Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5850,2,Mod(5149,5850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5850.5149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5850.e (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: | \(46.7124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1950) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5149.4 | ||
Root | \(2.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5850.5149 |
Dual form | 5850.2.e.bi.5149.1 |
$q$-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 \(\left(\mathbb{Z}/5850\mathbb{Z}\right)^\times\).
\(n\) | \(2251\) | \(3251\) | \(3277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70156i | 0.643130i | 0.946888 | + | 0.321565i | \(0.104209\pi\) | ||||
−0.946888 | + | 0.321565i | \(0.895791\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70156 | 0.513040 | 0.256520 | − | 0.966539i | \(-0.417424\pi\) | ||||
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −1.70156 | −0.454762 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.70156i | 1.38283i | 0.722457 | + | 0.691416i | \(0.243013\pi\) | ||||
−0.722457 | + | 0.691416i | \(0.756987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.70156 | −1.07861 | −0.539306 | − | 0.842110i | \(-0.681313\pi\) | ||||
−0.539306 | + | 0.842110i | \(0.681313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.70156i | 0.362774i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 1.70156i | − 0.321565i | ||||||||
\(29\) | 6.40312 | 1.18903 | 0.594515 | − | 0.804084i | \(-0.297344\pi\) | ||||
0.594515 | + | 0.804084i | \(0.297344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.10469 | 1.63525 | 0.817625 | − | 0.575751i | \(-0.195290\pi\) | ||||
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.70156 | −0.977810 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.70156i | − 0.772932i | −0.922304 | − | 0.386466i | \(-0.873696\pi\) | ||||
0.922304 | − | 0.386466i | \(-0.126304\pi\) | |||||||
\(38\) | − 4.70156i | − 0.762694i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.70156 | −0.421913 | −0.210957 | − | 0.977495i | \(-0.567658\pi\) | ||||
−0.210957 | + | 0.977495i | \(0.567658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.40312i | 0.213974i | 0.994260 | + | 0.106987i | \(0.0341204\pi\) | ||||
−0.994260 | + | 0.106987i | \(0.965880\pi\) | |||||||
\(44\) | −1.70156 | −0.256520 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00000i | 1.02105i | 0.859861 | + | 0.510527i | \(0.170550\pi\) | ||||
−0.859861 | + | 0.510527i | \(0.829450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.10469 | 0.586384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | 10.4031i | 1.42898i | 0.699646 | + | 0.714490i | \(0.253341\pi\) | ||||
−0.699646 | + | 0.714490i | \(0.746659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.70156 | 0.227381 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.40312i | 0.840771i | ||||||||
\(59\) | −3.70156 | −0.481902 | −0.240951 | − | 0.970537i | \(-0.577459\pi\) | ||||
−0.240951 | + | 0.970537i | \(0.577459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.10469 | −0.653588 | −0.326794 | − | 0.945096i | \(-0.605968\pi\) | ||||
−0.326794 | + | 0.945096i | \(0.605968\pi\) | |||||||
\(62\) | 9.10469i | 1.15630i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.40312i | − 0.782266i | −0.920334 | − | 0.391133i | \(-0.872083\pi\) | ||||
0.920334 | − | 0.391133i | \(-0.127917\pi\) | |||||||
\(68\) | − 5.70156i | − 0.691416i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.70156 | −0.557973 | −0.278986 | − | 0.960295i | \(-0.589998\pi\) | ||||
−0.278986 | + | 0.960295i | \(0.589998\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.0000i | − 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | 4.70156 | 0.546545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.70156 | 0.539306 | ||||||||
\(77\) | 2.89531i | 0.329952i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.701562 | −0.0789319 | −0.0394660 | − | 0.999221i | \(-0.512566\pi\) | ||||
−0.0394660 | + | 0.999221i | \(0.512566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 2.70156i | − 0.298338i | ||||||||
\(83\) | 4.29844i | 0.471815i | 0.971776 | + | 0.235907i | \(0.0758062\pi\) | ||||
−0.971776 | + | 0.235907i | \(0.924194\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.40312 | −0.151303 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 1.70156i | − 0.181387i | ||||||||
\(89\) | −1.40312 | −0.148731 | −0.0743654 | − | 0.997231i | \(-0.523693\pi\) | ||||
−0.0743654 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.70156 | 0.178372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4031i | 1.56395i | 0.623310 | + | 0.781975i | \(0.285788\pi\) | ||||
−0.623310 | + | 0.781975i | \(0.714212\pi\) | |||||||
\(98\) | 4.10469i | 0.414636i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.298438 | −0.0296957 | −0.0148478 | − | 0.999890i | \(-0.504726\pi\) | ||||
−0.0148478 | + | 0.999890i | \(0.504726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 11.4031i | − 1.12358i | −0.827279 | − | 0.561792i | \(-0.810112\pi\) | ||||
0.827279 | − | 0.561792i | \(-0.189888\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4031 | −1.01044 | ||||||||
\(107\) | − 0.104686i | − 0.0101204i | −0.999987 | − | 0.00506021i | \(-0.998389\pi\) | ||||
0.999987 | − | 0.00506021i | \(-0.00161072\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7016 | −1.02502 | −0.512512 | − | 0.858680i | \(-0.671285\pi\) | ||||
−0.512512 | + | 0.858680i | \(0.671285\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.70156i | 0.160783i | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.40312 | −0.594515 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 3.70156i | − 0.340756i | ||||||||
\(119\) | −9.70156 | −0.889341 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.10469 | −0.736790 | ||||||||
\(122\) | − 5.10469i | − 0.462157i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.10469 | −0.817625 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7016i | 1.12708i | 0.826088 | + | 0.563541i | \(0.190561\pi\) | ||||
−0.826088 | + | 0.563541i | \(0.809439\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.50781 | 0.830701 | 0.415351 | − | 0.909661i | \(-0.363659\pi\) | ||||
0.415351 | + | 0.909661i | \(0.363659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 8.00000i | − 0.693688i | ||||||||
\(134\) | 6.40312 | 0.553146 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.70156 | 0.488905 | ||||||||
\(137\) | 7.29844i | 0.623548i | 0.950156 | + | 0.311774i | \(0.100923\pi\) | ||||
−0.950156 | + | 0.311774i | \(0.899077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.40312 | 0.288649 | 0.144325 | − | 0.989530i | \(-0.453899\pi\) | ||||
0.144325 | + | 0.989530i | \(0.453899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 4.70156i | − 0.394546i | ||||||||
\(143\) | − 1.70156i | − 0.142292i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.70156i | 0.386466i | ||||||||
\(149\) | 19.4031 | 1.58957 | 0.794783 | − | 0.606894i | \(-0.207585\pi\) | ||||
0.794783 | + | 0.606894i | \(0.207585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.10469 | 0.415413 | 0.207707 | − | 0.978191i | \(-0.433400\pi\) | ||||
0.207707 | + | 0.978191i | \(0.433400\pi\) | |||||||
\(152\) | 4.70156i | 0.381347i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.89531 | −0.233311 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2984i | 1.30076i | 0.759610 | + | 0.650378i | \(0.225390\pi\) | ||||
−0.759610 | + | 0.650378i | \(0.774610\pi\) | |||||||
\(158\) | − 0.701562i | − 0.0558133i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.80625i | 0.533107i | 0.963820 | + | 0.266553i | \(0.0858848\pi\) | ||||
−0.963820 | + | 0.266553i | \(0.914115\pi\) | |||||||
\(164\) | 2.70156 | 0.210957 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.29844 | −0.333623 | ||||||||
\(167\) | 18.1047i | 1.40098i | 0.713661 | + | 0.700491i | \(0.247036\pi\) | ||||
−0.713661 | + | 0.700491i | \(0.752964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1.40312i | − 0.106987i | ||||||||
\(173\) | 25.8062i | 1.96201i | 0.193976 | + | 0.981006i | \(0.437862\pi\) | ||||
−0.193976 | + | 0.981006i | \(0.562138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.70156 | 0.128260 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 1.40312i | − 0.105169i | ||||||||
\(179\) | 14.2094 | 1.06206 | 0.531029 | − | 0.847354i | \(-0.321805\pi\) | ||||
0.531029 | + | 0.847354i | \(0.321805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7016 | 1.31575 | 0.657873 | − | 0.753129i | \(-0.271456\pi\) | ||||
0.657873 | + | 0.753129i | \(0.271456\pi\) | |||||||
\(182\) | 1.70156i | 0.126128i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.70156i | 0.709448i | ||||||||
\(188\) | − 7.00000i | − 0.510527i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8062 | −0.926628 | −0.463314 | − | 0.886194i | \(-0.653340\pi\) | ||||
−0.463314 | + | 0.886194i | \(0.653340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 22.2094i | − 1.59867i | −0.600889 | − | 0.799333i | \(-0.705186\pi\) | ||||
0.600889 | − | 0.799333i | \(-0.294814\pi\) | |||||||
\(194\) | −15.4031 | −1.10588 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.10469 | −0.293192 | ||||||||
\(197\) | 7.40312i | 0.527451i | 0.964598 | + | 0.263725i | \(0.0849513\pi\) | ||||
−0.964598 | + | 0.263725i | \(0.915049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7016 | −1.04217 | −0.521083 | − | 0.853506i | \(-0.674472\pi\) | ||||
−0.521083 | + | 0.853506i | \(0.674472\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 0.298438i | − 0.0209980i | ||||||||
\(203\) | 10.8953i | 0.764701i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.4031 | 0.794493 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1.00000i | − 0.0693375i | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8062 | −1.29468 | −0.647338 | − | 0.762203i | \(-0.724118\pi\) | ||||
−0.647338 | + | 0.762203i | \(0.724118\pi\) | |||||||
\(212\) | − 10.4031i | − 0.714490i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.104686 | 0.00715621 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.4922i | 1.05168i | ||||||||
\(218\) | − 10.7016i | − 0.724801i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70156 | 0.383529 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.40312i | − 0.0939601i | −0.998896 | − | 0.0469801i | \(-0.985040\pi\) | ||||
0.998896 | − | 0.0469801i | \(-0.0149597\pi\) | |||||||
\(224\) | −1.70156 | −0.113690 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 3.10469i | 0.206065i | 0.994678 | + | 0.103033i | \(0.0328546\pi\) | ||||
−0.994678 | + | 0.103033i | \(0.967145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.29844 | −0.614458 | −0.307229 | − | 0.951636i | \(-0.599402\pi\) | ||||
−0.307229 | + | 0.951636i | \(0.599402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 6.40312i | − 0.420386i | ||||||||
\(233\) | − 18.2094i | − 1.19294i | −0.802637 | − | 0.596468i | \(-0.796570\pi\) | ||||
0.802637 | − | 0.596468i | \(-0.203430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.70156 | 0.240951 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 9.70156i | − 0.628859i | ||||||||
\(239\) | −13.1047 | −0.847672 | −0.423836 | − | 0.905739i | \(-0.639317\pi\) | ||||
−0.423836 | + | 0.905739i | \(0.639317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4031 | −0.992202 | −0.496101 | − | 0.868265i | \(-0.665236\pi\) | ||||
−0.496101 | + | 0.868265i | \(0.665236\pi\) | |||||||
\(242\) | − 8.10469i | − 0.520989i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.10469 | 0.326794 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.70156i | 0.299153i | ||||||||
\(248\) | − 9.10469i | − 0.578148i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.70156 | −0.422999 | −0.211499 | − | 0.977378i | \(-0.567835\pi\) | ||||
−0.211499 | + | 0.977378i | \(0.567835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.7016 | −0.796967 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 21.7016i | − 1.35371i | −0.736118 | − | 0.676853i | \(-0.763343\pi\) | ||||
0.736118 | − | 0.676853i | \(-0.236657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.50781i | 0.587395i | ||||||||
\(263\) | − 2.00000i | − 0.123325i | −0.998097 | − | 0.0616626i | \(-0.980360\pi\) | ||||
0.998097 | − | 0.0616626i | \(-0.0196403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.40312i | 0.391133i | ||||||||
\(269\) | −7.20937 | −0.439563 | −0.219782 | − | 0.975549i | \(-0.570534\pi\) | ||||
−0.219782 | + | 0.975549i | \(0.570534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5078 | −0.759795 | −0.379898 | − | 0.925029i | \(-0.624041\pi\) | ||||
−0.379898 | + | 0.925029i | \(0.624041\pi\) | |||||||
\(272\) | 5.70156i | 0.345708i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.29844 | −0.440915 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000i | 1.32185i | 0.750451 | + | 0.660926i | \(0.229836\pi\) | ||||
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(278\) | 3.40312i | 0.204106i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9109 | −1.36675 | −0.683376 | − | 0.730067i | \(-0.739489\pi\) | ||||
−0.683376 | + | 0.730067i | \(0.739489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.59688i | 0.511031i | 0.966805 | + | 0.255516i | \(0.0822452\pi\) | ||||
−0.966805 | + | 0.255516i | \(0.917755\pi\) | |||||||
\(284\) | 4.70156 | 0.278986 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.70156 | 0.100615 | ||||||||
\(287\) | − 4.59688i | − 0.271345i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5078 | −0.912224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.0000i | 0.702247i | ||||||||
\(293\) | − 8.59688i | − 0.502235i | −0.967957 | − | 0.251117i | \(-0.919202\pi\) | ||||
0.967957 | − | 0.251117i | \(-0.0807980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.70156 | −0.273273 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.4031i | 1.12399i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.38750 | −0.137613 | ||||||||
\(302\) | 5.10469i | 0.293742i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.70156 | −0.269653 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.701562i | − 0.0400403i | −0.999800 | − | 0.0200201i | \(-0.993627\pi\) | ||||
0.999800 | − | 0.0200201i | \(-0.00637303\pi\) | |||||||
\(308\) | − 2.89531i | − 0.164976i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0000 | −1.70114 | −0.850572 | − | 0.525859i | \(-0.823744\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2094i | 0.972731i | 0.873755 | + | 0.486366i | \(0.161678\pi\) | ||||
−0.873755 | + | 0.486366i | \(0.838322\pi\) | |||||||
\(314\) | −16.2984 | −0.919774 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.701562 | 0.0394660 | ||||||||
\(317\) | 26.8062i | 1.50559i | 0.658256 | + | 0.752794i | \(0.271295\pi\) | ||||
−0.658256 | + | 0.752794i | \(0.728705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8953 | 0.610020 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 26.8062i | − 1.49154i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.80625 | −0.376963 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.70156i | 0.149169i | ||||||||
\(329\) | −11.9109 | −0.656671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | − 4.29844i | − 0.235907i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.1047 | −0.990644 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1047i | 0.604911i | 0.953164 | + | 0.302455i | \(0.0978063\pi\) | ||||
−0.953164 | + | 0.302455i | \(0.902194\pi\) | |||||||
\(338\) | − 1.00000i | − 0.0543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4922 | 0.838949 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8953i | 1.02025i | ||||||||
\(344\) | 1.40312 | 0.0756514 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.8062 | −1.38735 | ||||||||
\(347\) | − 21.5078i | − 1.15460i | −0.816532 | − | 0.577300i | \(-0.804106\pi\) | ||||
0.816532 | − | 0.577300i | \(-0.195894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.40312 | −0.0751075 | −0.0375538 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375538 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.70156i | 0.0906936i | ||||||||
\(353\) | 17.5078i | 0.931847i | 0.884825 | + | 0.465923i | \(0.154278\pi\) | ||||
−0.884825 | + | 0.465923i | \(0.845722\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.40312 | 0.0743654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.2094i | 0.750989i | ||||||||
\(359\) | 16.6125 | 0.876774 | 0.438387 | − | 0.898786i | \(-0.355550\pi\) | ||||
0.438387 | + | 0.898786i | \(0.355550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.10469 | 0.163405 | ||||||||
\(362\) | 17.7016i | 0.930373i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.70156 | −0.0891861 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.70156i | 0.454218i | 0.973869 | + | 0.227109i | \(0.0729273\pi\) | ||||
−0.973869 | + | 0.227109i | \(0.927073\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.7016 | −0.919019 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7016i | 0.605884i | 0.953009 | + | 0.302942i | \(0.0979688\pi\) | ||||
−0.953009 | + | 0.302942i | \(0.902031\pi\) | |||||||
\(374\) | −9.70156 | −0.501656 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | − 6.40312i | − 0.329778i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.1047 | 1.70047 | 0.850237 | − | 0.526400i | \(-0.176459\pi\) | ||||
0.850237 | + | 0.526400i | \(0.176459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 12.8062i | − 0.655225i | ||||||||
\(383\) | − 0.492189i | − 0.0251497i | −0.999921 | − | 0.0125749i | \(-0.995997\pi\) | ||||
0.999921 | − | 0.0125749i | \(-0.00400281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.2094 | 1.13043 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 15.4031i | − 0.781975i | ||||||||
\(389\) | −7.89531 | −0.400308 | −0.200154 | − | 0.979764i | \(-0.564144\pi\) | ||||
−0.200154 | + | 0.979764i | \(0.564144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − 4.10469i | − 0.207318i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.40312 | −0.372964 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 22.9109i | − 1.14987i | −0.818200 | − | 0.574933i | \(-0.805028\pi\) | ||||
0.818200 | − | 0.574933i | \(-0.194972\pi\) | |||||||
\(398\) | − 14.7016i | − 0.736923i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.2094 | 1.00921 | 0.504604 | − | 0.863351i | \(-0.331639\pi\) | ||||
0.504604 | + | 0.863351i | \(0.331639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.10469i | − 0.453537i | ||||||||
\(404\) | 0.298438 | 0.0148478 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.8953 | −0.540725 | ||||||||
\(407\) | − 8.00000i | − 0.396545i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5969 | −0.820663 | −0.410331 | − | 0.911937i | \(-0.634587\pi\) | ||||
−0.410331 | + | 0.911937i | \(0.634587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.4031i | 0.561792i | ||||||||
\(413\) | − 6.29844i | − 0.309926i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 8.00000i | − 0.391293i | ||||||||
\(419\) | −34.9109 | −1.70551 | −0.852755 | − | 0.522310i | \(-0.825070\pi\) | ||||
−0.852755 | + | 0.522310i | \(0.825070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.4031 | −0.653228 | −0.326614 | − | 0.945158i | \(-0.605908\pi\) | ||||
−0.326614 | + | 0.945158i | \(0.605908\pi\) | |||||||
\(422\) | − 18.8062i | − 0.915474i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4031 | 0.505220 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8.68594i | − 0.420342i | ||||||||
\(428\) | 0.104686i | 0.00506021i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.3141 | 1.07483 | 0.537415 | − | 0.843318i | \(-0.319401\pi\) | ||||
0.537415 | + | 0.843318i | \(0.319401\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.10469i | 0.389486i | 0.980854 | + | 0.194743i | \(0.0623873\pi\) | ||||
−0.980854 | + | 0.194743i | \(0.937613\pi\) | |||||||
\(434\) | −15.4922 | −0.743649 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.7016 | 0.512512 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7016 | 0.797122 | 0.398561 | − | 0.917142i | \(-0.369510\pi\) | ||||
0.398561 | + | 0.917142i | \(0.369510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.70156i | 0.271196i | ||||||||
\(443\) | − 0.492189i | − 0.0233846i | −0.999932 | − | 0.0116923i | \(-0.996278\pi\) | ||||
0.999932 | − | 0.0116923i | \(-0.00372186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.40312 | 0.0664399 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1.70156i | − 0.0803913i | ||||||||
\(449\) | 8.70156 | 0.410652 | 0.205326 | − | 0.978694i | \(-0.434175\pi\) | ||||
0.205326 | + | 0.978694i | \(0.434175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.59688 | −0.216458 | ||||||||
\(452\) | − 14.0000i | − 0.658505i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.10469 | −0.145710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4031i | 0.720528i | 0.932850 | + | 0.360264i | \(0.117313\pi\) | ||||
−0.932850 | + | 0.360264i | \(0.882687\pi\) | |||||||
\(458\) | − 9.29844i | − 0.434487i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.20937 | 0.102901 | 0.0514504 | − | 0.998676i | \(-0.483616\pi\) | ||||
0.0514504 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 27.7016i | − 1.28740i | −0.765278 | − | 0.643700i | \(-0.777398\pi\) | ||||
0.765278 | − | 0.643700i | \(-0.222602\pi\) | |||||||
\(464\) | 6.40312 | 0.297258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.2094 | 0.843533 | ||||||||
\(467\) | 36.7016i | 1.69835i | 0.528115 | + | 0.849173i | \(0.322899\pi\) | ||||
−0.528115 | + | 0.849173i | \(0.677101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8953 | 0.503099 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.70156i | 0.170378i | ||||||||
\(473\) | 2.38750i | 0.109778i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.70156 | 0.444670 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 13.1047i | − 0.599394i | ||||||||
\(479\) | 10.6125 | 0.484897 | 0.242449 | − | 0.970164i | \(-0.422049\pi\) | ||||
0.242449 | + | 0.970164i | \(0.422049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.70156 | −0.214373 | ||||||||
\(482\) | − 15.4031i | − 0.701593i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.10469 | 0.368395 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.1047i | 1.22823i | 0.789216 | + | 0.614115i | \(0.210487\pi\) | ||||
−0.789216 | + | 0.614115i | \(0.789513\pi\) | |||||||
\(488\) | 5.10469i | 0.231078i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.5969 | −0.929524 | −0.464762 | − | 0.885436i | \(-0.653860\pi\) | ||||
−0.464762 | + | 0.885436i | \(0.653860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.5078i | 1.64423i | ||||||||
\(494\) | −4.70156 | −0.211533 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.10469 | 0.408812 | ||||||||
\(497\) | − 8.00000i | − 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2094 | 0.949462 | 0.474731 | − | 0.880131i | \(-0.342545\pi\) | ||||
0.474731 | + | 0.880131i | \(0.342545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 6.70156i | − 0.299105i | ||||||||
\(503\) | − 26.2094i | − 1.16862i | −0.811531 | − | 0.584309i | \(-0.801366\pi\) | ||||
0.811531 | − | 0.584309i | \(-0.198634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 12.7016i | − 0.563541i | ||||||||
\(509\) | 7.40312 | 0.328138 | 0.164069 | − | 0.986449i | \(-0.447538\pi\) | ||||
0.164069 | + | 0.986449i | \(0.447538\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4187 | 0.903272 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.7016 | 0.957215 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.9109i | 0.523842i | ||||||||
\(518\) | 8.00000i | 0.351500i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.20937 | −0.0967944 | −0.0483972 | − | 0.998828i | \(-0.515411\pi\) | ||||
−0.0483972 | + | 0.998828i | \(0.515411\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.806248i | 0.0352548i | 0.999845 | + | 0.0176274i | \(0.00561126\pi\) | ||||
−0.999845 | + | 0.0176274i | \(0.994389\pi\) | |||||||
\(524\) | −9.50781 | −0.415351 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | 51.9109i | 2.26128i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000i | 0.346844i | ||||||||
\(533\) | 2.70156i | 0.117018i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.40312 | −0.276573 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 7.20937i | − 0.310818i | ||||||||
\(539\) | 6.98438 | 0.300838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.2094 | −1.72874 | −0.864368 | − | 0.502860i | \(-0.832281\pi\) | ||||
−0.864368 | + | 0.502860i | \(0.832281\pi\) | |||||||
\(542\) | − 12.5078i | − 0.537256i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.70156 | −0.244452 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19.6125i | − 0.838570i | −0.907855 | − | 0.419285i | \(-0.862281\pi\) | ||||
0.907855 | − | 0.419285i | \(-0.137719\pi\) | |||||||
\(548\) | − 7.29844i | − 0.311774i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.1047 | −1.28250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.19375i | − 0.0507635i | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.40312 | −0.144325 | ||||||||
\(557\) | − 8.80625i | − 0.373133i | −0.982442 | − | 0.186566i | \(-0.940264\pi\) | ||||
0.982442 | − | 0.186566i | \(-0.0597359\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.40312 | 0.0593458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 22.9109i | − 0.966439i | ||||||||
\(563\) | 0.492189i | 0.0207433i | 0.999946 | + | 0.0103717i | \(0.00330146\pi\) | ||||
−0.999946 | + | 0.0103717i | \(0.996699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.59688 | −0.361354 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.70156i | 0.197273i | ||||||||
\(569\) | −17.7016 | −0.742088 | −0.371044 | − | 0.928615i | \(-0.621000\pi\) | ||||
−0.371044 | + | 0.928615i | \(0.621000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 1.70156i | 0.0711459i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.59688 | 0.191870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2094i | 0.591544i | 0.955259 | + | 0.295772i | \(0.0955769\pi\) | ||||
−0.955259 | + | 0.295772i | \(0.904423\pi\) | |||||||
\(578\) | − 15.5078i | − 0.645040i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.31406 | −0.303438 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.7016i | 0.733124i | ||||||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.59688 | 0.355134 | ||||||||
\(587\) | 24.5078i | 1.01155i | 0.862667 | + | 0.505773i | \(0.168793\pi\) | ||||
−0.862667 | + | 0.505773i | \(0.831207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.8062 | −1.76380 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 4.70156i | − 0.193233i | ||||||||
\(593\) | 26.9109i | 1.10510i | 0.833480 | + | 0.552550i | \(0.186345\pi\) | ||||
−0.833480 | + | 0.552550i | \(0.813655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.4031 | −0.794783 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.2094 | −1.23432 | −0.617161 | − | 0.786837i | \(-0.711717\pi\) | ||||
−0.617161 | + | 0.786837i | \(0.711717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.6125 | −1.65662 | −0.828309 | − | 0.560271i | \(-0.810697\pi\) | ||||
−0.828309 | + | 0.560271i | \(0.810697\pi\) | |||||||
\(602\) | − 2.38750i | − 0.0973074i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.10469 | −0.207707 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8953i | 0.645171i | 0.946540 | + | 0.322585i | \(0.104552\pi\) | ||||
−0.946540 | + | 0.322585i | \(0.895448\pi\) | |||||||
\(608\) | − 4.70156i | − 0.190674i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.00000 | 0.283190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.8062i | 0.517240i | 0.965979 | + | 0.258620i | \(0.0832677\pi\) | ||||
−0.965979 | + | 0.258620i | \(0.916732\pi\) | |||||||
\(614\) | 0.701562 | 0.0283127 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.89531 | 0.116656 | ||||||||
\(617\) | − 7.89531i | − 0.317853i | −0.987290 | − | 0.158927i | \(-0.949197\pi\) | ||||
0.987290 | − | 0.158927i | \(-0.0508033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.8062 | 1.55975 | 0.779877 | − | 0.625932i | \(-0.215281\pi\) | ||||
0.779877 | + | 0.625932i | \(0.215281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 30.0000i | − 1.20289i | ||||||||
\(623\) | − 2.38750i | − 0.0956533i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.2094 | −0.687825 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 16.2984i | − 0.650378i | ||||||||
\(629\) | 26.8062 | 1.06884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6125 | −0.701142 | −0.350571 | − | 0.936536i | \(-0.614013\pi\) | ||||
−0.350571 | + | 0.936536i | \(0.614013\pi\) | |||||||
\(632\) | 0.701562i | 0.0279066i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.8062 | −1.06461 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.10469i | − 0.162634i | ||||||||
\(638\) | 10.8953i | 0.431350i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5078 | 1.04700 | 0.523498 | − | 0.852027i | \(-0.324627\pi\) | ||||
0.523498 | + | 0.852027i | \(0.324627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 16.7016i | − 0.658645i | −0.944217 | − | 0.329323i | \(-0.893180\pi\) | ||||
0.944217 | − | 0.329323i | \(-0.106820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.8062 | 1.05468 | ||||||||
\(647\) | − 24.0000i | − 0.943537i | −0.881722 | − | 0.471769i | \(-0.843616\pi\) | ||||
0.881722 | − | 0.471769i | \(-0.156384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.29844 | −0.247235 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 6.80625i | − 0.266553i | ||||||||
\(653\) | 27.7016i | 1.08405i | 0.840364 | + | 0.542023i | \(0.182341\pi\) | ||||
−0.840364 | + | 0.542023i | \(0.817659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.70156 | −0.105478 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 11.9109i | − 0.464337i | ||||||||
\(659\) | 38.3141 | 1.49250 | 0.746252 | − | 0.665664i | \(-0.231851\pi\) | ||||
0.746252 | + | 0.665664i | \(0.231851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.1203 | 1.67719 | 0.838593 | − | 0.544759i | \(-0.183379\pi\) | ||||
0.838593 | + | 0.544759i | \(0.183379\pi\) | |||||||
\(662\) | − 12.0000i | − 0.466393i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.29844 | 0.166812 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − 18.1047i | − 0.700491i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.68594 | −0.335317 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 28.0156i | − 1.07992i | −0.841690 | − | 0.539961i | \(-0.818439\pi\) | ||||
0.841690 | − | 0.539961i | \(-0.181561\pi\) | |||||||
\(674\) | −11.1047 | −0.427737 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − 19.6125i | − 0.753769i | −0.926260 | − | 0.376885i | \(-0.876995\pi\) | ||||
0.926260 | − | 0.376885i | \(-0.123005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.2094 | −1.00582 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.4922i | 0.593227i | ||||||||
\(683\) | − 38.2984i | − 1.46545i | −0.680525 | − | 0.732724i | \(-0.738248\pi\) | ||||
0.680525 | − | 0.732724i | \(-0.261752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.8953 | −0.721426 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.40312i | 0.0534936i | ||||||||
\(689\) | 10.4031 | 0.396327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8062 | −1.81864 | −0.909318 | − | 0.416103i | \(-0.863396\pi\) | ||||
−0.909318 | + | 0.416103i | \(0.863396\pi\) | |||||||
\(692\) | − 25.8062i | − 0.981006i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.5078 | 0.816425 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 15.4031i | − 0.583435i | ||||||||
\(698\) | − 1.40312i | − 0.0531090i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.9109 | 0.525409 | 0.262704 | − | 0.964876i | \(-0.415386\pi\) | ||||
0.262704 | + | 0.964876i | \(0.415386\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.1047i | 0.833694i | ||||||||
\(704\) | −1.70156 | −0.0641300 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.5078 | −0.658915 | ||||||||
\(707\) | − 0.507811i | − 0.0190982i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.6125 | 1.33746 | 0.668728 | − | 0.743507i | \(-0.266839\pi\) | ||||
0.668728 | + | 0.743507i | \(0.266839\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.40312i | 0.0525843i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.2094 | −0.531029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.6125i | 0.619973i | ||||||||
\(719\) | 53.0156 | 1.97715 | 0.988575 | − | 0.150733i | \(-0.0481633\pi\) | ||||
0.988575 | + | 0.150733i | \(0.0481633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.4031 | 0.722610 | ||||||||
\(722\) | 3.10469i | 0.115544i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.7016 | −0.657873 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 46.2094i | − 1.71381i | −0.515474 | − | 0.856905i | \(-0.672384\pi\) | ||||
0.515474 | − | 0.856905i | \(-0.327616\pi\) | |||||||
\(728\) | − 1.70156i | − 0.0630641i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.08907i | 0.114097i | 0.998371 | + | 0.0570486i | \(0.0181690\pi\) | ||||
−0.998371 | + | 0.0570486i | \(0.981831\pi\) | |||||||
\(734\) | −8.70156 | −0.321181 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 10.8953i | − 0.401334i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.6125 | 1.71467 | 0.857334 | − | 0.514760i | \(-0.172119\pi\) | ||||
0.857334 | + | 0.514760i | \(0.172119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 17.7016i | − 0.649845i | ||||||||
\(743\) | − 20.6125i | − 0.756199i | −0.925765 | − | 0.378100i | \(-0.876578\pi\) | ||||
0.925765 | − | 0.378100i | \(-0.123422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.7016 | −0.428425 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 9.70156i | − 0.354724i | ||||||||
\(749\) | 0.178130 | 0.00650874 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5078 | −0.857812 | −0.428906 | − | 0.903349i | \(-0.641101\pi\) | ||||
−0.428906 | + | 0.903349i | \(0.641101\pi\) | |||||||
\(752\) | 7.00000i | 0.255264i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.40312 | 0.233188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1047i | 1.34859i | 0.738461 | + | 0.674296i | \(0.235553\pi\) | ||||
−0.738461 | + | 0.674296i | \(0.764447\pi\) | |||||||
\(758\) | 33.1047i | 1.20242i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.7172 | −1.58475 | −0.792373 | − | 0.610036i | \(-0.791155\pi\) | ||||
−0.792373 | + | 0.610036i | \(0.791155\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 18.2094i | − 0.659224i | ||||||||
\(764\) | 12.8062 | 0.463314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.492189 | 0.0177835 | ||||||||
\(767\) | 3.70156i | 0.133656i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00000 | 0.288487 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.2094i | 0.799333i | ||||||||
\(773\) | − 39.4031i | − 1.41723i | −0.705594 | − | 0.708616i | \(-0.749320\pi\) | ||||
0.705594 | − | 0.708616i | \(-0.250680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.4031 | 0.552940 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 7.89531i | − 0.283061i | ||||||||
\(779\) | 12.7016 | 0.455081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.10469 | 0.146596 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 53.1047i | − 1.89298i | −0.322737 | − | 0.946489i | \(-0.604603\pi\) | ||||
0.322737 | − | 0.946489i | \(-0.395397\pi\) | |||||||
\(788\) | − 7.40312i | − 0.263725i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.8219 | −0.847008 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.10469i | 0.181273i | ||||||||
\(794\) | 22.9109 | 0.813079 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.7016 | 0.521083 | ||||||||
\(797\) | − 41.9109i | − 1.48456i | −0.670089 | − | 0.742281i | \(-0.733744\pi\) | ||||
0.670089 | − | 0.742281i | \(-0.266256\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.9109 | −1.41195 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.2094i | 0.713618i | ||||||||
\(803\) | − 20.4187i | − 0.720562i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.10469 | 0.320699 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.298438i | 0.0104990i | ||||||||
\(809\) | 32.8062 | 1.15341 | 0.576703 | − | 0.816954i | \(-0.304339\pi\) | ||||
0.576703 | + | 0.816954i | \(0.304339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.2984 | 1.48530 | 0.742650 | − | 0.669680i | \(-0.233569\pi\) | ||||
0.742650 | + | 0.669680i | \(0.233569\pi\) | |||||||
\(812\) | − 10.8953i | − 0.382351i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 6.59688i | − 0.230795i | ||||||||
\(818\) | − 16.5969i | − 0.580296i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.4031 | 1.16578 | 0.582889 | − | 0.812552i | \(-0.301922\pi\) | ||||
0.582889 | + | 0.812552i | \(0.301922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.10469i | − 0.0733648i | −0.999327 | − | 0.0366824i | \(-0.988321\pi\) | ||||
0.999327 | − | 0.0366824i | \(-0.0116790\pi\) | |||||||
\(824\) | −11.4031 | −0.397247 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.29844 | 0.219151 | ||||||||
\(827\) | 14.2984i | 0.497205i | 0.968606 | + | 0.248603i | \(0.0799713\pi\) | ||||
−0.968606 | + | 0.248603i | \(0.920029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.5078 | −0.920654 | −0.460327 | − | 0.887749i | \(-0.652268\pi\) | ||||
−0.460327 | + | 0.887749i | \(0.652268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 23.4031i | 0.810870i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.00000 | 0.276686 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 34.9109i | − 1.20598i | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0000 | 0.413793 | ||||||||
\(842\) | − 13.4031i | − 0.461902i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.8062 | 0.647338 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 13.7906i | − 0.473852i | ||||||||
\(848\) | 10.4031i | 0.357245i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 31.5078i | − 1.07881i | −0.842047 | − | 0.539403i | \(-0.818650\pi\) | ||||
0.842047 | − | 0.539403i | \(-0.181350\pi\) | |||||||
\(854\) | 8.68594 | 0.297227 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.104686 | −0.00357811 | ||||||||
\(857\) | 43.6125i | 1.48977i | 0.667190 | + | 0.744887i | \(0.267497\pi\) | ||||
−0.667190 | + | 0.744887i | \(0.732503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2094 | −1.09897 | −0.549485 | − | 0.835504i | \(-0.685176\pi\) | ||||
−0.549485 | + | 0.835504i | \(0.685176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.3141i | 0.760020i | ||||||||
\(863\) | 48.2250i | 1.64160i | 0.571217 | + | 0.820799i | \(0.306471\pi\) | ||||
−0.571217 | + | 0.820799i | \(0.693529\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.10469 | −0.275408 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 15.4922i | − 0.525839i | ||||||||
\(869\) | −1.19375 | −0.0404952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.40312 | −0.216962 | ||||||||
\(872\) | 10.7016i | 0.362401i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 27.7172i | − 0.935943i | −0.883744 | − | 0.467971i | \(-0.844985\pi\) | ||||
0.883744 | − | 0.467971i | \(-0.155015\pi\) | |||||||
\(878\) | 16.7016i | 0.563650i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.7172 | −1.03489 | −0.517444 | − | 0.855717i | \(-0.673116\pi\) | ||||
−0.517444 | + | 0.855717i | \(0.673116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 5.61250i | − 0.188876i | −0.995531 | − | 0.0944378i | \(-0.969895\pi\) | ||||
0.995531 | − | 0.0944378i | \(-0.0301053\pi\) | |||||||
\(884\) | −5.70156 | −0.191764 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.492189 | 0.0165354 | ||||||||
\(887\) | − 20.0000i | − 0.671534i | −0.941945 | − | 0.335767i | \(-0.891004\pi\) | ||||
0.941945 | − | 0.335767i | \(-0.108996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.6125 | −0.724860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.40312i | 0.0469801i | ||||||||
\(893\) | − 32.9109i | − 1.10132i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.70156 | 0.0568452 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.70156i | 0.290375i | ||||||||
\(899\) | 58.2984 | 1.94436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.3141 | −1.97604 | ||||||||
\(902\) | − 4.59688i | − 0.153059i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 39.0156i | − 1.29549i | −0.761856 | − | 0.647746i | \(-0.775712\pi\) | ||||
0.761856 | − | 0.647746i | \(-0.224288\pi\) | |||||||
\(908\) | − 3.10469i | − 0.103033i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.79063 | −0.125589 | −0.0627945 | − | 0.998026i | \(-0.520001\pi\) | ||||
−0.0627945 | + | 0.998026i | \(0.520001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.31406i | 0.242060i | ||||||||
\(914\) | −15.4031 | −0.509490 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.29844 | 0.307229 | ||||||||
\(917\) | 16.1781i | 0.534249i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.1047 | 0.795140 | 0.397570 | − | 0.917572i | \(-0.369854\pi\) | ||||
0.397570 | + | 0.917572i | \(0.369854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.20937i | 0.0727618i | ||||||||
\(923\) | 4.70156i | 0.154754i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27.7016 | 0.910330 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.40312i | 0.210193i | ||||||||
\(929\) | 58.7016 | 1.92594 | 0.962968 | − | 0.269616i | \(-0.0868968\pi\) | ||||
0.962968 | + | 0.269616i | \(0.0868968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.2984 | −0.632481 | ||||||||
\(932\) | 18.2094i | 0.596468i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.7016 | −1.20091 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.9109i | 0.977148i | 0.872523 | + | 0.488574i | \(0.162483\pi\) | ||||
−0.872523 | + | 0.488574i | \(0.837517\pi\) | |||||||
\(938\) | 10.8953i | 0.355745i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.4187 | 1.57841 | 0.789203 | − | 0.614132i | \(-0.210494\pi\) | ||||
0.789203 | + | 0.614132i | \(0.210494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.70156 | −0.120476 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.38750 | −0.0776244 | ||||||||
\(947\) | 15.4922i | 0.503429i | 0.967802 | + | 0.251714i | \(0.0809943\pi\) | ||||
−0.967802 | + | 0.251714i | \(0.919006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.70156i | 0.314429i | ||||||||
\(953\) | 37.7016i | 1.22127i | 0.791911 | + | 0.610637i | \(0.209086\pi\) | ||||
−0.791911 | + | 0.610637i | \(0.790914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.1047 | 0.423836 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.6125i | 0.342874i | ||||||||
\(959\) | −12.4187 | −0.401022 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.8953 | 1.67404 | ||||||||
\(962\) | − 4.70156i | − 0.151584i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.4031 | 0.496101 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 49.1047i | − 1.57910i | −0.613686 | − | 0.789550i | \(-0.710314\pi\) | ||||
0.613686 | − | 0.789550i | \(-0.289686\pi\) | |||||||
\(968\) | 8.10469i | 0.260494i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.1047 | 1.80049 | 0.900243 | − | 0.435389i | \(-0.143389\pi\) | ||||
0.900243 | + | 0.435389i | \(0.143389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.79063i | 0.185639i | ||||||||
\(974\) | −27.1047 | −0.868490 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.10469 | −0.163397 | ||||||||
\(977\) | − 10.5969i | − 0.339024i | −0.985528 | − | 0.169512i | \(-0.945781\pi\) | ||||
0.985528 | − | 0.169512i | \(-0.0542192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.38750 | −0.0763049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 20.5969i | − 0.657273i | ||||||||
\(983\) | − 24.5078i | − 0.781678i | −0.920459 | − | 0.390839i | \(-0.872185\pi\) | ||||
0.920459 | − | 0.390839i | \(-0.127815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36.5078 | −1.16265 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 4.70156i | − 0.149577i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1047 | 0.320986 | 0.160493 | − | 0.987037i | \(-0.448692\pi\) | ||||
0.160493 | + | 0.987037i | \(0.448692\pi\) | |||||||
\(992\) | 9.10469i | 0.289074i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.5078i | 1.34624i | 0.739535 | + | 0.673118i | \(0.235045\pi\) | ||||
−0.739535 | + | 0.673118i | \(0.764955\pi\) | |||||||
\(998\) | 21.2094i | 0.671371i | ||||||||
\(999\) | 0 | 0 |
(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 | 5850.2.e.bi.5149.4 | 4 | ||
3.2 | odd | 2 | 1950.2.e.p.1249.2 | 4 | |||
5.2 | odd | 4 | 5850.2.a.cg.1.1 | 2 | |||
5.3 | odd | 4 | 5850.2.a.cj.1.2 | 2 | |||
5.4 | even | 2 | inner | 5850.2.e.bi.5149.1 | 4 | ||
15.2 | even | 4 | 1950.2.a.bg.1.1 | yes | 2 | ||
15.8 | even | 4 | 1950.2.a.bc.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 1950.2.e.p.1249.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.a.bc.1.2 | ✓ | 2 | 15.8 | even | 4 | ||
1950.2.a.bg.1.1 | yes | 2 | 15.2 | even | 4 | ||
1950.2.e.p.1249.2 | 4 | 3.2 | odd | 2 | |||
1950.2.e.p.1249.3 | 4 | 15.14 | odd | 2 | |||
5850.2.a.cg.1.1 | 2 | 5.2 | odd | 4 | |||
5850.2.a.cj.1.2 | 2 | 5.3 | odd | 4 | |||
5850.2.e.bi.5149.1 | 4 | 5.4 | even | 2 | inner | ||
5850.2.e.bi.5149.4 | 4 | 1.1 | even | 1 | trivial |