Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{113})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 59x^{2} + 60x + 674 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(7.22929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | 6.54802 | 0.420055 | 0.210028 | − | 0.977695i | \(-0.432645\pi\) | ||||
0.210028 | + | 0.977695i | \(0.432645\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 45.9910 | 0.822713 | 0.411356 | − | 0.911475i | \(-0.365055\pi\) | ||||
0.411356 | + | 0.911475i | \(0.365055\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −200.123 | −0.823553 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 551.781 | 1.37494 | 0.687472 | − | 0.726211i | \(-0.258720\pi\) | ||||
0.687472 | + | 0.726211i | \(0.258720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1094.10 | −1.79555 | −0.897776 | − | 0.440453i | \(-0.854818\pi\) | ||||
−0.897776 | + | 0.440453i | \(0.854818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 301.150 | 0.345585 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1180.71 | 0.990883 | 0.495442 | − | 0.868641i | \(-0.335006\pi\) | ||||
0.495442 | + | 0.868641i | \(0.335006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1166.13 | −0.741074 | −0.370537 | − | 0.928818i | \(-0.620826\pi\) | ||||
−0.370537 | + | 0.928818i | \(0.620826\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −44.3851 | −0.0174951 | −0.00874757 | − | 0.999962i | \(-0.502784\pi\) | ||||
−0.00874757 | + | 0.999962i | \(0.502784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1009.82 | −0.323143 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2901.58 | −0.765993 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3329.02 | 0.735057 | 0.367529 | − | 0.930012i | \(-0.380204\pi\) | ||||
0.367529 | + | 0.930012i | \(0.380204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8784.01 | 1.64168 | 0.820841 | − | 0.571157i | \(-0.193505\pi\) | ||||
0.820841 | + | 0.571157i | \(0.193505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3613.07 | 0.577552 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2557.12 | −0.307077 | −0.153539 | − | 0.988143i | \(-0.549067\pi\) | ||||
−0.153539 | + | 0.988143i | \(0.549067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7164.17 | −0.754231 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12761.3 | 1.18559 | 0.592794 | − | 0.805354i | \(-0.298025\pi\) | ||||
0.592794 | + | 0.805354i | \(0.298025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 96.7714 | 0.00798135 | 0.00399067 | − | 0.999992i | \(-0.498730\pi\) | ||||
0.00399067 | + | 0.999992i | \(0.498730\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9203.89 | −0.677548 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7679.15 | 0.507071 | 0.253535 | − | 0.967326i | \(-0.418407\pi\) | ||||
0.253535 | + | 0.967326i | \(0.418407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7731.33 | 0.416226 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11953.3 | −0.584520 | −0.292260 | − | 0.956339i | \(-0.594407\pi\) | ||||
−0.292260 | + | 0.956339i | \(0.594407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25377.0 | 1.13118 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7635.81 | −0.311292 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9857.24 | 0.368659 | 0.184330 | − | 0.982864i | \(-0.440989\pi\) | ||||
0.184330 | + | 0.982864i | \(0.440989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38517.9 | 1.32537 | 0.662686 | − | 0.748897i | \(-0.269416\pi\) | ||||
0.662686 | + | 0.748897i | \(0.269416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −50318.7 | −1.47722 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 67548.9 | 1.83836 | 0.919182 | − | 0.393833i | \(-0.128851\pi\) | ||||
0.919182 | + | 0.393833i | \(0.128851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −290.634 | −0.00734893 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61374.6 | 1.44492 | 0.722458 | − | 0.691415i | \(-0.243012\pi\) | ||||
0.722458 | + | 0.691415i | \(0.243012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1850.40 | −0.0406404 | −0.0203202 | − | 0.999794i | \(-0.506469\pi\) | ||||
−0.0203202 | + | 0.999794i | \(0.506469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6612.34 | −0.135738 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.52913 | 0.000153758 0 | 7.68788e−5 | − | 1.00000i | \(-0.499976\pi\) | ||||
7.68788e−5 | 1.00000i | \(0.499976\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29630.4 | 0.501794 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −95039.3 | −1.51429 | −0.757143 | − | 0.653249i | \(-0.773405\pi\) | ||||
−0.757143 | + | 0.653249i | \(0.773405\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54302.3 | 0.815212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21798.5 | 0.308765 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −53605.6 | −0.717357 | −0.358678 | − | 0.933461i | \(-0.616773\pi\) | ||||
−0.358678 | + | 0.933461i | \(0.616773\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 57517.9 | 0.689597 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −53631.4 | −0.609691 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3110.79 | −0.0335693 | −0.0167846 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167846 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −110424. | −1.13234 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −21835.9 | −0.212994 | −0.106497 | − | 0.994313i | \(-0.533963\pi\) | ||||
−0.106497 | + | 0.994313i | \(0.533963\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 65341.4 | 0.606870 | 0.303435 | − | 0.952852i | \(-0.401866\pi\) | ||||
0.303435 | + | 0.952852i | \(0.401866\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 108957. | 0.920020 | 0.460010 | − | 0.887914i | \(-0.347846\pi\) | ||||
0.460010 | + | 0.887914i | \(0.347846\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 86728.7 | 0.699192 | 0.349596 | − | 0.936901i | \(-0.386319\pi\) | ||||
0.349596 | + | 0.936901i | \(0.386319\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16744.1 | −0.128989 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −101496. | −0.747746 | −0.373873 | − | 0.927480i | \(-0.621970\pi\) | ||||
−0.373873 | + | 0.927480i | \(0.621970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2041.32 | −0.0143935 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 218955. | 1.47873 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 143411. | 0.890470 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 83560.9 | 0.498013 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −190165. | −1.08857 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3094.61 | 0.0170253 | 0.00851267 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851267 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 633.661 | 0.00335261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 253431. | 1.29027 | 0.645136 | − | 0.764067i | \(-0.276801\pi\) | ||||
0.645136 | + | 0.764067i | \(0.276801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −133447. | −0.630193 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −97152.9 | −0.442236 | −0.221118 | − | 0.975247i | \(-0.570971\pi\) | ||||
−0.221118 | + | 0.975247i | \(0.570971\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 210308. | 0.923249 | 0.461624 | − | 0.887076i | \(-0.347267\pi\) | ||||
0.461624 | + | 0.887076i | \(0.347267\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 50283.2 | 0.212998 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −603702. | −2.46878 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 153105. | 0.604741 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 140406. | 0.518109 | 0.259055 | − | 0.965863i | \(-0.416589\pi\) | ||||
0.259055 | + | 0.965863i | \(0.416589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −119696. | −0.427205 | −0.213603 | − | 0.976921i | \(-0.568520\pi\) | ||||
−0.213603 | + | 0.976921i | \(0.568520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −236289. | −0.816045 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 403986. | 1.35063 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −97616.9 | −0.316065 | −0.158032 | − | 0.987434i | \(-0.550515\pi\) | ||||
−0.158032 | + | 0.987434i | \(0.550515\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −78270.6 | −0.245531 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −182678. | −0.538539 | −0.269270 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269270 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 166169. | 0.475160 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −451674. | −1.25324 | −0.626619 | − | 0.779326i | \(-0.715562\pi\) | ||||
−0.626619 | + | 0.779326i | \(0.715562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 825757. | 2.22400 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 233369. | 0.610314 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −371647. | −0.944095 | −0.472047 | − | 0.881573i | \(-0.656485\pi\) | ||||
−0.472047 | + | 0.881573i | \(0.656485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 64545.4 | 0.154857 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −85003.4 | −0.198291 | −0.0991457 | − | 0.995073i | \(-0.531611\pi\) | ||||
−0.0991457 | + | 0.995073i | \(0.531611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 379442. | 0.860892 | 0.430446 | − | 0.902616i | \(-0.358356\pi\) | ||||
0.430446 | + | 0.902616i | \(0.358356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 252216. | 0.556730 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −117605. | −0.252636 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 651496. | 1.36241 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 922196. | 1.82911 | 0.914555 | − | 0.404462i | \(-0.132541\pi\) | ||||
0.914555 | + | 0.404462i | \(0.132541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 505107. | 0.976090 | 0.488045 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488045 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −329488. | −0.620516 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 251505. | 0.461723 | 0.230861 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230861 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −208033. | −0.372392 | −0.186196 | − | 0.982513i | \(-0.559616\pi\) | ||||
−0.186196 | + | 0.982513i | \(0.559616\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 442311. | 0.772215 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 586904. | 0.975399 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8882.50 | 0.0144082 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −643446. | −1.01893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 640577. | 0.990525 | 0.495262 | − | 0.868744i | \(-0.335072\pi\) | ||||
0.495262 | + | 0.868744i | \(0.335072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 401882. | 0.606945 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4450.62 | 0.00656636 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12116.4 | −0.0170712 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.29182e6 | −1.77918 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 390135. | 0.525354 | 0.262677 | − | 0.964884i | \(-0.415395\pi\) | ||||
0.262677 | + | 0.964884i | \(0.415395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 202089. | 0.266126 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 291353. | 0.375279 | 0.187639 | − | 0.982238i | \(-0.439916\pi\) | ||||
0.187639 | + | 0.982238i | \(0.439916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.23040e6 | 1.55045 | 0.775227 | − | 0.631682i | \(-0.217635\pi\) | ||||
0.775227 | + | 0.631682i | \(0.217635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 114279. | 0.137903 | 0.0689517 | − | 0.997620i | \(-0.478035\pi\) | ||||
0.0689517 | + | 0.997620i | \(0.478035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 353172. | 0.417174 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 55.8489 | 6.45867e−5 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.14782e6 | 1.29981 | 0.649906 | − | 0.760014i | \(-0.274808\pi\) | ||||
0.649906 | + | 0.760014i | \(0.274808\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −812708. | −0.901346 | −0.450673 | − | 0.892689i | \(-0.648816\pi\) | ||||
−0.450673 | + | 0.892689i | \(0.648816\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 899104. | 0.976775 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.27586e6 | 1.33064 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −622318. | −0.636084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −406772. | −0.407537 | −0.203768 | − | 0.979019i | \(-0.565319\pi\) | ||||
−0.203768 | + | 0.979019i | \(0.565319\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24490.8 | −0.0240548 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 355572. | 0.342434 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.69712e6 | 1.60281 | 0.801403 | − | 0.598125i | \(-0.204087\pi\) | ||||
0.801403 | + | 0.598125i | \(0.204087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −666215. | −0.605359 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −205694. | −0.183372 | −0.0916859 | − | 0.995788i | \(-0.529226\pi\) | ||||
−0.0916859 | + | 0.995788i | \(0.529226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −549746. | −0.480892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −351010. | −0.301330 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.73425e6 | −1.46127 | −0.730635 | − | 0.682769i | \(-0.760776\pi\) | ||||
−0.730635 | + | 0.682769i | \(0.760776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 369042. | 0.305248 | 0.152624 | − | 0.988284i | \(-0.451228\pi\) | ||||
0.152624 | + | 0.988284i | \(0.451228\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −557201. | −0.444304 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22767e6 | 0.961351 | 0.480676 | − | 0.876899i | \(-0.340391\pi\) | ||||
0.480676 | + | 0.876899i | \(0.340391\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.75789e6 | −1.35201 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00671e6 | 1.51607 | 0.758035 | − | 0.652214i | \(-0.226159\pi\) | ||||
0.758035 | + | 0.652214i | \(0.226159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.78581e6 | −1.32547 | −0.662734 | − | 0.748855i | \(-0.730604\pi\) | ||||
−0.662734 | + | 0.748855i | \(0.730604\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −351179. | −0.256104 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25770.8 | −0.0181503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20369.5 | −0.0141009 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −853248. | −0.580639 | −0.290319 | − | 0.956930i | \(-0.593762\pi\) | ||||
−0.290319 | + | 0.956930i | \(0.593762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 453345. | 0.303301 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.60104e6 | −1.05320 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 48561.6 | 0.0314134 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −142982. | −0.0894693 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.77148e6 | 1.09040 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.96068e6 | −1.18730 | −0.593652 | − | 0.804722i | \(-0.702314\pi\) | ||||
−0.593652 | + | 0.804722i | \(0.702314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 427857. | 0.254919 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 863604. | 0.506307 | 0.253153 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253153 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.10047e6 | −0.634918 | −0.317459 | − | 0.948272i | \(-0.602830\pi\) | ||||
−0.317459 | + | 0.948272i | \(0.602830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.49591e6 | 0.836097 | 0.418048 | − | 0.908425i | \(-0.362714\pi\) | ||||
0.418048 | + | 0.908425i | \(0.362714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.83689e6 | 1.01066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 713454. | 0.386459 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.37686e6 | −0.734318 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.10485e6 | 0.580221 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 567901. | 0.293699 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74015e6 | 1.37469 | 0.687345 | − | 0.726331i | \(-0.258776\pi\) | ||||
0.687345 | + | 0.726331i | \(0.258776\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 511741. | 0.252894 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.10665e6 | 1.51245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.31353e6 | −1.10968 | −0.554842 | − | 0.831956i | \(-0.687221\pi\) | ||||
−0.554842 | + | 0.831956i | \(0.687221\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −664600. | −0.314095 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.84685e6 | 2.25722 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13366.6 | −0.00604606 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.05926e6 | 1.36393 | 0.681966 | − | 0.731384i | \(-0.261125\pi\) | ||||
0.681966 | + | 0.731384i | \(0.261125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 210232. | 0.0923921 | 0.0461961 | − | 0.998932i | \(-0.485290\pi\) | ||||
0.0461961 | + | 0.998932i | \(0.485290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.17461e6 | 1.37538 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.76790e6 | 1.60939 | 0.804697 | − | 0.593686i | \(-0.202328\pi\) | ||||
0.804697 | + | 0.593686i | \(0.202328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.82268e6 | 1.18875 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.00722e6 | −0.412465 | −0.206232 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206232 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.11625e6 | −0.450809 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 939058. | 0.374047 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −85101.8 | −0.0334354 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.52650e6 | −0.591603 | −0.295802 | − | 0.955249i | \(-0.595587\pi\) | ||||
−0.295802 | + | 0.955249i | \(0.595587\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.55383e6 | −0.976396 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.86297e6 | 1.80980 | 0.904898 | − | 0.425629i | \(-0.139947\pi\) | ||||
0.904898 | + | 0.425629i | \(0.139947\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.24520e6 | −0.457258 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.64227e6 | −1.31983 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −630878. | −0.225604 | −0.112802 | − | 0.993617i | \(-0.535983\pi\) | ||||
−0.112802 | + | 0.993617i | \(0.535983\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20263.5 | 0.00715159 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 565644. | 0.197036 | 0.0985182 | − | 0.995135i | \(-0.468590\pi\) | ||||
0.0985182 | + | 0.995135i | \(0.468590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19366.2 | −0.00657306 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 592212. | 0.198428 | 0.0992140 | − | 0.995066i | \(-0.468367\pi\) | ||||
0.0992140 | + | 0.995066i | \(0.468367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52406.1 | −0.0173356 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.65947e6 | 0.541986 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 392.264 | 0.000126498 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.34312e6 | −0.427698 | −0.213849 | − | 0.976867i | \(-0.568600\pi\) | ||||
−0.213849 | + | 0.976867i | \(0.568600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.68716e6 | −1.14507 | −0.572534 | − | 0.819881i | \(-0.694040\pi\) | ||||
−0.572534 | + | 0.819881i | \(0.694040\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.61057e6 | −2.94772 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.36273e6 | 0.412832 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.41097e6 | −0.422214 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.45630e6 | −0.430470 | −0.215235 | − | 0.976562i | \(-0.569052\pi\) | ||||
−0.215235 | + | 0.976562i | \(0.569052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −636159. | −0.185764 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.37096e6 | −1.24582 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.37710e6 | 0.387816 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.92192e6 | −0.813080 | −0.406540 | − | 0.913633i | \(-0.633265\pi\) | ||||
−0.406540 | + | 0.913633i | \(0.633265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.01999e6 | 0.555450 | 0.277725 | − | 0.960661i | \(-0.410420\pi\) | ||||
0.277725 | + | 0.960661i | \(0.410420\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.53678e6 | −0.417600 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.19231e6 | −0.320197 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.95305e6 | −1.03703 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.43800e6 | 1.41009 | 0.705043 | − | 0.709164i | \(-0.250928\pi\) | ||||
0.705043 | + | 0.709164i | \(0.250928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.77335e6 | 0.967179 | 0.483590 | − | 0.875295i | \(-0.339333\pi\) | ||||
0.483590 | + | 0.875295i | \(0.339333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.00253e6 | 0.254025 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 51758.6 | 0.0129652 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.35150e6 | 0.582350 | 0.291175 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291175 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.80377e6 | −1.16298 | −0.581491 | − | 0.813553i | \(-0.697530\pi\) | ||||
−0.581491 | + | 0.813553i | \(0.697530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.46538e6 | −0.590179 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 919383. | 0.217634 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.76805e6 | −0.647975 | −0.323987 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323987 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.04142e6 | 1.63012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −783770. | −0.179450 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 241566. | 0.0541061 | 0.0270530 | − | 0.999634i | \(-0.491388\pi\) | ||||
0.0270530 | + | 0.999634i | \(0.491388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.42594e6 | −0.759010 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −990579. | −0.217088 | −0.108544 | − | 0.994092i | \(-0.534619\pi\) | ||||
−0.108544 | + | 0.994092i | \(0.534619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.20488e6 | −1.34518 | −0.672591 | − | 0.740014i | \(-0.734819\pi\) | ||||
−0.672591 | + | 0.740014i | \(0.734819\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.64531e6 | 0.567340 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.88497e6 | −1.46086 | −0.730432 | − | 0.682985i | \(-0.760681\pi\) | ||||
−0.730432 | + | 0.682985i | \(0.760681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −639197. | −0.132765 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53396.6 | 0.0109739 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.17758e6 | 0.239473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.39214e6 | 0.481383 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.41288e6 | −1.07793 | −0.538963 | − | 0.842329i | \(-0.681184\pi\) | ||||
−0.538963 | + | 0.842329i | \(0.681184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.79774e6 | 0.551373 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −143069. | −0.0276179 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.01043e6 | 0.575182 | 0.287591 | − | 0.957753i | \(-0.407146\pi\) | ||||
0.287591 | + | 0.957753i | \(0.407146\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.19618e6 | −0.226216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.24498e6 | 1.35623 | 0.678115 | − | 0.734956i | \(-0.262797\pi\) | ||||
0.678115 | + | 0.734956i | \(0.262797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.93062e6 | 0.728356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.07853e6 | −0.931591 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.12788e6 | 0.921906 | 0.460953 | − | 0.887425i | \(-0.347508\pi\) | ||||
0.460953 | + | 0.887425i | \(0.347508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.95757e6 | −0.526429 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.05978e7 | 1.86766 | 0.933830 | − | 0.357718i | \(-0.116445\pi\) | ||||
0.933830 | + | 0.357718i | \(0.116445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00426e6 | −0.175233 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.40707e6 | 0.934205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.78840e6 | −1.50354 | −0.751770 | − | 0.659425i | \(-0.770800\pi\) | ||||
−0.751770 | + | 0.659425i | \(0.770800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.38361e6 | 0.567658 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.00512e6 | 0.499280 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.23721e6 | 0.697194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.43355e6 | −0.396572 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −162133. | −0.0261684 | −0.0130842 | − | 0.999914i | \(-0.504165\pi\) | ||||
−0.0130842 | + | 0.999914i | \(0.504165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.14844e6 | −1.14277 | −0.571383 | − | 0.820684i | \(-0.693593\pi\) | ||||
−0.571383 | + | 0.820684i | \(0.693593\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03714e7 | 1.62671 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.43437e6 | −0.999694 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.97267e6 | −0.303611 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.39621e7 | −2.12879 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.01106e6 | 0.756912 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −556604. | −0.0832934 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.83604e6 | −0.710390 | −0.355195 | − | 0.934792i | \(-0.615586\pi\) | ||||
−0.355195 | + | 0.934792i | \(0.615586\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.48459e6 | 0.361622 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.98874e6 | 0.575234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.98777e6 | −1.42725 | −0.713626 | − | 0.700527i | \(-0.752948\pi\) | ||||
−0.713626 | + | 0.700527i | \(0.752948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.70833e6 | −1.09151 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.88205e6 | −0.544732 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −770078. | −0.106121 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.74619e6 | 0.238481 | 0.119241 | − | 0.992865i | \(-0.461954\pi\) | ||||
0.119241 | + | 0.992865i | \(0.461954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −105877. | −0.0143309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.26600e6 | 0.572287 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −755218. | −0.100416 | −0.0502078 | − | 0.998739i | \(-0.515988\pi\) | ||||
−0.0502078 | + | 0.998739i | \(0.515988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.66792e6 | −0.615181 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.39534e6 | −0.569131 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.16104e7 | −1.49024 | −0.745121 | − | 0.666930i | \(-0.767608\pi\) | ||||
−0.745121 | + | 0.666930i | \(0.767608\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.03855e6 | 0.768327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44821.1 | 0.00565344 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.06643e7 | −1.33350 | −0.666748 | − | 0.745283i | \(-0.732314\pi\) | ||||
−0.666748 | + | 0.745283i | \(0.732314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.30745e6 | 0.410012 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.59562e6 | −0.803682 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00700e7 | 1.21657 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.39482e7 | −1.67079 | −0.835396 | − | 0.549648i | \(-0.814762\pi\) | ||||
−0.835396 | + | 0.549648i | \(0.814762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.02433e7 | −1.21661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.64686e6 | 0.193949 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.17933e7 | −1.37720 | −0.688600 | − | 0.725142i | \(-0.741774\pi\) | ||||
−0.688600 | + | 0.725142i | \(0.741774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.36220e6 | −0.156425 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.38057e6 | 0.498843 | 0.249421 | − | 0.968395i | \(-0.419760\pi\) | ||||
0.249421 | + | 0.968395i | \(0.419760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −688570. | −0.0777610 | −0.0388805 | − | 0.999244i | \(-0.512379\pi\) | ||||
−0.0388805 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.35181e7 | −1.51399 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.59563e6 | 0.732601 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.37319e6 | −1.03256 | −0.516281 | − | 0.856420i | \(-0.672684\pi\) | ||||
−0.516281 | + | 0.856420i | \(0.672684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.40174e6 | −0.910472 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.16685e6 | −0.232904 | −0.116452 | − | 0.993196i | \(-0.537152\pi\) | ||||
−0.116452 | + | 0.993196i | \(0.537152\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.84306e6 | 0.409722 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.07951e6 | −0.537166 | −0.268583 | − | 0.963256i | \(-0.586555\pi\) | ||||
−0.268583 | + | 0.963256i | \(0.586555\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.19034e6 | −0.229766 | −0.114883 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114883 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 128787. | 0.0134012 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.59018e6 | −0.572435 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.21329e6 | −0.428009 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.01923e6 | −0.304278 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.18693e6 | 0.718572 | 0.359286 | − | 0.933228i | \(-0.383020\pi\) | ||||
0.359286 | + | 0.933228i | \(0.383020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.19451e6 | 0.416075 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 142324. | 0.0140070 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.22825e7 | −1.18997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.76500e7 | −1.69668 | −0.848340 | − | 0.529452i | \(-0.822398\pi\) | ||||
−0.848340 | + | 0.529452i | \(0.822398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 898309. | 0.0856837 | 0.0428419 | − | 0.999082i | \(-0.486359\pi\) | ||||
0.0428419 | + | 0.999082i | \(0.486359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29142.7 | 0.00275823 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.38642e6 | −0.130207 | −0.0651035 | − | 0.997879i | \(-0.520738\pi\) | ||||
−0.0651035 | + | 0.997879i | \(0.520738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.43904e6 | 0.506886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.75425e7 | −1.60994 | −0.804968 | − | 0.593318i | \(-0.797818\pi\) | ||||
−0.804968 | + | 0.593318i | \(0.797818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.16556e7 | 1.06152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 370308. | 0.0334696 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.87522e6 | −0.885795 | −0.442898 | − | 0.896572i | \(-0.646050\pi\) | ||||
−0.442898 | + | 0.896572i | \(0.646050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.06792e6 | 0.718221 | 0.359110 | − | 0.933295i | \(-0.383080\pi\) | ||||
0.359110 | + | 0.933295i | \(0.383080\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.45884e6 | −0.747355 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −147759. | −0.0128599 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.55461e6 | 0.220678 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.12534e7 | 1.82231 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.12772e7 | −0.959762 | −0.479881 | − | 0.877334i | \(-0.659320\pi\) | ||||
−0.479881 | + | 0.877334i | \(0.659320\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.93008e6 | 0.247526 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.20372e6 | −0.436357 | −0.218179 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218179 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.90778e6 | 0.157638 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.05915e6 | −0.497004 | −0.248502 | − | 0.968631i | \(-0.579938\pi\) | ||||
−0.248502 | + | 0.968631i | \(0.579938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.46816e6 | −0.363833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.05671e6 | 0.651277 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.30781e7 | 1.04954 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.36498e6 | 0.586781 | 0.293391 | − | 0.955993i | \(-0.405216\pi\) | ||||
0.293391 | + | 0.955993i | \(0.405216\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.67228e6 | 0.759569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50674e7 | 1.17478 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 748298. | 0.0579271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.80919e6 | 0.600221 | 0.300110 | − | 0.953904i | \(-0.402977\pi\) | ||||
0.300110 | + | 0.953904i | \(0.402977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.98193e6 | 0.227567 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.31258e6 | 0.175236 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.75650e7 | 1.31230 | 0.656150 | − | 0.754631i | \(-0.272184\pi\) | ||||
0.656150 | + | 0.754631i | \(0.272184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1706.88 | −0.000126628 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −389879. | −0.0287214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.77649e7 | −2.03110 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.51597e6 | 0.545993 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.09220e6 | −0.583773 | −0.291887 | − | 0.956453i | \(-0.594283\pi\) | ||||
−0.291887 | + | 0.956453i | \(0.594283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.32162e6 | −0.378615 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.36172e6 | −0.237529 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.51986e7 | 1.06652 | 0.533258 | − | 0.845952i | \(-0.320967\pi\) | ||||
0.533258 | + | 0.845952i | \(0.320967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.31285e6 | −0.0914944 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 114259. | 0.00790858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.83402e6 | −0.401059 | −0.200530 | − | 0.979688i | \(-0.564266\pi\) | ||||
−0.200530 | + | 0.979688i | \(0.564266\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.72722e7 | 2.52765 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.47719e6 | −0.436290 | −0.218145 | − | 0.975916i | \(-0.570001\pi\) | ||||
−0.218145 | + | 0.975916i | \(0.570001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.35433e6 | 0.558941 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.50899e7 | 1.00280 | 0.501401 | − | 0.865215i | \(-0.332818\pi\) | ||||
0.501401 | + | 0.865215i | \(0.332818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.45744e6 | 0.426255 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.90196e7 | 1.24710 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13997e6 | 0.138455 | 0.0692273 | − | 0.997601i | \(-0.477947\pi\) | ||||
0.0692273 | + | 0.997601i | \(0.477947\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.66355e6 | −0.171188 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.50494e6 | −0.351467 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.10943e7 | 1.33791 | 0.668954 | − | 0.743304i | \(-0.266742\pi\) | ||||
0.668954 | + | 0.743304i | \(0.266742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −160366. | −0.0101044 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.79958e6 | −0.613403 | −0.306701 | − | 0.951806i | \(-0.599225\pi\) | ||||
−0.306701 | + | 0.951806i | \(0.599225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.08672e7 | −0.671371 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.07848e7 | −0.661947 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.23493e7 | 1.97265 | 0.986323 | − | 0.164825i | \(-0.0527060\pi\) | ||||
0.986323 | + | 0.164825i | \(0.0527060\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.11128e7 | 0.673267 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.19713e6 | −0.553609 | −0.276805 | − | 0.960926i | \(-0.589276\pi\) | ||||
−0.276805 | + | 0.960926i | \(0.589276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.87030e6 | −0.530499 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.48812e7 | −0.878609 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.38653e7 | 1.98668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.65941e6 | −0.563049 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.48950e6 | −0.260030 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.46950e7 | 0.845731 | 0.422866 | − | 0.906192i | \(-0.361024\pi\) | ||||
0.422866 | + | 0.906192i | \(0.361024\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.34689e6 | −0.0770263 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.21423e7 | −2.37977 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.59975e6 | −0.202001 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.33344e7 | −1.30122 | −0.650610 | − | 0.759412i | \(-0.725487\pi\) | ||||
−0.650610 | + | 0.759412i | \(0.725487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.06688e6 | 0.502448 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.07277e7 | 0.590782 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.02101e6 | −0.0558783 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.13559e7 | −0.613814 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.69301e6 | 0.0909468 | 0.0454734 | − | 0.998966i | \(-0.485520\pi\) | ||||
0.0454734 | + | 0.998966i | \(0.485520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.12400e7 | −1.13397 | −0.566987 | − | 0.823727i | \(-0.691891\pi\) | ||||
−0.566987 | + | 0.823727i | \(0.691891\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.41649e6 | 0.128221 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.40155e6 | −0.443063 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −112848. | −0.00591477 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.73550e6 | 0.452304 | 0.226152 | − | 0.974092i | \(-0.427385\pi\) | ||||
0.226152 | + | 0.974092i | \(0.427385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.27964e7 | 1.68782 | 0.843910 | − | 0.536485i | \(-0.180248\pi\) | ||||
0.843910 | + | 0.536485i | \(0.180248\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.64856e6 | −0.186632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.31248e7 | −0.667311 | −0.333656 | − | 0.942695i | \(-0.608282\pi\) | ||||
−0.333656 | + | 0.942695i | \(0.608282\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.05402e7 | −1.03805 | −0.519026 | − | 0.854759i | \(-0.673705\pi\) | ||||
−0.519026 | + | 0.854759i | \(0.673705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.03880e6 | 0.403821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.07729e7 | −1.03106 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.54875e7 | −1.25752 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.83736e7 | 1.39159 | 0.695793 | − | 0.718243i | \(-0.255053\pi\) | ||||
0.695793 | + | 0.718243i | \(0.255053\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.42879e6 | −0.459691 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.31400e7 | 0.636834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.79774e7 | 1.82972 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.16935e7 | −0.556770 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 113498. | 0.00537236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.02093e7 | −0.480424 | −0.240212 | − | 0.970720i | \(-0.577217\pi\) | ||||
−0.240212 | + | 0.970720i | \(0.577217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.07329e7 | 0.502113 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.33206e6 | 0.387525 | 0.193763 | − | 0.981048i | \(-0.437931\pi\) | ||||
0.193763 | + | 0.981048i | \(0.437931\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.12766e7 | 1.44623 | 0.723113 | − | 0.690729i | \(-0.242710\pi\) | ||||
0.723113 | + | 0.690729i | \(0.242710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.73573e7 | 1.70745 | 0.853726 | − | 0.520722i | \(-0.174337\pi\) | ||||
0.853726 | + | 0.520722i | \(0.174337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.70924e7 | −0.776719 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −168747. | −0.00762411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4706.21 | 0.000211408 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.39051e7 | −3.30088 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 622543. | 0.0276461 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38996.7 | 0.00171210 | 0.000856049 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000856049 | 1.00000i | \(0.499728\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.58708e6 | −0.243900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.15554e7 | −1.36973 | −0.684864 | − | 0.728671i | \(-0.740138\pi\) | ||||
−0.684864 | + | 0.728671i | \(0.740138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.42253e7 | 1.47722 | 0.738611 | − | 0.674132i | \(-0.235482\pi\) | ||||
0.738611 | + | 0.674132i | \(0.235482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.96851e6 | 0.127403 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.69886e7 | −1.15178 | −0.575892 | − | 0.817526i | \(-0.695345\pi\) | ||||
−0.575892 | + | 0.817526i | \(0.695345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.63495e7 | 0.689938 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.95486e6 | −0.375777 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.90940e6 | −0.163137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 317982. | 0.0131954 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.92421e7 | 1.20673 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.41135e7 | −0.579191 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.74509e7 | 0.708267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.92103e7 | −0.775381 | −0.387690 | − | 0.921790i | \(-0.626727\pi\) | ||||
−0.387690 | + | 0.921790i | \(0.626727\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.36988e6 | 0.175412 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.86013e7 | −1.14180 | −0.570899 | − | 0.821020i | \(-0.693405\pi\) | ||||
−0.570899 | + | 0.821020i | \(0.693405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.24408e7 | −2.08206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.15997e7 | 0.458029 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.21754e7 | 1.64729 | 0.823645 | − | 0.567106i | \(-0.191937\pi\) | ||||
0.823645 | + | 0.567106i | \(0.191937\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.28386e7 | −0.498733 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.71498e7 | −2.59442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.58224e6 | 0.0992299 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.30764e7 | −0.499790 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.01886e7 | 1.14763 | 0.573817 | − | 0.818983i | \(-0.305462\pi\) | ||||
0.573817 | + | 0.818983i | \(0.305462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.65489e6 | 0.212677 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.99630e7 | 1.12087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.64068e6 | 0.135467 | 0.0677335 | − | 0.997703i | \(-0.478423\pi\) | ||||
0.0677335 | + | 0.997703i | \(0.478423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.20589e6 | −0.266701 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.88601e7 | −0.694336 | −0.347168 | − | 0.937803i | \(-0.612857\pi\) | ||||
−0.347168 | + | 0.937803i | \(0.612857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −566410. | −0.0207420 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.82172e7 | 0.660094 | 0.330047 | − | 0.943965i | \(-0.392935\pi\) | ||||
0.330047 | + | 0.943965i | \(0.392935\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.02452e6 | 0.0729720 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.79522e6 | 0.351207 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.76898e7 | 0.987616 | 0.493808 | − | 0.869571i | \(-0.335604\pi\) | ||||
0.493808 | + | 0.869571i | \(0.335604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.24127e7 | 1.50483 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.20280e7 | 0.424534 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.85298e7 | 1.69512 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.18049e7 | −0.757685 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.32304e7 | 0.803042 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.44768e7 | 0.841761 | 0.420881 | − | 0.907116i | \(-0.361721\pi\) | ||||
0.420881 | + | 0.907116i | \(0.361721\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.01571e6 | −0.308454 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.50151e6 | 0.323403 | 0.161702 | − | 0.986840i | \(-0.448302\pi\) | ||||
0.161702 | + | 0.986840i | \(0.448302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.23455e6 | 0.243725 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.69012e7 | 1.57198 | 0.785991 | − | 0.618238i | \(-0.212153\pi\) | ||||
0.785991 | + | 0.618238i | \(0.212153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.95785e7 | −0.986325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.73564e7 | −0.575822 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.35382e7 | 0.776945 | 0.388473 | − | 0.921460i | \(-0.373003\pi\) | ||||
0.388473 | + | 0.921460i | \(0.373003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.15670e7 | 0.379865 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4295.21 | −0.000139635 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.64104e7 | 0.854261 | 0.427130 | − | 0.904190i | \(-0.359525\pi\) | ||||
0.427130 | + | 0.904190i | \(0.359525\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.79426e7 | 0.577446 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.56766e6 | −0.306371 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.95164e7 | 0.621815 | 0.310907 | − | 0.950440i | \(-0.399367\pi\) | ||||
0.310907 | + | 0.950440i | \(0.399367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.41970e6 | 0.235219 |
(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 | 784.6.a.bf.1.3 | 4 | ||
4.3 | odd | 2 | 49.6.a.g.1.3 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 784.6.a.bf.1.2 | 4 | ||
12.11 | even | 2 | 441.6.a.z.1.1 | 4 | |||
28.3 | even | 6 | 49.6.c.h.30.1 | 8 | |||
28.11 | odd | 6 | 49.6.c.h.30.2 | 8 | |||
28.19 | even | 6 | 49.6.c.h.18.1 | 8 | |||
28.23 | odd | 6 | 49.6.c.h.18.2 | 8 | |||
28.27 | even | 2 | 49.6.a.g.1.4 | yes | 4 | ||
84.83 | odd | 2 | 441.6.a.z.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.g.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
49.6.a.g.1.4 | yes | 4 | 28.27 | even | 2 | ||
49.6.c.h.18.1 | 8 | 28.19 | even | 6 | |||
49.6.c.h.18.2 | 8 | 28.23 | odd | 6 | |||
49.6.c.h.30.1 | 8 | 28.3 | even | 6 | |||
49.6.c.h.30.2 | 8 | 28.11 | odd | 6 | |||
441.6.a.z.1.1 | 4 | 12.11 | even | 2 | |||
441.6.a.z.1.2 | 4 | 84.83 | odd | 2 | |||
784.6.a.bf.1.2 | 4 | 7.6 | odd | 2 | inner | ||
784.6.a.bf.1.3 | 4 | 1.1 | even | 1 | trivial |