Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,6,Mod(1,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, 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("688.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.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: | \(110.344068031\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.38824\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.1 |
$q$-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 | ||||||||
\(3\) | −25.0462 | −1.60671 | −0.803357 | − | 0.595497i | \(-0.796955\pi\) | ||||
−0.803357 | + | 0.595497i | \(0.796955\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.456695 | −0.00816961 | −0.00408481 | − | 0.999992i | \(-0.501300\pi\) | ||||
−0.00408481 | + | 0.999992i | \(0.501300\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −166.517 | −1.28444 | −0.642221 | − | 0.766519i | \(-0.721987\pi\) | ||||
−0.642221 | + | 0.766519i | \(0.721987\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 384.312 | 1.58153 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 65.6764 | 0.163654 | 0.0818272 | − | 0.996647i | \(-0.473924\pi\) | ||||
0.0818272 | + | 0.996647i | \(0.473924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −689.371 | −1.13134 | −0.565672 | − | 0.824630i | \(-0.691383\pi\) | ||||
−0.565672 | + | 0.824630i | \(0.691383\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.4385 | 0.0131262 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 737.385 | 0.618831 | 0.309415 | − | 0.950927i | \(-0.399867\pi\) | ||||
0.309415 | + | 0.950927i | \(0.399867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 609.887 | 0.387583 | 0.193792 | − | 0.981043i | \(-0.437921\pi\) | ||||
0.193792 | + | 0.981043i | \(0.437921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4170.63 | 2.06373 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1312.45 | −0.517326 | −0.258663 | − | 0.965968i | \(-0.583282\pi\) | ||||
−0.258663 | + | 0.965968i | \(0.583282\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3124.79 | −0.999933 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3539.34 | −0.934357 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8969.74 | −1.98055 | −0.990273 | − | 0.139137i | \(-0.955567\pi\) | ||||
−0.990273 | + | 0.139137i | \(0.955567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5858.93 | −1.09500 | −0.547500 | − | 0.836806i | \(-0.684420\pi\) | ||||
−0.547500 | + | 0.836806i | \(0.684420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1644.94 | −0.262946 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 76.0477 | 0.0104934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −55.9069 | −0.00671369 | −0.00335685 | − | 0.999994i | \(-0.501069\pi\) | ||||
−0.00335685 | + | 0.999994i | \(0.501069\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17266.1 | 1.81775 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10450.3 | −0.970889 | −0.485445 | − | 0.874267i | \(-0.661342\pi\) | ||||
−0.485445 | + | 0.874267i | \(0.661342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −175.514 | −0.0129205 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1942.82 | −0.128288 | −0.0641442 | − | 0.997941i | \(-0.520432\pi\) | ||||
−0.0641442 | + | 0.997941i | \(0.520432\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10921.1 | 0.649792 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18468.7 | −0.994284 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30129.2 | 1.47332 | 0.736661 | − | 0.676262i | \(-0.236401\pi\) | ||||
0.736661 | + | 0.676262i | \(0.236401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −29.9941 | −0.00133699 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15275.3 | −0.622736 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −52167.4 | −1.95106 | −0.975528 | − | 0.219877i | \(-0.929434\pi\) | ||||
−0.975528 | + | 0.219877i | \(0.929434\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14040.1 | −0.483108 | −0.241554 | − | 0.970387i | \(-0.577657\pi\) | ||||
−0.241554 | + | 0.970387i | \(0.577657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63994.7 | −2.03139 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 314.832 | 0.00924264 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −51437.7 | −1.39989 | −0.699946 | − | 0.714196i | \(-0.746792\pi\) | ||||
−0.699946 | + | 0.714196i | \(0.746792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 32872.0 | 0.831196 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11268.6 | −0.265292 | −0.132646 | − | 0.991163i | \(-0.542347\pi\) | ||||
−0.132646 | + | 0.991163i | \(0.542347\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −61124.5 | −1.34248 | −0.671241 | − | 0.741239i | \(-0.734238\pi\) | ||||
−0.671241 | + | 0.741239i | \(0.734238\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 78264.2 | 1.60661 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10936.3 | −0.210205 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −96018.3 | −1.73096 | −0.865478 | − | 0.500947i | \(-0.832985\pi\) | ||||
−0.865478 | + | 0.500947i | \(0.832985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4740.91 | −0.0802878 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −30378.0 | −0.484021 | −0.242010 | − | 0.970274i | \(-0.577807\pi\) | ||||
−0.242010 | + | 0.970274i | \(0.577807\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −336.760 | −0.00505561 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 224658. | 3.18217 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −65040.4 | −0.870378 | −0.435189 | − | 0.900339i | \(-0.643319\pi\) | ||||
−0.435189 | + | 0.900339i | \(0.643319\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 114792. | 1.45315 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 146744. | 1.75935 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −278.532 | −0.00316641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12067.6 | 0.130224 | 0.0651119 | − | 0.997878i | \(-0.479260\pi\) | ||||
0.0651119 | + | 0.997878i | \(0.479260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25240.2 | 0.258825 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107046. | 1.04416 | 0.522079 | − | 0.852897i | \(-0.325157\pi\) | ||||
0.522079 | + | 0.852897i | \(0.325157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 86209.7 | 0.800688 | 0.400344 | − | 0.916365i | \(-0.368891\pi\) | ||||
0.400344 | + | 0.916365i | \(0.368891\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1904.71 | −0.0168599 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −197153. | −1.66473 | −0.832365 | − | 0.554227i | \(-0.813014\pi\) | ||||
−0.832365 | + | 0.554227i | \(0.813014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 165311. | 1.33271 | 0.666355 | − | 0.745634i | \(-0.267853\pi\) | ||||
0.666355 | + | 0.745634i | \(0.267853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1400.26 | 0.0107870 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −179790. | −1.32455 | −0.662275 | − | 0.749260i | \(-0.730409\pi\) | ||||
−0.662275 | + | 0.749260i | \(0.730409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 599.391 | 0.00422635 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −264934. | −1.78926 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −122787. | −0.794852 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −156738. | −0.973217 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 261741. | 1.55994 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2854.25 | 0.0163387 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 286585. | 1.57668 | 0.788341 | − | 0.615238i | \(-0.210940\pi\) | ||||
0.788341 | + | 0.615238i | \(0.210940\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 46310.4 | 0.245022 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −67619.1 | −0.344263 | −0.172132 | − | 0.985074i | \(-0.555065\pi\) | ||||
−0.172132 | + | 0.985074i | \(0.555065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −101557. | −0.497829 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1616.40 | 0.00763333 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 133580. | 0.608050 | 0.304025 | − | 0.952664i | \(-0.401669\pi\) | ||||
0.304025 | + | 0.952664i | \(0.401669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 262195. | 1.15103 | 0.575516 | − | 0.817790i | \(-0.304801\pi\) | ||||
0.575516 | + | 0.817790i | \(0.304801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48660.2 | 0.206123 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −45275.4 | −0.185149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4096.44 | 0.0161803 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −273531. | −1.04403 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 187414. | 0.691569 | 0.345785 | − | 0.938314i | \(-0.387613\pi\) | ||||
0.345785 | + | 0.938314i | \(0.387613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 131632. | 0.469807 | 0.234904 | − | 0.972019i | \(-0.424523\pi\) | ||||
0.234904 | + | 0.972019i | \(0.424523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 283386. | 0.978701 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2675.75 | 0.00894573 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −252270. | −0.816800 | −0.408400 | − | 0.912803i | \(-0.633913\pi\) | ||||
−0.408400 | + | 0.912803i | \(0.633913\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −754622. | −2.36721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 218547. | 0.664476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 518121. | 1.52743 | 0.763717 | − | 0.645552i | \(-0.223373\pi\) | ||||
0.763717 | + | 0.645552i | \(0.223373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 751.238 | 0.00214817 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 681328. | 1.89045 | 0.945224 | − | 0.326422i | \(-0.105843\pi\) | ||||
0.945224 | + | 0.326422i | \(0.105843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 103939. | 0.279939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 234387. | 0.612976 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −148596. | −0.377478 | −0.188739 | − | 0.982027i | \(-0.560440\pi\) | ||||
−0.188739 | + | 0.982027i | \(0.560440\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 520332. | 1.28436 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.30660e6 | 3.13479 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −103068. | −0.240432 | −0.120216 | − | 0.992748i | \(-0.538359\pi\) | ||||
−0.120216 | + | 0.992748i | \(0.538359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 309316. | 0.701789 | 0.350894 | − | 0.936415i | \(-0.385878\pi\) | ||||
0.350894 | + | 0.936415i | \(0.385878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 351650. | 0.776217 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.5324 | 5.48483e−5 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 48428.8 | 0.101274 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 589362. | 1.20013 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −373258. | −0.740330 | −0.370165 | − | 0.928966i | \(-0.620699\pi\) | ||||
−0.370165 | + | 0.928966i | \(0.620699\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 85782.8 | 0.165770 | 0.0828852 | − | 0.996559i | \(-0.473587\pi\) | ||||
0.0828852 | + | 0.996559i | \(0.473587\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7885.36 | −0.0148503 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −178146. | −0.327047 | −0.163523 | − | 0.986539i | \(-0.552286\pi\) | ||||
−0.163523 | + | 0.986539i | \(0.552286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −154725. | −0.276967 | −0.138484 | − | 0.990365i | \(-0.544223\pi\) | ||||
−0.138484 | + | 0.990365i | \(0.544223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.28832e6 | 2.24923 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.49362e6 | 2.54390 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4772.61 | 0.00793179 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −504392. | −0.818168 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40055.2 | 0.0634297 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 682180. | 1.05485 | 0.527427 | − | 0.849600i | \(-0.323157\pi\) | ||||
0.527427 | + | 0.849600i | \(0.323157\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 282236. | 0.426249 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 844.429 | 0.00124585 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 975615. | 1.40647 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.53094e6 | 2.15698 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −508332. | −0.700110 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 464004. | 0.624827 | 0.312413 | − | 0.949946i | \(-0.398863\pi\) | ||||
0.312413 | + | 0.949946i | \(0.398863\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.20090e6 | −1.58143 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.13876e6 | −1.46679 | −0.733396 | − | 0.679801i | \(-0.762066\pi\) | ||||
−0.733396 | + | 0.679801i | \(0.762066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 648718. | 0.817462 | 0.408731 | − | 0.912655i | \(-0.365971\pi\) | ||||
0.408731 | + | 0.912655i | \(0.365971\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 273912. | 0.337739 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −588684. | −0.710383 | −0.355191 | − | 0.934794i | \(-0.615584\pi\) | ||||
−0.355191 | + | 0.934794i | \(0.615584\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 887.275 | 0.00104807 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.40489e6 | 2.78115 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −739129. | −0.837000 | −0.418500 | − | 0.908217i | \(-0.637444\pi\) | ||||
−0.418500 | + | 0.908217i | \(0.637444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.57360e6 | −1.74523 | −0.872615 | − | 0.488409i | \(-0.837577\pi\) | ||||
−0.872615 | + | 0.488409i | \(0.837577\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 978801. | 1.06336 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4987.60 | −0.00530855 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −420438. | −0.438490 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 760854. | 0.777684 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −456789. | −0.457648 | −0.228824 | − | 0.973468i | \(-0.573488\pi\) | ||||
−0.228824 | + | 0.973468i | \(0.573488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −86197.3 | −0.0846627 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8434.56 | 0.00812292 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.12132e6 | 1.05900 | 0.529499 | − | 0.848310i | \(-0.322380\pi\) | ||||
0.529499 | + | 0.848310i | \(0.322380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9309.48 | 0.00862335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.44718e6 | −3.13230 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.75620e6 | −1.56562 | −0.782808 | − | 0.622263i | \(-0.786214\pi\) | ||||
−0.782808 | + | 0.622263i | \(0.786214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13759.9 | −0.0120365 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.62901e6 | 1.39845 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.22933e6 | 1.03583 | 0.517915 | − | 0.855432i | \(-0.326708\pi\) | ||||
0.517915 | + | 0.855432i | \(0.326708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.32305e6 | −1.09435 | −0.547173 | − | 0.837020i | \(-0.684296\pi\) | ||||
−0.547173 | + | 0.837020i | \(0.684296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.87511e6 | −2.33479 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −205225. | −0.163643 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.96854e6 | 1.54151 | 0.770754 | − | 0.637133i | \(-0.219880\pi\) | ||||
0.770754 | + | 0.637133i | \(0.219880\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.25166e6 | −1.73178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.11820e6 | −0.844801 | −0.422400 | − | 0.906409i | \(-0.638812\pi\) | ||||
−0.422400 | + | 0.906409i | \(0.638812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.25727e6 | −0.933174 | −0.466587 | − | 0.884475i | \(-0.654517\pi\) | ||||
−0.466587 | + | 0.884475i | \(0.654517\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6976.18 | 0.00508751 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.74016e6 | 1.24705 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −876121. | −0.617049 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −302247. | −0.209233 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −260406. | −0.177207 | −0.0886037 | − | 0.996067i | \(-0.528240\pi\) | ||||
−0.0886037 | + | 0.996067i | \(0.528240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23824.6 | 0.0159394 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −232451. | −0.152912 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 904768. | 0.585274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 307891. | 0.195876 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.68109e6 | −1.67766 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6412.03 | 0.00394681 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.56144e6 | 0.945536 | 0.472768 | − | 0.881187i | \(-0.343255\pi\) | ||||
0.472768 | + | 0.881187i | \(0.343255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.15923e6 | −1.28648 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −655137. | −0.384088 | −0.192044 | − | 0.981386i | \(-0.561512\pi\) | ||||
−0.192044 | + | 0.981386i | \(0.561512\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −212890. | −0.122827 | −0.0614136 | − | 0.998112i | \(-0.519561\pi\) | ||||
−0.0614136 | + | 0.998112i | \(0.519561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29226.1 | 0.0165956 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −385858. | −0.215665 | −0.107832 | − | 0.994169i | \(-0.534391\pi\) | ||||
−0.107832 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −589100. | −0.324125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.93794e6 | 2.67475 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 449721. | 0.239849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.15414e6 | 1.13127 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.14042e6 | −2.14129 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 323513. | 0.164779 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.62905e6 | 0.817269 | 0.408634 | − | 0.912698i | \(-0.366005\pi\) | ||||
0.408634 | + | 0.912698i | \(0.366005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21485.7 | −0.0106179 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23491.3 | 0.0114366 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.32344e6 | −1.11444 | −0.557220 | − | 0.830365i | \(-0.688132\pi\) | ||||
−0.557220 | + | 0.830365i | \(0.688132\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.50305e6 | 2.12818 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −384794. | −0.179202 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 980112. | 0.449822 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15012.5 | −0.00679055 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.45789e6 | 1.09582 | 0.547910 | − | 0.836537i | \(-0.315424\pi\) | ||||
0.547910 | + | 0.836537i | \(0.315424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.36489e6 | −1.91827 | −0.959135 | − | 0.282950i | \(-0.908687\pi\) | ||||
−0.959135 | + | 0.282950i | \(0.908687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.43992e6 | 1.05708 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 898354. | 0.383717 | 0.191858 | − | 0.981423i | \(-0.438549\pi\) | ||||
0.191858 | + | 0.981423i | \(0.438549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5146.32 | 0.00216734 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.07536e6 | 1.27710 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.81866e6 | −0.744759 | −0.372379 | − | 0.928081i | \(-0.621458\pi\) | ||||
−0.372379 | + | 0.928081i | \(0.621458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.10414e6 | −0.849779 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.92568e6 | 1.56368 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27915.3 | 0.0109675 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.34762e6 | 0.909836 | 0.454918 | − | 0.890533i | \(-0.349669\pi\) | ||||
0.454918 | + | 0.890533i | \(0.349669\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.01619e6 | −1.53549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.01703e6 | −1.89240 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.97881e6 | 1.10859 | 0.554295 | − | 0.832321i | \(-0.312988\pi\) | ||||
0.554295 | + | 0.832321i | \(0.312988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −71488.1 | −0.0262516 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.18348e6 | 2.24068 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.77718e6 | −0.635527 | −0.317764 | − | 0.948170i | \(-0.602932\pi\) | ||||
−0.317764 | + | 0.948170i | \(0.602932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.17787e6 | −2.53328 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.08193e6 | 0.725220 | 0.362610 | − | 0.931941i | \(-0.381886\pi\) | ||||
0.362610 | + | 0.931941i | \(0.381886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4994.54 | 0.00171729 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −710594. | −0.241181 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.81080e6 | −0.606730 | −0.303365 | − | 0.952874i | \(-0.598110\pi\) | ||||
−0.303365 | + | 0.952874i | \(0.598110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −967784. | −0.320137 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.69360e6 | 0.553133 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43851.1 | 0.0141412 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 185900. | 0.0591975 | 0.0295988 | − | 0.999562i | \(-0.490577\pi\) | ||||
0.0295988 | + | 0.999562i | \(0.490577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.54361e6 | 0.799869 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.41892e6 | −1.06176 | −0.530882 | − | 0.847446i | \(-0.678139\pi\) | ||||
−0.530882 | + | 0.847446i | \(0.678139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.03898e6 | 1.23882 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2165.15 | 0.000655920 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3671.77 | −0.00109873 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −428179. | −0.126566 | −0.0632830 | − | 0.997996i | \(-0.520157\pi\) | ||||
−0.0632830 | + | 0.997996i | \(0.520157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.34567e6 | −0.976963 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.68679e6 | 2.50602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13873.5 | 0.00395426 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.56699e6 | −1.84938 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.84011e6 | −1.06858 | −0.534292 | − | 0.845300i | \(-0.679422\pi\) | ||||
−0.534292 | + | 0.845300i | \(0.679422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.05884e6 | 1.94101 | 0.970506 | − | 0.241078i | \(-0.0775010\pi\) | ||||
0.970506 | + | 0.241078i | \(0.0775010\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −746649. | −0.202892 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.30417e6 | −0.618789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.33792e6 | 0.620525 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.13398e6 | 0.297482 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.11813e6 | 0.549237 | 0.274619 | − | 0.961553i | \(-0.411448\pi\) | ||||
0.274619 | + | 0.961553i | \(0.411448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.58858e6 | −0.407182 | −0.203591 | − | 0.979056i | \(-0.565261\pi\) | ||||
−0.203591 | + | 0.979056i | \(0.565261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −102600. | −0.0259971 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −800448. | −0.200507 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.11302e6 | −1.76154 | −0.880771 | − | 0.473543i | \(-0.842975\pi\) | ||||
−0.880771 | + | 0.473543i | \(0.842975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.19710e6 | 1.02767 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.52423e6 | −0.611110 | −0.305555 | − | 0.952174i | \(-0.598842\pi\) | ||||
−0.305555 | + | 0.952174i | \(0.598842\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29703.6 | 0.00711065 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.69400e6 | −1.11115 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −471868. | −0.110460 | −0.0552300 | − | 0.998474i | \(-0.517589\pi\) | ||||
−0.0552300 | + | 0.998474i | \(0.517589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −686339. | −0.158890 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.29689e6 | −0.754846 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −52425.1 | −0.0118716 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.11039e6 | −1.36861 | −0.684303 | − | 0.729198i | \(-0.739893\pi\) | ||||
−0.684303 | + | 0.729198i | \(0.739893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.60985e6 | −0.578209 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.47383e6 | 1.63791 | 0.818957 | − | 0.573855i | \(-0.194553\pi\) | ||||
0.818957 | + | 0.573855i | \(0.194553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.14981e6 | 0.899654 | 0.449827 | − | 0.893116i | \(-0.351486\pi\) | ||||
0.449827 | + | 0.893116i | \(0.351486\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −67017.3 | −0.0143732 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.18789e6 | 0.252048 | 0.126024 | − | 0.992027i | \(-0.459778\pi\) | ||||
0.126024 | + | 0.992027i | \(0.459778\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.56527e6 | 1.79808 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.31840e6 | 1.31237 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −121436. | −0.0249571 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.90577e6 | −0.387558 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.15790e7 | 2.33011 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.74102e6 | −0.744992 | −0.372496 | − | 0.928034i | \(-0.621498\pi\) | ||||
−0.372496 | + | 0.928034i | \(0.621498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38540.6 | 0.00759549 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.47376e6 | −1.06762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5511.20 | −0.00106388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.18109e6 | −1.37204 | −0.686021 | − | 0.727581i | \(-0.740644\pi\) | ||||
−0.686021 | + | 0.727581i | \(0.740644\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.29770e7 | −2.45415 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.37443e6 | 1.38046 | 0.690231 | − | 0.723589i | \(-0.257509\pi\) | ||||
0.690231 | + | 0.723589i | \(0.257509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.61415e6 | −1.22562 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11527.1 | −0.00211450 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.87642e6 | 0.340753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.61086e6 | −0.469388 | −0.234694 | − | 0.972069i | \(-0.575409\pi\) | ||||
−0.234694 | + | 0.972069i | \(0.575409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.70647e7 | −3.03741 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 398438. | 0.0702167 | 0.0351084 | − | 0.999384i | \(-0.488822\pi\) | ||||
0.0351084 | + | 0.999384i | \(0.488822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48887.3 | −0.00853036 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.60329e6 | −0.449782 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 556201. | 0.0951563 | 0.0475781 | − | 0.998868i | \(-0.484850\pi\) | ||||
0.0475781 | + | 0.998868i | \(0.484850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.01783e7 | 1.72434 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.15860e6 | −0.362141 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39371.6 | −0.00654131 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −127597. | −0.0209950 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.72176e6 | 0.606499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.39465e6 | 0.547898 | 0.273949 | − | 0.961744i | \(-0.411670\pi\) | ||||
0.273949 | + | 0.961744i | \(0.411670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40326e6 | 1.50323 | 0.751613 | − | 0.659605i | \(-0.229276\pi\) | ||||
0.751613 | + | 0.659605i | \(0.229276\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.30323e7 | −2.06359 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.32029e6 | −0.677620 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.71381e6 | −0.732373 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00486e7 | −3.08566 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.20414e6 | 1.09841 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 90038.8 | 0.0136002 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.58147e6 | 0.386306 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 717256. | 0.106341 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.76159e6 | 0.699453 | 0.349727 | − | 0.936852i | \(-0.386274\pi\) | ||||
0.349727 | + | 0.936852i | \(0.386274\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.74720e6 | −1.12757 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −75496.8 | −0.0108877 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.68380e6 | −0.669314 | −0.334657 | − | 0.942340i | \(-0.608621\pi\) | ||||
−0.334657 | + | 0.942340i | \(0.608621\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.39577e6 | −0.764051 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.47053e6 | −0.767627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.59887e7 | 2.22331 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −639.490 | −8.81255e−5 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.37082e6 | 0.596931 | 0.298466 | − | 0.954420i | \(-0.403525\pi\) | ||||
0.298466 | + | 0.954420i | \(0.403525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.27465e6 | 0.172528 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.21296e6 | −0.162719 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.98439e6 | 1.32755 | 0.663774 | − | 0.747933i | \(-0.268954\pi\) | ||||
0.663774 | + | 0.747933i | \(0.268954\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 82109.1 | 0.0108211 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 789445. | 0.103125 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.03616e6 | −0.393137 | −0.196568 | − | 0.980490i | \(-0.562980\pi\) | ||||
−0.196568 | + | 0.980490i | \(0.562980\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.66426e6 | 0.598677 | 0.299339 | − | 0.954147i | \(-0.403234\pi\) | ||||
0.299339 | + | 0.954147i | \(0.403234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.34869e6 | 1.18950 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.10115e6 | 0.517292 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.53940e6 | 0.317536 | 0.158768 | − | 0.987316i | \(-0.449248\pi\) | ||||
0.158768 | + | 0.987316i | \(0.449248\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.14853e6 | −0.266346 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.05847e6 | 0.621697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.97878e6 | 0.241116 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 120994. | 0.0146175 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.18921e7 | −1.42450 | −0.712248 | − | 0.701927i | \(-0.752323\pi\) | ||||
−0.712248 | + | 0.701927i | \(0.752323\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.57329e6 | −0.424404 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.46187e6 | 0.525471 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.49053e6 | 0.174062 | 0.0870311 | − | 0.996206i | \(-0.472262\pi\) | ||||
0.0870311 | + | 0.996206i | \(0.472262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 56076.4 | 0.00649363 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.87528e6 | 0.445008 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.13339e7 | 1.29066 | 0.645328 | − | 0.763905i | \(-0.276721\pi\) | ||||
0.645328 | + | 0.763905i | \(0.276721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.07157e7 | 1.21014 | 0.605069 | − | 0.796173i | \(-0.293145\pi\) | ||||
0.605069 | + | 0.796173i | \(0.293145\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.97681e7 | −2.21397 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 71581.3 | 0.00795081 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 871321. | 0.0959857 | 0.0479929 | − | 0.998848i | \(-0.484718\pi\) | ||||
0.0479929 | + | 0.998848i | \(0.484718\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.74095e7 | −4.08732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33932e6 | 0.145138 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.62264e7 | −1.74410 | −0.872051 | − | 0.489415i | \(-0.837210\pi\) | ||||
−0.872051 | + | 0.489415i | \(0.837210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −119536. | −0.0127441 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.18192e6 | 0.124990 | 0.0624950 | − | 0.998045i | \(-0.480094\pi\) | ||||
0.0624950 | + | 0.998045i | \(0.480094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.78346e7 | −1.87084 | −0.935418 | − | 0.353544i | \(-0.884977\pi\) | ||||
−0.935418 | + | 0.353544i | \(0.884977\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.64522e6 | 0.483367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.08304e7 | 1.11795 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.76367e6 | 0.999800 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.00323e6 | −0.101913 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41224.9 | −0.00415464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.56569e7 | 1.56543 | 0.782715 | − | 0.622381i | \(-0.213834\pi\) | ||||
0.782715 | + | 0.622381i | \(0.213834\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.70860e7 | −1.69485 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −130882. | −0.0128809 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.52866e6 | −0.735139 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.33067e6 | −0.419568 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.56677e6 | −0.919645 | −0.459822 | − | 0.888011i | \(-0.652087\pi\) | ||||
−0.459822 | + | 0.888011i | \(0.652087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.58449e6 | −0.628050 | −0.314025 | − | 0.949415i | \(-0.601678\pi\) | ||||
−0.314025 | + | 0.949415i | \(0.601678\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21149.7 | −0.00200173 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.77942e6 | 0.542779 | 0.271390 | − | 0.962470i | \(-0.412517\pi\) | ||||
0.271390 | + | 0.962470i | \(0.412517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.42617e6 | −0.319299 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.44354e7 | −2.25979 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.76847e7 | −1.62298 | −0.811492 | − | 0.584364i | \(-0.801344\pi\) | ||||
−0.811492 | + | 0.584364i | \(0.801344\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30881.3 | 0.00281250 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.34909e7 | −2.12318 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.07891e7 | −0.967769 | −0.483884 | − | 0.875132i | \(-0.660774\pi\) | ||||
−0.483884 | + | 0.875132i | \(0.660774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.27678e7 | −1.13662 | −0.568308 | − | 0.822816i | \(-0.692402\pi\) | ||||
−0.568308 | + | 0.822816i | \(0.692402\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.27318e7 | 1.12488 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 46380.5 | 0.00406707 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17724e7 | 1.02459 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.16215e7 | −1.00392 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −922101. | −0.0790628 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.05831e6 | 0.430495 | 0.215247 | − | 0.976560i | \(-0.430944\pi\) | ||||
0.215247 | + | 0.976560i | \(0.430944\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.10597e7 | 0.934294 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.48127e7 | 1.24211 | 0.621057 | − | 0.783766i | \(-0.286704\pi\) | ||||
0.621057 | + | 0.783766i | \(0.286704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00946e6 | −0.167265 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.85217e7 | 2.35672 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.52658e6 | 0.781421 | 0.390711 | − | 0.920514i | \(-0.372229\pi\) | ||||
0.390711 | + | 0.920514i | \(0.372229\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −61005.2 | −0.00496753 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.62479e7 | −1.31343 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.07702e7 | −1.66683 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.04497e6 | 0.322270 | 0.161135 | − | 0.986932i | \(-0.448484\pi\) | ||||
0.161135 | + | 0.986932i | \(0.448484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.20294e6 | −0.332445 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −119743. | −0.00940349 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.70590e6 | −0.600816 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.47443e7 | 1.14138 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.78401e6 | 0.137120 | 0.0685602 | − | 0.997647i | \(-0.478159\pi\) | ||||
0.0685602 | + | 0.997647i | \(0.478159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34096.9 | −0.00260212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22222.9 | −0.00168394 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.78250e7 | −1.34116 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.22322e7 | −0.913878 | −0.456939 | − | 0.889498i | \(-0.651054\pi\) | ||||
−0.456939 | + | 0.889498i | \(0.651054\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.69010e7 | −2.73756 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.68958e6 | 0.566473 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20677.1 | 0.00151260 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.85124e7 | 1.34482 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.42924e6 | −0.608088 | −0.304044 | − | 0.952658i | \(-0.598337\pi\) | ||||
−0.304044 | + | 0.952658i | \(0.598337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.43554e7 | −1.02844 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.94128e7 | 2.80409 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.80286e7 | 1.98041 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.10329e7 | −0.774201 | −0.387101 | − | 0.922037i | \(-0.626523\pi\) | ||||
−0.387101 | + | 0.922037i | \(0.626523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.33632e7 | −1.62822 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.36342e6 | −0.0943708 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.02000e6 | −0.345099 | −0.172550 | − | 0.985001i | \(-0.555201\pi\) | ||||
−0.172550 | + | 0.985001i | \(0.555201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 124920. | 0.00852933 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.37824e6 | −0.229098 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.49061e6 | −0.167762 | −0.0838810 | − | 0.996476i | \(-0.526732\pi\) | ||||
−0.0838810 | + | 0.996476i | \(0.526732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.05304e7 | 0.704529 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.21111e7 | 0.804847 | 0.402423 | − | 0.915454i | \(-0.368168\pi\) | ||||
0.402423 | + | 0.915454i | \(0.368168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −85590.9 | −0.00564985 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.16746e7 | −0.765495 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.28294e7 | 2.13825 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.21669e7 | −1.43418 | −0.717092 | − | 0.696978i | \(-0.754528\pi\) | ||||
−0.717092 | + | 0.696978i | \(0.754528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.14408e7 | 0.735310 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −60115.8 | −0.00383814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.03112e7 | 0.653986 | 0.326993 | − | 0.945027i | \(-0.393965\pi\) | ||||
0.326993 | + | 0.945027i | \(0.393965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.15891e6 | 0.136029 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.23003e6 | 0.327373 | 0.163686 | − | 0.986512i | \(-0.447661\pi\) | ||||
0.163686 | + | 0.986512i | \(0.447661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.75272e7 | −1.71179 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −129421. | −0.00799560 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.59627e7 | 2.20731 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.16812e7 | 0.712315 | 0.356157 | − | 0.934426i | \(-0.384087\pi\) | ||||
0.356157 | + | 0.934426i | \(0.384087\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.80847e7 | −1.70151 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.35127e7 | 0.813379 | 0.406690 | − | 0.913566i | \(-0.366683\pi\) | ||||
0.406690 | + | 0.913566i | \(0.366683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.83079e7 | 1.09493 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −233167. | −0.0138553 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.37351e6 | −0.376301 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −740082. | −0.0434162 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.17470e7 | 1.85054 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 115210. | 0.00667294 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.08780e7 | 1.20158 | 0.600789 | − | 0.799407i | \(-0.294853\pi\) | ||||
0.600789 | + | 0.799407i | \(0.294853\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.39862e7 | 2.51550 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.99381e7 | 1.70131 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.67881e6 | 0.546562 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 344632. | 0.0193392 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.17024e7 | −0.652573 | −0.326286 | − | 0.945271i | \(-0.605797\pi\) | ||||
−0.326286 | + | 0.945271i | \(0.605797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.43260e6 | −0.0793888 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.49958e7 | −1.37653 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.01444e6 | −0.219703 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −99809.1 | −0.00542851 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.07901e7 | −1.66428 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.76467e7 | −1.48516 | −0.742578 | − | 0.669760i | \(-0.766397\pi\) | ||||
−0.742578 | + | 0.669760i | \(0.766397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.32113e6 | 0.444253 | 0.222126 | − | 0.975018i | \(-0.428700\pi\) | ||||
0.222126 | + | 0.975018i | \(0.428700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.31375e7 | 1.75830 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −236623. | −0.0124785 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.12768e6 | −0.0591059 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.41161e7 | 2.29820 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.01626e6 | 0.415063 | 0.207531 | − | 0.978228i | \(-0.433457\pi\) | ||||
0.207531 | + | 0.978228i | \(0.433457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.63830e6 | −0.238704 | −0.119352 | − | 0.992852i | \(-0.538082\pi\) | ||||
−0.119352 | + | 0.992852i | \(0.538082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.14011e6 | 0.262928 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.55667e6 | −0.282521 | −0.141261 | − | 0.989972i | \(-0.545116\pi\) | ||||
−0.141261 | + | 0.989972i | \(0.545116\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.47536e7 | 1.25098 | 0.625491 | − | 0.780231i | \(-0.284899\pi\) | ||||
0.625491 | + | 0.780231i | \(0.284899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.93046e7 | −2.47676 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.05302e6 | 0.402111 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −311159. | −0.0154442 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.07367e7 | 1.02312 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.24512e7 | 1.59157 | 0.795785 | − | 0.605579i | \(-0.207058\pi\) | ||||
0.795785 | + | 0.605579i | \(0.207058\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.99451e7 | 2.92256 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.80067e7 | 1.35735 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47468.6 | −0.00228699 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.60995e7 | 1.25004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.14899e7 | 1.49935 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 73375.3 | 0.00347317 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.47564e7 | 1.16497 | 0.582485 | − | 0.812841i | \(-0.302080\pi\) | ||||
0.582485 | + | 0.812841i | \(0.302080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −107043. | −0.00500777 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.28652e7 | 0.598363 | 0.299182 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299182 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.98227e6 | −0.0916601 | −0.0458300 | − | 0.998949i | \(-0.514593\pi\) | ||||
−0.0458300 | + | 0.998949i | \(0.514593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.35844e7 | −2.00366 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.11840e6 | 0.142529 | 0.0712647 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712647 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 67863.0 | 0.00308384 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.19435e7 | 0.991421 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.30613e6 | −0.283279 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.54596e7 | 1.58376 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.63772e6 | 0.205953 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −475282. | −0.0209861 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.15790e7 | −0.947398 | −0.473699 | − | 0.880687i | \(-0.657082\pi\) | ||||
−0.473699 | + | 0.880687i | \(0.657082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.52218e6 | 0.284722 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.27720e7 | −0.554393 | −0.277196 | − | 0.960813i | \(-0.589405\pi\) | ||||
−0.277196 | + | 0.960813i | \(0.589405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.80113e6 | −0.379871 | −0.189936 | − | 0.981797i | \(-0.560828\pi\) | ||||
−0.189936 | + | 0.981797i | \(0.560828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −596716. | −0.0256100 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.47818e7 | 1.48437 | 0.742187 | − | 0.670192i | \(-0.233788\pi\) | ||||
0.742187 | + | 0.670192i | \(0.233788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.77214e7 | −2.02516 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −311366. | −0.0131394 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.18490e6 | −0.0497225 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47070.8 | 0.00196424 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.26610e7 | −0.940368 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.25531e7 | 2.16870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.22168e7 | 0.911737 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.71150e6 | −0.314716 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −141263. | −0.00573334 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.91865e7 | −0.774420 | −0.387210 | − | 0.921992i | \(-0.626561\pi\) | ||||
−0.387210 | + | 0.921992i | \(0.626561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.11390e7 | 1.65137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −834307. | −0.0333066 | −0.0166533 | − | 0.999861i | \(-0.505301\pi\) | ||||
−0.0166533 | + | 0.999861i | \(0.505301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.99512e6 | −0.0792121 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −160597. | −0.00634139 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.12598e7 | 0.442187 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.11037e7 | −0.433690 | −0.216845 | − | 0.976206i | \(-0.569577\pi\) | ||||
−0.216845 | + | 0.976206i | \(0.569577\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.91080e7 | −1.51921 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.76826e6 | 0.300137 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 174698. | 0.00671324 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.31315e7 | 1.26631 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.03857e7 | −0.394816 | −0.197408 | − | 0.980321i | \(-0.563252\pi\) | ||||
−0.197408 | + | 0.980321i | \(0.563252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.66061e6 | 0.251849 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.64087e7 | 0.617120 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22117.2 | −0.000827372 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.10627e7 | −0.783729 | −0.391865 | − | 0.920023i | \(-0.628170\pi\) | ||||
−0.391865 | + | 0.920023i | \(0.628170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.33209e6 | 0.197348 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.67199e7 | −1.35185 | −0.675924 | − | 0.736971i | \(-0.736255\pi\) | ||||
−0.675924 | + | 0.736971i | \(0.736255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.37156e7 | 0.502267 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −269159. | −0.00980457 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.07332e7 | −0.388914 | −0.194457 | − | 0.980911i | \(-0.562294\pi\) | ||||
−0.194457 | + | 0.980911i | \(0.562294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.21375e7 | 1.51881 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.66428e6 | 0.346512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.10240e7 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238772\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238772\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 170465. | 0.00604821 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.47547e7 | 0.520776 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.22434e7 | −0.781005 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.69795e6 | 0.199026 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.57683e7 | −2.63283 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39176.6 | −0.00135428 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.93253e7 | −1.00850 | −0.504251 | − | 0.863557i | \(-0.668231\pi\) | ||||
−0.504251 | + | 0.863557i | \(0.668231\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.12638e7 | −0.385368 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.44554e6 | −0.117276 | −0.0586381 | − | 0.998279i | \(-0.518676\pi\) | ||||
−0.0586381 | + | 0.998279i | \(0.518676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.36601e7 | −1.47843 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.39530e7 | −1.81763 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.77647e7 | 1.26576 | 0.632878 | − | 0.774252i | \(-0.281874\pi\) | ||||
0.632878 | + | 0.774252i | \(0.281874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.27162e6 | −0.142441 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.35311e7 | 2.10772 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.69058e7 | −0.558024 | −0.279012 | − | 0.960288i | \(-0.590007\pi\) | ||||
−0.279012 | + | 0.960288i | \(0.590007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 81358.2 | 0.00267184 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.10277e6 | −0.264753 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.42673e6 | 0.0788915 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.83818e7 | −0.594570 | −0.297285 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297285 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.08016e7 | −1.31312 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 70662.3 | 0.00226272 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.05937e7 | −0.656139 | −0.328069 | − | 0.944654i | \(-0.606398\pi\) | ||||
−0.328069 | + | 0.944654i | \(0.606398\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 197874. | 0.00627298 |
(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 | 688.6.a.h.1.2 | 10 | ||
4.3 | odd | 2 | 43.6.a.b.1.7 | ✓ | 10 | ||
12.11 | even | 2 | 387.6.a.e.1.4 | 10 | |||
20.19 | odd | 2 | 1075.6.a.b.1.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.b.1.7 | ✓ | 10 | 4.3 | odd | 2 | ||
387.6.a.e.1.4 | 10 | 12.11 | even | 2 | |||
688.6.a.h.1.2 | 10 | 1.1 | even | 1 | trivial | ||
1075.6.a.b.1.4 | 10 | 20.19 | odd | 2 |