Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(81,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.81");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{90}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 81.8 | ||
Root | \(-2.80358 + 2.85306i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.81 |
Dual form | 160.6.d.a.81.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 10.7455i | − 0.689323i | −0.938727 | − | 0.344662i | \(-0.887994\pi\) | ||||
0.938727 | − | 0.344662i | \(-0.112006\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −198.733 | −1.53294 | −0.766470 | − | 0.642280i | \(-0.777989\pi\) | ||||
−0.766470 | + | 0.642280i | \(0.777989\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 127.535 | 0.524833 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 85.9303i | − 0.214124i | −0.994252 | − | 0.107062i | \(-0.965856\pi\) | ||||
0.994252 | − | 0.107062i | \(-0.0341443\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 407.120i | 0.668134i | 0.942549 | + | 0.334067i | \(0.108421\pi\) | ||||
−0.942549 | + | 0.334067i | \(0.891579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 268.637 | 0.308275 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1206.02 | 1.01212 | 0.506062 | − | 0.862497i | \(-0.331101\pi\) | ||||
0.506062 | + | 0.862497i | \(0.331101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 206.036i | 0.130936i | 0.997855 | + | 0.0654680i | \(0.0208540\pi\) | ||||
−0.997855 | + | 0.0654680i | \(0.979146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2135.48i | 1.05669i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2595.25 | 1.02296 | 0.511482 | − | 0.859294i | \(-0.329097\pi\) | ||||
0.511482 | + | 0.859294i | \(0.329097\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3981.57i | − 1.05110i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6195.27i | 1.36794i | 0.729512 | + | 0.683968i | \(0.239747\pi\) | ||||
−0.729512 | + | 0.683968i | \(0.760253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1862.42 | 0.348075 | 0.174038 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174038 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −923.363 | −0.147600 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 4968.33i | − 0.685552i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 14708.1i | − 1.76625i | −0.469142 | − | 0.883123i | \(-0.655437\pi\) | ||||
0.469142 | − | 0.883123i | \(-0.344563\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4374.70 | 0.460560 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18098.0 | 1.68140 | 0.840699 | − | 0.541503i | \(-0.182144\pi\) | ||||
0.840699 | + | 0.541503i | \(0.182144\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9260.46i | 0.763768i | 0.924210 | + | 0.381884i | \(0.124725\pi\) | ||||
−0.924210 | + | 0.381884i | \(0.875275\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3188.36i | 0.234713i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24363.7 | 1.60879 | 0.804395 | − | 0.594095i | \(-0.202490\pi\) | ||||
0.804395 | + | 0.594095i | \(0.202490\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22687.9 | 1.34991 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 12959.3i | − 0.697680i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 12764.8i | − 0.624202i | −0.950049 | − | 0.312101i | \(-0.898967\pi\) | ||||
0.950049 | − | 0.312101i | \(-0.101033\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2148.26 | 0.0957590 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2213.96 | 0.0902572 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20719.7i | 0.774913i | 0.921888 | + | 0.387457i | \(0.126646\pi\) | ||||
−0.921888 | + | 0.387457i | \(0.873354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11368.5i | 0.391183i | 0.980686 | + | 0.195591i | \(0.0626626\pi\) | ||||
−0.980686 | + | 0.195591i | \(0.937337\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25345.3 | −0.804538 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10178.0 | −0.298799 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62614.9i | 1.70408i | 0.523475 | + | 0.852041i | \(0.324635\pi\) | ||||
−0.523475 | + | 0.852041i | \(0.675365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 27887.3i | − 0.705153i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61208.1 | 1.44100 | 0.720498 | − | 0.693457i | \(-0.243913\pi\) | ||||
0.720498 | + | 0.693457i | \(0.243913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 23236.4 | 0.510342 | 0.255171 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255171 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6715.93i | 0.137865i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17077.2i | 0.328239i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29172.5 | −0.525904 | −0.262952 | − | 0.964809i | \(-0.584696\pi\) | ||||
−0.262952 | + | 0.964809i | \(0.584696\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11793.1 | −0.199717 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 48099.7i | − 0.766386i | −0.923668 | − | 0.383193i | \(-0.874824\pi\) | ||||
0.923668 | − | 0.383193i | \(-0.125176\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 30150.6i | 0.452635i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 66571.2 | 0.942950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30118.4 | 0.403048 | 0.201524 | − | 0.979484i | \(-0.435411\pi\) | ||||
0.201524 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 80908.2i | − 1.02421i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 20012.6i | − 0.239937i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5150.90 | −0.0585563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −113676. | −1.22670 | −0.613351 | − | 0.789811i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789811i | \(0.710179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 10959.1i | − 0.112379i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 21867.4i | 0.213302i | 0.994297 | + | 0.106651i | \(0.0340127\pi\) | ||||
−0.994297 | + | 0.106651i | \(0.965987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −156608. | −1.45452 | −0.727262 | − | 0.686360i | \(-0.759208\pi\) | ||||
−0.727262 | + | 0.686360i | \(0.759208\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −53387.1 | −0.472567 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 91401.1i | − 0.771777i | −0.922545 | − | 0.385889i | \(-0.873895\pi\) | ||||
0.922545 | − | 0.385889i | \(-0.126105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 48973.9i | 0.394819i | 0.980321 | + | 0.197410i | \(0.0632529\pi\) | ||||
−0.980321 | + | 0.197410i | \(0.936747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −158045. | −1.21751 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −153638. | −1.13188 | −0.565942 | − | 0.824445i | \(-0.691487\pi\) | ||||
−0.565942 | + | 0.824445i | \(0.691487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 64881.4i | 0.457483i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 51921.8i | 0.350659i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −239677. | −1.55152 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 153667. | 0.954151 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 194472.i | − 1.15903i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 15625.0i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 122092. | 0.671705 | 0.335852 | − | 0.941915i | \(-0.390976\pi\) | ||||
0.335852 | + | 0.941915i | \(0.390976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 99508.2 | 0.526483 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 179438.i | 0.913560i | 0.889580 | + | 0.456780i | \(0.150997\pi\) | ||||
−0.889580 | + | 0.456780i | \(0.849003\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 40946.2i | − 0.200717i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 99539.3 | 0.470068 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −327113. | −1.48900 | −0.744502 | − | 0.667620i | \(-0.767313\pi\) | ||||
−0.744502 | + | 0.667620i | \(0.767313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 359354.i | 1.57756i | 0.614678 | + | 0.788778i | \(0.289286\pi\) | ||||
−0.614678 | + | 0.788778i | \(0.710714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 261800.i | − 1.10898i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34983.9 | 0.143063 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −154882. | −0.611759 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 243792.i | − 0.930522i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 494795.i | 1.82583i | 0.408152 | + | 0.912914i | \(0.366173\pi\) | ||||
−0.408152 | + | 0.912914i | \(0.633827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9960.81 | 0.0355511 | 0.0177755 | − | 0.999842i | \(-0.494342\pi\) | ||||
0.0177755 | + | 0.999842i | \(0.494342\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 153810. | 0.531196 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 46560.5i | 0.155664i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 243819.i | − 0.789439i | −0.918802 | − | 0.394719i | \(-0.870842\pi\) | ||||
0.918802 | − | 0.394719i | \(-0.129158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −137164. | −0.430277 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −515763. | −1.56814 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 268182.i | 0.790608i | 0.918550 | + | 0.395304i | \(0.129361\pi\) | ||||
−0.918550 | + | 0.395304i | \(0.870639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 23084.1i | − 0.0660089i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17404.1 | 0.0482905 | 0.0241452 | − | 0.999708i | \(-0.492314\pi\) | ||||
0.0241452 | + | 0.999708i | \(0.492314\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 205547. | 0.553597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26276.7i | 0.0687195i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 534365.i | − 1.35745i | −0.734394 | − | 0.678723i | \(-0.762534\pi\) | ||||
0.734394 | − | 0.678723i | \(-0.237466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 124208. | 0.306588 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 222643. | 0.534166 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 342831.i | 0.799738i | 0.916572 | + | 0.399869i | \(0.130944\pi\) | ||||
−0.916572 | + | 0.399869i | \(0.869056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 593221.i | − 1.34592i | −0.739678 | − | 0.672961i | \(-0.765022\pi\) | ||||
0.739678 | − | 0.672961i | \(-0.234978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 122160. | 0.269651 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 367701. | 0.789889 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 103634.i | − 0.216720i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 791271.i | 1.61128i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1448.97 | 0.00287392 | 0.00143696 | − | 0.999999i | \(-0.499543\pi\) | ||||
0.00143696 | + | 0.999999i | \(0.499543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 888526. | 1.71703 | 0.858513 | − | 0.512791i | \(-0.171388\pi\) | ||||
0.858513 | + | 0.512791i | \(0.171388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 109367.i | 0.205969i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 356565.i | 0.654595i | 0.944921 | + | 0.327298i | \(0.106138\pi\) | ||||
−0.944921 | + | 0.327298i | \(0.893862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 406304. | 0.727307 | 0.363654 | − | 0.931534i | \(-0.381529\pi\) | ||||
0.363654 | + | 0.931534i | \(0.381529\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 672827. | 1.17466 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.23121e6i | − 2.09696i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 452450.i | 0.751944i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 330984. | 0.536886 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17704.7 | 0.0280365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 582646.i | − 0.900945i | −0.892790 | − | 0.450473i | \(-0.851256\pi\) | ||||
0.892790 | − | 0.450473i | \(-0.148744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 657711.i | − 0.993312i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −231512. | −0.341568 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −370125. | −0.533579 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 249686.i | − 0.351791i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 490996.i | 0.676234i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 789020. | 1.06249 | 0.531246 | − | 0.847218i | \(-0.321724\pi\) | ||||
0.531246 | + | 0.847218i | \(0.321724\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −79709.1 | −0.104967 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 872412.i | 1.12372i | 0.827233 | + | 0.561858i | \(0.189913\pi\) | ||||
−0.827233 | + | 0.561858i | \(0.810087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 404072.i | − 0.509178i | −0.967049 | − | 0.254589i | \(-0.918060\pi\) | ||||
0.967049 | − | 0.254589i | \(-0.0819402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 183503. | 0.226263 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −198854. | −0.239963 | −0.119982 | − | 0.992776i | \(-0.538284\pi\) | ||||
−0.119982 | + | 0.992776i | \(0.538284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 609093.i | 0.719472i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 313473.i | 0.362518i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 388433. | 0.439868 | 0.219934 | − | 0.975515i | \(-0.429416\pi\) | ||||
0.219934 | + | 0.975515i | \(0.429416\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −714818. | −0.792780 | −0.396390 | − | 0.918082i | \(-0.629737\pi\) | ||||
−0.396390 | + | 0.918082i | \(0.629737\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 840800.i | − 0.913434i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 567197.i | 0.603696i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −83881.3 | −0.0874828 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −516855. | −0.528287 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.57948e6i | − 1.58244i | −0.611529 | − | 0.791222i | \(-0.709445\pi\) | ||||
0.611529 | − | 0.791222i | \(-0.290555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 223011.i | − 0.219041i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 323983. | 0.312012 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.80546e6 | 1.70512 | 0.852558 | − | 0.522632i | \(-0.175050\pi\) | ||||
0.852558 | + | 0.522632i | \(0.175050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.92298e6i | 2.70755i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 790111.i | 0.717938i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −185503. | −0.165372 | −0.0826860 | − | 0.996576i | \(-0.526350\pi\) | ||||
−0.0826860 | + | 0.996576i | \(0.526350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 319121. | 0.279152 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 323637.i | − 0.277830i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.12615e6i | 0.948887i | 0.880286 | + | 0.474444i | \(0.157351\pi\) | ||||
−0.880286 | + | 0.474444i | \(0.842649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −157610. | −0.130365 | −0.0651825 | − | 0.997873i | \(-0.520763\pi\) | ||||
−0.0651825 | + | 0.997873i | \(0.520763\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −869398. | −0.706012 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 53706.4i | 0.0428247i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.93510e6i | − 1.51532i | −0.652650 | − | 0.757660i | \(-0.726343\pi\) | ||||
0.652650 | − | 0.757660i | \(-0.273657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 237523. | 0.182682 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 394102. | 0.297744 | 0.148872 | − | 0.988856i | \(-0.452436\pi\) | ||||
0.148872 | + | 0.988856i | \(0.452436\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 538592.i | − 0.399755i | −0.979821 | − | 0.199878i | \(-0.935946\pi\) | ||||
0.979821 | − | 0.199878i | \(-0.0640545\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 55348.9i | 0.0403642i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.59667e6 | −2.57748 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34635.4 | 0.0243936 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.22150e6i | 0.845594i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.25662e6i | − 0.855134i | −0.903984 | − | 0.427567i | \(-0.859371\pi\) | ||||
0.903984 | − | 0.427567i | \(-0.140629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −517992. | −0.346552 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −342138. | −0.225066 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.05658e6i | 0.683477i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.84036e6i | − 1.17081i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 234976. | 0.147034 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −284213. | −0.174942 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 227401.i | 0.137704i | 0.997627 | + | 0.0688519i | \(0.0219336\pi\) | ||||
−0.997627 | + | 0.0688519i | \(0.978066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.68283e6i | 1.00264i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.13530e6 | −0.665593 | −0.332796 | − | 0.942999i | \(-0.607992\pi\) | ||||
−0.332796 | + | 0.942999i | \(0.607992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.32737e6 | −1.34278 | −0.671390 | − | 0.741105i | \(-0.734302\pi\) | ||||
−0.671390 | + | 0.741105i | \(0.734302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 633633.i | − 0.359800i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.50212e6i | − 0.839570i | −0.907624 | − | 0.419785i | \(-0.862106\pi\) | ||||
0.907624 | − | 0.419785i | \(-0.137894\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 532362. | 0.292907 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −982149. | −0.532004 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 248484.i | 0.132523i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 254450.i | − 0.133627i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 526248. | 0.272158 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.84188e6 | −2.46618 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.72477e6i | − 1.36697i | −0.729964 | − | 0.683486i | \(-0.760463\pi\) | ||||
0.729964 | − | 0.683486i | \(-0.239537\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.87578e6i | − 0.926984i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.56537e6 | −0.762089 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.04270e6 | 0.979784 | 0.489892 | − | 0.871783i | \(-0.337036\pi\) | ||||
0.489892 | + | 0.871783i | \(0.337036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.65091e6i | 0.780234i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 160038.i | − 0.0745312i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.16872e6 | −0.536385 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 697182. | 0.315354 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.57456e6i | − 1.14783i | −0.818914 | − | 0.573916i | \(-0.805423\pi\) | ||||
0.818914 | − | 0.573916i | \(-0.194577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.97991e6i | 0.870125i | 0.900400 | + | 0.435062i | \(0.143274\pi\) | ||||
−0.900400 | + | 0.435062i | \(0.856726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.62098e6 | 0.702278 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.02870e6 | −0.439394 | −0.219697 | − | 0.975568i | \(-0.570507\pi\) | ||||
−0.219697 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.53020e6i | 0.644433i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.57544e6i | 1.06950i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 979196. | 0.400990 | 0.200495 | − | 0.979695i | \(-0.435745\pi\) | ||||
0.200495 | + | 0.979695i | \(0.435745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.43365e6 | 0.982856 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.65123e6i | − 0.657719i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 580909.i | 0.228232i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.07920e6 | 0.418250 | 0.209125 | − | 0.977889i | \(-0.432938\pi\) | ||||
0.209125 | + | 0.977889i | \(0.432938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.30812e6 | 0.882454 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.53679e6i | 0.956864i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.65291e6i | 1.35946i | 0.733461 | + | 0.679731i | \(0.237904\pi\) | ||||
−0.733461 | + | 0.679731i | \(0.762096\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −167898. | −0.0616550 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.52222e6 | −0.913964 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 2.99413e6i | − 1.07071i | −0.844627 | − | 0.535355i | \(-0.820178\pi\) | ||||
0.844627 | − | 0.535355i | \(-0.179822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.31194e6i | − 0.463022i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.15754e6 | −1.44824 | −0.724119 | − | 0.689675i | \(-0.757753\pi\) | ||||
−0.724119 | + | 0.689675i | \(0.757753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −426930. | −0.146793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.18103e6i | 0.400851i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.08421e6i | 0.363278i | 0.983365 | + | 0.181639i | \(0.0581402\pi\) | ||||
−0.983365 | + | 0.181639i | \(0.941860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.12994e6 | 1.03537 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.92815e6 | 0.629739 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 729313.i | − 0.235191i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.11966e6i | 0.993415i | 0.867918 | + | 0.496708i | \(0.165458\pi\) | ||||
−0.867918 | + | 0.496708i | \(0.834542\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −439987. | −0.138359 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.18432e6 | −0.988908 | −0.494454 | − | 0.869204i | \(-0.664632\pi\) | ||||
−0.494454 | + | 0.869204i | \(0.664632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 758228.i | 0.232561i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 294827.i | − 0.0893160i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.26387e6 | −0.378195 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.76338e6 | 1.11242 | 0.556211 | − | 0.831041i | \(-0.312255\pi\) | ||||
0.556211 | + | 0.831041i | \(0.312255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.51499e6i | 1.02641i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.11769e6i | − 1.18790i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20249e6 | 0.342738 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.86143e6 | 1.08745 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.73449e6i | − 0.760924i | −0.924797 | − | 0.380462i | \(-0.875765\pi\) | ||||
0.924797 | − | 0.380462i | \(-0.124235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 450371.i | − 0.123841i | −0.998081 | − | 0.0619206i | \(-0.980277\pi\) | ||||
0.998081 | − | 0.0619206i | \(-0.0197225\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.10722e6 | 0.844346 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −753765. | −0.202425 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.25930e6i | − 0.599659i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 375919.i | − 0.0986169i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −517327. | −0.134144 | −0.0670721 | − | 0.997748i | \(-0.521366\pi\) | ||||
−0.0670721 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.24867e6 | 0.576375 | 0.288188 | − | 0.957574i | \(-0.406947\pi\) | ||||
0.288188 | + | 0.957574i | \(0.406947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.66428e6i | 0.421700i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 534716.i | 0.133943i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −862979. | −0.213717 | −0.106858 | − | 0.994274i | \(-0.534079\pi\) | ||||
−0.106858 | + | 0.994274i | \(0.534079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.89349e6 | 0.708476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 972329.i | − 0.235399i | −0.993049 | − | 0.117699i | \(-0.962448\pi\) | ||||
0.993049 | − | 0.117699i | \(-0.0375519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 752959.i | 0.180248i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.31682e6 | 1.25859 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28297.9 | −0.00662428 | −0.00331214 | − | 0.999995i | \(-0.501054\pi\) | ||||
−0.00331214 | + | 0.999995i | \(0.501054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.55516e6i | − 0.360027i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 107034.i | − 0.0245062i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.02270e6 | 0.458041 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 456269. | 0.102195 | 0.0510976 | − | 0.998694i | \(-0.483728\pi\) | ||||
0.0510976 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.80187e6i | − 1.06385i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11198.5i | 0.00245418i | 0.999999 | + | 0.00122709i | \(0.000390595\pi\) | ||||
−0.999999 | + | 0.00122709i | \(0.999609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.93015e6 | 1.71921 | 0.859605 | − | 0.510959i | \(-0.170710\pi\) | ||||
0.859605 | + | 0.510959i | \(0.170710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 500315. | 0.107303 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.59151e6i | 1.39860i | 0.714830 | + | 0.699298i | \(0.246504\pi\) | ||||
−0.714830 | + | 0.699298i | \(0.753496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.24437e7i | − 2.61226i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.61995e6 | −0.544179 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 795754. | 0.163541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 128772.i | − 0.0261872i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.62796e6i | − 0.327602i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.60702e6 | 0.320023 | 0.160012 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160012 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.98794e6 | 1.18009 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.54213e6i | 1.08096i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2.84190e6i | − 0.548597i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.81230e6 | 0.346264 | 0.173132 | − | 0.984899i | \(-0.444611\pi\) | ||||
0.173132 | + | 0.984899i | \(0.444611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.88175e6 | 0.544985 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 292083.i | − 0.0546768i | −0.999626 | − | 0.0273384i | \(-0.991297\pi\) | ||||
0.999626 | − | 0.0273384i | \(-0.00870317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.47164e6i | 1.38452i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 273977. | 0.0502575 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.21641e7 | −2.20896 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.47619e6i | 1.52388i | 0.647650 | + | 0.761938i | \(0.275752\pi\) | ||||
−0.647650 | + | 0.761938i | \(0.724248\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 187016.i | − 0.0332877i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.07725e6 | −0.366074 | −0.183037 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183037 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −546686. | −0.0953914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.20870e6i | − 0.381607i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 739081.i | − 0.126444i | −0.997999 | − | 0.0632219i | \(-0.979862\pi\) | ||||
0.997999 | − | 0.0632219i | \(-0.0201376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.61784e6 | −0.782324 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 820347. | 0.137627 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.91520e6i | − 0.650483i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.09358e6i | − 0.344480i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.74201e6 | −0.935719 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.18449e6 | −1.15958 | −0.579791 | − | 0.814765i | \(-0.696866\pi\) | ||||
−0.579791 | + | 0.814765i | \(0.696866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.94687e6i | − 0.311231i | −0.987818 | − | 0.155616i | \(-0.950264\pi\) | ||||
0.987818 | − | 0.155616i | \(-0.0497361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.33468e6i | − 0.211338i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.24612e6 | 0.352295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 299003. | 0.0464554 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.64247e6i | 0.406700i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.36804e6i | 1.12340i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.28503e6 | 0.345149 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.68389e6 | 0.551278 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.94958e6i | − 0.289047i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.18585e7i | 1.74195i | 0.491330 | + | 0.870973i | \(0.336511\pi\) | ||||
−0.491330 | + | 0.870973i | \(0.663489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.37445e6 | −0.927776 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.22435e6 | −0.176569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.10343e6i | − 0.300580i | −0.988642 | − | 0.150290i | \(-0.951979\pi\) | ||||
0.988642 | − | 0.150290i | \(-0.0480207\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.44988e6i | 0.205306i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.27645e6 | −0.179112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.79755e6 | 0.806179 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 3.95113e6i | − 0.544489i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.61967e6i | − 0.630918i | −0.948939 | − | 0.315459i | \(-0.897842\pi\) | ||||
0.948939 | − | 0.315459i | \(-0.102158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.77012e6 | −0.510300 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.11360e6 | −0.149390 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.23357e7i | 1.64019i | 0.572227 | + | 0.820096i | \(0.306080\pi\) | ||||
−0.572227 | + | 0.820096i | \(0.693920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.84095e6i | − 0.506194i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.34367e6 | 0.306154 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.85222e6 | 1.01674 | 0.508372 | − | 0.861138i | \(-0.330247\pi\) | ||||
0.508372 | + | 0.861138i | \(0.330247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.14825e7i | − 1.47383i | −0.675984 | − | 0.736916i | \(-0.736281\pi\) | ||||
0.675984 | − | 0.736916i | \(-0.263719\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 15569.8i | − 0.00198106i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.62203e6 | −0.204593 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.10508e7 | −1.38183 | −0.690913 | − | 0.722938i | \(-0.742791\pi\) | ||||
−0.690913 | + | 0.722938i | \(0.742791\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9.54765e6i | − 1.18359i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.55901e6i | 1.17482i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.09689e6 | −0.133656 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.29805e6 | −0.156820 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.22974e6i | 0.147305i | 0.997284 | + | 0.0736524i | \(0.0234655\pi\) | ||||
−0.997284 | + | 0.0736524i | \(0.976534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 383725.i | 0.0455756i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.83146e6 | 0.451228 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.14520e6 | 0.484071 | 0.242035 | − | 0.970267i | \(-0.422185\pi\) | ||||
0.242035 | + | 0.970267i | \(0.422185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 5.99192e6i | − 0.693863i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.36593e6i | − 0.501350i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.54313e7 | −1.75726 | −0.878629 | − | 0.477505i | \(-0.841541\pi\) | ||||
−0.878629 | + | 0.477505i | \(0.841541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.20526e7 | −1.36111 | −0.680556 | − | 0.732696i | \(-0.738262\pi\) | ||||
−0.680556 | + | 0.732696i | \(0.738262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.98556e6i | 0.894359i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.84167e6i | 0.426709i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.95296e6 | −0.876107 | −0.438053 | − | 0.898949i | \(-0.644332\pi\) | ||||
−0.438053 | + | 0.898949i | \(0.644332\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.32299e7 | −1.44549 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.91895e6i | 1.07489i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.04301e7i | 1.12108i | 0.828128 | + | 0.560538i | \(0.189406\pi\) | ||||
−0.828128 | + | 0.560538i | \(0.810594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.86179e6 | 0.518333 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.91606e6 | −0.731384 | −0.365692 | − | 0.930736i | \(-0.619168\pi\) | ||||
−0.365692 | + | 0.930736i | \(0.619168\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.15145e7i | − 1.20786i | −0.797037 | − | 0.603931i | \(-0.793600\pi\) | ||||
0.797037 | − | 0.603931i | \(-0.206400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1.03332e7i | − 1.07524i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.98552e6 | −0.617848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 190246.i | − 0.0193262i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.77383e7i | − 1.78766i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.76766e6 | −0.576669 | −0.288334 | − | 0.957530i | \(-0.593101\pi\) | ||||
−0.288334 | + | 0.957530i | \(0.593101\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.26081e6 | −0.621042 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.05230e6i | 0.300396i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.23668e6i | 0.901919i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.80614e6 | 0.756283 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −518990. | −0.0498901 | −0.0249450 | − | 0.999689i | \(-0.507941\pi\) | ||||
−0.0249450 | + | 0.999689i | \(0.507941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.52874e6i | − 0.622733i | −0.950290 | − | 0.311367i | \(-0.899213\pi\) | ||||
0.950290 | − | 0.311367i | \(-0.100787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.48770e6i | 0.235450i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.41651e6 | 0.602613 | 0.301306 | − | 0.953527i | \(-0.402577\pi\) | ||||
0.301306 | + | 0.953527i | \(0.402577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.78045e6 | 0.165927 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.97717e6i | 0.367808i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 9.11065e6i | − 0.836116i | −0.908420 | − | 0.418058i | \(-0.862711\pi\) | ||||
0.908420 | − | 0.418058i | \(-0.137289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.48596e6 | −0.408557 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.96344e6 | 0.267844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.97306e7i | − 1.76981i | −0.465775 | − | 0.884903i | \(-0.654224\pi\) | ||||
0.465775 | − | 0.884903i | \(-0.345776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.04530e6i | 0.805228i | 0.915370 | + | 0.402614i | \(0.131898\pi\) | ||||
−0.915370 | + | 0.402614i | \(0.868102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.27599e6 | 0.466144 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.02365e6 | 0.0897634 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.60783e7i | 1.39935i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 8.47840e6i | − 0.732401i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 976900. | 0.0837614 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.11387e7 | −0.947974 | −0.473987 | − | 0.880532i | \(-0.657186\pi\) | ||||
−0.473987 | + | 0.880532i | \(0.657186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.48848e6i | 0.210221i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.13338e7i | 0.950395i | 0.879879 | + | 0.475198i | \(0.157623\pi\) | ||||
−0.879879 | + | 0.475198i | \(0.842377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.25912e7 | 1.88046 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.37449e6 | 0.774604 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.06005e7i | 0.869514i | 0.900548 | + | 0.434757i | \(0.143166\pi\) | ||||
−0.900548 | + | 0.434757i | \(0.856834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.17782e6i | − 0.665903i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.34195e6 | −0.350988 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.19681e6 | 0.417051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18528e7i | 0.944331i | 0.881510 | + | 0.472165i | \(0.156527\pi\) | ||||
−0.881510 | + | 0.472165i | \(0.843473\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.17793e6i | 0.172271i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.98384e6 | −0.705505 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.18266e7 | 1.70178 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.13678e6i | 0.165412i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.42728e7i | − 1.09702i | −0.836144 | − | 0.548511i | \(-0.815195\pi\) | ||||
0.836144 | − | 0.548511i | \(-0.184805\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.03039e6 | 0.231265 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.54500e6 | 0.495949 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.34578e6i | − 0.326979i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.40052e7i | − 1.04635i | −0.852227 | − | 0.523173i | \(-0.824748\pi\) | ||||
0.852227 | − | 0.523173i | \(-0.175252\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.72050e6 | −0.276012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.83345e6 | 0.356069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 874598.i | 0.0639799i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4.17391e6i | − 0.303211i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.28309e6 | −0.525404 | −0.262702 | − | 0.964877i | \(-0.584614\pi\) | ||||
−0.262702 | + | 0.964877i | \(0.584614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.11232e7 | 2.22970 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.68107e6i | 0.546482i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.87205e6i | − 0.273587i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.41888e6 | −0.239910 | −0.119955 | − | 0.992779i | \(-0.538275\pi\) | ||||
−0.119955 | + | 0.992779i | \(0.538275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.19005e7 | −0.829368 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.11683e7i | 0.773028i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.11502e6i | 0.145397i | 0.997354 | + | 0.0726983i | \(0.0231610\pi\) | ||||
−0.997354 | + | 0.0726983i | \(0.976839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.09481e6 | 0.416142 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.38051e6 | 0.364884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.97420e6i | 0.335052i | 0.985868 | + | 0.167526i | \(0.0535778\pi\) | ||||
−0.985868 | + | 0.167526i | \(0.946422\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 901345.i | 0.0603039i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.04483e6 | −0.401709 | −0.200855 | − | 0.979621i | \(-0.564372\pi\) | ||||
−0.200855 | + | 0.979621i | \(0.564372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.23699e7 | −0.816535 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.13437e6i | − 0.402225i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.81644e7i | 1.18309i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.14521e7 | 1.38794 | 0.693970 | − | 0.720004i | \(-0.255860\pi\) | ||||
0.693970 | + | 0.720004i | \(0.255860\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.69722e7 | −1.09082 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 249020.i | 0.0158989i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22790e7i | 0.778794i | 0.921070 | + | 0.389397i | \(0.127317\pi\) | ||||
−0.921070 | + | 0.389397i | \(0.872683\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.39636e6 | −0.150990 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.38648e7 | −0.867867 | −0.433933 | − | 0.900945i | \(-0.642875\pi\) | ||||
−0.433933 | + | 0.900945i | \(0.642875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.73273e6i | − 0.605234i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.84524e6i | 0.237558i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.43539e6 | −0.517746 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.92248e6 | 0.117232 | 0.0586158 | − | 0.998281i | \(-0.481331\pi\) | ||||
0.0586158 | + | 0.998281i | \(0.481331\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.94005e7i | − 1.17538i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.66728e7i | 1.60554i | 0.596291 | + | 0.802768i | \(0.296640\pi\) | ||||
−0.596291 | + | 0.802768i | \(0.703360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.16401e6 | −0.0696151 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.14088e7 | 1.86638 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.72883e6i | 0.220155i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 5.25963e6i | − 0.308551i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.46669e7 | 1.43784 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.09548e6 | 0.353048 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.22979e6i | − 0.416092i | −0.978119 | − | 0.208046i | \(-0.933290\pi\) | ||||
0.978119 | − | 0.208046i | \(-0.0667103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.99332e6i | 0.113995i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.05329e7 | 1.73511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.62835e6 | −0.261362 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 3.42911e6i | − 0.192426i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 4.41257e6i | − 0.246062i | −0.992403 | − | 0.123031i | \(-0.960738\pi\) | ||||
0.992403 | − | 0.123031i | \(-0.0392615\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.93832e7 | 1.62829 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.84113e6 | 0.211533 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.99671e6i | − 0.109276i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.28941e7i | − 0.701295i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.21010e7 | 0.654090 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.04388e6 | 0.324672 | 0.162336 | − | 0.986736i | \(-0.448097\pi\) | ||||
0.162336 | + | 0.986736i | \(0.448097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.40664e7i | 1.28487i | 0.766340 | + | 0.642435i | \(0.222076\pi\) | ||||
−0.766340 | + | 0.642435i | \(0.777924\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.69360e6i | 0.0898636i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.70456e6 | −0.353571 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.90799e6 | −0.100005 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.03186e7i | − 0.537540i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.16527e7i | − 0.603350i | −0.953411 | − | 0.301675i | \(-0.902454\pi\) | ||||
0.953411 | − | 0.301675i | \(-0.0975458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 161156. | 0.00829369 | 0.00414684 | − | 0.999991i | \(-0.498680\pi\) | ||||
0.00414684 | + | 0.999991i | \(0.498680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 577102. | 0.0295201 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.85594e7i | − 1.45206i | −0.687661 | − | 0.726031i | \(-0.741363\pi\) | ||||
0.687661 | − | 0.726031i | \(-0.258637\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.49564e7i | 0.755859i | 0.925834 | + | 0.377929i | \(0.123364\pi\) | ||||
−0.925834 | + | 0.377929i | \(0.876636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.07936e7 | −1.04455 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.73621e7 | 1.36627 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 435104.i | 0.0215962i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7.41536e6i | − 0.365863i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.76445e7 | 0.865374 | 0.432687 | − | 0.901544i | \(-0.357565\pi\) | ||||
0.432687 | + | 0.901544i | \(0.357565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78703e7 | −0.871246 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.23482e6i | − 0.205242i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.13866e6i | 0.247576i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.05387e7 | −1.46266 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.78744e6 | −0.275561 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.81711e7i | − 1.80681i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.43356e7i | − 1.61574i | −0.589361 | − | 0.807870i | \(-0.700620\pi\) | ||||
0.589361 | − | 0.807870i | \(-0.299380\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −656917. | −0.0307323 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.27760e7 | −0.594216 | −0.297108 | − | 0.954844i | \(-0.596022\pi\) | ||||
−0.297108 | + | 0.954844i | \(0.596022\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.23768e7i | 1.49710i | 0.663077 | + | 0.748551i | \(0.269250\pi\) | ||||
−0.663077 | + | 0.748551i | \(0.730750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.86480e7i | 1.77672i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.57138e7 | −1.17527 | −0.587637 | − | 0.809125i | \(-0.699942\pi\) | ||||
−0.587637 | + | 0.809125i | \(0.699942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.33591e7 | 0.607068 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 372174.i | − 0.0168151i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.50680e6i | 0.112608i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.54917e7 | −1.13856 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.44976e7 | −0.643814 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.10521e6i | 0.137110i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.69271e6i | − 0.206027i | −0.994680 | − | 0.103014i | \(-0.967151\pi\) | ||||
0.994680 | − | 0.103014i | \(-0.0328485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.35030e7 | −0.589464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 446984. | 0.0194023 | 0.00970113 | − | 0.999953i | \(-0.496912\pi\) | ||||
0.00970113 | + | 0.999953i | \(0.496912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.04436e7i | − 1.31400i | −0.753892 | − | 0.656999i | \(-0.771826\pi\) | ||||
0.753892 | − | 0.656999i | \(-0.228174\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.56608e6i | 0.238886i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.40477e7 | 0.599508 | 0.299754 | − | 0.954016i | \(-0.403095\pi\) | ||||
0.299754 | + | 0.954016i | \(0.403095\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.42638e7 | −1.02968 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.01338e6i | 0.0427640i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.01980e6i | 0.210648i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.57078e6 | −0.357654 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.13535e7 | 0.471137 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.15382e7i | 0.476145i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.53947e7i | − 0.631769i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.97756e7 | −0.807067 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.48305e7 | 0.601915 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.03623e7i | 1.22551i | 0.790273 | + | 0.612755i | \(0.209939\pi\) | ||||
−0.790273 | + | 0.612755i | \(0.790061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.78885e6i | 0.111948i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.87844e7 | 0.749896 | 0.374948 | − | 0.927046i | \(-0.377661\pi\) | ||||
0.374948 | + | 0.927046i | \(0.377661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.13322e6 | −0.164101 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.05401e6i | 0.120592i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.56604e7i | − 1.40043i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.38053e7 | −1.71095 | −0.855476 | − | 0.517842i | \(-0.826735\pi\) | ||||
−0.855476 | + | 0.517842i | \(0.826735\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.44353e6 | 0.0949224 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.49190e7i | 0.962779i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.19253e6i | 0.353249i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.99729e7 | −0.763383 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.88925e7 | −0.718208 | −0.359104 | − | 0.933298i | \(-0.616918\pi\) | ||||
−0.359104 | + | 0.933298i | \(0.616918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.67452e6i | 0.176751i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.21993e7i | 0.458809i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.59085e6 | 0.0969199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.00651e7 | −1.11870 | −0.559350 | − | 0.828931i | \(-0.688949\pi\) | ||||
−0.559350 | + | 0.828931i | \(0.688949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.50087e7i | 0.925609i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 368874.i | − 0.0135801i | −0.999977 | − | 0.00679006i | \(-0.997839\pi\) | ||||
0.999977 | − | 0.00679006i | \(-0.00216136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.69689e7 | 1.72001 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.97818e7 | −0.720586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.31548e6i | 0.120135i | 0.998194 | + | 0.0600677i | \(0.0191317\pi\) | ||||
−0.998194 | + | 0.0600677i | \(0.980868\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.45999e6i | 0.340977i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.61410e7 | −0.578735 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.89980e7 | 0.677604 | 0.338802 | − | 0.940858i | \(-0.389978\pi\) | ||||
0.338802 | + | 0.940858i | \(0.389978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36224.1i | 0.00128526i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.72049e6i | − 0.201908i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.50082e7 | 2.28256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.51605e7 | −0.878844 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.16568e7i | − 0.405054i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.22132e7i | 0.767878i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00131e7 | −0.344354 | −0.172177 | − | 0.985066i | \(-0.555080\pi\) | ||||
−0.172177 | + | 0.985066i | \(0.555080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.67008e6 | 0.0913514 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.66607e6i | − 0.0907453i | −0.998970 | − | 0.0453726i | \(-0.985552\pi\) | ||||
0.998970 | − | 0.0453726i | \(-0.0144475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 7.14155e7i | − 2.41830i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.73419e6 | −0.0921121 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.15935e6 | −0.105891 | −0.0529457 | − | 0.998597i | \(-0.516861\pi\) | ||||
−0.0529457 | + | 0.998597i | \(0.516861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2.58808e6i | − 0.0863021i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.24586e6i | 0.207214i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.50171e6 | −0.0825758 | −0.0412879 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412879 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.91412e6 | −0.292744 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.20284e7i | 1.69999i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.40333e7i | 0.781307i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.14173e7 | −1.33967 | −0.669835 | − | 0.742510i | \(-0.733635\pi\) | ||||
−0.669835 | + | 0.742510i | \(0.733635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.92790e7 | −0.942286 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.01576e7i | 0.325262i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.80654e7i | 1.21281i | 0.795156 | + | 0.606405i | \(0.207389\pi\) | ||||
−0.795156 | + | 0.606405i | \(0.792611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.85612e7 | −1.85651 |
(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 | 160.6.d.a.81.8 | 20 | ||
4.3 | odd | 2 | 40.6.d.a.21.9 | ✓ | 20 | ||
5.2 | odd | 4 | 800.6.f.c.49.7 | 20 | |||
5.3 | odd | 4 | 800.6.f.b.49.14 | 20 | |||
5.4 | even | 2 | 800.6.d.c.401.13 | 20 | |||
8.3 | odd | 2 | 40.6.d.a.21.10 | yes | 20 | ||
8.5 | even | 2 | inner | 160.6.d.a.81.13 | 20 | ||
12.11 | even | 2 | 360.6.k.b.181.12 | 20 | |||
20.3 | even | 4 | 200.6.f.c.149.1 | 20 | |||
20.7 | even | 4 | 200.6.f.b.149.20 | 20 | |||
20.19 | odd | 2 | 200.6.d.b.101.12 | 20 | |||
24.11 | even | 2 | 360.6.k.b.181.11 | 20 | |||
40.3 | even | 4 | 200.6.f.b.149.19 | 20 | |||
40.13 | odd | 4 | 800.6.f.c.49.8 | 20 | |||
40.19 | odd | 2 | 200.6.d.b.101.11 | 20 | |||
40.27 | even | 4 | 200.6.f.c.149.2 | 20 | |||
40.29 | even | 2 | 800.6.d.c.401.8 | 20 | |||
40.37 | odd | 4 | 800.6.f.b.49.13 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.d.a.21.9 | ✓ | 20 | 4.3 | odd | 2 | ||
40.6.d.a.21.10 | yes | 20 | 8.3 | odd | 2 | ||
160.6.d.a.81.8 | 20 | 1.1 | even | 1 | trivial | ||
160.6.d.a.81.13 | 20 | 8.5 | even | 2 | inner | ||
200.6.d.b.101.11 | 20 | 40.19 | odd | 2 | |||
200.6.d.b.101.12 | 20 | 20.19 | odd | 2 | |||
200.6.f.b.149.19 | 20 | 40.3 | even | 4 | |||
200.6.f.b.149.20 | 20 | 20.7 | even | 4 | |||
200.6.f.c.149.1 | 20 | 20.3 | even | 4 | |||
200.6.f.c.149.2 | 20 | 40.27 | even | 4 | |||
360.6.k.b.181.11 | 20 | 24.11 | even | 2 | |||
360.6.k.b.181.12 | 20 | 12.11 | even | 2 | |||
800.6.d.c.401.8 | 20 | 40.29 | even | 2 | |||
800.6.d.c.401.13 | 20 | 5.4 | even | 2 | |||
800.6.f.b.49.13 | 20 | 40.37 | odd | 4 | |||
800.6.f.b.49.14 | 20 | 5.3 | odd | 4 | |||
800.6.f.c.49.7 | 20 | 5.2 | odd | 4 | |||
800.6.f.c.49.8 | 20 | 40.13 | odd | 4 |