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.10340e7 | −0.812851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63138e7 | 1.19341 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.89915e6 | 0.428540 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.15621e7 | −0.834096 | −0.417048 | − | 0.908885i | \(-0.636935\pi\) | ||||
−0.417048 | + | 0.908885i | \(0.636935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.88047e7 | 1.33789 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.63702e6 | 0.539608 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.06100e7 | 1.44624 | 0.723122 | − | 0.690720i | \(-0.242706\pi\) | ||||
0.723122 | + | 0.690720i | \(0.242706\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.71780e7 | 1.19716 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 313149. | 0.0216749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.55344e6 | −0.519260 | −0.259630 | − | 0.965708i | \(-0.583601\pi\) | ||||
−0.259630 | + | 0.965708i | \(0.583601\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.12647e7 | 2.12024 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.50829e7 | −1.01595 | −0.507975 | − | 0.861372i | \(-0.669606\pi\) | ||||
−0.507975 | + | 0.861372i | \(0.669606\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.39989e7 | 2.27468 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −971810. | −0.0645817 | −0.0322908 | − | 0.999479i | \(-0.510280\pi\) | ||||
−0.0322908 | + | 0.999479i | \(0.510280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.97402e6 | −0.460355 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.75939e7 | −1.80930 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.59178e6 | −0.102987 | −0.0514937 | − | 0.998673i | \(-0.516398\pi\) | ||||
−0.0514937 | + | 0.998673i | \(0.516398\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.00852e6 | −0.129089 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.98376e7 | 1.26655 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.50784e7 | −1.59060 | −0.795298 | − | 0.606219i | \(-0.792685\pi\) | ||||
−0.795298 | + | 0.606219i | \(0.792685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.72831e7 | −3.60929 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.26521e6 | −0.517359 | −0.258680 | − | 0.965963i | \(-0.583287\pi\) | ||||
−0.258680 | + | 0.965963i | \(0.583287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.21440e6 | −0.0750252 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.75045e6 | −0.107439 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.49439e7 | 1.52107 | 0.760535 | − | 0.649297i | \(-0.224937\pi\) | ||||
0.760535 | + | 0.649297i | \(0.224937\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.63099e6 | 0.583492 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.58183e7 | 1.55410 | 0.777049 | − | 0.629440i | \(-0.216716\pi\) | ||||
0.777049 | + | 0.629440i | \(0.216716\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00896e6 | 0.179954 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.36489e7 | 1.39626 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.09758e7 | −1.81717 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.49394e7 | −4.95113 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.66295e6 | −0.443836 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.16838e7 | −0.672431 | −0.336216 | − | 0.941785i | \(-0.609147\pi\) | ||||
−0.336216 | + | 0.941785i | \(0.609147\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.59181e7 | 1.48221 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.71980e6 | 0.266526 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.69967e7 | 0.953779 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.49383e7 | −0.833019 | −0.416509 | − | 0.909131i | \(-0.636747\pi\) | ||||
−0.416509 | + | 0.909131i | \(0.636747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −651691. | −0.0361139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.84197e7 | −4.86931 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00492e7 | −1.64454 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.93364e7 | 2.66676 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.78022e7 | 0.956320 | 0.478160 | − | 0.878273i | \(-0.341304\pi\) | ||||
0.478160 | + | 0.878273i | \(0.341304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.49528e7 | 0.798307 | 0.399154 | − | 0.916884i | \(-0.369304\pi\) | ||||
0.399154 | + | 0.916884i | \(0.369304\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.01695e6 | −0.107021 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.12304e7 | −0.592247 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.63760e7 | −1.38246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.78509e7 | −1.44205 | −0.721027 | − | 0.692907i | \(-0.756330\pi\) | ||||
−0.721027 | + | 0.692907i | \(0.756330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56865.0 | 0.00292648 | 0.00146324 | − | 0.999999i | \(-0.499534\pi\) | ||||
0.00146324 | + | 0.999999i | \(0.499534\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.56210e7 | 0.799049 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.32146e7 | −0.671878 | −0.335939 | − | 0.941884i | \(-0.609054\pi\) | ||||
−0.335939 | + | 0.941884i | \(0.609054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.67763e7 | 1.35321 | 0.676604 | − | 0.736347i | \(-0.263451\pi\) | ||||
0.676604 | + | 0.736347i | \(0.263451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.61834e7 | 0.812957 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.09943e7 | −1.53839 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.34658e7 | −1.65116 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.78838e7 | 1.36756 | 0.683781 | − | 0.729687i | \(-0.260334\pi\) | ||||
0.683781 | + | 0.729687i | \(0.260334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.96852e7 | 2.42235 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.42316e7 | 1.17439 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.16580e7 | −0.561671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.30842e7 | 2.52753 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.71740e6 | 0.128626 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.57318e7 | −1.21087 | −0.605436 | − | 0.795894i | \(-0.707001\pi\) | ||||
−0.605436 | + | 0.795894i | \(0.707001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.02287e8 | 4.78524 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.30602e6 | 0.386315 | 0.193157 | − | 0.981168i | \(-0.438127\pi\) | ||||
0.193157 | + | 0.981168i | \(0.438127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.15556e7 | 0.996731 | 0.498365 | − | 0.866967i | \(-0.333934\pi\) | ||||
0.498365 | + | 0.866967i | \(0.333934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.12531e7 | −0.514334 | −0.257167 | − | 0.966367i | \(-0.582789\pi\) | ||||
−0.257167 | + | 0.966367i | \(0.582789\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.93832e6 | 0.224408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.10360e7 | 1.85403 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.73285e7 | 2.12605 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.28664e7 | 1.02130 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.75692e7 | 0.780220 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.42464e7 | 1.50354 | 0.751771 | − | 0.659424i | \(-0.229200\pi\) | ||||
0.751771 | + | 0.659424i | \(0.229200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.08637e6 | 0.309351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.79016e6 | 0.294741 | 0.147370 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147370 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.66001e7 | −1.57972 | −0.789861 | − | 0.613285i | \(-0.789848\pi\) | ||||
−0.789861 | + | 0.613285i | \(0.789848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.42238e6 | −0.318555 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.33180e7 | 0.568369 | 0.284185 | − | 0.958770i | \(-0.408277\pi\) | ||||
0.284185 | + | 0.958770i | \(0.408277\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.82809e7 | −3.72539 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.48908e7 | 2.30341 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.95506e7 | −0.815836 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.18958e7 | −1.73856 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.76571e7 | 1.14132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 297883. | 0.0122246 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.33923e7 | −0.543544 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.70149e7 | −0.686769 | −0.343385 | − | 0.939195i | \(-0.611573\pi\) | ||||
−0.343385 | + | 0.939195i | \(0.611573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.29861e7 | −2.52834 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.07087e6 | −0.322199 | −0.161100 | − | 0.986938i | \(-0.551504\pi\) | ||||
−0.161100 | + | 0.986938i | \(0.551504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.75474e7 | 1.09371 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.00132e7 | 0.790250 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.58766e7 | −1.40127 | −0.700637 | − | 0.713518i | \(-0.747101\pi\) | ||||
−0.700637 | + | 0.713518i | \(0.747101\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.14696e7 | −0.445553 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.26552e7 | −0.875312 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −741029. | −0.0284761 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.58604e7 | 0.606198 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.86363e7 | −0.708468 | −0.354234 | − | 0.935157i | \(-0.615258\pi\) | ||||
−0.354234 | + | 0.935157i | \(0.615258\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.19178e7 | 2.32869 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.21235e6 | 0.0453523 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.78637e7 | −0.664697 | −0.332348 | − | 0.943157i | \(-0.607841\pi\) | ||||
−0.332348 | + | 0.943157i | \(0.607841\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.38371e7 | −3.47305 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.37739e7 | 1.24339 | 0.621695 | − | 0.783260i | \(-0.286444\pi\) | ||||
0.621695 | + | 0.783260i | \(0.286444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.91418e7 | −1.06718 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.53291e7 | 1.28014 | 0.640070 | − | 0.768317i | \(-0.278905\pi\) | ||||
0.640070 | + | 0.768317i | \(0.278905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.19774e7 | −0.792157 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.62856e7 | 2.73522 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.03334e7 | −1.08190 | −0.540952 | − | 0.841053i | \(-0.681936\pi\) | ||||
−0.540952 | + | 0.841053i | \(0.681936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.77005e7 | 1.33764 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.43582e8 | 5.06780 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.77323e7 | −0.619380 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.44262e7 | −2.23870 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.34984e7 | −0.812307 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.48744e7 | 1.54323 | 0.771617 | − | 0.636087i | \(-0.219448\pi\) | ||||
0.771617 | + | 0.636087i | \(0.219448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.52662e6 | 0.0864430 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.01491e7 | 0.685817 | 0.342909 | − | 0.939369i | \(-0.388588\pi\) | ||||
0.342909 | + | 0.939369i | \(0.388588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.14249e7 | 0.384894 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.29285e7 | 1.43883 | 0.719415 | − | 0.694580i | \(-0.244410\pi\) | ||||
0.719415 | + | 0.694580i | \(0.244410\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.82707e7 | 2.94347 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.55714e7 | −1.51189 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.91728e7 | 1.62308 | 0.811542 | − | 0.584294i | \(-0.198629\pi\) | ||||
0.811542 | + | 0.584294i | \(0.198629\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.91193e7 | −0.956292 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.25023e7 | 1.05663 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.92457e7 | −1.26943 | −0.634714 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634714 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.30536e7 | −1.70742 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.82216e7 | −0.903698 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.79147e7 | −1.84523 | −0.922616 | − | 0.385721i | \(-0.873953\pi\) | ||||
−0.922616 | + | 0.385721i | \(0.873953\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.24177e6 | 0.261280 |
(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 | 392.6.a.h.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 784.6.a.bh.1.4 | 4 | |||
7.2 | even | 3 | 392.6.i.m.361.4 | 8 | |||
7.3 | odd | 6 | 392.6.i.m.177.1 | 8 | |||
7.4 | even | 3 | 392.6.i.m.177.4 | 8 | |||
7.5 | odd | 6 | 392.6.i.m.361.1 | 8 | |||
7.6 | odd | 2 | inner | 392.6.a.h.1.4 | yes | 4 | |
28.27 | even | 2 | 784.6.a.bh.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.6.a.h.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
392.6.a.h.1.4 | yes | 4 | 7.6 | odd | 2 | inner | |
392.6.i.m.177.1 | 8 | 7.3 | odd | 6 | |||
392.6.i.m.177.4 | 8 | 7.4 | even | 3 | |||
392.6.i.m.361.1 | 8 | 7.5 | odd | 6 | |||
392.6.i.m.361.4 | 8 | 7.2 | even | 3 | |||
784.6.a.bh.1.1 | 4 | 28.27 | even | 2 | |||
784.6.a.bh.1.4 | 4 | 4.3 | odd | 2 |