Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(1,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.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: | \(7.85880717084\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(7.22929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.81507 | 0.497639 | 0.248820 | − | 0.968550i | \(-0.419957\pi\) | ||||
0.248820 | + | 0.968550i | \(0.419957\pi\) | |||||||
\(3\) | 6.54802 | 0.420055 | 0.210028 | − | 0.977695i | \(-0.432645\pi\) | ||||
0.210028 | + | 0.977695i | \(0.432645\pi\) | |||||||
\(4\) | −24.0754 | −0.752355 | ||||||||
\(5\) | −45.9910 | −0.822713 | −0.411356 | − | 0.911475i | \(-0.634945\pi\) | ||||
−0.411356 | + | 0.911475i | \(0.634945\pi\) | |||||||
\(6\) | 18.4331 | 0.209036 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −157.856 | −0.872041 | ||||||||
\(9\) | −200.123 | −0.823553 | ||||||||
\(10\) | −129.468 | −0.409414 | ||||||||
\(11\) | −551.781 | −1.37494 | −0.687472 | − | 0.726211i | \(-0.741280\pi\) | ||||
−0.687472 | + | 0.726211i | \(0.741280\pi\) | |||||||
\(12\) | −157.646 | −0.316031 | ||||||||
\(13\) | 1094.10 | 1.79555 | 0.897776 | − | 0.440453i | \(-0.145182\pi\) | ||||
0.897776 | + | 0.440453i | \(0.145182\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −301.150 | −0.345585 | ||||||||
\(16\) | 326.035 | 0.318393 | ||||||||
\(17\) | −1180.71 | −0.990883 | −0.495442 | − | 0.868641i | \(-0.664994\pi\) | ||||
−0.495442 | + | 0.868641i | \(0.664994\pi\) | |||||||
\(18\) | −563.362 | −0.409833 | ||||||||
\(19\) | −1166.13 | −0.741074 | −0.370537 | − | 0.928818i | \(-0.620826\pi\) | ||||
−0.370537 | + | 0.928818i | \(0.620826\pi\) | |||||||
\(20\) | 1107.25 | 0.618972 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1553.30 | −0.684226 | ||||||||
\(23\) | 44.3851 | 0.0174951 | 0.00874757 | − | 0.999962i | \(-0.497216\pi\) | ||||
0.00874757 | + | 0.999962i | \(0.497216\pi\) | |||||||
\(24\) | −1033.65 | −0.366305 | ||||||||
\(25\) | −1009.82 | −0.323143 | ||||||||
\(26\) | 3079.97 | 0.893537 | ||||||||
\(27\) | −2901.58 | −0.765993 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3329.02 | 0.735057 | 0.367529 | − | 0.930012i | \(-0.380204\pi\) | ||||
0.367529 | + | 0.930012i | \(0.380204\pi\) | |||||||
\(30\) | −847.759 | −0.171977 | ||||||||
\(31\) | 8784.01 | 1.64168 | 0.820841 | − | 0.571157i | \(-0.193505\pi\) | ||||
0.820841 | + | 0.571157i | \(0.193505\pi\) | |||||||
\(32\) | 5969.21 | 1.03049 | ||||||||
\(33\) | −3613.07 | −0.577552 | ||||||||
\(34\) | −3323.80 | −0.493102 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4818.05 | 0.619605 | ||||||||
\(37\) | −2557.12 | −0.307077 | −0.153539 | − | 0.988143i | \(-0.549067\pi\) | ||||
−0.153539 | + | 0.988143i | \(0.549067\pi\) | |||||||
\(38\) | −3282.73 | −0.368787 | ||||||||
\(39\) | 7164.17 | 0.754231 | ||||||||
\(40\) | 7259.97 | 0.717439 | ||||||||
\(41\) | −12761.3 | −1.18559 | −0.592794 | − | 0.805354i | \(-0.701975\pi\) | ||||
−0.592794 | + | 0.805354i | \(0.701975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −96.7714 | −0.00798135 | −0.00399067 | − | 0.999992i | \(-0.501270\pi\) | ||||
−0.00399067 | + | 0.999992i | \(0.501270\pi\) | |||||||
\(44\) | 13284.3 | 1.03445 | ||||||||
\(45\) | 9203.89 | 0.677548 | ||||||||
\(46\) | 124.947 | 0.00870627 | ||||||||
\(47\) | 7679.15 | 0.507071 | 0.253535 | − | 0.967326i | \(-0.418407\pi\) | ||||
0.253535 | + | 0.967326i | \(0.418407\pi\) | |||||||
\(48\) | 2134.88 | 0.133743 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2842.73 | −0.160809 | ||||||||
\(51\) | −7731.33 | −0.416226 | ||||||||
\(52\) | −26340.8 | −1.35089 | ||||||||
\(53\) | −11953.3 | −0.584520 | −0.292260 | − | 0.956339i | \(-0.594407\pi\) | ||||
−0.292260 | + | 0.956339i | \(0.594407\pi\) | |||||||
\(54\) | −8168.16 | −0.381188 | ||||||||
\(55\) | 25377.0 | 1.13118 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7635.81 | −0.311292 | ||||||||
\(58\) | 9371.43 | 0.365793 | ||||||||
\(59\) | 9857.24 | 0.368659 | 0.184330 | − | 0.982864i | \(-0.440989\pi\) | ||||
0.184330 | + | 0.982864i | \(0.440989\pi\) | |||||||
\(60\) | 7250.30 | 0.260003 | ||||||||
\(61\) | −38517.9 | −1.32537 | −0.662686 | − | 0.748897i | \(-0.730584\pi\) | ||||
−0.662686 | + | 0.748897i | \(0.730584\pi\) | |||||||
\(62\) | 24727.6 | 0.816965 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6370.65 | 0.194417 | ||||||||
\(65\) | −50318.7 | −1.47722 | ||||||||
\(66\) | −10171.1 | −0.287413 | ||||||||
\(67\) | −67548.9 | −1.83836 | −0.919182 | − | 0.393833i | \(-0.871149\pi\) | ||||
−0.919182 | + | 0.393833i | \(0.871149\pi\) | |||||||
\(68\) | 28426.1 | 0.745496 | ||||||||
\(69\) | 290.634 | 0.00734893 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61374.6 | −1.44492 | −0.722458 | − | 0.691415i | \(-0.756988\pi\) | ||||
−0.722458 | + | 0.691415i | \(0.756988\pi\) | |||||||
\(72\) | 31590.7 | 0.718172 | ||||||||
\(73\) | 1850.40 | 0.0406404 | 0.0203202 | − | 0.999794i | \(-0.493531\pi\) | ||||
0.0203202 | + | 0.999794i | \(0.493531\pi\) | |||||||
\(74\) | −7198.49 | −0.152814 | ||||||||
\(75\) | −6612.34 | −0.135738 | ||||||||
\(76\) | 28074.9 | 0.557551 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 20167.7 | 0.375335 | ||||||||
\(79\) | −8.52913 | −0.000153758 0 | −7.68788e−5 | − | 1.00000i | \(-0.500024\pi\) | ||||
−7.68788e−5 | 1.00000i | \(0.500024\pi\) | ||||||||
\(80\) | −14994.7 | −0.261946 | ||||||||
\(81\) | 29630.4 | 0.501794 | ||||||||
\(82\) | −35923.9 | −0.589996 | ||||||||
\(83\) | −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 | ||||||||
\(86\) | −272.419 | −0.00397183 | ||||||||
\(87\) | 21798.5 | 0.308765 | ||||||||
\(88\) | 87102.1 | 1.19901 | ||||||||
\(89\) | 53605.6 | 0.717357 | 0.358678 | − | 0.933461i | \(-0.383227\pi\) | ||||
0.358678 | + | 0.933461i | \(0.383227\pi\) | |||||||
\(90\) | 25909.6 | 0.337175 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1068.59 | −0.0131626 | ||||||||
\(93\) | 57517.9 | 0.689597 | ||||||||
\(94\) | 21617.4 | 0.252338 | ||||||||
\(95\) | 53631.4 | 0.609691 | ||||||||
\(96\) | 39086.5 | 0.432861 | ||||||||
\(97\) | 3110.79 | 0.0335693 | 0.0167846 | − | 0.999859i | \(-0.494657\pi\) | ||||
0.0167846 | + | 0.999859i | \(0.494657\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 110424. | 1.13234 | ||||||||
\(100\) | 24311.9 | 0.243119 | ||||||||
\(101\) | 21835.9 | 0.212994 | 0.106497 | − | 0.994313i | \(-0.466037\pi\) | ||||
0.106497 | + | 0.994313i | \(0.466037\pi\) | |||||||
\(102\) | −21764.3 | −0.207130 | ||||||||
\(103\) | 65341.4 | 0.606870 | 0.303435 | − | 0.952852i | \(-0.401866\pi\) | ||||
0.303435 | + | 0.952852i | \(0.401866\pi\) | |||||||
\(104\) | −172710. | −1.56579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −33649.5 | −0.290880 | ||||||||
\(107\) | −108957. | −0.920020 | −0.460010 | − | 0.887914i | \(-0.652154\pi\) | ||||
−0.460010 | + | 0.887914i | \(0.652154\pi\) | |||||||
\(108\) | 69856.6 | 0.576299 | ||||||||
\(109\) | 86728.7 | 0.699192 | 0.349596 | − | 0.936901i | \(-0.386319\pi\) | ||||
0.349596 | + | 0.936901i | \(0.386319\pi\) | |||||||
\(110\) | 71438.1 | 0.562922 | ||||||||
\(111\) | −16744.1 | −0.128989 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −101496. | −0.747746 | −0.373873 | − | 0.927480i | \(-0.621970\pi\) | ||||
−0.373873 | + | 0.927480i | \(0.621970\pi\) | |||||||
\(114\) | −21495.4 | −0.154911 | ||||||||
\(115\) | −2041.32 | −0.0143935 | ||||||||
\(116\) | −80147.3 | −0.553024 | ||||||||
\(117\) | −218955. | −1.47873 | ||||||||
\(118\) | 27748.9 | 0.183459 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 47538.4 | 0.301364 | ||||||||
\(121\) | 143411. | 0.890470 | ||||||||
\(122\) | −108431. | −0.659557 | ||||||||
\(123\) | −83560.9 | −0.498013 | ||||||||
\(124\) | −211478. | −1.23513 | ||||||||
\(125\) | 190165. | 1.08857 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3094.61 | −0.0170253 | −0.00851267 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851267 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(128\) | −173081. | −0.933736 | ||||||||
\(129\) | −633.661 | −0.00335261 | ||||||||
\(130\) | −141651. | −0.735124 | ||||||||
\(131\) | 253431. | 1.29027 | 0.645136 | − | 0.764067i | \(-0.276801\pi\) | ||||
0.645136 | + | 0.764067i | \(0.276801\pi\) | |||||||
\(132\) | 86986.0 | 0.434525 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −190155. | −0.914842 | ||||||||
\(135\) | 133447. | 0.630193 | ||||||||
\(136\) | 186383. | 0.864091 | ||||||||
\(137\) | −97152.9 | −0.442236 | −0.221118 | − | 0.975247i | \(-0.570971\pi\) | ||||
−0.221118 | + | 0.975247i | \(0.570971\pi\) | |||||||
\(138\) | 818.156 | 0.00365711 | ||||||||
\(139\) | 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 | ||||||||
\(142\) | −172774. | −0.719047 | ||||||||
\(143\) | −603702. | −2.46878 | ||||||||
\(144\) | −65247.2 | −0.262214 | ||||||||
\(145\) | −153105. | −0.604741 | ||||||||
\(146\) | 5209.01 | 0.0202243 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 61563.7 | 0.231031 | ||||||||
\(149\) | 140406. | 0.518109 | 0.259055 | − | 0.965863i | \(-0.416589\pi\) | ||||
0.259055 | + | 0.965863i | \(0.416589\pi\) | |||||||
\(150\) | −18614.2 | −0.0675486 | ||||||||
\(151\) | 119696. | 0.427205 | 0.213603 | − | 0.976921i | \(-0.431480\pi\) | ||||
0.213603 | + | 0.976921i | \(0.431480\pi\) | |||||||
\(152\) | 184080. | 0.646247 | ||||||||
\(153\) | 236289. | 0.816045 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −403986. | −1.35063 | ||||||||
\(156\) | −172480. | −0.567450 | ||||||||
\(157\) | 97616.9 | 0.316065 | 0.158032 | − | 0.987434i | \(-0.449485\pi\) | ||||
0.158032 | + | 0.987434i | \(0.449485\pi\) | |||||||
\(158\) | −24.0101 | −7.65159e−5 0 | ||||||||
\(159\) | −78270.6 | −0.245531 | ||||||||
\(160\) | −274530. | −0.847794 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 83411.8 | 0.249712 | ||||||||
\(163\) | 182678. | 0.538539 | 0.269270 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269270 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(164\) | 307232. | 0.891984 | ||||||||
\(165\) | 166169. | 0.475160 | ||||||||
\(166\) | −267542. | −0.753568 | ||||||||
\(167\) | −451674. | −1.25324 | −0.626619 | − | 0.779326i | \(-0.715562\pi\) | ||||
−0.626619 | + | 0.779326i | \(0.715562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 825757. | 2.22400 | ||||||||
\(170\) | 152865. | 0.405682 | ||||||||
\(171\) | 233369. | 0.610314 | ||||||||
\(172\) | 2329.81 | 0.00600481 | ||||||||
\(173\) | 371647. | 0.944095 | 0.472047 | − | 0.881573i | \(-0.343515\pi\) | ||||
0.472047 | + | 0.881573i | \(0.343515\pi\) | |||||||
\(174\) | 61364.2 | 0.153653 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −179900. | −0.437773 | ||||||||
\(177\) | 64545.4 | 0.154857 | ||||||||
\(178\) | 150904. | 0.356985 | ||||||||
\(179\) | 85003.4 | 0.198291 | 0.0991457 | − | 0.995073i | \(-0.468389\pi\) | ||||
0.0991457 | + | 0.995073i | \(0.468389\pi\) | |||||||
\(180\) | −221587. | −0.509757 | ||||||||
\(181\) | −379442. | −0.860892 | −0.430446 | − | 0.902616i | \(-0.641644\pi\) | ||||
−0.430446 | + | 0.902616i | \(0.641644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −252216. | −0.556730 | ||||||||
\(184\) | −7006.46 | −0.0152565 | ||||||||
\(185\) | 117605. | 0.252636 | ||||||||
\(186\) | 161917. | 0.343171 | ||||||||
\(187\) | 651496. | 1.36241 | ||||||||
\(188\) | −184878. | −0.381497 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 150976. | 0.303406 | ||||||||
\(191\) | −922196. | −1.82911 | −0.914555 | − | 0.404462i | \(-0.867459\pi\) | ||||
−0.914555 | + | 0.404462i | \(0.867459\pi\) | |||||||
\(192\) | 41715.1 | 0.0816658 | ||||||||
\(193\) | 505107. | 0.976090 | 0.488045 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488045 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(194\) | 8757.11 | 0.0167054 | ||||||||
\(195\) | −329488. | −0.620516 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 251505. | 0.461723 | 0.230861 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230861 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(198\) | 310853. | 0.563497 | ||||||||
\(199\) | −208033. | −0.372392 | −0.186196 | − | 0.982513i | \(-0.559616\pi\) | ||||
−0.186196 | + | 0.982513i | \(0.559616\pi\) | |||||||
\(200\) | 159407. | 0.281794 | ||||||||
\(201\) | −442311. | −0.772215 | ||||||||
\(202\) | 61469.7 | 0.105994 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 186135. | 0.313150 | ||||||||
\(205\) | 586904. | 0.975399 | ||||||||
\(206\) | 183941. | 0.302002 | ||||||||
\(207\) | −8882.50 | −0.0144082 | ||||||||
\(208\) | 356714. | 0.571692 | ||||||||
\(209\) | 643446. | 1.01893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −640577. | −0.990525 | −0.495262 | − | 0.868744i | \(-0.664928\pi\) | ||||
−0.495262 | + | 0.868744i | \(0.664928\pi\) | |||||||
\(212\) | 287781. | 0.439767 | ||||||||
\(213\) | −401882. | −0.606945 | ||||||||
\(214\) | −306723. | −0.457838 | ||||||||
\(215\) | 4450.62 | 0.00656636 | ||||||||
\(216\) | 458032. | 0.667977 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 244148. | 0.347945 | ||||||||
\(219\) | 12116.4 | 0.0170712 | ||||||||
\(220\) | −610960. | −0.851052 | ||||||||
\(221\) | −1.29182e6 | −1.77918 | ||||||||
\(222\) | −47135.8 | −0.0641902 | ||||||||
\(223\) | 390135. | 0.525354 | 0.262677 | − | 0.964884i | \(-0.415395\pi\) | ||||
0.262677 | + | 0.964884i | \(0.415395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 202089. | 0.266126 | ||||||||
\(226\) | −285720. | −0.372108 | ||||||||
\(227\) | 291353. | 0.375279 | 0.187639 | − | 0.982238i | \(-0.439916\pi\) | ||||
0.187639 | + | 0.982238i | \(0.439916\pi\) | |||||||
\(228\) | 183835. | 0.234202 | ||||||||
\(229\) | −1.23040e6 | −1.55045 | −0.775227 | − | 0.631682i | \(-0.782365\pi\) | ||||
−0.775227 | + | 0.631682i | \(0.782365\pi\) | |||||||
\(230\) | −5746.45 | −0.00716276 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −525506. | −0.641000 | ||||||||
\(233\) | 114279. | 0.137903 | 0.0689517 | − | 0.997620i | \(-0.478035\pi\) | ||||
0.0689517 | + | 0.997620i | \(0.478035\pi\) | |||||||
\(234\) | −616373. | −0.735875 | ||||||||
\(235\) | −353172. | −0.417174 | ||||||||
\(236\) | −237317. | −0.277363 | ||||||||
\(237\) | −55.8489 | −6.45867e−5 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.14782e6 | −1.29981 | −0.649906 | − | 0.760014i | \(-0.725192\pi\) | ||||
−0.649906 | + | 0.760014i | \(0.725192\pi\) | |||||||
\(240\) | −98185.4 | −0.110032 | ||||||||
\(241\) | 812708. | 0.901346 | 0.450673 | − | 0.892689i | \(-0.351184\pi\) | ||||
0.450673 | + | 0.892689i | \(0.351184\pi\) | |||||||
\(242\) | 403713. | 0.443133 | ||||||||
\(243\) | 899104. | 0.976775 | ||||||||
\(244\) | 927332. | 0.997150 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −235230. | −0.247831 | ||||||||
\(247\) | −1.27586e6 | −1.33064 | ||||||||
\(248\) | −1.38661e6 | −1.43161 | ||||||||
\(249\) | −622318. | −0.636084 | ||||||||
\(250\) | 535328. | 0.541714 | ||||||||
\(251\) | −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 | ||||||||
\(254\) | −8711.54 | −0.00847248 | ||||||||
\(255\) | 355572. | 0.342434 | ||||||||
\(256\) | −691096. | −0.659081 | ||||||||
\(257\) | −1.69712e6 | −1.60281 | −0.801403 | − | 0.598125i | \(-0.795913\pi\) | ||||
−0.801403 | + | 0.598125i | \(0.795913\pi\) | |||||||
\(258\) | −1783.80 | −0.00166839 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.21144e6 | 1.11140 | ||||||||
\(261\) | −666215. | −0.605359 | ||||||||
\(262\) | 713427. | 0.642090 | ||||||||
\(263\) | 205694. | 0.183372 | 0.0916859 | − | 0.995788i | \(-0.470774\pi\) | ||||
0.0916859 | + | 0.995788i | \(0.470774\pi\) | |||||||
\(264\) | 570346. | 0.503649 | ||||||||
\(265\) | 549746. | 0.480892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 351010. | 0.301330 | ||||||||
\(268\) | 1.62627e6 | 1.38310 | ||||||||
\(269\) | 1.73425e6 | 1.46127 | 0.730635 | − | 0.682769i | \(-0.239224\pi\) | ||||
0.730635 | + | 0.682769i | \(0.239224\pi\) | |||||||
\(270\) | 375662. | 0.313609 | ||||||||
\(271\) | 369042. | 0.305248 | 0.152624 | − | 0.988284i | \(-0.451228\pi\) | ||||
0.152624 | + | 0.988284i | \(0.451228\pi\) | |||||||
\(272\) | −384954. | −0.315491 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −273492. | −0.220074 | ||||||||
\(275\) | 557201. | 0.444304 | ||||||||
\(276\) | −6997.12 | −0.00552900 | ||||||||
\(277\) | 1.22767e6 | 0.961351 | 0.480676 | − | 0.876899i | \(-0.340391\pi\) | ||||
0.480676 | + | 0.876899i | \(0.340391\pi\) | |||||||
\(278\) | 592032. | 0.459445 | ||||||||
\(279\) | −1.75789e6 | −1.35201 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00671e6 | 1.51607 | 0.758035 | − | 0.652214i | \(-0.226159\pi\) | ||||
0.758035 | + | 0.652214i | \(0.226159\pi\) | |||||||
\(282\) | 141551. | 0.105996 | ||||||||
\(283\) | −1.78581e6 | −1.32547 | −0.662734 | − | 0.748855i | \(-0.730604\pi\) | ||||
−0.662734 | + | 0.748855i | \(0.730604\pi\) | |||||||
\(284\) | 1.47762e6 | 1.08709 | ||||||||
\(285\) | 351179. | 0.256104 | ||||||||
\(286\) | −1.69947e6 | −1.22856 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.19458e6 | −0.848660 | ||||||||
\(289\) | −25770.8 | −0.0181503 | ||||||||
\(290\) | −431002. | −0.300943 | ||||||||
\(291\) | 20369.5 | 0.0141009 | ||||||||
\(292\) | −44549.0 | −0.0305760 | ||||||||
\(293\) | 853248. | 0.580639 | 0.290319 | − | 0.956930i | \(-0.406238\pi\) | ||||
0.290319 | + | 0.956930i | \(0.406238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −453345. | −0.303301 | ||||||||
\(296\) | 403658. | 0.267784 | ||||||||
\(297\) | 1.60104e6 | 1.05320 | ||||||||
\(298\) | 395254. | 0.257831 | ||||||||
\(299\) | 48561.6 | 0.0314134 | ||||||||
\(300\) | 159194. | 0.102123 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 336952. | 0.212594 | ||||||||
\(303\) | 142982. | 0.0894693 | ||||||||
\(304\) | −380198. | −0.235953 | ||||||||
\(305\) | 1.77148e6 | 1.09040 | ||||||||
\(306\) | 665170. | 0.406096 | ||||||||
\(307\) | −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 | ||||||||
\(310\) | −1.13725e6 | −0.672128 | ||||||||
\(311\) | 863604. | 0.506307 | 0.253153 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253153 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(312\) | −1.13091e6 | −0.657720 | ||||||||
\(313\) | 1.10047e6 | 0.634918 | 0.317459 | − | 0.948272i | \(-0.397170\pi\) | ||||
0.317459 | + | 0.948272i | \(0.397170\pi\) | |||||||
\(314\) | 274799. | 0.157286 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 205.342 | 0.000115680 0 | ||||||||
\(317\) | 1.49591e6 | 0.836097 | 0.418048 | − | 0.908425i | \(-0.362714\pi\) | ||||
0.418048 | + | 0.908425i | \(0.362714\pi\) | |||||||
\(318\) | −220337. | −0.122186 | ||||||||
\(319\) | −1.83689e6 | −1.01066 | ||||||||
\(320\) | −292993. | −0.159949 | ||||||||
\(321\) | −713454. | −0.386459 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37686e6 | 0.734318 | ||||||||
\(324\) | −713363. | −0.377527 | ||||||||
\(325\) | −1.10485e6 | −0.580221 | ||||||||
\(326\) | 514252. | 0.267998 | ||||||||
\(327\) | 567901. | 0.293699 | ||||||||
\(328\) | 2.01445e6 | 1.03388 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 467777. | 0.236458 | ||||||||
\(331\) | −2.74015e6 | −1.37469 | −0.687345 | − | 0.726331i | \(-0.741224\pi\) | ||||
−0.687345 | + | 0.726331i | \(0.741224\pi\) | |||||||
\(332\) | 2.28810e6 | 1.13928 | ||||||||
\(333\) | 511741. | 0.252894 | ||||||||
\(334\) | −1.27149e6 | −0.623661 | ||||||||
\(335\) | 3.10665e6 | 1.51245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.31353e6 | −1.10968 | −0.554842 | − | 0.831956i | \(-0.687221\pi\) | ||||
−0.554842 | + | 0.831956i | \(0.687221\pi\) | |||||||
\(338\) | 2.32457e6 | 1.10675 | ||||||||
\(339\) | −664600. | −0.314095 | ||||||||
\(340\) | −1.30735e6 | −0.613329 | ||||||||
\(341\) | −4.84685e6 | −2.25722 | ||||||||
\(342\) | 656951. | 0.303716 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15276.0 | 0.00696006 | ||||||||
\(345\) | −13366.6 | −0.00604606 | ||||||||
\(346\) | 1.04621e6 | 0.469819 | ||||||||
\(347\) | −3.05926e6 | −1.36393 | −0.681966 | − | 0.731384i | \(-0.738875\pi\) | ||||
−0.681966 | + | 0.731384i | \(0.738875\pi\) | |||||||
\(348\) | −524806. | −0.232301 | ||||||||
\(349\) | −210232. | −0.0923921 | −0.0461961 | − | 0.998932i | \(-0.514710\pi\) | ||||
−0.0461961 | + | 0.998932i | \(0.514710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.17461e6 | −1.37538 | ||||||||
\(352\) | −3.29370e6 | −1.41686 | ||||||||
\(353\) | −3.76790e6 | −1.60939 | −0.804697 | − | 0.593686i | \(-0.797672\pi\) | ||||
−0.804697 | + | 0.593686i | \(0.797672\pi\) | |||||||
\(354\) | 181700. | 0.0770631 | ||||||||
\(355\) | 2.82268e6 | 1.18875 | ||||||||
\(356\) | −1.29057e6 | −0.539707 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 239291. | 0.0986776 | ||||||||
\(359\) | 1.00722e6 | 0.412465 | 0.206232 | − | 0.978503i | \(-0.433880\pi\) | ||||
0.206232 | + | 0.978503i | \(0.433880\pi\) | |||||||
\(360\) | −1.45289e6 | −0.590850 | ||||||||
\(361\) | −1.11625e6 | −0.450809 | ||||||||
\(362\) | −1.06816e6 | −0.428414 | ||||||||
\(363\) | 939058. | 0.374047 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −85101.8 | −0.0334354 | ||||||||
\(366\) | −710005. | −0.277050 | ||||||||
\(367\) | −1.52650e6 | −0.591603 | −0.295802 | − | 0.955249i | \(-0.595587\pi\) | ||||
−0.295802 | + | 0.955249i | \(0.595587\pi\) | |||||||
\(368\) | 14471.1 | 0.00557034 | ||||||||
\(369\) | 2.55383e6 | 0.976396 | ||||||||
\(370\) | 331066. | 0.125722 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38476e6 | −0.518822 | ||||||||
\(373\) | 4.86297e6 | 1.80980 | 0.904898 | − | 0.425629i | \(-0.139947\pi\) | ||||
0.904898 | + | 0.425629i | \(0.139947\pi\) | |||||||
\(374\) | 1.83401e6 | 0.677988 | ||||||||
\(375\) | 1.24520e6 | 0.457258 | ||||||||
\(376\) | −1.21220e6 | −0.442186 | ||||||||
\(377\) | 3.64227e6 | 1.31983 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 630878. | 0.225604 | 0.112802 | − | 0.993617i | \(-0.464017\pi\) | ||||
0.112802 | + | 0.993617i | \(0.464017\pi\) | |||||||
\(380\) | −1.29119e6 | −0.458704 | ||||||||
\(381\) | −20263.5 | −0.00715159 | ||||||||
\(382\) | −2.59605e6 | −0.910237 | ||||||||
\(383\) | 565644. | 0.197036 | 0.0985182 | − | 0.995135i | \(-0.468590\pi\) | ||||
0.0985182 | + | 0.995135i | \(0.468590\pi\) | |||||||
\(384\) | −1.13334e6 | −0.392221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.42191e6 | 0.485741 | ||||||||
\(387\) | 19366.2 | 0.00657306 | ||||||||
\(388\) | −74893.5 | −0.0252560 | ||||||||
\(389\) | 592212. | 0.198428 | 0.0992140 | − | 0.995066i | \(-0.468367\pi\) | ||||
0.0992140 | + | 0.995066i | \(0.468367\pi\) | |||||||
\(390\) | −927532. | −0.308793 | ||||||||
\(391\) | −52406.1 | −0.0173356 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.65947e6 | 0.541986 | ||||||||
\(394\) | 708005. | 0.229771 | ||||||||
\(395\) | 392.264 | 0.000126498 0 | ||||||||
\(396\) | −2.65851e6 | −0.851922 | ||||||||
\(397\) | 1.34312e6 | 0.427698 | 0.213849 | − | 0.976867i | \(-0.431400\pi\) | ||||
0.213849 | + | 0.976867i | \(0.431400\pi\) | |||||||
\(398\) | −585629. | −0.185317 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −329238. | −0.102887 | ||||||||
\(401\) | −3.68716e6 | −1.14507 | −0.572534 | − | 0.819881i | \(-0.694040\pi\) | ||||
−0.572534 | + | 0.819881i | \(0.694040\pi\) | |||||||
\(402\) | −1.24514e6 | −0.384284 | ||||||||
\(403\) | 9.61057e6 | 2.94772 | ||||||||
\(404\) | −525707. | −0.160247 | ||||||||
\(405\) | −1.36273e6 | −0.412832 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.41097e6 | 0.422214 | ||||||||
\(408\) | 1.22044e6 | 0.362966 | ||||||||
\(409\) | 1.45630e6 | 0.430470 | 0.215235 | − | 0.976562i | \(-0.430948\pi\) | ||||
0.215235 | + | 0.976562i | \(0.430948\pi\) | |||||||
\(410\) | 1.65218e6 | 0.485397 | ||||||||
\(411\) | −636159. | −0.185764 | ||||||||
\(412\) | −1.57312e6 | −0.456582 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −25004.9 | −0.00717008 | ||||||||
\(415\) | 4.37096e6 | 1.24582 | ||||||||
\(416\) | 6.53090e6 | 1.85029 | ||||||||
\(417\) | 1.37710e6 | 0.387816 | ||||||||
\(418\) | 1.81135e6 | 0.507062 | ||||||||
\(419\) | −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 | \(0.410420\pi\) | |||||||
\(422\) | −1.80327e6 | −0.492924 | ||||||||
\(423\) | −1.53678e6 | −0.417600 | ||||||||
\(424\) | 1.88691e6 | 0.509725 | ||||||||
\(425\) | 1.19231e6 | 0.320197 | ||||||||
\(426\) | −1.13133e6 | −0.302040 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.62319e6 | 0.692182 | ||||||||
\(429\) | −3.95305e6 | −1.03703 | ||||||||
\(430\) | 12528.8 | 0.00326768 | ||||||||
\(431\) | −5.43800e6 | −1.41009 | −0.705043 | − | 0.709164i | \(-0.749072\pi\) | ||||
−0.705043 | + | 0.709164i | \(0.749072\pi\) | |||||||
\(432\) | −946016. | −0.243887 | ||||||||
\(433\) | −3.77335e6 | −0.967179 | −0.483590 | − | 0.875295i | \(-0.660667\pi\) | ||||
−0.483590 | + | 0.875295i | \(0.660667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.00253e6 | −0.254025 | ||||||||
\(436\) | −2.08802e6 | −0.526041 | ||||||||
\(437\) | −51758.6 | −0.0129652 | ||||||||
\(438\) | 34108.7 | 0.00849531 | ||||||||
\(439\) | 2.35150e6 | 0.582350 | 0.291175 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291175 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(440\) | −4.00591e6 | −0.986439 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.63656e6 | −0.885391 | ||||||||
\(443\) | 4.80377e6 | 1.16298 | 0.581491 | − | 0.813553i | \(-0.302470\pi\) | ||||
0.581491 | + | 0.813553i | \(0.302470\pi\) | |||||||
\(444\) | 403120. | 0.0970458 | ||||||||
\(445\) | −2.46538e6 | −0.590179 | ||||||||
\(446\) | 1.09826e6 | 0.261437 | ||||||||
\(447\) | 919383. | 0.217634 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.76805e6 | −0.647975 | −0.323987 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323987 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(450\) | 568896. | 0.132435 | ||||||||
\(451\) | 7.04142e6 | 1.63012 | ||||||||
\(452\) | 2.44356e6 | 0.562571 | ||||||||
\(453\) | 783770. | 0.179450 | ||||||||
\(454\) | 820179. | 0.186754 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.20536e6 | 0.271459 | ||||||||
\(457\) | 241566. | 0.0541061 | 0.0270530 | − | 0.999634i | \(-0.491388\pi\) | ||||
0.0270530 | + | 0.999634i | \(0.491388\pi\) | |||||||
\(458\) | −3.46368e6 | −0.771567 | ||||||||
\(459\) | 3.42594e6 | 0.759010 | ||||||||
\(460\) | 49145.4 | 0.0108290 | ||||||||
\(461\) | 990579. | 0.217088 | 0.108544 | − | 0.994092i | \(-0.465381\pi\) | ||||
0.108544 | + | 0.994092i | \(0.465381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.20488e6 | 1.34518 | 0.672591 | − | 0.740014i | \(-0.265181\pi\) | ||||
0.672591 | + | 0.740014i | \(0.265181\pi\) | |||||||
\(464\) | 1.08538e6 | 0.234037 | ||||||||
\(465\) | −2.64531e6 | −0.567340 | ||||||||
\(466\) | 321702. | 0.0686261 | ||||||||
\(467\) | −6.88497e6 | −1.46086 | −0.730432 | − | 0.682985i | \(-0.760681\pi\) | ||||
−0.730432 | + | 0.682985i | \(0.760681\pi\) | |||||||
\(468\) | 5.27141e6 | 1.11253 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −994206. | −0.207602 | ||||||||
\(471\) | 639197. | 0.132765 | ||||||||
\(472\) | −1.55603e6 | −0.321486 | ||||||||
\(473\) | 53396.6 | 0.0109739 | ||||||||
\(474\) | −157.219 | −3.21409e−5 0 | ||||||||
\(475\) | 1.17758e6 | 0.239473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.39214e6 | 0.481383 | ||||||||
\(478\) | −3.23121e6 | −0.646838 | ||||||||
\(479\) | −5.41288e6 | −1.07793 | −0.538963 | − | 0.842329i | \(-0.681184\pi\) | ||||
−0.538963 | + | 0.842329i | \(0.681184\pi\) | |||||||
\(480\) | −1.79763e6 | −0.356120 | ||||||||
\(481\) | −2.79774e6 | −0.551373 | ||||||||
\(482\) | 2.28783e6 | 0.448545 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.45268e6 | −0.669950 | ||||||||
\(485\) | −143069. | −0.0276179 | ||||||||
\(486\) | 2.53104e6 | 0.486081 | ||||||||
\(487\) | −3.01043e6 | −0.575182 | −0.287591 | − | 0.957753i | \(-0.592854\pi\) | ||||
−0.287591 | + | 0.957753i | \(0.592854\pi\) | |||||||
\(488\) | 6.08029e6 | 1.15578 | ||||||||
\(489\) | 1.19618e6 | 0.226216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.24498e6 | −1.35623 | −0.678115 | − | 0.734956i | \(-0.737203\pi\) | ||||
−0.678115 | + | 0.734956i | \(0.737203\pi\) | |||||||
\(492\) | 2.01176e6 | 0.374683 | ||||||||
\(493\) | −3.93062e6 | −0.728356 | ||||||||
\(494\) | −3.59163e6 | −0.662177 | ||||||||
\(495\) | −5.07853e6 | −0.931591 | ||||||||
\(496\) | 2.86389e6 | 0.522700 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.75187e6 | −0.316540 | ||||||||
\(499\) | −5.12788e6 | −0.921906 | −0.460953 | − | 0.887425i | \(-0.652492\pi\) | ||||
−0.460953 | + | 0.887425i | \(0.652492\pi\) | |||||||
\(500\) | −4.57829e6 | −0.818989 | ||||||||
\(501\) | −2.95757e6 | −0.526429 | ||||||||
\(502\) | −1.14509e6 | −0.202806 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | −68943.5 | −0.0119706 | ||||||||
\(507\) | 5.40707e6 | 0.934205 | ||||||||
\(508\) | 74503.8 | 0.0128091 | ||||||||
\(509\) | 8.78840e6 | 1.50354 | 0.751770 | − | 0.659425i | \(-0.229200\pi\) | ||||
0.751770 | + | 0.659425i | \(0.229200\pi\) | |||||||
\(510\) | 1.00096e6 | 0.170409 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.59310e6 | 0.605752 | ||||||||
\(513\) | 3.38361e6 | 0.567658 | ||||||||
\(514\) | −4.77753e6 | −0.797619 | ||||||||
\(515\) | −3.00512e6 | −0.499280 | ||||||||
\(516\) | 15255.6 | 0.00252235 | ||||||||
\(517\) | −4.23721e6 | −0.697194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.43355e6 | 0.396572 | ||||||||
\(520\) | 7.94312e6 | 1.28820 | ||||||||
\(521\) | 162133. | 0.0261684 | 0.0130842 | − | 0.999914i | \(-0.495835\pi\) | ||||
0.0130842 | + | 0.999914i | \(0.495835\pi\) | |||||||
\(522\) | −1.87544e6 | −0.301250 | ||||||||
\(523\) | −7.14844e6 | −1.14277 | −0.571383 | − | 0.820684i | \(-0.693593\pi\) | ||||
−0.571383 | + | 0.820684i | \(0.693593\pi\) | |||||||
\(524\) | −6.10144e6 | −0.970743 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 579044. | 0.0912530 | ||||||||
\(527\) | −1.03714e7 | −1.62671 | ||||||||
\(528\) | −1.17799e6 | −0.183889 | ||||||||
\(529\) | −6.43437e6 | −0.999694 | ||||||||
\(530\) | 1.54758e6 | 0.239311 | ||||||||
\(531\) | −1.97267e6 | −0.303611 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.39621e7 | −2.12879 | ||||||||
\(534\) | 988120. | 0.149953 | ||||||||
\(535\) | 5.01106e6 | 0.756912 | ||||||||
\(536\) | 1.06630e7 | 1.60313 | ||||||||
\(537\) | 556604. | 0.0832934 | ||||||||
\(538\) | 4.88203e6 | 0.727185 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.21278e6 | −0.474129 | ||||||||
\(541\) | −4.83604e6 | −0.710390 | −0.355195 | − | 0.934792i | \(-0.615586\pi\) | ||||
−0.355195 | + | 0.934792i | \(0.615586\pi\) | |||||||
\(542\) | 1.03888e6 | 0.151903 | ||||||||
\(543\) | −2.48459e6 | −0.361622 | ||||||||
\(544\) | −7.04793e6 | −1.02109 | ||||||||
\(545\) | −3.98874e6 | −0.575234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.98777e6 | 1.42725 | 0.713626 | − | 0.700527i | \(-0.247052\pi\) | ||||
0.713626 | + | 0.700527i | \(0.247052\pi\) | |||||||
\(548\) | 2.33899e6 | 0.332719 | ||||||||
\(549\) | 7.70833e6 | 1.09151 | ||||||||
\(550\) | 1.56856e6 | 0.221103 | ||||||||
\(551\) | −3.88205e6 | −0.544732 | ||||||||
\(552\) | −45878.4 | −0.00640856 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.45598e6 | 0.478406 | ||||||||
\(555\) | 770078. | 0.106121 | ||||||||
\(556\) | −5.06324e6 | −0.694611 | ||||||||
\(557\) | 1.74619e6 | 0.238481 | 0.119241 | − | 0.992865i | \(-0.461954\pi\) | ||||
0.119241 | + | 0.992865i | \(0.461954\pi\) | |||||||
\(558\) | −4.94858e6 | −0.672814 | ||||||||
\(559\) | −105877. | −0.0143309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.26600e6 | 0.572287 | ||||||||
\(562\) | 5.64904e6 | 0.754456 | ||||||||
\(563\) | −755218. | −0.100416 | −0.0502078 | − | 0.998739i | \(-0.515988\pi\) | ||||
−0.0502078 | + | 0.998739i | \(0.515988\pi\) | |||||||
\(564\) | −1.21059e6 | −0.160250 | ||||||||
\(565\) | 4.66792e6 | 0.615181 | ||||||||
\(566\) | −5.02719e6 | −0.659605 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.68836e6 | 1.26003 | ||||||||
\(569\) | −4.39534e6 | −0.569131 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(570\) | 988594. | 0.127447 | ||||||||
\(571\) | 1.16104e7 | 1.49024 | 0.745121 | − | 0.666930i | \(-0.232392\pi\) | ||||
0.745121 | + | 0.666930i | \(0.232392\pi\) | |||||||
\(572\) | 1.45344e7 | 1.85740 | ||||||||
\(573\) | −6.03855e6 | −0.768327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −44821.1 | −0.00565344 | ||||||||
\(576\) | −1.27492e6 | −0.160113 | ||||||||
\(577\) | 1.06643e7 | 1.33350 | 0.666748 | − | 0.745283i | \(-0.267686\pi\) | ||||
0.666748 | + | 0.745283i | \(0.267686\pi\) | |||||||
\(578\) | −72546.6 | −0.00903228 | ||||||||
\(579\) | 3.30745e6 | 0.410012 | ||||||||
\(580\) | 3.68606e6 | 0.454980 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 57341.7 | 0.00701719 | ||||||||
\(583\) | 6.59562e6 | 0.803682 | ||||||||
\(584\) | −292097. | −0.0354401 | ||||||||
\(585\) | 1.00700e7 | 1.21657 | ||||||||
\(586\) | 2.40195e6 | 0.288949 | ||||||||
\(587\) | −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 | ||||||||
\(590\) | −1.27620e6 | −0.150934 | ||||||||
\(591\) | 1.64686e6 | 0.193949 | ||||||||
\(592\) | −833711. | −0.0977713 | ||||||||
\(593\) | 1.17933e7 | 1.37720 | 0.688600 | − | 0.725142i | \(-0.258226\pi\) | ||||
0.688600 | + | 0.725142i | \(0.258226\pi\) | |||||||
\(594\) | 4.50703e6 | 0.524113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.38033e6 | −0.389802 | ||||||||
\(597\) | −1.36220e6 | −0.156425 | ||||||||
\(598\) | 136705. | 0.0156326 | ||||||||
\(599\) | −4.38057e6 | −0.498843 | −0.249421 | − | 0.968395i | \(-0.580240\pi\) | ||||
−0.249421 | + | 0.968395i | \(0.580240\pi\) | |||||||
\(600\) | 1.04380e6 | 0.118369 | ||||||||
\(601\) | 688570. | 0.0777610 | 0.0388805 | − | 0.999244i | \(-0.487621\pi\) | ||||
0.0388805 | + | 0.999244i | \(0.487621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.35181e7 | 1.51399 | ||||||||
\(604\) | −2.88172e6 | −0.321410 | ||||||||
\(605\) | −6.59563e6 | −0.732601 | ||||||||
\(606\) | 402504. | 0.0445235 | ||||||||
\(607\) | −9.37319e6 | −1.03256 | −0.516281 | − | 0.856420i | \(-0.672684\pi\) | ||||
−0.516281 | + | 0.856420i | \(0.672684\pi\) | |||||||
\(608\) | −6.96085e6 | −0.763666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.98684e6 | 0.542626 | ||||||||
\(611\) | 8.40174e6 | 0.910472 | ||||||||
\(612\) | −5.68874e6 | −0.613956 | ||||||||
\(613\) | −2.16685e6 | −0.232904 | −0.116452 | − | 0.993196i | \(-0.537152\pi\) | ||||
−0.116452 | + | 0.993196i | \(0.537152\pi\) | |||||||
\(614\) | −5.51947e6 | −0.590849 | ||||||||
\(615\) | 3.84306e6 | 0.409722 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.07951e6 | −0.537166 | −0.268583 | − | 0.963256i | \(-0.586555\pi\) | ||||
−0.268583 | + | 0.963256i | \(0.586555\pi\) | |||||||
\(618\) | 1.20445e6 | 0.126858 | ||||||||
\(619\) | −2.19034e6 | −0.229766 | −0.114883 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114883 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(620\) | 9.72611e6 | 1.01616 | ||||||||
\(621\) | −128787. | −0.0134012 | ||||||||
\(622\) | 2.43111e6 | 0.251958 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.33577e6 | 0.240142 | ||||||||
\(625\) | −5.59018e6 | −0.572435 | ||||||||
\(626\) | 3.09790e6 | 0.315960 | ||||||||
\(627\) | 4.21329e6 | 0.428009 | ||||||||
\(628\) | −2.35016e6 | −0.237793 | ||||||||
\(629\) | 3.01923e6 | 0.304278 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.18693e6 | −0.718572 | −0.359286 | − | 0.933228i | \(-0.616980\pi\) | ||||
−0.359286 | + | 0.933228i | \(0.616980\pi\) | |||||||
\(632\) | 1346.38 | 0.000134083 0 | ||||||||
\(633\) | −4.19451e6 | −0.416075 | ||||||||
\(634\) | 4.21109e6 | 0.416075 | ||||||||
\(635\) | 142324. | 0.0140070 | ||||||||
\(636\) | 1.88439e6 | 0.184726 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.17097e6 | −0.502945 | ||||||||
\(639\) | 1.22825e7 | 1.18997 | ||||||||
\(640\) | 7.96017e6 | 0.768197 | ||||||||
\(641\) | −1.76500e7 | −1.69668 | −0.848340 | − | 0.529452i | \(-0.822398\pi\) | ||||
−0.848340 | + | 0.529452i | \(0.822398\pi\) | |||||||
\(642\) | −2.00843e6 | −0.192317 | ||||||||
\(643\) | 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 | ||||||||
\(646\) | 3.87597e6 | 0.365425 | ||||||||
\(647\) | −1.38642e6 | −0.130207 | −0.0651035 | − | 0.997879i | \(-0.520738\pi\) | ||||
−0.0651035 | + | 0.997879i | \(0.520738\pi\) | |||||||
\(648\) | −4.67735e6 | −0.437585 | ||||||||
\(649\) | −5.43904e6 | −0.506886 | ||||||||
\(650\) | −3.11022e6 | −0.288741 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.39804e6 | −0.405173 | ||||||||
\(653\) | −1.75425e7 | −1.60994 | −0.804968 | − | 0.593318i | \(-0.797818\pi\) | ||||
−0.804968 | + | 0.593318i | \(0.797818\pi\) | |||||||
\(654\) | 1.59868e6 | 0.146156 | ||||||||
\(655\) | −1.16556e7 | −1.06152 | ||||||||
\(656\) | −4.16062e6 | −0.377484 | ||||||||
\(657\) | −370308. | −0.0334696 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.87522e6 | 0.885795 | 0.442898 | − | 0.896572i | \(-0.353950\pi\) | ||||
0.442898 | + | 0.896572i | \(0.353950\pi\) | |||||||
\(660\) | −4.00058e6 | −0.357489 | ||||||||
\(661\) | −8.06792e6 | −0.718221 | −0.359110 | − | 0.933295i | \(-0.616920\pi\) | ||||
−0.359110 | + | 0.933295i | \(0.616920\pi\) | |||||||
\(662\) | −7.71373e6 | −0.684100 | ||||||||
\(663\) | −8.45884e6 | −0.747355 | ||||||||
\(664\) | 1.50025e7 | 1.32052 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.44059e6 | 0.125850 | ||||||||
\(667\) | 147759. | 0.0128599 | ||||||||
\(668\) | 1.08742e7 | 0.942880 | ||||||||
\(669\) | 2.55461e6 | 0.220678 | ||||||||
\(670\) | 8.74544e6 | 0.752652 | ||||||||
\(671\) | 2.12534e7 | 1.82231 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.12772e7 | −0.959762 | −0.479881 | − | 0.877334i | \(-0.659320\pi\) | ||||
−0.479881 | + | 0.877334i | \(0.659320\pi\) | |||||||
\(674\) | −6.51274e6 | −0.552223 | ||||||||
\(675\) | 2.93008e6 | 0.247526 | ||||||||
\(676\) | −1.98804e7 | −1.67324 | ||||||||
\(677\) | 5.20372e6 | 0.436357 | 0.218179 | − | 0.975909i | \(-0.429988\pi\) | ||||
0.218179 | + | 0.975909i | \(0.429988\pi\) | |||||||
\(678\) | −1.87090e6 | −0.156306 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.57196e6 | −0.710899 | ||||||||
\(681\) | 1.90778e6 | 0.157638 | ||||||||
\(682\) | −1.36442e7 | −1.12328 | ||||||||
\(683\) | 6.05915e6 | 0.497004 | 0.248502 | − | 0.968631i | \(-0.420062\pi\) | ||||
0.248502 | + | 0.968631i | \(0.420062\pi\) | |||||||
\(684\) | −5.61845e6 | −0.459173 | ||||||||
\(685\) | 4.46816e6 | 0.363833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.05671e6 | −0.651277 | ||||||||
\(688\) | −31550.9 | −0.00254121 | ||||||||
\(689\) | −1.30781e7 | −1.04954 | ||||||||
\(690\) | −37627.9 | −0.00300876 | ||||||||
\(691\) | 7.36498e6 | 0.586781 | 0.293391 | − | 0.955993i | \(-0.405216\pi\) | ||||
0.293391 | + | 0.955993i | \(0.405216\pi\) | |||||||
\(692\) | −8.94754e6 | −0.710295 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.61204e6 | −0.678746 | ||||||||
\(695\) | −9.67228e6 | −0.759569 | ||||||||
\(696\) | −3.44102e6 | −0.269255 | ||||||||
\(697\) | 1.50674e7 | 1.17478 | ||||||||
\(698\) | −591818. | −0.0459779 | ||||||||
\(699\) | 748298. | 0.0579271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.80919e6 | 0.600221 | 0.300110 | − | 0.953904i | \(-0.402977\pi\) | ||||
0.300110 | + | 0.953904i | \(0.402977\pi\) | |||||||
\(702\) | −8.93676e6 | −0.684443 | ||||||||
\(703\) | 2.98193e6 | 0.227567 | ||||||||
\(704\) | −3.51520e6 | −0.267312 | ||||||||
\(705\) | −2.31258e6 | −0.175236 | ||||||||
\(706\) | −1.06069e7 | −0.800898 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.55395e6 | −0.116508 | ||||||||
\(709\) | 1.75650e7 | 1.31230 | 0.656150 | − | 0.754631i | \(-0.272184\pi\) | ||||
0.656150 | + | 0.754631i | \(0.272184\pi\) | |||||||
\(710\) | 7.94606e6 | 0.591569 | ||||||||
\(711\) | 1706.88 | 0.000126628 0 | ||||||||
\(712\) | −8.46198e6 | −0.625564 | ||||||||
\(713\) | 389879. | 0.0287214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.77649e7 | 2.03110 | ||||||||
\(716\) | −2.04649e6 | −0.149186 | ||||||||
\(717\) | −7.51597e6 | −0.545993 | ||||||||
\(718\) | 2.83539e6 | 0.205259 | ||||||||
\(719\) | −8.09220e6 | −0.583773 | −0.291887 | − | 0.956453i | \(-0.594283\pi\) | ||||
−0.291887 | + | 0.956453i | \(0.594283\pi\) | |||||||
\(720\) | 3.00079e6 | 0.215727 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.14232e6 | −0.224341 | ||||||||
\(723\) | 5.32162e6 | 0.378615 | ||||||||
\(724\) | 9.13520e6 | 0.647697 | ||||||||
\(725\) | −3.36172e6 | −0.237529 | ||||||||
\(726\) | 2.64352e6 | 0.186140 | ||||||||
\(727\) | 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 | ||||||||
\(730\) | −239568. | −0.0166388 | ||||||||
\(731\) | 114259. | 0.00790858 | ||||||||
\(732\) | 6.07218e6 | 0.418858 | ||||||||
\(733\) | 5.83402e6 | 0.401059 | 0.200530 | − | 0.979688i | \(-0.435734\pi\) | ||||
0.200530 | + | 0.979688i | \(0.435734\pi\) | |||||||
\(734\) | −4.29720e6 | −0.294405 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 264944. | 0.0180285 | ||||||||
\(737\) | 3.72722e7 | 2.52765 | ||||||||
\(738\) | 7.18921e6 | 0.485893 | ||||||||
\(739\) | 6.47719e6 | 0.436290 | 0.218145 | − | 0.975916i | \(-0.429999\pi\) | ||||
0.218145 | + | 0.975916i | \(0.429999\pi\) | |||||||
\(740\) | −2.83138e6 | −0.190072 | ||||||||
\(741\) | −8.35433e6 | −0.558941 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.50899e7 | −1.00280 | −0.501401 | − | 0.865215i | \(-0.667182\pi\) | ||||
−0.501401 | + | 0.865215i | \(0.667182\pi\) | |||||||
\(744\) | −9.07955e6 | −0.601357 | ||||||||
\(745\) | −6.45744e6 | −0.426255 | ||||||||
\(746\) | 1.36896e7 | 0.900626 | ||||||||
\(747\) | 1.90196e7 | 1.24710 | ||||||||
\(748\) | −1.56850e7 | −1.02502 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.50534e6 | 0.227550 | ||||||||
\(751\) | −2.13997e6 | −0.138455 | −0.0692273 | − | 0.997601i | \(-0.522053\pi\) | ||||
−0.0692273 | + | 0.997601i | \(0.522053\pi\) | |||||||
\(752\) | 2.50367e6 | 0.161448 | ||||||||
\(753\) | −2.66355e6 | −0.171188 | ||||||||
\(754\) | 1.02533e7 | 0.656801 | ||||||||
\(755\) | −5.50494e6 | −0.351467 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.10943e7 | 1.33791 | 0.668954 | − | 0.743304i | \(-0.266742\pi\) | ||||
0.668954 | + | 0.743304i | \(0.266742\pi\) | |||||||
\(758\) | 1.77597e6 | 0.112270 | ||||||||
\(759\) | −160366. | −0.0101044 | ||||||||
\(760\) | −8.46605e6 | −0.531675 | ||||||||
\(761\) | 9.79958e6 | 0.613403 | 0.306701 | − | 0.951806i | \(-0.400775\pi\) | ||||
0.306701 | + | 0.951806i | \(0.400775\pi\) | |||||||
\(762\) | −57043.3 | −0.00355891 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.22022e7 | 1.37614 | ||||||||
\(765\) | −1.08672e7 | −0.671371 | ||||||||
\(766\) | 1.59233e6 | 0.0980530 | ||||||||
\(767\) | 1.07848e7 | 0.661947 | ||||||||
\(768\) | −4.52531e6 | −0.276850 | ||||||||
\(769\) | −3.23493e7 | −1.97265 | −0.986323 | − | 0.164825i | \(-0.947294\pi\) | ||||
−0.986323 | + | 0.164825i | \(0.947294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.11128e7 | −0.673267 | ||||||||
\(772\) | −1.21606e7 | −0.734366 | ||||||||
\(773\) | 9.19713e6 | 0.553609 | 0.276805 | − | 0.960926i | \(-0.410724\pi\) | ||||
0.276805 | + | 0.960926i | \(0.410724\pi\) | |||||||
\(774\) | 54517.4 | 0.00327102 | ||||||||
\(775\) | −8.87030e6 | −0.530499 | ||||||||
\(776\) | −491058. | −0.0292738 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.66712e6 | 0.0987456 | ||||||||
\(779\) | 1.48812e7 | 0.878609 | ||||||||
\(780\) | 7.93254e6 | 0.466848 | ||||||||
\(781\) | 3.38653e7 | 1.98668 | ||||||||
\(782\) | −147527. | −0.00862690 | ||||||||
\(783\) | −9.65941e6 | −0.563049 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.48950e6 | −0.260030 | ||||||||
\(786\) | 4.67153e6 | 0.269713 | ||||||||
\(787\) | 1.46950e7 | 0.845731 | 0.422866 | − | 0.906192i | \(-0.361024\pi\) | ||||
0.422866 | + | 0.906192i | \(0.361024\pi\) | |||||||
\(788\) | −6.05508e6 | −0.347379 | ||||||||
\(789\) | 1.34689e6 | 0.0770263 | ||||||||
\(790\) | 1104.25 | 6.29506e−5 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.74312e7 | −0.987446 | ||||||||
\(793\) | −4.21423e7 | −2.37977 | ||||||||
\(794\) | 3.78097e6 | 0.212839 | ||||||||
\(795\) | 3.59975e6 | 0.202001 | ||||||||
\(796\) | 5.00847e6 | 0.280171 | ||||||||
\(797\) | 2.33344e7 | 1.30122 | 0.650610 | − | 0.759412i | \(-0.274513\pi\) | ||||
0.650610 | + | 0.759412i | \(0.274513\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.06688e6 | −0.502448 | ||||||||
\(800\) | −6.02785e6 | −0.332995 | ||||||||
\(801\) | −1.07277e7 | −0.590782 | ||||||||
\(802\) | −1.03796e7 | −0.569831 | ||||||||
\(803\) | −1.02101e6 | −0.0558783 | ||||||||
\(804\) | 1.06488e7 | 0.580980 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.70545e7 | 1.46690 | ||||||||
\(807\) | 1.13559e7 | 0.613814 | ||||||||
\(808\) | −3.44693e6 | −0.185740 | ||||||||
\(809\) | 1.69301e6 | 0.0909468 | 0.0454734 | − | 0.998966i | \(-0.485520\pi\) | ||||
0.0454734 | + | 0.998966i | \(0.485520\pi\) | |||||||
\(810\) | −3.83620e6 | −0.205442 | ||||||||
\(811\) | −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 | ||||||||
\(814\) | 3.97199e6 | 0.210110 | ||||||||
\(815\) | −8.40155e6 | −0.443063 | ||||||||
\(816\) | −2.52068e6 | −0.132524 | ||||||||
\(817\) | 112848. | 0.00591477 | ||||||||
\(818\) | 4.09960e6 | 0.214219 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.41299e7 | −0.733847 | ||||||||
\(821\) | 8.73550e6 | 0.452304 | 0.226152 | − | 0.974092i | \(-0.427385\pi\) | ||||
0.226152 | + | 0.974092i | \(0.427385\pi\) | |||||||
\(822\) | −1.79083e6 | −0.0924433 | ||||||||
\(823\) | −3.27964e7 | −1.68782 | −0.843910 | − | 0.536485i | \(-0.819752\pi\) | ||||
−0.843910 | + | 0.536485i | \(0.819752\pi\) | |||||||
\(824\) | −1.03146e7 | −0.529215 | ||||||||
\(825\) | 3.64856e6 | 0.186632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.31248e7 | 0.667311 | 0.333656 | − | 0.942695i | \(-0.391718\pi\) | ||||
0.333656 | + | 0.942695i | \(0.391718\pi\) | |||||||
\(828\) | 213849. | 0.0108401 | ||||||||
\(829\) | 2.05402e7 | 1.03805 | 0.519026 | − | 0.854759i | \(-0.326295\pi\) | ||||
0.519026 | + | 0.854759i | \(0.326295\pi\) | |||||||
\(830\) | 1.23046e7 | 0.619970 | ||||||||
\(831\) | 8.03880e6 | 0.403821 | ||||||||
\(832\) | 6.97012e6 | 0.349085 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.87664e6 | 0.192992 | ||||||||
\(835\) | 2.07729e7 | 1.03106 | ||||||||
\(836\) | −1.54912e7 | −0.766601 | ||||||||
\(837\) | −2.54875e7 | −1.25752 | ||||||||
\(838\) | −8.22542e6 | −0.404621 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 5.68643e6 | 0.276414 | ||||||||
\(843\) | 1.31400e7 | 0.636834 | ||||||||
\(844\) | 1.54221e7 | 0.745226 | ||||||||
\(845\) | −3.79774e7 | −1.82972 | ||||||||
\(846\) | −4.32614e6 | −0.207814 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.89720e6 | −0.186107 | ||||||||
\(849\) | −1.16935e7 | −0.556770 | ||||||||
\(850\) | 3.35645e6 | 0.159343 | ||||||||
\(851\) | −113498. | −0.00537236 | ||||||||
\(852\) | 9.67545e6 | 0.456638 | ||||||||
\(853\) | 1.02093e7 | 0.480424 | 0.240212 | − | 0.970720i | \(-0.422783\pi\) | ||||
0.240212 | + | 0.970720i | \(0.422783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.07329e7 | −0.502113 | ||||||||
\(856\) | 1.71996e7 | 0.802295 | ||||||||
\(857\) | −8.33206e6 | −0.387525 | −0.193763 | − | 0.981048i | \(-0.562069\pi\) | ||||
−0.193763 | + | 0.981048i | \(0.562069\pi\) | |||||||
\(858\) | −1.11281e7 | −0.516064 | ||||||||
\(859\) | 3.12766e7 | 1.44623 | 0.723113 | − | 0.690729i | \(-0.242710\pi\) | ||||
0.723113 | + | 0.690729i | \(0.242710\pi\) | |||||||
\(860\) | −107150. | −0.00494023 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.53084e7 | −0.701714 | ||||||||
\(863\) | −3.73573e7 | −1.70745 | −0.853726 | − | 0.520722i | \(-0.825663\pi\) | ||||
−0.853726 | + | 0.520722i | \(0.825663\pi\) | |||||||
\(864\) | −1.73201e7 | −0.789345 | ||||||||
\(865\) | −1.70924e7 | −0.776719 | ||||||||
\(866\) | −1.06222e7 | −0.481306 | ||||||||
\(867\) | −168747. | −0.00762411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4706.21 | 0.000211408 0 | ||||||||
\(870\) | −2.82221e6 | −0.126413 | ||||||||
\(871\) | −7.39051e7 | −3.30088 | ||||||||
\(872\) | −1.36907e7 | −0.609724 | ||||||||
\(873\) | −622543. | −0.0276461 | ||||||||
\(874\) | −145704. | −0.00645199 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −291708. | −0.0128436 | ||||||||
\(877\) | 38996.7 | 0.00171210 | 0.000856049 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000856049 | 1.00000i | \(0.499728\pi\) | ||||||||
\(878\) | 6.61965e6 | 0.289800 | ||||||||
\(879\) | 5.58708e6 | 0.243900 | ||||||||
\(880\) | 8.27378e6 | 0.360162 | ||||||||
\(881\) | 3.15554e7 | 1.36973 | 0.684864 | − | 0.728671i | \(-0.259862\pi\) | ||||
0.684864 | + | 0.728671i | \(0.259862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.42253e7 | −1.47722 | −0.738611 | − | 0.674132i | \(-0.764518\pi\) | ||||
−0.738611 | + | 0.674132i | \(0.764518\pi\) | |||||||
\(884\) | 3.11010e7 | 1.33858 | ||||||||
\(885\) | −2.96851e6 | −0.127403 | ||||||||
\(886\) | 1.35230e7 | 0.578745 | ||||||||
\(887\) | −2.69886e7 | −1.15178 | −0.575892 | − | 0.817526i | \(-0.695345\pi\) | ||||
−0.575892 | + | 0.817526i | \(0.695345\pi\) | |||||||
\(888\) | 2.64316e6 | 0.112484 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.94022e6 | −0.293696 | ||||||||
\(891\) | −1.63495e7 | −0.689938 | ||||||||
\(892\) | −9.39263e6 | −0.395253 | ||||||||
\(893\) | −8.95486e6 | −0.375777 | ||||||||
\(894\) | 2.58813e6 | 0.108303 | ||||||||
\(895\) | −3.90940e6 | −0.163137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 317982. | 0.0131954 | ||||||||
\(898\) | −7.79226e6 | −0.322458 | ||||||||
\(899\) | 2.92421e7 | 1.20673 | ||||||||
\(900\) | −4.86538e6 | −0.200221 | ||||||||
\(901\) | 1.41135e7 | 0.579191 | ||||||||
\(902\) | 1.98221e7 | 0.811211 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.60218e7 | 0.652065 | ||||||||
\(905\) | 1.74509e7 | 0.708267 | ||||||||
\(906\) | 2.20637e6 | 0.0893013 | ||||||||
\(907\) | 1.92103e7 | 0.775381 | 0.387690 | − | 0.921790i | \(-0.373273\pi\) | ||||
0.387690 | + | 0.921790i | \(0.373273\pi\) | |||||||
\(908\) | −7.01442e6 | −0.282343 | ||||||||
\(909\) | −4.36988e6 | −0.175412 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.86013e7 | 1.14180 | 0.570899 | − | 0.821020i | \(-0.306595\pi\) | ||||
0.570899 | + | 0.821020i | \(0.306595\pi\) | |||||||
\(912\) | −2.48954e6 | −0.0991133 | ||||||||
\(913\) | 5.24408e7 | 2.08206 | ||||||||
\(914\) | 680027. | 0.0269253 | ||||||||
\(915\) | 1.15997e7 | 0.458029 | ||||||||
\(916\) | 2.96224e7 | 1.16649 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.64426e6 | 0.377713 | ||||||||
\(919\) | −4.21754e7 | −1.64729 | −0.823645 | − | 0.567106i | \(-0.808063\pi\) | ||||
−0.823645 | + | 0.567106i | \(0.808063\pi\) | |||||||
\(920\) | 322235. | 0.0125517 | ||||||||
\(921\) | −1.28386e7 | −0.498733 | ||||||||
\(922\) | 2.78855e6 | 0.108032 | ||||||||
\(923\) | −6.71498e7 | −2.59442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.58224e6 | 0.0992299 | ||||||||
\(926\) | 1.74672e7 | 0.669416 | ||||||||
\(927\) | −1.30764e7 | −0.499790 | ||||||||
\(928\) | 1.98716e7 | 0.757466 | ||||||||
\(929\) | −3.01886e7 | −1.14763 | −0.573817 | − | 0.818983i | \(-0.694538\pi\) | ||||
−0.573817 | + | 0.818983i | \(0.694538\pi\) | |||||||
\(930\) | −7.44673e6 | −0.282331 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.75130e6 | −0.103752 | ||||||||
\(933\) | 5.65489e6 | 0.212677 | ||||||||
\(934\) | −1.93817e7 | −0.726984 | ||||||||
\(935\) | −2.99630e7 | −1.12087 | ||||||||
\(936\) | 3.45634e7 | 1.28952 | ||||||||
\(937\) | −3.64068e6 | −0.135467 | −0.0677335 | − | 0.997703i | \(-0.521577\pi\) | ||||
−0.0677335 | + | 0.997703i | \(0.521577\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.20589e6 | 0.266701 | ||||||||
\(940\) | 8.50275e6 | 0.313863 | ||||||||
\(941\) | 1.88601e7 | 0.694336 | 0.347168 | − | 0.937803i | \(-0.387143\pi\) | ||||
0.347168 | + | 0.937803i | \(0.387143\pi\) | |||||||
\(942\) | 1.79939e6 | 0.0660689 | ||||||||
\(943\) | −566410. | −0.0207420 | ||||||||
\(944\) | 3.21380e6 | 0.117379 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 150315. | 0.00546104 | ||||||||
\(947\) | −1.82172e7 | −0.660094 | −0.330047 | − | 0.943965i | \(-0.607065\pi\) | ||||
−0.330047 | + | 0.943965i | \(0.607065\pi\) | |||||||
\(948\) | 1344.58 | 4.85922e−5 0 | ||||||||
\(949\) | 2.02452e6 | 0.0729720 | ||||||||
\(950\) | 3.31498e6 | 0.119171 | ||||||||
\(951\) | 9.79522e6 | 0.351207 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.76898e7 | 0.987616 | 0.493808 | − | 0.869571i | \(-0.335604\pi\) | ||||
0.493808 | + | 0.869571i | \(0.335604\pi\) | |||||||
\(954\) | 6.73406e6 | 0.239555 | ||||||||
\(955\) | 4.24127e7 | 1.50483 | ||||||||
\(956\) | 2.76343e7 | 0.977921 | ||||||||
\(957\) | −1.20280e7 | −0.424534 | ||||||||
\(958\) | −1.52376e7 | −0.536419 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.91852e6 | −0.0671875 | ||||||||
\(961\) | 4.85298e7 | 1.69512 | ||||||||
\(962\) | −7.87585e6 | −0.274385 | ||||||||
\(963\) | 2.18049e7 | 0.757685 | ||||||||
\(964\) | −1.95662e7 | −0.678133 | ||||||||
\(965\) | −2.32304e7 | −0.803042 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.44768e7 | −0.841761 | −0.420881 | − | 0.907116i | \(-0.638279\pi\) | ||||
−0.420881 | + | 0.907116i | \(0.638279\pi\) | |||||||
\(968\) | −2.26383e7 | −0.776526 | ||||||||
\(969\) | 9.01571e6 | 0.308454 | ||||||||
\(970\) | −402749. | −0.0137437 | ||||||||
\(971\) | 9.50151e6 | 0.323403 | 0.161702 | − | 0.986840i | \(-0.448302\pi\) | ||||
0.161702 | + | 0.986840i | \(0.448302\pi\) | |||||||
\(972\) | −2.16463e7 | −0.734881 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.47457e6 | −0.286233 | ||||||||
\(975\) | −7.23455e6 | −0.243725 | ||||||||
\(976\) | −1.25582e7 | −0.421990 | ||||||||
\(977\) | 4.69012e7 | 1.57198 | 0.785991 | − | 0.618238i | \(-0.212153\pi\) | ||||
0.785991 | + | 0.618238i | \(0.212153\pi\) | |||||||
\(978\) | 3.36733e6 | 0.112574 | ||||||||
\(979\) | −2.95785e7 | −0.986325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.73564e7 | −0.575822 | ||||||||
\(982\) | −2.03951e7 | −0.674914 | ||||||||
\(983\) | 2.35382e7 | 0.776945 | 0.388473 | − | 0.921460i | \(-0.373003\pi\) | ||||
0.388473 | + | 0.921460i | \(0.373003\pi\) | |||||||
\(984\) | 1.31906e7 | 0.434288 | ||||||||
\(985\) | −1.15670e7 | −0.379865 | ||||||||
\(986\) | −1.10650e7 | −0.362458 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.07167e7 | 1.00111 | ||||||||
\(989\) | −4295.21 | −0.000139635 0 | ||||||||
\(990\) | −1.42964e7 | −0.463596 | ||||||||
\(991\) | −2.64104e7 | −0.854261 | −0.427130 | − | 0.904190i | \(-0.640475\pi\) | ||||
−0.427130 | + | 0.904190i | \(0.640475\pi\) | |||||||
\(992\) | 5.24336e7 | 1.69173 | ||||||||
\(993\) | −1.79426e7 | −0.577446 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.56766e6 | 0.306371 | ||||||||
\(996\) | 1.49825e7 | 0.478561 | ||||||||
\(997\) | −1.95164e7 | −0.621815 | −0.310907 | − | 0.950440i | \(-0.600633\pi\) | ||||
−0.310907 | + | 0.950440i | \(0.600633\pi\) | |||||||
\(998\) | −1.44354e7 | −0.458777 | ||||||||
\(999\) | 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 | 49.6.a.g.1.4 | yes | 4 | |
3.2 | odd | 2 | 441.6.a.z.1.2 | 4 | |||
4.3 | odd | 2 | 784.6.a.bf.1.2 | 4 | |||
7.2 | even | 3 | 49.6.c.h.18.1 | 8 | |||
7.3 | odd | 6 | 49.6.c.h.30.2 | 8 | |||
7.4 | even | 3 | 49.6.c.h.30.1 | 8 | |||
7.5 | odd | 6 | 49.6.c.h.18.2 | 8 | |||
7.6 | odd | 2 | inner | 49.6.a.g.1.3 | ✓ | 4 | |
21.20 | even | 2 | 441.6.a.z.1.1 | 4 | |||
28.27 | even | 2 | 784.6.a.bf.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.g.1.3 | ✓ | 4 | 7.6 | odd | 2 | inner | |
49.6.a.g.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
49.6.c.h.18.1 | 8 | 7.2 | even | 3 | |||
49.6.c.h.18.2 | 8 | 7.5 | odd | 6 | |||
49.6.c.h.30.1 | 8 | 7.4 | even | 3 | |||
49.6.c.h.30.2 | 8 | 7.3 | odd | 6 | |||
441.6.a.z.1.1 | 4 | 21.20 | even | 2 | |||
441.6.a.z.1.2 | 4 | 3.2 | odd | 2 | |||
784.6.a.bf.1.2 | 4 | 4.3 | odd | 2 | |||
784.6.a.bf.1.3 | 4 | 28.27 | even | 2 |