Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,8,Mod(1,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.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: | \(94.9650477472\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{633}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 158 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(13.0797\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.1 |
$q$-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 | ||||||||
\(3\) | −3.23924 | −0.0692657 | −0.0346329 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346329 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −312.472 | −1.11793 | −0.558967 | − | 0.829190i | \(-0.688802\pi\) | ||||
−0.558967 | + | 0.829190i | \(0.688802\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 766.767 | 0.844929 | 0.422465 | − | 0.906379i | \(-0.361165\pi\) | ||||
0.422465 | + | 0.906379i | \(0.361165\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2176.51 | −0.995202 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −252.042 | −0.0570950 | −0.0285475 | − | 0.999592i | \(-0.509088\pi\) | ||||
−0.0285475 | + | 0.999592i | \(0.509088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1065.19 | −0.134471 | −0.0672353 | − | 0.997737i | \(-0.521418\pi\) | ||||
−0.0672353 | + | 0.997737i | \(0.521418\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1012.17 | 0.0774345 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18769.7 | −0.926589 | −0.463295 | − | 0.886204i | \(-0.653333\pi\) | ||||
−0.463295 | + | 0.886204i | \(0.653333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2483.74 | −0.0585246 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11559.9 | −0.198109 | −0.0990546 | − | 0.995082i | \(-0.531582\pi\) | ||||
−0.0990546 | + | 0.995082i | \(0.531582\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19513.8 | 0.249777 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14134.4 | 0.138199 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −46290.0 | −0.352448 | −0.176224 | − | 0.984350i | \(-0.556388\pi\) | ||||
−0.176224 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46848.2 | −0.282441 | −0.141220 | − | 0.989978i | \(-0.545103\pi\) | ||||
−0.141220 | + | 0.989978i | \(0.545103\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 816.422 | 0.00395472 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −239593. | −0.944575 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −182916. | −0.593672 | −0.296836 | − | 0.954928i | \(-0.595932\pi\) | ||||
−0.296836 | + | 0.954928i | \(0.595932\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3450.42 | 0.00931420 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 819661. | 1.85734 | 0.928669 | − | 0.370910i | \(-0.120954\pi\) | ||||
0.928669 | + | 0.370910i | \(0.120954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −477471. | −0.915814 | −0.457907 | − | 0.889000i | \(-0.651401\pi\) | ||||
−0.457907 | + | 0.889000i | \(0.651401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 680098. | 1.11257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −992580. | −1.39451 | −0.697257 | − | 0.716821i | \(-0.745596\pi\) | ||||
−0.697257 | + | 0.716821i | \(0.745596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −235611. | −0.286095 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 60799.7 | 0.0641809 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −852516. | −0.786569 | −0.393285 | − | 0.919417i | \(-0.628661\pi\) | ||||
−0.393285 | + | 0.919417i | \(0.628661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 78756.0 | 0.0638284 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22217.9 | −0.0158906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.92404e6 | 1.21964 | 0.609821 | − | 0.792539i | \(-0.291241\pi\) | ||||
0.609821 | + | 0.792539i | \(0.291241\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 209564. | 0.118212 | 0.0591062 | − | 0.998252i | \(-0.481175\pi\) | ||||
0.0591062 | + | 0.998252i | \(0.481175\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.66887e6 | −0.840875 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 332843. | 0.150329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.32447e6 | 0.944198 | 0.472099 | − | 0.881546i | \(-0.343497\pi\) | ||||
0.472099 | + | 0.881546i | \(0.343497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 37445.1 | 0.0137222 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.37237e6 | 1.78140 | 0.890700 | − | 0.454591i | \(-0.150215\pi\) | ||||
0.890700 | + | 0.454591i | \(0.150215\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.71614e6 | −1.11805 | −0.559027 | − | 0.829150i | \(-0.688825\pi\) | ||||
−0.559027 | + | 0.829150i | \(0.688825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −63209.9 | −0.0173010 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −193257. | −0.0482412 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.30851e6 | 0.298596 | 0.149298 | − | 0.988792i | \(-0.452299\pi\) | ||||
0.149298 | + | 0.988792i | \(0.452299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.71424e6 | 0.985630 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.51683e6 | 1.25102 | 0.625508 | − | 0.780218i | \(-0.284892\pi\) | ||||
0.625508 | + | 0.780218i | \(0.284892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.86502e6 | 1.03587 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 149944. | 0.0244125 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.99586e6 | 0.600822 | 0.300411 | − | 0.953810i | \(-0.402876\pi\) | ||||
0.300411 | + | 0.953810i | \(0.402876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −816756. | −0.113618 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 151753. | 0.0195635 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.14325e6 | −0.256472 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.90391e6 | −0.768058 | −0.384029 | − | 0.923321i | \(-0.625464\pi\) | ||||
−0.384029 | + | 0.923321i | \(0.625464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 548570. | 0.0568210 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.81610e6 | 0.271971 | 0.135986 | − | 0.990711i | \(-0.456580\pi\) | ||||
0.135986 | + | 0.990711i | \(0.456580\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.86273e6 | −0.708995 | −0.354497 | − | 0.935057i | \(-0.615348\pi\) | ||||
−0.354497 | + | 0.935057i | \(0.615348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 776100. | 0.0654267 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −611626. | −0.0482662 | −0.0241331 | − | 0.999709i | \(-0.507683\pi\) | ||||
−0.0241331 | + | 0.999709i | \(0.507683\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.23210e6 | 0.386976 | 0.193488 | − | 0.981103i | \(-0.438020\pi\) | ||||
0.193488 | + | 0.981103i | \(0.438020\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 592510. | 0.0411211 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.58527e6 | −0.233747 | −0.116874 | − | 0.993147i | \(-0.537287\pi\) | ||||
−0.116874 | + | 0.993147i | \(0.537287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.61213e6 | 0.221473 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.31840e6 | 0.133825 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.43920e7 | −0.782902 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94236e7 | −0.996740 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.65508e6 | −0.128650 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.83144e7 | 0.838700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.99465e7 | 1.29728 | 0.648639 | − | 0.761096i | \(-0.275339\pi\) | ||||
0.648639 | + | 0.761096i | \(0.275339\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.54664e6 | 0.0634345 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.11292e6 | 0.315303 | 0.157651 | − | 0.987495i | \(-0.449608\pi\) | ||||
0.157651 | + | 0.987495i | \(0.449608\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.25926e6 | 0.193840 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.41662e6 | −0.154498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.44157e7 | 0.478977 | 0.239488 | − | 0.970899i | \(-0.423020\pi\) | ||||
0.239488 | + | 0.970899i | \(0.423020\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.77446e7 | 1.19207 | 0.596036 | − | 0.802957i | \(-0.296741\pi\) | ||||
0.596036 | + | 0.802957i | \(0.296741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.21520e6 | 0.0965920 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 268473. | 0.00767759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.44643e7 | 0.394013 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 763200. | 0.0198165 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.30679e7 | 1.80957 | 0.904784 | − | 0.425872i | \(-0.140033\pi\) | ||||
0.904784 | + | 0.425872i | \(0.140033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.14056e7 | 0.978678 | 0.489339 | − | 0.872094i | \(-0.337238\pi\) | ||||
0.489339 | + | 0.872094i | \(0.337238\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.08525e7 | 0.922144 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.46388e7 | 0.315750 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.93945e7 | 0.606203 | 0.303101 | − | 0.952958i | \(-0.401978\pi\) | ||||
0.303101 | + | 0.952958i | \(0.401978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.76150e6 | 0.0544823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.86371e6 | −0.167388 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.03924e6 | −0.163484 | −0.0817420 | − | 0.996654i | \(-0.526048\pi\) | ||||
−0.0817420 | + | 0.996654i | \(0.526048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −255109. | −0.00442112 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.16728e7 | 1.35697 | 0.678484 | − | 0.734615i | \(-0.262637\pi\) | ||||
0.678484 | + | 0.734615i | \(0.262637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.16139e7 | −0.981918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.49287e7 | −0.228315 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.33191e8 | 1.95575 | 0.977874 | − | 0.209197i | \(-0.0670849\pi\) | ||||
0.977874 | + | 0.209197i | \(0.0670849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.49626e7 | 0.211044 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.23243e6 | −0.0844794 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.90910e7 | 0.639759 | 0.319879 | − | 0.947458i | \(-0.396358\pi\) | ||||
0.319879 | + | 0.947458i | \(0.396358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.11979e7 | 1.01782 | 0.508908 | − | 0.860821i | \(-0.330049\pi\) | ||||
0.508908 | + | 0.860821i | \(0.330049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −678828. | −0.00818806 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.71563e7 | 0.663686 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.73076e6 | 0.0529036 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.08378e7 | 0.116768 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.40713e7 | −0.769190 | −0.384595 | − | 0.923086i | \(-0.625659\pi\) | ||||
−0.384595 | + | 0.923086i | \(0.625659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.70125e7 | −0.971353 | −0.485676 | − | 0.874139i | \(-0.661427\pi\) | ||||
−0.485676 | + | 0.874139i | \(0.661427\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.07816e6 | −0.0104127 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.34770e7 | −0.405161 | −0.202581 | − | 0.979266i | \(-0.564933\pi\) | ||||
−0.202581 | + | 0.979266i | \(0.564933\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.89651e7 | −0.350502 | −0.175251 | − | 0.984524i | \(-0.556074\pi\) | ||||
−0.175251 | + | 0.984524i | \(0.556074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.52952e6 | −0.0654005 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.54937e7 | −0.297793 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.56121e8 | −2.07638 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.51601e7 | 0.197159 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.72875e6 | −0.0130985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.85264e7 | 0.282339 | 0.141169 | − | 0.989985i | \(-0.454914\pi\) | ||||
0.141169 | + | 0.989985i | \(0.454914\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.74024e7 | −0.123390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.49196e8 | 1.02382 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.59217e7 | −0.238642 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.20375e7 | 0.0774428 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.99934e7 | 0.124599 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.03401e8 | 1.22825 | 0.614124 | − | 0.789209i | \(-0.289509\pi\) | ||||
0.614124 | + | 0.789209i | \(0.289509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.24720e7 | −0.248579 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.24944e8 | −1.27639 | −0.638195 | − | 0.769875i | \(-0.720319\pi\) | ||||
−0.638195 | + | 0.769875i | \(0.720319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.38882e8 | −1.31450 | −0.657248 | − | 0.753674i | \(-0.728280\pi\) | ||||
−0.657248 | + | 0.753674i | \(0.728280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 626006. | 0.00334146 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.23019e8 | 1.67295 | 0.836475 | − | 0.548005i | \(-0.184613\pi\) | ||||
0.836475 | + | 0.548005i | \(0.184613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.10153e8 | 1.55897 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.23859e6 | −0.0206825 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.18160e7 | 0.245511 | 0.122756 | − | 0.992437i | \(-0.460827\pi\) | ||||
0.122756 | + | 0.992437i | \(0.460827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.15926e8 | 0.533484 | 0.266742 | − | 0.963768i | \(-0.414053\pi\) | ||||
0.266742 | + | 0.963768i | \(0.414053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.61825e7 | −0.206469 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.36219e7 | 0.319835 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.30617e6 | −0.0308497 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.11096e7 | −0.0866525 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.03761e7 | 0.161163 | 0.0805817 | − | 0.996748i | \(-0.474322\pi\) | ||||
0.0805817 | + | 0.996748i | \(0.474322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.91356e6 | 0.0113110 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.89982e7 | −0.0717500 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.67661e8 | 0.983602 | 0.491801 | − | 0.870708i | \(-0.336339\pi\) | ||||
0.491801 | + | 0.870708i | \(0.336339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.40254e8 | −0.501611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00751e8 | 0.350757 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.12778e8 | −1.73814 | −0.869068 | − | 0.494692i | \(-0.835281\pi\) | ||||
−0.869068 | + | 0.494692i | \(0.835281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.66387e8 | 0.879333 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.29435e7 | −0.0416163 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.75792e8 | 1.80357 | 0.901784 | − | 0.432187i | \(-0.142258\pi\) | ||||
0.901784 | + | 0.432187i | \(0.142258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.24839e8 | −1.60189 | −0.800946 | − | 0.598737i | \(-0.795670\pi\) | ||||
−0.800946 | + | 0.598737i | \(0.795670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.64567e6 | 0.00786984 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.91829e6 | −0.0142610 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.64620e8 | −1.31347 | −0.656733 | − | 0.754123i | \(-0.728062\pi\) | ||||
−0.656733 | + | 0.754123i | \(0.728062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.01966e8 | 0.281086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75429e8 | −0.471660 | −0.235830 | − | 0.971794i | \(-0.575781\pi\) | ||||
−0.235830 | + | 0.971794i | \(0.575781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.44948e8 | −0.380154 | −0.190077 | − | 0.981769i | \(-0.560874\pi\) | ||||
−0.190077 | + | 0.981769i | \(0.560874\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.94248e6 | 0.0177647 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.28489e8 | 1.56932 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.80353e7 | −0.141433 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.23634e7 | 0.0532001 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.24522e8 | −0.985970 | −0.492985 | − | 0.870038i | \(-0.664094\pi\) | ||||
−0.492985 | + | 0.870038i | \(0.664094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.01210e8 | −1.36348 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.56247e6 | −0.00789047 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.23135e7 | 0.0266399 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.66109e8 | −0.773798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.12200e6 | −0.0188383 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.54830e7 | −0.132154 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.27528e8 | −0.843297 | −0.421649 | − | 0.906759i | \(-0.638548\pi\) | ||||
−0.421649 | + | 0.906759i | \(0.638548\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.54692e7 | 0.0491090 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.70275e8 | 0.320989 | 0.160495 | − | 0.987037i | \(-0.448691\pi\) | ||||
0.160495 | + | 0.987037i | \(0.448691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.02143e8 | −0.741269 | −0.370634 | − | 0.928779i | \(-0.620860\pi\) | ||||
−0.370634 | + | 0.928779i | \(0.620860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.21477e8 | 0.940043 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.90630e8 | −0.336112 | −0.168056 | − | 0.985777i | \(-0.553749\pi\) | ||||
−0.168056 | + | 0.985777i | \(0.553749\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16670e7 | 0.0201230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.98120e6 | 0.00334319 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.28742e8 | −0.212574 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.07860e7 | −0.0335876 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.69480e7 | −0.0268041 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.61077e8 | −1.17827 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.12008e8 | 0.624464 | 0.312232 | − | 0.950006i | \(-0.398923\pi\) | ||||
0.312232 | + | 0.950006i | \(0.398923\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.98119e8 | 0.590824 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.26333e8 | −1.05555 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.99272e8 | −0.995271 | −0.497636 | − | 0.867386i | \(-0.665798\pi\) | ||||
−0.497636 | + | 0.867386i | \(0.665798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.16135e7 | 0.0161907 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.18077e7 | 0.0161259 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.12125e8 | −1.08666 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.17005e7 | −0.0153405 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.29885e8 | 1.19475 | 0.597374 | − | 0.801963i | \(-0.296211\pi\) | ||||
0.597374 | + | 0.801963i | \(0.296211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.43776e8 | −0.558823 | −0.279412 | − | 0.960171i | \(-0.590139\pi\) | ||||
−0.279412 | + | 0.960171i | \(0.590139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.50559e7 | −0.0185837 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.49388e9 | −1.80761 | −0.903804 | − | 0.427946i | \(-0.859237\pi\) | ||||
−0.903804 | + | 0.427946i | \(0.859237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.67872e9 | −1.99149 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.66192e7 | 0.0542283 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.77937e8 | 0.202972 | 0.101486 | − | 0.994837i | \(-0.467640\pi\) | ||||
0.101486 | + | 0.994837i | \(0.467640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.29178e7 | 0.0690399 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.16119e9 | 1.24991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37515e9 | 1.45218 | 0.726088 | − | 0.687601i | \(-0.241336\pi\) | ||||
0.726088 | + | 0.687601i | \(0.241336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.78400e9 | −1.84843 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.53681e8 | −0.664595 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.55845e9 | 1.55493 | 0.777466 | − | 0.628925i | \(-0.216505\pi\) | ||||
0.777466 | + | 0.628925i | \(0.216505\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.93245e7 | −0.0580932 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.93079e7 | 0.0473938 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.84549e8 | −0.834613 | −0.417306 | − | 0.908766i | \(-0.637026\pi\) | ||||
−0.417306 | + | 0.908766i | \(0.637026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.70038e7 | −0.0898569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.44573e9 | −1.31490 | −0.657449 | − | 0.753499i | \(-0.728365\pi\) | ||||
−0.657449 | + | 0.753499i | \(0.728365\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.03875e7 | 0.0539305 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.03922e9 | 0.911420 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.02164e9 | −0.879986 | −0.439993 | − | 0.898001i | \(-0.645019\pi\) | ||||
−0.439993 | + | 0.898001i | \(0.645019\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.16975e8 | 0.183566 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.62797e7 | −0.0218397 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.08874e8 | −0.333811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.80050e8 | 0.144419 | 0.0722097 | − | 0.997389i | \(-0.476995\pi\) | ||||
0.0722097 | + | 0.997389i | \(0.476995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.70360e7 | −0.0134265 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.06670e8 | 0.392392 | 0.196196 | − | 0.980565i | \(-0.437141\pi\) | ||||
0.196196 | + | 0.980565i | \(0.437141\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.99025e7 | 0.0379799 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.47307e9 | −1.10187 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.61026e7 | 0.0338957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.14898e9 | 0.830388 | 0.415194 | − | 0.909733i | \(-0.363714\pi\) | ||||
0.415194 | + | 0.909733i | \(0.363714\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.66959e7 | −0.0331767 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.47529e9 | 1.03051 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.03633e9 | −1.39855 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.22264e8 | −0.0825698 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.02289e9 | −1.34346 | −0.671729 | − | 0.740797i | \(-0.734448\pi\) | ||||
−0.671729 | + | 0.740797i | \(0.734448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.55503e9 | 1.66882 | 0.834408 | − | 0.551147i | \(-0.185810\pi\) | ||||
0.834408 | + | 0.551147i | \(0.185810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.16036e9 | 1.38782 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.66269e8 | −0.231441 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.60687e8 | 0.0998811 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −869648. | −0.000531794 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.47316e9 | −0.886295 | −0.443147 | − | 0.896449i | \(-0.646138\pi\) | ||||
−0.443147 | + | 0.896449i | \(0.646138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.33243e8 | −0.552443 | −0.276221 | − | 0.961094i | \(-0.589082\pi\) | ||||
−0.276221 | + | 0.961094i | \(0.589082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.68534e7 | −0.0272916 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.92890e7 | −0.0454494 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.94411e9 | 1.09672 | 0.548358 | − | 0.836244i | \(-0.315253\pi\) | ||||
0.548358 | + | 0.836244i | \(0.315253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.12809e8 | 0.284722 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.35592e9 | 1.28750 | 0.643751 | − | 0.765235i | \(-0.277377\pi\) | ||||
0.643751 | + | 0.765235i | \(0.277377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.24860e9 | −0.671679 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.36684e8 | −0.125341 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.83374e9 | −0.956042 | −0.478021 | − | 0.878349i | \(-0.658646\pi\) | ||||
−0.478021 | + | 0.878349i | \(0.658646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.06589e8 | −0.106045 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.34123e8 | −0.0677889 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.55213e8 | 0.127018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.76683e9 | −1.84616 | −0.923079 | − | 0.384611i | \(-0.874336\pi\) | ||||
−0.923079 | + | 0.384611i | \(0.874336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.65300e8 | −0.128054 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.30560e9 | 1.57144 | 0.785720 | − | 0.618583i | \(-0.212293\pi\) | ||||
0.785720 | + | 0.618583i | \(0.212293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.66326e9 | 1.71528 | 0.857638 | − | 0.514253i | \(-0.171931\pi\) | ||||
0.857638 | + | 0.514253i | \(0.171931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.74184e7 | −0.0218707 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.22674e9 | 1.01172 | 0.505860 | − | 0.862616i | \(-0.331175\pi\) | ||||
0.505860 | + | 0.862616i | \(0.331175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.78233e9 | 0.797780 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.52159e7 | −0.0419891 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.20342e8 | 0.0522883 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.33845e8 | 0.0573028 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.85551e9 | 0.782796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.43508e9 | −0.596625 | −0.298313 | − | 0.954468i | \(-0.596424\pi\) | ||||
−0.298313 | + | 0.954468i | \(0.596424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94842e8 | 0.0798314 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.87117e7 | 0.0115943 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.15728e9 | 0.858638 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.11642e9 | 0.830330 | 0.415165 | − | 0.909746i | \(-0.363724\pi\) | ||||
0.415165 | + | 0.909746i | \(0.363724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.92802e7 | 0.0113238 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.07105e9 | −1.55211 | −0.776053 | − | 0.630668i | \(-0.782781\pi\) | ||||
−0.776053 | + | 0.630668i | \(0.782781\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.68852e8 | 0.326574 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.71413e8 | −0.0635222 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.11935e9 | 1.50516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.93039e9 | −1.41607 | −0.708034 | − | 0.706178i | \(-0.750418\pi\) | ||||
−0.708034 | + | 0.706178i | \(0.750418\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.64558e8 | −0.0939914 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.70030e9 | 0.595714 | 0.297857 | − | 0.954610i | \(-0.403728\pi\) | ||||
0.297857 | + | 0.954610i | \(0.403728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.79952e8 | −0.304046 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.99582e8 | 0.0680132 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.62955e8 | −0.0883830 | −0.0441915 | − | 0.999023i | \(-0.514071\pi\) | ||||
−0.0441915 | + | 0.999023i | \(0.514071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.84942e9 | −0.944676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.69481e7 | 0.0317051 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.45688e9 | 0.792609 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.50171e8 | 0.0796197 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.31436e8 | −0.135466 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.86990e9 | −0.579277 | −0.289639 | − | 0.957136i | \(-0.593535\pi\) | ||||
−0.289639 | + | 0.957136i | \(0.593535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.49460e9 | 1.67950 | 0.839750 | − | 0.542972i | \(-0.182701\pi\) | ||||
0.839750 | + | 0.542972i | \(0.182701\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.84673e7 | −0.0146181 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.79329e8 | 0.261706 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.27120e9 | −0.960753 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.18769e9 | −1.21379 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.73098e8 | −0.249757 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.91116e8 | 0.0539584 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.59017e8 | −0.0443133 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.93838e7 | 0.0163346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.97892e9 | 1.89495 | 0.947475 | − | 0.319830i | \(-0.103626\pi\) | ||||
0.947475 | + | 0.319830i | \(0.103626\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.63019e8 | −0.0704998 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.63489e9 | −0.432613 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.87859e9 | 1.53574 | 0.767870 | − | 0.640606i | \(-0.221317\pi\) | ||||
0.767870 | + | 0.640606i | \(0.221317\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.56118e8 | −0.117645 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.17503e8 | −0.0808570 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.00333e9 | 0.252292 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.85143e8 | −0.0459707 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.03155e9 | −0.498119 | −0.249060 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249060 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.08599e8 | 0.123150 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.53240e7 | −0.00366440 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.68161e9 | −0.397142 | −0.198571 | − | 0.980087i | \(-0.563630\pi\) | ||||
−0.198571 | + | 0.980087i | \(0.563630\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.12030e9 | 0.261314 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.61472e9 | 0.832787 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.57746e9 | −1.04167 | −0.520837 | − | 0.853656i | \(-0.674380\pi\) | ||||
−0.520837 | + | 0.853656i | \(0.674380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.79221e9 | 1.30202 | 0.651010 | − | 0.759069i | \(-0.274345\pi\) | ||||
0.651010 | + | 0.759069i | \(0.274345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.39935e8 | 0.0532785 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.25577e8 | −0.0494831 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.74692e9 | −0.812005 | −0.406003 | − | 0.913872i | \(-0.633078\pi\) | ||||
−0.406003 | + | 0.913872i | \(0.633078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.14246e8 | 0.0672814 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.99689e9 | 1.05702 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.14869e8 | 0.0449091 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.24436e8 | −0.149608 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.69193e9 | 1.16152 | 0.580760 | − | 0.814075i | \(-0.302756\pi\) | ||||
0.580760 | + | 0.814075i | \(0.302756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.21332e8 | −0.0647963 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.40832e8 | 0.0280638 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.45596e9 | 0.286720 | 0.143360 | − | 0.989671i | \(-0.454209\pi\) | ||||
0.143360 | + | 0.989671i | \(0.454209\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.49711e9 | 0.875233 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.26217e8 | 0.0242778 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.21735e9 | 1.18198 | 0.590992 | − | 0.806677i | \(-0.298736\pi\) | ||||
0.590992 | + | 0.806677i | \(0.298736\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.98776e9 | 1.87675 | 0.938377 | − | 0.345613i | \(-0.112329\pi\) | ||||
0.938377 | + | 0.345613i | \(0.112329\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.05924e9 | −0.939668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.06935e9 | 1.11429 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.17827e9 | −0.576807 | −0.288404 | − | 0.957509i | \(-0.593124\pi\) | ||||
−0.288404 | + | 0.957509i | \(0.593124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.14972e8 | 0.0206269 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.05729e9 | 0.187521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.34969e8 | −0.111337 | −0.0556687 | − | 0.998449i | \(-0.517729\pi\) | ||||
−0.0556687 | + | 0.998449i | \(0.517729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.29637e8 | 0.143822 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.48835e7 | −0.00769287 | −0.00384643 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384643 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.79132e8 | 0.165930 | 0.0829648 | − | 0.996552i | \(-0.473561\pi\) | ||||
0.0829648 | + | 0.996552i | \(0.473561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.63392e8 | −0.0273785 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.06390e9 | 0.507652 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.24724e9 | −1.18739 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.59984e6 | 0.000907276 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.43330e9 | 0.550090 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.42563e9 | 0.384345 | 0.192172 | − | 0.981361i | \(-0.438447\pi\) | ||||
0.192172 | + | 0.981361i | \(0.438447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.24796e8 | −0.0195564 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.35744e9 | −1.45027 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.50972e8 | 0.0384713 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.16930e10 | −1.77285 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.23132e8 | 0.138440 | 0.0692199 | − | 0.997601i | \(-0.477949\pi\) | ||||
0.0692199 | + | 0.997601i | \(0.477949\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.86334e9 | −1.01812 | −0.509058 | − | 0.860732i | \(-0.670006\pi\) | ||||
−0.509058 | + | 0.860732i | \(0.670006\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.83282e8 | −0.0709156 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.02399e8 | −0.0729262 | −0.0364631 | − | 0.999335i | \(-0.511609\pi\) | ||||
−0.0364631 | + | 0.999335i | \(0.511609\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.84939e8 | −0.0696355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.16359e8 | 0.0165297 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.23523e9 | 0.595225 | 0.297612 | − | 0.954687i | \(-0.403810\pi\) | ||||
0.297612 | + | 0.954687i | \(0.403810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.53506e9 | −0.352488 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.08822e9 | 1.11269 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.34554e10 | 1.83146 | 0.915731 | − | 0.401791i | \(-0.131612\pi\) | ||||
0.915731 | + | 0.401791i | \(0.131612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.23518e10 | 1.66351 | 0.831753 | − | 0.555146i | \(-0.187338\pi\) | ||||
0.831753 | + | 0.555146i | \(0.187338\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.47634e7 | −0.00863043 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.64337e9 | −0.216700 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.35106e8 | 0.0698231 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.58864e8 | −0.0850755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.28189e7 | −0.00674933 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.52638e9 | −0.193024 | −0.0965119 | − | 0.995332i | \(-0.530769\pi\) | ||||
−0.0965119 | + | 0.995332i | \(0.530769\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.75817e8 | 0.0345189 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.55415e9 | −0.192500 | −0.0962502 | − | 0.995357i | \(-0.530685\pi\) | ||||
−0.0962502 | + | 0.995357i | \(0.530685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.29369e9 | −0.648954 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.28646e8 | 0.0884100 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.21824e9 | 0.386497 | 0.193249 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193249 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.50451e9 | −0.535465 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.73796e8 | 0.0910495 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.08095e8 | 0.105770 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.15999e9 | −1.05614 | −0.528071 | − | 0.849200i | \(-0.677084\pi\) | ||||
−0.528071 | + | 0.849200i | \(0.677084\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.20626e8 | 0.0480098 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.17941e10 | −1.33266 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.53848e10 | −1.72099 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.04634e9 | −0.115878 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.97717e9 | −0.874653 | −0.437327 | − | 0.899303i | \(-0.644075\pi\) | ||||
−0.437327 | + | 0.899303i | \(0.644075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.25462e9 | −0.136198 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.00466e9 | −0.107984 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.15929e9 | 0.229796 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.97010e9 | 0.839851 | 0.419925 | − | 0.907559i | \(-0.362056\pi\) | ||||
0.419925 | + | 0.907559i | \(0.362056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.84799e9 | −0.297163 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.41559e8 | 0.0559541 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.38904e7 | −0.00858304 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.67844e8 | −0.0170055 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.00263e10 | −1.00598 | −0.502991 | − | 0.864292i | \(-0.667767\pi\) | ||||
−0.502991 | + | 0.864292i | \(0.667767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.02888e9 | −0.599050 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.75512e8 | −0.0369522 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.03295e8 | −0.0880333 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.65401e10 | 1.59650 | 0.798248 | − | 0.602329i | \(-0.205760\pi\) | ||||
0.798248 | + | 0.602329i | \(0.205760\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.01604e10 | −0.971329 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.96200e9 | 0.848583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.81994e9 | 0.920969 | 0.460484 | − | 0.887668i | \(-0.347676\pi\) | ||||
0.460484 | + | 0.887668i | \(0.347676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.38479e8 | −0.0221536 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.85864e8 | −0.0539089 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.41304e9 | −0.493385 | −0.246692 | − | 0.969094i | \(-0.579344\pi\) | ||||
−0.246692 | + | 0.969094i | \(0.579344\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.36664e7 | 0.00213682 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.26105e9 | 0.738881 | 0.369440 | − | 0.929254i | \(-0.379549\pi\) | ||||
0.369440 | + | 0.929254i | \(0.379549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.28317e10 | −2.02298 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.41839e10 | −1.24501 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.68975e8 | −0.0407815 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.44332e10 | 1.24343 | 0.621715 | − | 0.783243i | \(-0.286436\pi\) | ||||
0.621715 | + | 0.783243i | \(0.286436\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.30788e8 | −0.0111631 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.29381e10 | −1.09410 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.31294e9 | −0.696496 | −0.348248 | − | 0.937402i | \(-0.613223\pi\) | ||||
−0.348248 | + | 0.937402i | \(0.613223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.43772e6 | −0.000783467 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.96636e10 | −1.61739 | −0.808697 | − | 0.588226i | \(-0.799827\pi\) | ||||
−0.808697 | + | 0.588226i | \(0.799827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.01180e9 | 0.326967 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.27653e10 | −1.03090 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.04948e9 | −0.164006 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.27102e10 | 1.00788 | 0.503942 | − | 0.863738i | \(-0.331883\pi\) | ||||
0.503942 | + | 0.863738i | \(0.331883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.67018e8 | −0.0681299 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.87614e9 | −0.223966 | −0.111983 | − | 0.993710i | \(-0.535720\pi\) | ||||
−0.111983 | + | 0.993710i | \(0.535720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.14188e8 | −0.0705472 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.54317e8 | 0.0347444 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.62206e9 | 0.426102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.35406e9 | −0.101709 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.54283e8 | −0.0487079 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.18498e9 | −0.677695 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.61813e9 | −0.410847 | −0.205424 | − | 0.978673i | \(-0.565857\pi\) | ||||
−0.205424 | + | 0.978673i | \(0.565857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.66101e9 | 0.120393 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.74906e9 | −0.197500 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.23227e8 | −0.0158961 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.62892e8 | −0.0609076 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.98926e9 | −0.349085 | −0.174543 | − | 0.984650i | \(-0.555845\pi\) | ||||
−0.174543 | + | 0.984650i | \(0.555845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.86305e10 | 1.29214 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.69703e9 | −0.597939 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.36623e8 | 0.0638352 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.76966e9 | 0.187129 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.86513e9 | −0.124925 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.60176e10 | 1.72762 | 0.863809 | − | 0.503820i | \(-0.168073\pi\) | ||||
0.863809 | + | 0.503820i | \(0.168073\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.36033e10 | −0.895513 | −0.447756 | − | 0.894156i | \(-0.647777\pi\) | ||||
−0.447756 | + | 0.894156i | \(0.647777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.70008e9 | 0.110956 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.82451e9 | 0.182764 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.27497e9 | −0.210102 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.77768e9 | 0.113073 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.59803e9 | 0.353048 | 0.176524 | − | 0.984296i | \(-0.443515\pi\) | ||||
0.176524 | + | 0.984296i | \(0.443515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.83609e10 | −1.77346 | −0.886728 | − | 0.462292i | \(-0.847027\pi\) | ||||
−0.886728 | + | 0.462292i | \(0.847027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.59315e7 | 0.000987799 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.94087e10 | 1.19324 | 0.596619 | − | 0.802524i | \(-0.296510\pi\) | ||||
0.596619 | + | 0.802524i | \(0.296510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.25701e10 | 0.766301 | 0.383150 | − | 0.923686i | \(-0.374839\pi\) | ||||
0.383150 | + | 0.923686i | \(0.374839\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.50501e9 | 0.0909781 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.42236e9 | 0.265092 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.55205e10 | −1.51700 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.62173e8 | −0.0390331 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.95535e10 | −1.14303 | −0.571515 | − | 0.820592i | \(-0.693644\pi\) | ||||
−0.571515 | + | 0.820592i | \(0.693644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.51071e10 | −0.875781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.68256e8 | 0.0326699 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.92526e10 | 1.09772 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.48934e10 | −0.842175 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.69521e8 | 0.0263316 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.11449e9 | 0.117612 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.14196e10 | 0.629986 | 0.314993 | − | 0.949094i | \(-0.397998\pi\) | ||||
0.314993 | + | 0.949094i | \(0.397998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.66479e9 | 0.255241 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.94401e10 | −1.05503 | −0.527516 | − | 0.849545i | \(-0.676877\pi\) | ||||
−0.527516 | + | 0.849545i | \(0.676877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.07841e10 | −0.580509 | −0.290254 | − | 0.956950i | \(-0.593740\pi\) | ||||
−0.290254 | + | 0.956950i | \(0.593740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.03583e9 | −0.108700 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.45236e8 | 0.0447651 | 0.0223826 | − | 0.999749i | \(-0.492875\pi\) | ||||
0.0223826 | + | 0.999749i | \(0.492875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.16184e10 | −2.18640 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.87990e8 | 0.00979643 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.29800e8 | −0.0170483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.47602e9 | −0.126967 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.50264e10 | 0.764373 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.40428e10 | 0.708642 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.17563e10 | 1.08915 | 0.544574 | − | 0.838713i | \(-0.316691\pi\) | ||||
0.544574 | + | 0.838713i | \(0.316691\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.37513e9 | 0.0682939 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.18056e10 | 1.07436 | 0.537182 | − | 0.843466i | \(-0.319489\pi\) | ||||
0.537182 | + | 0.843466i | \(0.319489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.25662e9 | −0.110305 | −0.0551526 | − | 0.998478i | \(-0.517565\pi\) | ||||
−0.0551526 | + | 0.998478i | \(0.517565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.94746e9 | 0.0944424 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.72271e10 | 0.828857 | 0.414428 | − | 0.910082i | \(-0.363982\pi\) | ||||
0.414428 | + | 0.910082i | \(0.363982\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.29620e10 | 1.09611 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.18818e9 | −0.0562745 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.80810e9 | −0.319923 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.53396e10 | −0.715208 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.98863e7 | −0.00184523 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.16861e9 | 0.0995455 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60015e10 | 0.728827 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.18591e9 | 0.0535976 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.53721e10 | −1.13785 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.32557e10 | −1.03491 | −0.517456 | − | 0.855710i | \(-0.673121\pi\) | ||||
−0.517456 | + | 0.855710i | \(0.673121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.12926e9 | −0.270666 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.22775e10 | 1.85266 | 0.926329 | − | 0.376715i | \(-0.122946\pi\) | ||||
0.926329 | + | 0.376715i | \(0.122946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.64251e9 | −0.0714267 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.12115e8 | 0.00915372 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.22072e9 | 0.266408 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.74897e10 | −1.16833 | −0.584164 | − | 0.811635i | \(-0.698578\pi\) | ||||
−0.584164 | + | 0.811635i | \(0.698578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.38487e9 | 0.0584116 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.72261e9 | −0.239546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.56940e9 | −0.148286 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.71133e10 | 0.705593 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.42814e10 | −0.993614 | −0.496807 | − | 0.867861i | \(-0.665494\pi\) | ||||
−0.496807 | + | 0.867861i | \(0.665494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.61606e9 | −0.0656346 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.51563e8 | −0.0222336 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.47823e9 | −0.0591427 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.53708e10 | −1.40461 | −0.702305 | − | 0.711876i | \(-0.747846\pi\) | ||||
−0.702305 | + | 0.711876i | \(0.747846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.30264e9 | 0.0513445 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.60255e10 | −1.40944 | −0.704719 | − | 0.709486i | \(-0.748927\pi\) | ||||
−0.704719 | + | 0.709486i | \(0.748927\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.47516e9 | −0.367956 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.38652e9 | −0.130539 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.20930e10 | 0.845336 | 0.422668 | − | 0.906285i | \(-0.361094\pi\) | ||||
0.422668 | + | 0.906285i | \(0.361094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.95842e9 | 0.150345 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.17496e8 | 0.0232810 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.36409e9 | −0.0884787 | −0.0442393 | − | 0.999021i | \(-0.514086\pi\) | ||||
−0.0442393 | + | 0.999021i | \(0.514086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.31452e10 | 0.859903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.77922e7 | −0.00139383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.10535e10 | 0.404702 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.53179e10 | −0.920227 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.33121e9 | 0.0480346 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.03137e10 | 1.08591 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.69098e10 | −0.957014 | −0.478507 | − | 0.878084i | \(-0.658822\pi\) | ||||
−0.478507 | + | 0.878084i | \(0.658822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.17025e8 | 0.0147241 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.71594e9 | 0.165311 | 0.0826553 | − | 0.996578i | \(-0.473660\pi\) | ||||
0.0826553 | + | 0.996578i | \(0.473660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.89413e10 | 1.00722 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.73308e7 | 0.00232647 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.79514e10 | 0.615839 | 0.307919 | − | 0.951412i | \(-0.400367\pi\) | ||||
0.307919 | + | 0.951412i | \(0.400367\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.00712e9 | −0.0343039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.13877e10 | −0.385119 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.39450e10 | −0.804039 | −0.402019 | − | 0.915631i | \(-0.631692\pi\) | ||||
−0.402019 | + | 0.915631i | \(0.631692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35854e10 | 0.452944 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.46531e9 | 0.0816134 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.51949e9 | 0.181431 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.07956e10 | −0.352362 | −0.176181 | − | 0.984358i | \(-0.556374\pi\) | ||||
−0.176181 | + | 0.984358i | \(0.556374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.33459e9 | −0.0432540 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.21755e10 | 0.391838 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.54933e10 | −1.13426 | −0.567131 | − | 0.823627i | \(-0.691947\pi\) | ||||
−0.567131 | + | 0.823627i | \(0.691947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.58542e9 | −0.0820450 |
(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 | 304.8.a.d.1.1 | 2 | ||
4.3 | odd | 2 | 38.8.a.d.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 342.8.a.g.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.8.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
304.8.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
342.8.a.g.1.2 | 2 | 12.11 | even | 2 |