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: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 200x^{3} - 99x^{2} + 5803x - 3615 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(5.14333\) 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 | ||||||||
\(3\) | 11.2867 | 0.724039 | 0.362020 | − | 0.932170i | \(-0.382087\pi\) | ||||
0.362020 | + | 0.932170i | \(0.382087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −26.0667 | −0.466295 | −0.233148 | − | 0.972441i | \(-0.574903\pi\) | ||||
−0.233148 | + | 0.972441i | \(0.574903\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −115.611 | −0.475767 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 434.865 | 1.08361 | 0.541805 | − | 0.840505i | \(-0.317741\pi\) | ||||
0.541805 | + | 0.840505i | \(0.317741\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −737.247 | −1.20992 | −0.604958 | − | 0.796258i | \(-0.706810\pi\) | ||||
−0.604958 | + | 0.796258i | \(0.706810\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −294.206 | −0.337616 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1413.04 | 1.18586 | 0.592929 | − | 0.805255i | \(-0.297972\pi\) | ||||
0.592929 | + | 0.805255i | \(0.297972\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1737.76 | 1.10435 | 0.552173 | − | 0.833729i | \(-0.313799\pi\) | ||||
0.552173 | + | 0.833729i | \(0.313799\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 929.808 | 0.366500 | 0.183250 | − | 0.983066i | \(-0.441338\pi\) | ||||
0.183250 | + | 0.983066i | \(0.441338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2445.53 | −0.782569 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4047.52 | −1.06851 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1630.63 | −0.360048 | −0.180024 | − | 0.983662i | \(-0.557617\pi\) | ||||
−0.180024 | + | 0.983662i | \(0.557617\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1872.16 | −0.349895 | −0.174948 | − | 0.984578i | \(-0.555976\pi\) | ||||
−0.174948 | + | 0.984578i | \(0.555976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4908.17 | 0.784575 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7931.14 | −0.952426 | −0.476213 | − | 0.879330i | \(-0.657991\pi\) | ||||
−0.476213 | + | 0.879330i | \(0.657991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8321.06 | −0.876026 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6325.76 | −0.587697 | −0.293848 | − | 0.955852i | \(-0.594936\pi\) | ||||
−0.293848 | + | 0.955852i | \(0.594936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20075.7 | 1.65577 | 0.827885 | − | 0.560898i | \(-0.189544\pi\) | ||||
0.827885 | + | 0.560898i | \(0.189544\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3013.61 | 0.221848 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10265.6 | 0.677857 | 0.338928 | − | 0.940812i | \(-0.389936\pi\) | ||||
0.338928 | + | 0.940812i | \(0.389936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15948.5 | 0.858608 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11967.4 | 0.585206 | 0.292603 | − | 0.956234i | \(-0.405479\pi\) | ||||
0.292603 | + | 0.956234i | \(0.405479\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11335.5 | −0.505282 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19613.5 | 0.799590 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −21184.5 | −0.792296 | −0.396148 | − | 0.918187i | \(-0.629653\pi\) | ||||
−0.396148 | + | 0.918187i | \(0.629653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 350.115 | 0.0120472 | 0.00602361 | − | 0.999982i | \(-0.498083\pi\) | ||||
0.00602361 | + | 0.999982i | \(0.498083\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19217.6 | 0.564178 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16206.0 | 0.441052 | 0.220526 | − | 0.975381i | \(-0.429223\pi\) | ||||
0.220526 | + | 0.975381i | \(0.429223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10494.4 | 0.265360 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72282.7 | −1.70172 | −0.850861 | − | 0.525392i | \(-0.823919\pi\) | ||||
−0.850861 | + | 0.525392i | \(0.823919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 83700.7 | 1.83832 | 0.919161 | − | 0.393881i | \(-0.128868\pi\) | ||||
0.919161 | + | 0.393881i | \(0.128868\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −27601.8 | −0.566610 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 47131.0 | 0.849648 | 0.424824 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424824 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −17589.4 | −0.297878 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 843.116 | 0.0134336 | 0.00671679 | − | 0.999977i | \(-0.497862\pi\) | ||||
0.00671679 | + | 0.999977i | \(0.497862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −36833.3 | −0.552960 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18404.3 | −0.260689 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 41349.9 | 0.553349 | 0.276675 | − | 0.960964i | \(-0.410768\pi\) | ||||
0.276675 | + | 0.960964i | \(0.410768\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21130.4 | −0.253338 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −45297.7 | −0.514952 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 155369. | 1.67662 | 0.838312 | − | 0.545191i | \(-0.183543\pi\) | ||||
0.838312 | + | 0.545191i | \(0.183543\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −50275.4 | −0.515546 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −31423.7 | −0.306517 | −0.153258 | − | 0.988186i | \(-0.548977\pi\) | ||||
−0.153258 | + | 0.988186i | \(0.548977\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 36353.3 | 0.337637 | 0.168819 | − | 0.985647i | \(-0.446005\pi\) | ||||
0.168819 | + | 0.985647i | \(0.446005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 210635. | 1.77857 | 0.889287 | − | 0.457350i | \(-0.151201\pi\) | ||||
0.889287 | + | 0.457350i | \(0.151201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 228714. | 1.84385 | 0.921927 | − | 0.387364i | \(-0.126614\pi\) | ||||
0.921927 | + | 0.387364i | \(0.126614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −89516.0 | −0.689594 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 240902. | 1.77478 | 0.887390 | − | 0.461019i | \(-0.152516\pi\) | ||||
0.887390 | + | 0.461019i | \(0.152516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24237.0 | −0.170897 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 85234.2 | 0.575638 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28056.5 | 0.174209 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −71396.7 | −0.425515 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 145205. | 0.831204 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 134747. | 0.741328 | 0.370664 | − | 0.928767i | \(-0.379130\pi\) | ||||
0.370664 | + | 0.928767i | \(0.379130\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 226588. | 1.19884 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −44321.1 | −0.225648 | −0.112824 | − | 0.993615i | \(-0.535990\pi\) | ||||
−0.112824 | + | 0.993615i | \(0.535990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 105506. | 0.498243 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −365483. | −1.66366 | −0.831832 | − | 0.555027i | \(-0.812708\pi\) | ||||
−0.831832 | + | 0.555027i | \(0.812708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −134487. | −0.590397 | −0.295198 | − | 0.955436i | \(-0.595386\pi\) | ||||
−0.295198 | + | 0.955436i | \(0.595386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 115864. | 0.490795 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −320603. | −1.31107 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 42505.1 | 0.167889 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −330148. | −1.21827 | −0.609134 | − | 0.793067i | \(-0.708483\pi\) | ||||
−0.609134 | + | 0.793067i | \(0.708483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −215976. | −0.770838 | −0.385419 | − | 0.922742i | \(-0.625943\pi\) | ||||
−0.385419 | + | 0.922742i | \(0.625943\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −163364. | −0.564192 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 48800.9 | 0.163154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 415250. | 1.34450 | 0.672249 | − | 0.740325i | \(-0.265328\pi\) | ||||
0.672249 | + | 0.740325i | \(0.265328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 135071. | 0.423712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −243823. | −0.718797 | −0.359399 | − | 0.933184i | \(-0.617018\pi\) | ||||
−0.359399 | + | 0.933184i | \(0.617018\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −127940. | −0.365844 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 622368. | 1.72685 | 0.863427 | − | 0.504473i | \(-0.168313\pi\) | ||||
0.863427 | + | 0.504473i | \(0.168313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 172241. | 0.463894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −200905. | −0.525412 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 195614. | 0.496919 | 0.248459 | − | 0.968642i | \(-0.420076\pi\) | ||||
0.248459 | + | 0.968642i | \(0.420076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −239102. | −0.573653 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −508181. | −1.18546 | −0.592729 | − | 0.805402i | \(-0.701949\pi\) | ||||
−0.592729 | + | 0.805402i | \(0.701949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 815807. | 1.85093 | 0.925467 | − | 0.378827i | \(-0.123673\pi\) | ||||
0.925467 | + | 0.378827i | \(0.123673\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3951.63 | 0.00872265 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 206739. | 0.444112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 614482. | 1.28501 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 289788. | 0.574774 | 0.287387 | − | 0.957815i | \(-0.407213\pi\) | ||||
0.287387 | + | 0.957815i | \(0.407213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −83053.9 | −0.160497 | −0.0802485 | − | 0.996775i | \(-0.525571\pi\) | ||||
−0.0802485 | + | 0.996775i | \(0.525571\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 216903. | 0.408487 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −758761. | −1.39296 | −0.696481 | − | 0.717575i | \(-0.745252\pi\) | ||||
−0.696481 | + | 0.717575i | \(0.745252\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 352538. | 0.631063 | 0.315532 | − | 0.948915i | \(-0.397817\pi\) | ||||
0.315532 | + | 0.948915i | \(0.397817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 182912. | 0.319339 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 164892. | 0.274040 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −107496. | −0.174369 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 755690. | 1.19668 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 74904.6 | 0.115825 | 0.0579125 | − | 0.998322i | \(-0.481556\pi\) | ||||
0.0579125 | + | 0.998322i | \(0.481556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −815830. | −1.23211 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −523308. | −0.772078 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 944700. | 1.33102 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.04176e6 | −1.43479 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 658048. | 0.886125 | 0.443063 | − | 0.896491i | \(-0.353892\pi\) | ||||
0.443063 | + | 0.896491i | \(0.353892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 282731. | 0.372320 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 516436. | 0.665200 | 0.332600 | − | 0.943068i | \(-0.392074\pi\) | ||||
0.332600 | + | 0.943068i | \(0.392074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 322948. | 0.406953 | 0.203476 | − | 0.979080i | \(-0.434776\pi\) | ||||
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.48011e6 | 1.78610 | 0.893050 | − | 0.449958i | \(-0.148561\pi\) | ||||
0.893050 | + | 0.449958i | \(0.148561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −267589. | −0.316082 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 531952. | 0.615179 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −209299. | −0.237014 | −0.118507 | − | 0.992953i | \(-0.537811\pi\) | ||||
−0.118507 | + | 0.992953i | \(0.537811\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.21271e6 | −1.34497 | −0.672487 | − | 0.740109i | \(-0.734774\pi\) | ||||
−0.672487 | + | 0.740109i | \(0.734774\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 785023. | 0.852838 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.28116e6 | −1.33617 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9515.96 | 0.00972644 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.64691e6 | 1.65001 | 0.825004 | − | 0.565126i | \(-0.191173\pi\) | ||||
0.825004 | + | 0.565126i | \(0.191173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 404341. | 0.397143 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −415725. | −0.400365 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18894.0 | −0.0178440 | −0.00892198 | − | 0.999960i | \(-0.502840\pi\) | ||||
−0.00892198 | + | 0.999960i | \(0.502840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 188519. | 0.171299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.25353e6 | −1.11749 | −0.558747 | − | 0.829338i | \(-0.688718\pi\) | ||||
−0.558747 | + | 0.829338i | \(0.688718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −311950. | −0.272879 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 466702. | 0.400647 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 954812. | 0.804521 | 0.402260 | − | 0.915525i | \(-0.368225\pi\) | ||||
0.402260 | + | 0.915525i | \(0.368225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 450312. | 0.372469 | 0.186235 | − | 0.982505i | \(-0.440372\pi\) | ||||
0.186235 | + | 0.982505i | \(0.440372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.06347e6 | −0.847998 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.72355e6 | −1.34966 | −0.674830 | − | 0.737973i | \(-0.735783\pi\) | ||||
−0.674830 | + | 0.737973i | \(0.735783\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 216443. | 0.166469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 503056. | 0.380059 | 0.190029 | − | 0.981778i | \(-0.439142\pi\) | ||||
0.190029 | + | 0.981778i | \(0.439142\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.59134e6 | 1.18113 | 0.590565 | − | 0.806990i | \(-0.298905\pi\) | ||||
0.590565 | + | 0.806990i | \(0.298905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −511259. | −0.372845 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 576829. | 0.406259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.75360e6 | 1.21394 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.73373e6 | −1.17981 | −0.589907 | − | 0.807471i | \(-0.700836\pi\) | ||||
−0.589907 | + | 0.807471i | \(0.700836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 552209. | 0.369444 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.76013e6 | −1.15785 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −685499. | −0.443434 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −354669. | −0.221930 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9126.35 | −0.00561756 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 955767. | 0.578770 | 0.289385 | − | 0.957213i | \(-0.406549\pi\) | ||||
0.289385 | + | 0.957213i | \(0.406549\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 410307. | 0.244463 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.87849e6 | 1.68758 | 0.843789 | − | 0.536674i | \(-0.180320\pi\) | ||||
0.843789 | + | 0.536674i | \(0.180320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.72591e6 | 1.57272 | 0.786358 | − | 0.617771i | \(-0.211964\pi\) | ||||
0.786358 | + | 0.617771i | \(0.211964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.86964e6 | 1.60391 | 0.801954 | − | 0.597385i | \(-0.203794\pi\) | ||||
0.801954 | + | 0.597385i | \(0.203794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −709103. | −0.390151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.37737e6 | 1.28776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.45553e6 | 1.30960 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.80296e6 | 0.946841 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.58142e6 | 1.33502 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 336903. | 0.169019 | 0.0845093 | − | 0.996423i | \(-0.473068\pi\) | ||||
0.0845093 | + | 0.996423i | \(0.473068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 916931. | 0.453133 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −422438. | −0.205660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16431.9 | −0.00788156 | −0.00394078 | − | 0.999992i | \(-0.501254\pi\) | ||||
−0.00394078 | + | 0.999992i | \(0.501254\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.71898e6 | 1.28501 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −814135. | −0.379149 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −273555. | −0.123736 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −639206. | −0.284982 | −0.142491 | − | 0.989796i | \(-0.545511\pi\) | ||||
−0.142491 | + | 0.989796i | \(0.545511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.22585e6 | −1.41769 | −0.708843 | − | 0.705366i | \(-0.750783\pi\) | ||||
−0.708843 | + | 0.705366i | \(0.750783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.98403e6 | 1.29281 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.00724e6 | −0.857359 | −0.428679 | − | 0.903457i | \(-0.641021\pi\) | ||||
−0.428679 | + | 0.903457i | \(0.641021\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.88417e6 | 0.793505 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.40344e6 | 1.80325 | 0.901626 | − | 0.432517i | \(-0.142374\pi\) | ||||
0.901626 | + | 0.432517i | \(0.142374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 543706. | 0.219582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 316664. | 0.126134 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.18180e6 | −0.857202 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.19731e6 | −1.62669 | −0.813347 | − | 0.581779i | \(-0.802357\pi\) | ||||
−0.813347 | + | 0.581779i | \(0.802357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 731331. | 0.279607 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.58823e6 | −0.591072 | −0.295536 | − | 0.955332i | \(-0.595498\pi\) | ||||
−0.295536 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.63888e6 | 0.601824 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.20218e6 | 0.435627 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.23384e6 | −0.798830 | −0.399415 | − | 0.916770i | \(-0.630787\pi\) | ||||
−0.399415 | + | 0.916770i | \(0.630787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.52085e6 | 0.536751 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 884438. | 0.308085 | 0.154042 | − | 0.988064i | \(-0.450771\pi\) | ||||
0.154042 | + | 0.988064i | \(0.450771\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.32098e6 | −0.787761 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.58074e6 | −0.529648 | −0.264824 | − | 0.964297i | \(-0.585314\pi\) | ||||
−0.264824 | + | 0.964297i | \(0.585314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.31386e6 | 0.434617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −500237. | −0.163378 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.22855e6 | −0.396187 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −978509. | −0.311594 | −0.155797 | − | 0.987789i | \(-0.549795\pi\) | ||||
−0.155797 | + | 0.987789i | \(0.549795\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.39959e6 | 1.05576 | 0.527880 | − | 0.849319i | \(-0.322987\pi\) | ||||
0.527880 | + | 0.849319i | \(0.322987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.38024e6 | 0.423343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 458498. | 0.138899 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.44897e6 | −1.03206 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −356468. | −0.105369 | −0.0526844 | − | 0.998611i | \(-0.516778\pi\) | ||||
−0.0526844 | + | 0.998611i | \(0.516778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.12508e6 | −1.20456 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21977.3 | −0.00626402 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.51791e6 | −0.427470 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 783777. | 0.218101 | 0.109050 | − | 0.994036i | \(-0.465219\pi\) | ||||
0.109050 | + | 0.994036i | \(0.465219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −543516. | −0.149454 | −0.0747270 | − | 0.997204i | \(-0.523809\pi\) | ||||
−0.0747270 | + | 0.997204i | \(0.523809\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.18682e6 | −0.322502 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.45563e6 | −0.928015 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.61854e6 | −0.949270 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 809955. | 0.210023 | 0.105012 | − | 0.994471i | \(-0.466512\pi\) | ||||
0.105012 | + | 0.994471i | \(0.466512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 894096. | 0.229174 | 0.114587 | − | 0.993413i | \(-0.463446\pi\) | ||||
0.114587 | + | 0.993413i | \(0.463446\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 479740. | 0.121558 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.61578e6 | 0.404743 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.97626e6 | −1.72767 | −0.863836 | − | 0.503773i | \(-0.831945\pi\) | ||||
−0.863836 | + | 0.503773i | \(0.831945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 466594. | 0.112961 | 0.0564807 | − | 0.998404i | \(-0.482012\pi\) | ||||
0.0564807 | + | 0.998404i | \(0.482012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07786e6 | −0.258024 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.72627e6 | −0.882074 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.68786e6 | 0.629203 | 0.314602 | − | 0.949224i | \(-0.398129\pi\) | ||||
0.314602 | + | 0.949224i | \(0.398129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.75085e6 | −0.636833 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.43765e6 | −0.558117 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −166961. | −0.0373959 | −0.0186979 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186979 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.71932e6 | −1.26710 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.53425e6 | 0.336236 | 0.168118 | − | 0.985767i | \(-0.446231\pi\) | ||||
0.168118 | + | 0.985767i | \(0.446231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.11226e6 | −1.54190 | −0.770949 | − | 0.636897i | \(-0.780217\pi\) | ||||
−0.770949 | + | 0.636897i | \(0.780217\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 550799. | 0.118130 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.88723e6 | 1.24916 | 0.624581 | − | 0.780960i | \(-0.285270\pi\) | ||||
0.624581 | + | 0.780960i | \(0.285270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.68678e6 | 0.973469 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.73022e6 | 1.79421 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.24974e6 | −0.864227 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.38356e6 | −0.278422 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −233079. | −0.0464156 | −0.0232078 | − | 0.999731i | \(-0.507388\pi\) | ||||
−0.0232078 | + | 0.999731i | \(0.507388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.84721e6 | 1.15235 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.04996e6 | −0.781802 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.29839e6 | −0.439139 | −0.219569 | − | 0.975597i | \(-0.570465\pi\) | ||||
−0.219569 | + | 0.975597i | \(0.570465\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.75195e6 | −0.520437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −268580. | −0.0502771 | −0.0251386 | − | 0.999684i | \(-0.508003\pi\) | ||||
−0.0251386 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.30415e6 | −0.426965 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.31051e6 | 0.240397 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.07781e6 | −1.45225 | −0.726127 | − | 0.687561i | \(-0.758681\pi\) | ||||
−0.726127 | + | 0.687561i | \(0.758681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.02445e6 | 1.25031 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.46801e6 | −1.13986 | −0.569929 | − | 0.821694i | \(-0.693029\pi\) | ||||
−0.569929 | + | 0.821694i | \(0.693029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 819113. | 0.142927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.94402e6 | 0.335878 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.61907e6 | 1.13241 | 0.566203 | − | 0.824266i | \(-0.308412\pi\) | ||||
0.566203 | + | 0.824266i | \(0.308412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.03362e6 | −1.18001 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −947610. | −0.157439 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.46413e6 | 0.734532 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.20783e6 | 0.359789 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.74672e6 | 0.927525 | 0.463763 | − | 0.885959i | \(-0.346499\pi\) | ||||
0.463763 | + | 0.885959i | \(0.346499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.63623e6 | −1.22074 | −0.610372 | − | 0.792115i | \(-0.708980\pi\) | ||||
−0.610372 | + | 0.792115i | \(0.708980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.64543e6 | −0.414926 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.57180e6 | −0.865678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.44917e6 | 0.376948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.66365e6 | 0.711063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.49057e6 | −0.829341 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.73566e6 | −0.858317 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.46588e6 | −0.656015 | −0.328008 | − | 0.944675i | \(-0.606377\pi\) | ||||
−0.328008 | + | 0.944675i | \(0.606377\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.20773e6 | 1.34015 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.96182e6 | −0.859781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −53981.3 | −0.00771391 | −0.00385696 | − | 0.999993i | \(-0.501228\pi\) | ||||
−0.00385696 | + | 0.999993i | \(0.501228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40477.3 | −0.00573167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.83364e6 | −0.397617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.33339e6 | 0.321555 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.19677e6 | 0.163446 | 0.0817228 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817228 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.48008e7 | −2.00334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.93545e6 | 0.930395 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.98924e6 | −1.32819 | −0.664097 | − | 0.747646i | \(-0.731184\pi\) | ||||
−0.664097 | + | 0.747646i | \(0.731184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.27953e6 | −0.827572 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.19320e7 | −1.54502 | −0.772509 | − | 0.635003i | \(-0.780999\pi\) | ||||
−0.772509 | + | 0.635003i | \(0.780999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.00650e7 | 1.29189 | 0.645943 | − | 0.763386i | \(-0.276465\pi\) | ||||
0.645943 | + | 0.763386i | \(0.276465\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.27074e6 | 0.416159 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.27387e6 | −0.286811 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.21284e6 | 1.15200 | 0.576002 | − | 0.817448i | \(-0.304612\pi\) | ||||
0.576002 | + | 0.817448i | \(0.304612\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −937401. | −0.116206 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.20418e6 | 0.634134 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.22178e6 | −0.268417 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.95647e6 | 0.593714 | 0.296857 | − | 0.954922i | \(-0.404062\pi\) | ||||
0.296857 | + | 0.954922i | \(0.404062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.25336e6 | −0.386405 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.56387e6 | −1.00856 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.24149e6 | −1.07921 | −0.539604 | − | 0.841919i | \(-0.681426\pi\) | ||||
−0.539604 | + | 0.841919i | \(0.681426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.97897e6 | 0.456914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.07648e7 | −1.22586 | −0.612929 | − | 0.790138i | \(-0.710009\pi\) | ||||
−0.612929 | + | 0.790138i | \(0.710009\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.54962e6 | −0.513794 | −0.256897 | − | 0.966439i | \(-0.582700\pi\) | ||||
−0.256897 | + | 0.966439i | \(0.582700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.87360e6 | −0.209838 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −731340. | −0.0812327 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −729167. | −0.0803258 | −0.0401629 | − | 0.999193i | \(-0.512788\pi\) | ||||
−0.0401629 | + | 0.999193i | \(0.512788\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.56826e6 | −0.820149 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.07089e7 | 1.15105 | 0.575526 | − | 0.817784i | \(-0.304797\pi\) | ||||
0.575526 | + | 0.817784i | \(0.304797\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.86108e6 | 0.198416 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.13441e7 | −1.19966 | −0.599828 | − | 0.800129i | \(-0.704764\pi\) | ||||
−0.599828 | + | 0.800129i | \(0.704764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.60974e7 | 1.68861 | 0.844303 | − | 0.535866i | \(-0.180015\pi\) | ||||
0.844303 | + | 0.535866i | \(0.180015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.76342e6 | −0.391610 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.85725e6 | 0.394982 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.52921e6 | 0.866443 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.12070e7 | −1.12944 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.09127e6 | −0.409058 | −0.204529 | − | 0.978861i | \(-0.565566\pi\) | ||||
−0.204529 | + | 0.978861i | \(0.565566\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 845422. | 0.0838618 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.51242e6 | −0.345678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.35671e6 | 0.809623 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.46808e6 | 0.621771 | 0.310885 | − | 0.950447i | \(-0.399375\pi\) | ||||
0.310885 | + | 0.950447i | \(0.399375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.35591e7 | −1.29331 | −0.646655 | − | 0.762783i | \(-0.723832\pi\) | ||||
−0.646655 | + | 0.762783i | \(0.723832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.90639e6 | −0.559015 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.04550e7 | −0.981890 | −0.490945 | − | 0.871190i | \(-0.663348\pi\) | ||||
−0.490945 | + | 0.871190i | \(0.663348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.21238e6 | −0.858539 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.64259e6 | −0.609613 | −0.304807 | − | 0.952414i | \(-0.598592\pi\) | ||||
−0.304807 | + | 0.952414i | \(0.598592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.15530e6 | 0.105219 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.67675e6 | −0.874614 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.80579e6 | 0.341375 | 0.170687 | − | 0.985325i | \(-0.445401\pi\) | ||||
0.170687 | + | 0.985325i | \(0.445401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.47727e7 | −1.31510 | −0.657548 | − | 0.753413i | \(-0.728406\pi\) | ||||
−0.657548 | + | 0.753413i | \(0.728406\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.17580e7 | −1.03884 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.51617e6 | −0.131957 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.42715e6 | 0.641589 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 152253. | 0.0130545 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.25733e7 | −1.07007 | −0.535033 | − | 0.844831i | \(-0.679701\pi\) | ||||
−0.535033 | + | 0.844831i | \(0.679701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.89833e6 | 0.836185 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.64300e7 | 1.37774 | 0.688868 | − | 0.724887i | \(-0.258108\pi\) | ||||
0.688868 | + | 0.724887i | \(0.258108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.82884e6 | 0.481631 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.16788e6 | 0.751999 | 0.376000 | − | 0.926620i | \(-0.377299\pi\) | ||||
0.376000 | + | 0.926620i | \(0.377299\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.52694e6 | 0.775759 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.64501e6 | 0.294650 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.82291e6 | −0.708049 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.33063e6 | 0.185686 | 0.0928429 | − | 0.995681i | \(-0.470405\pi\) | ||||
0.0928429 | + | 0.995681i | \(0.470405\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.50564e6 | 0.275299 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.93857e6 | −0.696925 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.67055e7 | 1.29321 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.64254e6 | −0.510551 | −0.255276 | − | 0.966868i | \(-0.582166\pi\) | ||||
−0.255276 | + | 0.966868i | \(0.582166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.37824e7 | −1.05181 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.02019e6 | −0.228855 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.41760e7 | 1.80621 | 0.903105 | − | 0.429419i | \(-0.141282\pi\) | ||||
0.903105 | + | 0.429419i | \(0.141282\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.44889e6 | −0.404235 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.74075e6 | −0.128236 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.35707e6 | 0.611348 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.36229e6 | −0.171607 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.33905e6 | 0.673721 | 0.336861 | − | 0.941554i | \(-0.390635\pi\) | ||||
0.336861 | + | 0.941554i | \(0.390635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.36874e7 | −0.973814 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.98774e6 | 0.281762 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.37712e7 | −0.966352 | −0.483176 | − | 0.875523i | \(-0.660517\pi\) | ||||
−0.483176 | + | 0.875523i | \(0.660517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.31345e7 | 0.915366 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.83678e7 | 1.96351 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.76967e6 | −0.396635 | −0.198318 | − | 0.980138i | \(-0.563548\pi\) | ||||
−0.198318 | + | 0.980138i | \(0.563548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.04743e6 | 0.477928 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.30308e7 | 0.877730 | 0.438865 | − | 0.898553i | \(-0.355381\pi\) | ||||
0.438865 | + | 0.898553i | \(0.355381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.44600e7 | −0.967436 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.50890e7 | −1.66729 | −0.833645 | − | 0.552300i | \(-0.813750\pi\) | ||||
−0.833645 | + | 0.552300i | \(0.813750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.60587e6 | 0.568073 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −97473.8 | −0.00639126 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.62435e6 | −0.622689 | −0.311345 | − | 0.950297i | \(-0.600779\pi\) | ||||
−0.311345 | + | 0.950297i | \(0.600779\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.85881e7 | 1.19467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.62978e6 | 0.359438 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.81324e7 | 1.15005 | 0.575023 | − | 0.818137i | \(-0.304993\pi\) | ||||
0.575023 | + | 0.818137i | \(0.304993\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.56366e6 | 0.287547 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.88507e6 | 0.493564 | 0.246782 | − | 0.969071i | \(-0.420627\pi\) | ||||
0.246782 | + | 0.969071i | \(0.420627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.25836e6 | 0.263080 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.56182e7 | 0.958610 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.50529e6 | −0.152771 | −0.0763857 | − | 0.997078i | \(-0.524338\pi\) | ||||
−0.0763857 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −213250. | −0.0129197 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.37371e7 | −0.826885 | −0.413443 | − | 0.910530i | \(-0.635674\pi\) | ||||
−0.413443 | + | 0.910530i | \(0.635674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.57841e6 | 0.273817 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.09926e7 | −0.649021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.14332e7 | −1.84400 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.60001e6 | 0.384716 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.08242e7 | −0.626934 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.44461e7 | 1.40693 | 0.703465 | − | 0.710730i | \(-0.251635\pi\) | ||||
0.703465 | + | 0.710730i | \(0.251635\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.41481e7 | −0.809109 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −258122. | −0.0145761 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.52087e6 | −0.197575 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.02154e7 | −1.68493 | −0.842466 | − | 0.538749i | \(-0.818897\pi\) | ||||
−0.842466 | + | 0.538749i | \(0.818897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.45057e7 | 0.803842 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.78052e6 | −0.263266 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.63985e7 | 1.99202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.07766e7 | 0.582505 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.33535e7 | −1.25453 | −0.627266 | − | 0.778805i | \(-0.715826\pi\) | ||||
−0.627266 | + | 0.778805i | \(0.715826\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 271769. | 0.0145093 | 0.00725466 | − | 0.999974i | \(-0.497691\pi\) | ||||
0.00725466 | + | 0.999974i | \(0.497691\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.08252e6 | 0.269682 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.35568e6 | 0.335172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.48867e7 | 1.82854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.26647e7 | −0.655747 | −0.327874 | − | 0.944722i | \(-0.606332\pi\) | ||||
−0.327874 | + | 0.944722i | \(0.606332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.66922e7 | −0.859041 | −0.429520 | − | 0.903057i | \(-0.641317\pi\) | ||||
−0.429520 | + | 0.903057i | \(0.641317\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.20031e7 | −0.613984 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.52342e7 | 1.28300 | 0.641500 | − | 0.767123i | \(-0.278313\pi\) | ||||
0.641500 | + | 0.767123i | \(0.278313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 839396. | 0.0424210 | 0.0212105 | − | 0.999775i | \(-0.493248\pi\) | ||||
0.0212105 | + | 0.999775i | \(0.493248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.94531e7 | −0.977207 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.62231e7 | −0.805224 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.57759e6 | 0.373868 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.27745e7 | −1.11698 | −0.558488 | − | 0.829512i | \(-0.688618\pi\) | ||||
−0.558488 | + | 0.829512i | \(0.688618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78522e7 | −0.870366 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.67782e6 | 0.275177 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.48975e6 | −0.216312 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.79610e7 | 0.855185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.37444e6 | −0.349064 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.56919e7 | 1.20899 | 0.604497 | − | 0.796607i | \(-0.293374\pi\) | ||||
0.604497 | + | 0.796607i | \(0.293374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.23693e6 | 0.244997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.17425e7 | −1.47635 | −0.738174 | − | 0.674610i | \(-0.764312\pi\) | ||||
−0.738174 | + | 0.674610i | \(0.764312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.46054e7 | −0.675354 | −0.337677 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337677 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.51398e6 | −0.343434 | −0.171717 | − | 0.985146i | \(-0.554931\pi\) | ||||
−0.171717 | + | 0.985146i | \(0.554931\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.09902e6 | −0.231711 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.51047e6 | 0.294147 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.04956e7 | 0.920687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.19479e7 | −0.533635 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.79625e7 | −0.797683 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.73823e6 | 0.295833 | 0.147917 | − | 0.989000i | \(-0.452743\pi\) | ||||
0.147917 | + | 0.989000i | \(0.452743\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.95681e7 | −0.854231 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26520e7 | 0.983256 | 0.491628 | − | 0.870805i | \(-0.336402\pi\) | ||||
0.491628 | + | 0.870805i | \(0.336402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.92988e6 | −0.342267 | −0.171133 | − | 0.985248i | \(-0.554743\pi\) | ||||
−0.171133 | + | 0.985248i | \(0.554743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.23259e6 | 0.267492 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −347573. | −0.0148333 | −0.00741663 | − | 0.999972i | \(-0.502361\pi\) | ||||
−0.00741663 | + | 0.999972i | \(0.502361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.64902e6 | −0.322784 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.78391e7 | 0.748589 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.32466e7 | 0.552773 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.73699e6 | −0.321063 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.05279e6 | 0.125979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.69104e7 | 0.693971 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.12654e7 | −0.863083 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.67448e7 | 0.675869 | 0.337935 | − | 0.941170i | \(-0.390272\pi\) | ||||
0.337935 | + | 0.941170i | \(0.390272\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.63294e6 | 0.145831 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.36320e6 | 0.333869 | 0.166935 | − | 0.985968i | \(-0.446613\pi\) | ||||
0.166935 | + | 0.985968i | \(0.446613\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 366641. | 0.0145568 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −103006. | −0.00406733 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.32444e7 | 0.907883 | 0.453942 | − | 0.891031i | \(-0.350017\pi\) | ||||
0.453942 | + | 0.891031i | \(0.350017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.07874e7 | 0.419052 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.32902e7 | 2.05894 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.93958e7 | 0.745339 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.20285e6 | −0.160637 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.65468e7 | −1.00919 | −0.504595 | − | 0.863356i | \(-0.668358\pi\) | ||||
−0.504595 | + | 0.863356i | \(0.668358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.24885e7 | 1.22187 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.60175e7 | −0.599193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.39209e7 | 1.63426 | 0.817132 | − | 0.576451i | \(-0.195563\pi\) | ||||
0.817132 | + | 0.576451i | \(0.195563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.07664e7 | 1.13871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.05536e7 | 0.756684 | 0.378342 | − | 0.925666i | \(-0.376494\pi\) | ||||
0.378342 | + | 0.925666i | \(0.376494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.88175e6 | −0.215391 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.11519e7 | 1.12878 | 0.564391 | − | 0.825507i | \(-0.309111\pi\) | ||||
0.564391 | + | 0.825507i | \(0.309111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.17081e7 | −2.22421 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.23887e7 | 1.16129 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.15913e7 | −1.48344 | −0.741721 | − | 0.670709i | \(-0.765990\pi\) | ||||
−0.741721 | + | 0.670709i | \(0.765990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.55383e6 | −0.268015 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.00340e6 | −0.282485 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.51242e7 | −0.877573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.43519e7 | −0.846187 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.16494e6 | 0.0748390 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.38061e7 | −1.50650 | −0.753249 | − | 0.657735i | \(-0.771515\pi\) | ||||
−0.753249 | + | 0.657735i | \(0.771515\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.77147e7 | 0.948200 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.71158e7 | 1.26331 | 0.631656 | − | 0.775249i | \(-0.282376\pi\) | ||||
0.631656 | + | 0.775249i | \(0.282376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.03494e7 | 0.685550 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.74795e7 | 0.585860 | 0.292930 | − | 0.956134i | \(-0.405370\pi\) | ||||
0.292930 | + | 0.956134i | \(0.405370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.79816e7 | 0.599614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.64420e7 | −0.877245 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.36400e7 | −1.77054 | −0.885268 | − | 0.465081i | \(-0.846025\pi\) | ||||
−0.885268 | + | 0.465081i | \(0.846025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.97784e7 | 0.649532 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.86666e7 | 0.606839 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.59845e7 | 0.840485 | 0.420242 | − | 0.907412i | \(-0.361945\pi\) | ||||
0.420242 | + | 0.907412i | \(0.361945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.80250e6 | 0.122376 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.18950e6 | −0.294262 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.23388e6 | 0.294203 | 0.147101 | − | 0.989121i | \(-0.453006\pi\) | ||||
0.147101 | + | 0.989121i | \(0.453006\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.21015e7 | 1.01768 |
(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.bl.1.4 | 5 | ||
4.3 | odd | 2 | 392.6.a.j.1.2 | 5 | |||
7.3 | odd | 6 | 112.6.i.f.65.4 | 10 | |||
7.5 | odd | 6 | 112.6.i.f.81.4 | 10 | |||
7.6 | odd | 2 | 784.6.a.bk.1.2 | 5 | |||
28.3 | even | 6 | 56.6.i.b.9.2 | ✓ | 10 | ||
28.11 | odd | 6 | 392.6.i.o.177.4 | 10 | |||
28.19 | even | 6 | 56.6.i.b.25.2 | yes | 10 | ||
28.23 | odd | 6 | 392.6.i.o.361.4 | 10 | |||
28.27 | even | 2 | 392.6.a.k.1.4 | 5 | |||
84.47 | odd | 6 | 504.6.s.b.361.4 | 10 | |||
84.59 | odd | 6 | 504.6.s.b.289.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.i.b.9.2 | ✓ | 10 | 28.3 | even | 6 | ||
56.6.i.b.25.2 | yes | 10 | 28.19 | even | 6 | ||
112.6.i.f.65.4 | 10 | 7.3 | odd | 6 | |||
112.6.i.f.81.4 | 10 | 7.5 | odd | 6 | |||
392.6.a.j.1.2 | 5 | 4.3 | odd | 2 | |||
392.6.a.k.1.4 | 5 | 28.27 | even | 2 | |||
392.6.i.o.177.4 | 10 | 28.11 | odd | 6 | |||
392.6.i.o.361.4 | 10 | 28.23 | odd | 6 | |||
504.6.s.b.289.4 | 10 | 84.59 | odd | 6 | |||
504.6.s.b.361.4 | 10 | 84.47 | odd | 6 | |||
784.6.a.bk.1.2 | 5 | 7.6 | odd | 2 | |||
784.6.a.bl.1.4 | 5 | 1.1 | even | 1 | trivial |