Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(319,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.j (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.389136420864.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.5 | ||
Root | \(-1.52274 - 1.29664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.319 |
Dual form | 960.3.j.e.319.6 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27492 | − | 2.59328i | −0.854983 | − | 0.518655i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.837253 | −0.119608 | −0.0598038 | − | 0.998210i | \(-0.519048\pi\) | ||||
−0.0598038 | + | 0.998210i | \(0.519048\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.7955i | 1.43596i | 0.696066 | + | 0.717978i | \(0.254932\pi\) | ||||
−0.696066 | + | 0.717978i | \(0.745068\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.18655i | 0.398966i | 0.979901 | + | 0.199483i | \(0.0639262\pi\) | ||||
−0.979901 | + | 0.199483i | \(0.936074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.40437 | − | 4.49169i | −0.493625 | − | 0.299446i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 27.3586i | − | 1.60933i | −0.593728 | − | 0.804666i | \(-0.702344\pi\) | ||
0.593728 | − | 0.804666i | \(-0.297656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 17.9667i | − | 0.945618i | −0.881165 | − | 0.472809i | \(-0.843240\pi\) | ||
0.881165 | − | 0.472809i | \(-0.156760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.45017 | −0.0690555 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.1101 | 0.830874 | 0.415437 | − | 0.909622i | \(-0.363629\pi\) | ||||
0.415437 | + | 0.909622i | \(0.363629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.5498 | + | 22.1721i | 0.461993 | + | 0.886883i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 45.6495 | 1.57412 | 0.787060 | − | 0.616876i | \(-0.211602\pi\) | ||||
0.787060 | + | 0.616876i | \(0.211602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.6243i | 0.439493i | 0.975557 | + | 0.219747i | \(0.0705230\pi\) | ||||
−0.975557 | + | 0.219747i | \(0.929477\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 27.3586i | 0.829050i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.57919 | + | 2.17123i | 0.102263 | + | 0.0620351i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 15.5597i | − | 0.420531i | −0.977644 | − | 0.210266i | \(-0.932567\pi\) | ||
0.977644 | − | 0.210266i | \(-0.0674329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.98337i | 0.230343i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.2990 | 0.324366 | 0.162183 | − | 0.986761i | \(-0.448147\pi\) | ||||
0.162183 | + | 0.986761i | \(0.448147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.9430 | 0.649837 | 0.324918 | − | 0.945742i | \(-0.394663\pi\) | ||||
0.324918 | + | 0.945742i | \(0.394663\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.8248 | − | 7.77983i | −0.284994 | − | 0.172885i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 55.6558 | 1.18417 | 0.592083 | − | 0.805877i | \(-0.298306\pi\) | ||||
0.592083 | + | 0.805877i | \(0.298306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.2990 | −0.985694 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 47.3865i | − | 0.929148i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 15.5597i | − | 0.293578i | −0.989168 | − | 0.146789i | \(-0.953106\pi\) | ||
0.989168 | − | 0.146789i | \(-0.0468939\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.9621 | − | 67.5245i | 0.744766 | − | 1.22772i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 31.1193i | − | 0.545953i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 87.6625i | − | 1.48581i | −0.669400 | − | 0.742903i | \(-0.733449\pi\) | ||
0.669400 | − | 0.742903i | \(-0.266551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38.0000 | −0.622951 | −0.311475 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311475 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.51176 | −0.0398692 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.4502 | − | 22.1721i | 0.206926 | − | 0.341109i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 92.2015 | 1.37614 | 0.688071 | − | 0.725643i | \(-0.258458\pi\) | ||||
0.688071 | + | 0.725643i | \(0.258458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 33.0997 | 0.479705 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 130.707i | − | 1.84094i | −0.390816 | − | 0.920469i | \(-0.627807\pi\) | ||
0.390816 | − | 0.920469i | \(-0.372193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 54.7173i | − | 0.749552i | −0.927115 | − | 0.374776i | \(-0.877720\pi\) | ||
0.927115 | − | 0.374776i | \(-0.122280\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.0049 | + | 38.4032i | 0.266732 | + | 0.512042i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.2249i | − | 0.171751i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.6243i | − | 0.172459i | −0.996275 | − | 0.0862297i | \(-0.972518\pi\) | ||
0.996275 | − | 0.0862297i | \(-0.0274819\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 59.0048 | 0.710901 | 0.355451 | − | 0.934695i | \(-0.384327\pi\) | ||||
0.355451 | + | 0.934695i | \(0.384327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −70.9485 | + | 116.956i | −0.834688 | + | 1.37595i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 79.0673 | 0.908819 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 39.8007 | 0.447198 | 0.223599 | − | 0.974681i | \(-0.428219\pi\) | ||||
0.223599 | + | 0.974681i | \(0.428219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.34246i | − | 0.0477193i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.5980i | 0.253741i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −46.5927 | + | 76.8064i | −0.490450 | + | 0.808488i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 168.821i | 1.74043i | 0.492675 | + | 0.870214i | \(0.336019\pi\) | ||||
−0.492675 | + | 0.870214i | \(0.663981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 47.3865i | 0.478652i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44.5498 | −0.441087 | −0.220544 | − | 0.975377i | \(-0.570783\pi\) | ||||
−0.220544 | + | 0.975377i | \(0.570783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 126.466 | 1.22782 | 0.613911 | − | 0.789375i | \(-0.289595\pi\) | ||||
0.613911 | + | 0.789375i | \(0.289595\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.19934 | + | 3.76068i | 0.0590413 | + | 0.0358160i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 104.383 | 0.975546 | 0.487773 | − | 0.872971i | \(-0.337809\pi\) | ||||
0.487773 | + | 0.872971i | \(0.337809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.501656 | 0.00460235 | 0.00230117 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00230117 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 26.9501i | − | 0.242794i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.9855i | 0.150314i | 0.997172 | + | 0.0751572i | \(0.0239459\pi\) | ||||
−0.997172 | + | 0.0751572i | \(0.976054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −81.6941 | − | 49.5578i | −0.710384 | − | 0.430937i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.5597i | 0.132989i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.9061i | 0.192488i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −128.498 | −1.06197 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.0346 | 0.187273 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.12376 | − | 124.736i | 0.0649901 | − | 0.997886i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.45598 | −0.0665825 | −0.0332913 | − | 0.999446i | \(-0.510599\pi\) | ||||
−0.0332913 | + | 0.999446i | \(0.510599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 48.3987 | 0.375184 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 51.7290i | − | 0.394878i | −0.980315 | − | 0.197439i | \(-0.936738\pi\) | ||
0.980315 | − | 0.197439i | \(-0.0632624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.0427i | 0.113103i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.2131 | − | 13.4751i | −0.164542 | − | 0.0998153i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 53.8083i | 0.392762i | 0.980528 | + | 0.196381i | \(0.0629189\pi\) | ||||
−0.980528 | + | 0.196381i | \(0.937081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.6243i | − | 0.0980165i | −0.998798 | − | 0.0490082i | \(-0.984394\pi\) | ||
0.998798 | − | 0.0490082i | \(-0.0156061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 96.3987 | 0.683679 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −81.9243 | −0.572897 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −195.148 | − | 118.382i | −1.34585 | − | 0.816426i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −83.6563 | −0.569091 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 33.6495 | 0.225836 | 0.112918 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112918 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 139.988i | 0.927076i | 0.886077 | + | 0.463538i | \(0.153420\pi\) | ||||
−0.886077 | + | 0.463538i | \(0.846580\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 82.0759i | − | 0.536444i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 35.3315 | − | 58.2427i | 0.227945 | − | 0.375759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.2631i | 0.135434i | 0.997705 | + | 0.0677170i | \(0.0215715\pi\) | ||||
−0.997705 | + | 0.0677170i | \(0.978428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 26.9501i | − | 0.169498i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −0.0993789 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −210.211 | −1.28964 | −0.644819 | − | 0.764335i | \(-0.723067\pi\) | ||||
−0.644819 | + | 0.764335i | \(0.723067\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 70.9485 | − | 116.956i | 0.429991 | − | 0.708824i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 238.384 | 1.42745 | 0.713725 | − | 0.700426i | \(-0.247006\pi\) | ||||
0.713725 | + | 0.700426i | \(0.247006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142.100 | 0.840826 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 53.9002i | − | 0.315206i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.33481i | − | 0.0134960i | −0.999977 | − | 0.00674800i | \(-0.997852\pi\) | ||
0.999977 | − | 0.00674800i | \(-0.00214797\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.67014 | − | 18.5637i | −0.0552579 | − | 0.106078i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 151.836i | − | 0.857830i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 227.054i | 1.26846i | 0.773145 | + | 0.634229i | \(0.218682\pi\) | ||||
−0.773145 | + | 0.634229i | \(0.781318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −114.096 | −0.630367 | −0.315183 | − | 0.949031i | \(-0.602066\pi\) | ||||
−0.315183 | + | 0.949031i | \(0.602066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −65.8179 | −0.359661 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40.3505 | + | 66.5163i | −0.218111 | + | 0.359547i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 432.144 | 2.31093 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.35050 | −0.0230185 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 139.392i | 0.729798i | 0.931047 | + | 0.364899i | \(0.118897\pi\) | ||||
−0.931047 | + | 0.364899i | \(0.881103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 182.046i | 0.943245i | 0.881801 | + | 0.471623i | \(0.156331\pi\) | ||||
−0.881801 | + | 0.471623i | \(0.843669\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.2964 | − | 38.4032i | 0.119469 | − | 0.196939i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 258.027i | 1.30978i | 0.755724 | + | 0.654890i | \(0.227285\pi\) | ||||
−0.755724 | + | 0.654890i | \(0.772715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 256.474i | − | 1.28881i | −0.764683 | − | 0.644407i | \(-0.777104\pi\) | ||
0.764683 | − | 0.644407i | \(-0.222896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 159.698 | 0.794516 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −38.2202 | −0.188277 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −56.8522 | − | 34.4880i | −0.277328 | − | 0.168234i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 57.3303 | 0.276958 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 283.794 | 1.35787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 211.855i | 1.00405i | 0.864852 | + | 0.502027i | \(0.167412\pi\) | ||||
−0.864852 | + | 0.502027i | \(0.832588\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 226.390i | − | 1.06287i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −119.454 | − | 72.4639i | −0.555600 | − | 0.337041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.4070i | − | 0.0525667i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 94.7731i | − | 0.432754i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 141.897 | 0.642068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −349.843 | −1.56880 | −0.784401 | − | 0.620255i | \(-0.787029\pi\) | ||||
−0.784401 | + | 0.620255i | \(0.787029\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 34.6495 | + | 66.5163i | 0.153998 | + | 0.295628i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −185.554 | −0.817418 | −0.408709 | − | 0.912665i | \(-0.634021\pi\) | ||||
−0.408709 | + | 0.912665i | \(0.634021\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −263.897 | −1.15239 | −0.576194 | − | 0.817313i | \(-0.695463\pi\) | ||||
−0.576194 | + | 0.817313i | \(0.695463\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 22.9061i | − | 0.0991607i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 58.4780i | − | 0.250978i | −0.992095 | − | 0.125489i | \(-0.959950\pi\) | ||
0.992095 | − | 0.125489i | \(-0.0400500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −237.924 | − | 144.331i | −1.01244 | − | 0.614174i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 23.5980i | − | 0.0995694i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 113.337i | − | 0.474212i | −0.971484 | − | 0.237106i | \(-0.923801\pi\) | ||
0.971484 | − | 0.237106i | \(-0.0761989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −77.7940 | −0.322797 | −0.161398 | − | 0.986889i | \(-0.551600\pi\) | ||||
−0.161398 | + | 0.986889i | \(0.551600\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 206.474 | + | 125.253i | 0.842752 | + | 0.511235i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 93.1855 | 0.377269 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 102.199 | 0.410439 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 106.226i | − | 0.423212i | −0.977355 | − | 0.211606i | \(-0.932131\pi\) | ||
0.977355 | − | 0.211606i | \(-0.0678693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 301.854i | 1.19310i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −122.886 | + | 202.574i | −0.481908 | + | 0.794406i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 381.078i | − | 1.48279i | −0.671067 | − | 0.741397i | \(-0.734164\pi\) | ||
0.671067 | − | 0.741397i | \(-0.265836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0274i | 0.0502988i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 136.949 | 0.524707 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4914 | 0.0436934 | 0.0218467 | − | 0.999761i | \(-0.493045\pi\) | ||||
0.0218467 | + | 0.999761i | \(0.493045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.3505 | + | 66.5163i | −0.152266 | + | 0.251005i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 68.9368 | 0.258190 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 77.9518 | 0.289784 | 0.144892 | − | 0.989447i | \(-0.453717\pi\) | ||||
0.144892 | + | 0.989447i | \(0.453717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 86.6851i | − | 0.319871i | −0.987127 | − | 0.159936i | \(-0.948871\pi\) | ||
0.987127 | − | 0.159936i | \(-0.0511287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7.52136i | − | 0.0275508i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −350.220 | + | 182.436i | −1.27353 | + | 0.663402i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 287.328i | − | 1.03729i | −0.854991 | − | 0.518643i | \(-0.826437\pi\) | ||
0.854991 | − | 0.518643i | \(-0.173563\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 40.8729i | 0.146498i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −224.598 | −0.799281 | −0.399641 | − | 0.916672i | \(-0.630865\pi\) | ||||
−0.399641 | + | 0.916672i | \(0.630865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −84.1224 | −0.297252 | −0.148626 | − | 0.988893i | \(-0.547485\pi\) | ||||
−0.148626 | + | 0.988893i | \(0.547485\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −80.7010 | + | 133.033i | −0.283161 | + | 0.466781i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.1346 | −0.0387967 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −459.495 | −1.58995 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 292.407i | 1.00484i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 246.620i | − | 0.841706i | −0.907129 | − | 0.420853i | \(-0.861731\pi\) | ||
0.907129 | − | 0.420853i | \(-0.138269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −227.333 | + | 374.750i | −0.770621 | + | 1.27034i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 82.0759i | 0.276350i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 99.1156i | 0.331490i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3954 | −0.0777255 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −77.1626 | −0.254662 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 162.447 | + | 98.5445i | 0.532613 | + | 0.323097i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −115.811 | −0.377236 | −0.188618 | − | 0.982051i | \(-0.560401\pi\) | ||||
−0.188618 | + | 0.982051i | \(0.560401\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 219.045 | 0.708883 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 203.767i | 0.655201i | 0.944816 | + | 0.327600i | \(0.106240\pi\) | ||||
−0.944816 | + | 0.327600i | \(0.893760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99.0614i | 0.316490i | 0.987400 | + | 0.158245i | \(0.0505836\pi\) | ||||
−0.987400 | + | 0.158245i | \(0.949416\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.7376 | + | 6.51369i | 0.0340875 | + | 0.0206784i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 471.192i | − | 1.48641i | −0.669063 | − | 0.743206i | \(-0.733304\pi\) | ||
0.669063 | − | 0.743206i | \(-0.266696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 721.057i | 2.26037i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 180.797 | 0.563232 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −491.546 | −1.52181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −114.997 | + | 59.9038i | −0.353836 | + | 0.184319i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.868893 | 0.00265717 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −46.5980 | −0.141635 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 270.695i | − | 0.817810i | −0.912577 | − | 0.408905i | \(-0.865911\pi\) | ||
0.912577 | − | 0.408905i | \(-0.134089\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 46.6790i | − | 0.140177i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −394.154 | − | 239.104i | −1.17658 | − | 0.713743i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 377.317i | 1.11964i | 0.828615 | + | 0.559818i | \(0.189129\pi\) | ||||
−0.828615 | + | 0.559818i | \(0.810871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.4198i | 0.0867841i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −215.203 | −0.631093 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 81.4639 | 0.237504 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −141.498 | − | 85.8366i | −0.410140 | − | 0.248802i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 462.222 | 1.33205 | 0.666025 | − | 0.745929i | \(-0.267994\pi\) | ||||
0.666025 | + | 0.745929i | \(0.267994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −200.598 | −0.574779 | −0.287390 | − | 0.957814i | \(-0.592787\pi\) | ||||
−0.287390 | + | 0.957814i | \(0.592787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.9501i | 0.0767810i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 250.897i | − | 0.710757i | −0.934722 | − | 0.355379i | \(-0.884352\pi\) | ||
0.934722 | − | 0.355379i | \(-0.115648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −338.958 | + | 558.760i | −0.954812 | + | 1.57397i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 39.6746i | 0.111133i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 215.601i | 0.600560i | 0.953851 | + | 0.300280i | \(0.0970801\pi\) | ||||
−0.953851 | + | 0.300280i | \(0.902920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.1960 | 0.105806 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −222.566 | −0.613129 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −141.897 | + | 233.912i | −0.388759 | + | 0.640854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 67.0637 | 0.182735 | 0.0913675 | − | 0.995817i | \(-0.470876\pi\) | ||||
0.0913675 | + | 0.995817i | \(0.470876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.8970 | 0.108122 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0274i | 0.0351142i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 567.402i | 1.52119i | 0.649230 | + | 0.760593i | \(0.275091\pi\) | ||||
−0.649230 | + | 0.760593i | \(0.724909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.0708 | − | 216.049i | 0.0375220 | − | 0.576130i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 236.764i | 0.628020i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 240.298i | 0.634031i | 0.948420 | + | 0.317016i | \(0.102681\pi\) | ||||
−0.948420 | + | 0.317016i | \(0.897319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6462 | −0.0384414 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −670.068 | −1.74952 | −0.874762 | − | 0.484553i | \(-0.838982\pi\) | ||||
−0.874762 | + | 0.484553i | \(0.838982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.2957 | + | 56.5351i | −0.0890797 | + | 0.146845i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 83.8290 | 0.216612 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 474.640 | 1.22015 | 0.610077 | − | 0.792342i | \(-0.291139\pi\) | ||||
0.610077 | + | 0.792342i | \(0.291139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 522.826i | − | 1.33715i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 89.5973i | − | 0.227983i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.3315 | + | 58.2427i | −0.0894469 | + | 0.147450i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 499.460i | 1.25809i | 0.777371 | + | 0.629043i | \(0.216553\pi\) | ||||
−0.777371 | + | 0.629043i | \(0.783447\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 26.0548i | 0.0653001i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 344.694 | 0.859587 | 0.429793 | − | 0.902927i | \(-0.358586\pi\) | ||||
0.429793 | + | 0.902927i | \(0.358586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −70.6631 | −0.175343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −38.4743 | − | 23.3395i | −0.0949982 | − | 0.0576284i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 245.773 | 0.603864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −501.890 | −1.22712 | −0.613558 | − | 0.789650i | \(-0.710262\pi\) | ||||
−0.613558 | + | 0.789650i | \(0.710262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 93.1988i | 0.226761i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 73.3957i | 0.177714i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −252.241 | − | 153.016i | −0.607809 | − | 0.368713i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 23.5980i | − | 0.0565898i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 218.369i | − | 0.521167i | −0.965451 | − | 0.260584i | \(-0.916085\pi\) | ||
0.965451 | − | 0.260584i | \(-0.0839150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −281.698 | −0.669116 | −0.334558 | − | 0.942375i | \(-0.608587\pi\) | ||||
−0.334558 | + | 0.942375i | \(0.608587\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 166.967 | 0.394722 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 606.598 | − | 315.988i | 1.42729 | − | 0.743501i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.8156 | 0.0745097 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −141.897 | −0.330762 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 441.081i | 1.02339i | 0.859167 | + | 0.511694i | \(0.170982\pi\) | ||||
−0.859167 | + | 0.511694i | \(0.829018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 123.443i | 0.285089i | 0.989788 | + | 0.142544i | \(0.0455283\pi\) | ||||
−0.989788 | + | 0.142544i | \(0.954472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −338.006 | − | 205.043i | −0.777025 | − | 0.471364i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 343.346i | − | 0.785690i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 330.728i | − | 0.753368i | −0.926342 | − | 0.376684i | \(-0.877064\pi\) | ||
0.926342 | − | 0.376684i | \(-0.122936\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −144.897 | −0.328565 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 154.952 | 0.349780 | 0.174890 | − | 0.984588i | \(-0.444043\pi\) | ||||
0.174890 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −170.145 | − | 103.214i | −0.382347 | − | 0.231942i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 58.2826 | 0.130386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −95.8970 | −0.213579 | −0.106790 | − | 0.994282i | \(-0.534057\pi\) | ||||
−0.106790 | + | 0.994282i | \(0.534057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 210.065i | 0.465775i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 242.467i | 0.535247i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.2612 | + | 18.5637i | −0.0247499 | + | 0.0407992i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 485.718i | − | 1.06284i | −0.847108 | − | 0.531420i | \(-0.821659\pi\) | ||
0.847108 | − | 0.531420i | \(-0.178341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 142.160i | − | 0.309716i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −353.650 | −0.767136 | −0.383568 | − | 0.923513i | \(-0.625305\pi\) | ||||
−0.383568 | + | 0.923513i | \(0.625305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −421.720 | −0.910842 | −0.455421 | − | 0.890276i | \(-0.650511\pi\) | ||||
−0.455421 | + | 0.890276i | \(0.650511\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 61.1960 | − | 100.879i | 0.131604 | − | 0.216945i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 640.974 | 1.37254 | 0.686268 | − | 0.727349i | \(-0.259248\pi\) | ||||
0.686268 | + | 0.727349i | \(0.259248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −77.1960 | −0.164597 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.8289i | 0.0781929i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 441.374i | 0.933137i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 398.360 | − | 207.513i | 0.838653 | − | 0.436869i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 46.6790i | − | 0.0978595i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 221.137i | 0.461664i | 0.972994 | + | 0.230832i | \(0.0741448\pi\) | ||||
−0.972994 | + | 0.230832i | \(0.925855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 80.7010 | 0.167778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.7128 | −0.0573764 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 437.801 | − | 721.698i | 0.902682 | − | 1.48804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 889.949 | 1.82741 | 0.913705 | − | 0.406377i | \(-0.133208\pi\) | ||||
0.913705 | + | 0.406377i | \(0.133208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −364.096 | −0.744573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 552.843i | 1.12595i | 0.826473 | + | 0.562977i | \(0.190344\pi\) | ||||
−0.826473 | + | 0.562977i | \(0.809656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1248.91i | − | 2.53328i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 122.886 | − | 202.574i | 0.248255 | − | 0.409240i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 109.435i | 0.220190i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 533.302i | − | 1.06874i | −0.845250 | − | 0.534371i | \(-0.820549\pi\) | ||
0.845250 | − | 0.534371i | \(-0.179451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 412.894 | 0.824139 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 574.914 | 1.14297 | 0.571485 | − | 0.820612i | \(-0.306367\pi\) | ||||
0.571485 | + | 0.820612i | \(0.306367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 190.447 | + | 115.530i | 0.377122 | + | 0.228772i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 246.124 | 0.485451 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −207.547 | −0.407753 | −0.203877 | − | 0.978997i | \(-0.565354\pi\) | ||||
−0.203877 | + | 0.978997i | \(0.565354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.8122i | 0.0896521i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 93.3580i | − | 0.181984i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −540.630 | − | 327.960i | −1.04977 | − | 0.636816i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 879.112i | 1.70041i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.04401i | − | 0.00779192i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −712.900 | −1.36833 | −0.684165 | − | 0.729327i | \(-0.739833\pi\) | ||||
−0.684165 | + | 0.729327i | \(0.739833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −139.548 | −0.266822 | −0.133411 | − | 0.991061i | \(-0.542593\pi\) | ||||
−0.133411 | + | 0.991061i | \(0.542593\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.7492 | − | 32.1532i | −0.0319032 | − | 0.0612442i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 372.742 | 0.707290 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −163.804 | −0.309648 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 262.988i | − | 0.495268i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 68.9760i | 0.129411i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −446.230 | − | 270.695i | −0.834075 | − | 0.505972i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 393.269i | 0.732345i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 762.908i | − | 1.41541i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 946.688 | 1.74988 | 0.874942 | − | 0.484227i | \(-0.160899\pi\) | ||||
0.874942 | + | 0.484227i | \(0.160899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −197.621 | −0.363942 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.14454 | − | 1.30093i | −0.00393493 | − | 0.00238703i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −50.3388 | −0.0920271 | −0.0460136 | − | 0.998941i | \(-0.514652\pi\) | ||||
−0.0460136 | + | 0.998941i | \(0.514652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −114.000 | −0.207650 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 820.173i | − | 1.48852i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4070i | 0.0206275i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −69.8891 | + | 115.210i | −0.125926 | + | 0.207585i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 790.157i | 1.41859i | 0.704910 | + | 0.709297i | \(0.250987\pi\) | ||||
−0.704910 | + | 0.709297i | \(0.749013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 144.928i | 0.259263i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 748.495 | 1.33422 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 354.133 | 0.629010 | 0.314505 | − | 0.949256i | \(-0.398162\pi\) | ||||
0.314505 | + | 0.949256i | \(0.398162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.0482 | − | 72.6117i | 0.0779614 | − | 0.128516i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.53528 | −0.0132897 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 55.4983 | 0.0975366 | 0.0487683 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487683 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 791.134i | − | 1.38552i | −0.721167 | − | 0.692762i | \(-0.756394\pi\) | ||
0.721167 | − | 0.692762i | \(-0.243606\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 241.433i | 0.421349i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 220.719 | + | 423.711i | 0.383858 | + | 0.736888i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 201.759i | − | 0.349668i | −0.984598 | − | 0.174834i | \(-0.944061\pi\) | ||
0.984598 | − | 0.174834i | \(-0.0559389\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 315.313i | 0.544583i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −49.4020 | −0.0850292 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 245.773 | 0.421566 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.3505 | − | 66.5163i | 0.0689752 | − | 0.113703i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 444.556 | 0.757335 | 0.378668 | − | 0.925533i | \(-0.376382\pi\) | ||||
0.378668 | + | 0.925533i | \(0.376382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 244.784 | 0.415593 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 446.915i | 0.756202i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 563.908i | − | 0.950942i | −0.879731 | − | 0.475471i | \(-0.842278\pi\) | ||
0.879731 | − | 0.475471i | \(-0.157722\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 59.4019 | − | 97.9217i | 0.0998351 | − | 0.164574i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 444.226i | − | 0.744097i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 845.034i | − | 1.41074i | −0.708839 | − | 0.705371i | \(-0.750781\pi\) | ||
0.708839 | − | 0.705371i | \(-0.249219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 672.296 | 1.11863 | 0.559314 | − | 0.828956i | \(-0.311065\pi\) | ||||
0.559314 | + | 0.828956i | \(0.311065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 276.604 | 0.458714 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 549.320 | + | 333.232i | 0.907967 | + | 0.550796i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 882.664 | 1.45414 | 0.727071 | − | 0.686562i | \(-0.240881\pi\) | ||||
0.727071 | + | 0.686562i | \(0.240881\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −66.1993 | −0.108702 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 288.662i | 0.472442i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 469.374i | − | 0.765701i | −0.923810 | − | 0.382850i | \(-0.874943\pi\) | ||
0.923810 | − | 0.382850i | \(-0.125057\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −98.4708 | − | 59.7350i | −0.160115 | − | 0.0971300i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 218.994i | − | 0.354934i | −0.984127 | − | 0.177467i | \(-0.943210\pi\) | ||
0.984127 | − | 0.177467i | \(-0.0567902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 879.610i | 1.42102i | 0.703689 | + | 0.710509i | \(0.251535\pi\) | ||||
−0.703689 | + | 0.710509i | \(0.748465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 99.2990 | 0.159902 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.3232 | −0.0534884 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −358.203 | + | 512.168i | −0.573124 | + | 0.819468i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 491.546 | 0.783964 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −425.691 | −0.676774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 635.566i | 1.00724i | 0.863926 | + | 0.503618i | \(0.167998\pi\) | ||||
−0.863926 | + | 0.503618i | \(0.832002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 366.944i | 0.579691i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.1486 | + | 21.9287i | 0.0569270 | + | 0.0345334i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 250.505i | − | 0.393258i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 392.120i | − | 0.613646i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −296.309 | −0.462260 | −0.231130 | − | 0.972923i | \(-0.574242\pi\) | ||||
−0.231130 | + | 0.972923i | \(0.574242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 591.032 | 0.919179 | 0.459590 | − | 0.888131i | \(-0.347997\pi\) | ||||
0.459590 | + | 0.888131i | \(0.347997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −206.900 | − | 125.511i | −0.320776 | − | 0.194591i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 166.507 | 0.257352 | 0.128676 | − | 0.991687i | \(-0.458927\pi\) | ||||
0.128676 | + | 0.991687i | \(0.458927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1384.67 | 2.13355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 19.7575i | − | 0.0303494i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 621.335i | 0.951509i | 0.879578 | + | 0.475754i | \(0.157825\pi\) | ||||
−0.879578 | + | 0.475754i | \(0.842175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −134.148 | + | 221.137i | −0.204806 | + | 0.337614i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 164.152i | − | 0.249851i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 702.113i | 1.06542i | 0.846297 | + | 0.532711i | \(0.178827\pi\) | ||||
−0.846297 | + | 0.532711i | \(0.821173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −358.193 | −0.541895 | −0.270948 | − | 0.962594i | \(-0.587337\pi\) | ||||
−0.270948 | + | 0.962594i | \(0.587337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 245.773 | 0.370698 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 39.0099 | − | 64.3064i | 0.0586616 | − | 0.0967013i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 872.367 | 1.30790 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −605.945 | −0.905748 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 600.230i | − | 0.894530i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 714.176i | − | 1.06118i | −0.847628 | − | 0.530592i | \(-0.821970\pi\) | ||
0.847628 | − | 0.530592i | \(-0.178030\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 60.0147 | + | 115.210i | 0.0889107 | + | 0.170681i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 509.833i | − | 0.753077i | −0.926401 | − | 0.376538i | \(-0.877114\pi\) | ||
0.926401 | − | 0.376538i | \(-0.122886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 141.346i | − | 0.208168i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −321.389 | −0.471936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1263.93 | −1.85055 | −0.925275 | − | 0.379298i | \(-0.876166\pi\) | ||||
−0.925275 | + | 0.379298i | \(0.876166\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 139.540 | − | 230.026i | 0.203708 | − | 0.335805i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −457.083 | −0.665332 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 80.7010 | 0.117128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 512.351i | − | 0.741463i | −0.928740 | − | 0.370731i | \(-0.879107\pi\) | ||
0.928740 | − | 0.370731i | \(-0.120893\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 39.6746i | − | 0.0572504i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.3315 | + | 58.2427i | −0.0508368 | + | 0.0838024i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 363.843i | − | 0.522012i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 101.287i | − | 0.144902i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1092.03 | −1.55781 | −0.778907 | − | 0.627139i | \(-0.784226\pi\) | ||||
−0.778907 | + | 0.627139i | \(0.784226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −279.556 | −0.397662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −412.096 | − | 249.988i | −0.584534 | − | 0.354593i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.2995 | 0.0527574 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −416.887 | −0.587993 | −0.293997 | − | 0.955806i | \(-0.594985\pi\) | ||||
−0.293997 | + | 0.955806i | \(0.594985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 40.8729i | − | 0.0574864i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 260.362i | 0.365163i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 350.220 | + | 212.452i | 0.489818 | + | 0.297136i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 196.305i | − | 0.273787i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 395.268i | − | 0.549747i | −0.961480 | − | 0.274874i | \(-0.911364\pi\) | ||
0.961480 | − | 0.274874i | \(-0.0886361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −105.884 | −0.146857 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −134.743 | −0.186367 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 527.244 | + | 1012.14i | 0.727233 | + | 1.39606i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 597.583 | 0.821985 | 0.410993 | − | 0.911639i | \(-0.365182\pi\) | ||||
0.410993 | + | 0.911639i | \(0.365182\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 764.482i | − | 1.04580i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.8650i | − | 0.0325580i | −0.999867 | − | 0.0162790i | \(-0.994818\pi\) | ||
0.999867 | − | 0.0162790i | \(-0.00518200\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 357.624 | + | 216.944i | 0.486563 | + | 0.295162i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1456.37i | 1.97608i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 125.767i | − | 0.170186i | −0.996373 | − | 0.0850928i | \(-0.972881\pi\) | ||
0.996373 | − | 0.0850928i | \(-0.0271187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 161.402 | 0.217816 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 148.841 | 0.200325 | 0.100162 | − | 0.994971i | \(-0.468064\pi\) | ||||
0.100162 | + | 0.994971i | \(0.468064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −143.849 | − | 87.2625i | −0.193086 | − | 0.117131i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 177.014 | 0.236967 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −87.3954 | −0.116683 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 463.390i | − | 0.617030i | −0.951219 | − | 0.308515i | \(-0.900168\pi\) | ||
0.951219 | − | 0.308515i | \(-0.0998321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 183.989i | − | 0.244341i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 363.029 | − | 598.439i | 0.480833 | − | 0.792634i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 719.363i | − | 0.950281i | −0.879910 | − | 0.475141i | \(-0.842397\pi\) | ||
0.879910 | − | 0.475141i | \(-0.157603\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 522.826i | 0.688836i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1107.49 | −1.45530 | −0.727651 | − | 0.685947i | \(-0.759388\pi\) | ||||
−0.727651 | + | 0.685947i | \(0.759388\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.420013 | −0.000550476 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −212.846 | + | 350.868i | −0.278229 | + | 0.458651i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 454.666 | 0.592785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −231.691 | −0.301289 | −0.150644 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150644 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 660.047i | − | 0.856092i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 519.956i | 0.672647i | 0.941746 | + | 0.336324i | \(0.109184\pi\) | ||||
−0.941746 | + | 0.336324i | \(0.890816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −302.079 | + | 157.358i | −0.389779 | + | 0.203043i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.5641i | 0.0290400i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 238.940i | − | 0.306726i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2064.58 | 2.64351 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 237.202 | 0.302940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.1412 | − | 90.8982i | 0.0702436 | − | 0.115794i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.0288 | −0.0584864 | −0.0292432 | − | 0.999572i | \(-0.509310\pi\) | ||||
−0.0292432 | + | 0.999572i | \(0.509310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.9036 | 0.0252264 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 14.2212i | − | 0.0179788i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 197.089i | − | 0.248536i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −69.8891 | + | 115.210i | −0.0879108 | + | 0.144918i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.3098i | 0.0192093i | 0.999954 | + | 0.00960463i | \(0.00305730\pi\) | ||||
−0.999954 | + | 0.00960463i | \(0.996943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1522.67i | − | 1.90572i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 119.402 | 0.149066 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 864.288 | 1.07632 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 68.3987 | + | 41.4924i | 0.0849673 | + | 0.0515434i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 135.017 | 0.167307 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −313.093 | −0.387012 | −0.193506 | − | 0.981099i | \(-0.561986\pi\) | ||||
−0.193506 | + | 0.981099i | \(0.561986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1056.89i | 1.30319i | 0.758566 | + | 0.651596i | \(0.225900\pi\) | ||||
−0.758566 | + | 0.651596i | \(0.774100\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 150.143i | − | 0.184678i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 898.635 | + | 545.136i | 1.10262 | + | 0.668878i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 502.045i | − | 0.614498i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 13.0274i | − | 0.0159064i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −308.659 | −0.375955 | −0.187978 | − | 0.982173i | \(-0.560193\pi\) | ||||
−0.187978 | + | 0.982173i | \(0.560193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 109.680 | 0.133269 | 0.0666344 | − | 0.997777i | \(-0.478774\pi\) | ||||
0.0666344 | + | 0.997777i | \(0.478774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −606.598 | + | 315.988i | −0.735270 | + | 0.383015i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 711.971 | 0.860908 | 0.430454 | − | 0.902613i | \(-0.358354\pi\) | ||||
0.430454 | + | 0.902613i | \(0.358354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 118.688 | 0.143170 | 0.0715849 | − | 0.997435i | \(-0.477194\pi\) | ||||
0.0715849 | + | 0.997435i | \(0.477194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 497.667i | − | 0.598877i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1321.40i | 1.58631i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1019.07 | − | 618.196i | −1.22045 | − | 0.740355i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 70.7939i | 0.0845805i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1413.67i | 1.68495i | 0.538736 | + | 0.842475i | \(0.318902\pi\) | ||||
−0.538736 | + | 0.842475i | \(0.681098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1242.88 | 1.47786 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −389.015 | −0.461465 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −607.464 | − | 368.504i | −0.718893 | − | 0.436099i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 107.586 | 0.127020 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −145.704 | −0.171619 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 297.347i | − | 0.349409i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1308.03i | 1.53344i | 0.641979 | + | 0.766722i | \(0.278114\pi\) | ||||
−0.641979 | + | 0.766722i | \(0.721886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −139.778 | + | 230.419i | −0.163483 | + | 0.269496i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 719.755i | − | 0.839854i | −0.907558 | − | 0.419927i | \(-0.862056\pi\) | ||
0.907558 | − | 0.419927i | \(-0.137944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1402.44i | − | 1.63264i | −0.577601 | − | 0.816319i | \(-0.696011\pi\) | ||
0.577601 | − | 0.816319i | \(-0.303989\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.2858 | −0.0223993 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 72.4412 | 0.0839411 | 0.0419706 | − | 0.999119i | \(-0.486636\pi\) | ||||
0.0419706 | + | 0.999119i | \(0.486636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.05480 | + | 9.98111i | −0.00699977 | + | 0.0115389i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −795.869 | −0.917957 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 215.203 | 0.247644 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 478.208i | 0.549033i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 506.464i | 0.580142i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.80164 | + | 104.435i | −0.00777331 | + | 0.119355i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1382.21i | − | 1.57606i | −0.615635 | − | 0.788032i | \(-0.711100\pi\) | ||
0.615635 | − | 0.788032i | \(-0.288900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 427.158i | − | 0.485959i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1131.38 | −1.28419 | −0.642097 | − | 0.766623i | \(-0.721936\pi\) | ||||
−0.642097 | + | 0.766623i | \(0.721936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1077.39 | 1.22014 | 0.610072 | − | 0.792346i | \(-0.291140\pi\) | ||||
0.610072 | + | 0.792346i | \(0.291140\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −393.752 | + | 649.086i | −0.444918 | + | 0.733430i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −766.896 | −0.864595 | −0.432297 | − | 0.901731i | \(-0.642297\pi\) | ||||
−0.432297 | + | 0.901731i | \(0.642297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.07980 | 0.00796378 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 142.160i | 0.159551i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 999.954i | − | 1.11977i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 588.814 | − | 970.637i | 0.657893 | − | 1.08451i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 171.673i | 0.191386i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 621.942i | 0.691815i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −425.691 | −0.472465 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.5220 | −0.0448748 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 487.752 | + | 295.883i | 0.538953 | + | 0.326943i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1086.43 | −1.19783 | −0.598913 | − | 0.800814i | \(-0.704400\pi\) | ||||
−0.598913 | + | 0.800814i | \(0.704400\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −133.650 | −0.147029 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 237.746i | 0.260973i | 0.991450 | + | 0.130486i | \(0.0416539\pi\) | ||||
−0.991450 | + | 0.130486i | \(0.958346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 932.012i | 1.02082i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 281.366 | + | 170.684i | 0.307504 | + | 0.186540i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.3103i | 0.0472304i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 344.517i | 0.374882i | 0.982276 | + | 0.187441i | \(0.0600194\pi\) | ||||
−0.982276 | + | 0.187441i | \(0.939981\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −200.591 | −0.217797 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 677.917 | 0.734471 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 344.990 | − | 179.711i | 0.372962 | − | 0.194283i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 379.397 | 0.409274 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1478.10 | 1.59106 | 0.795531 | − | 0.605913i | \(-0.207192\pi\) | ||||
0.795531 | + | 0.605913i | \(0.207192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 867.776i | 0.932090i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 352.935i | 0.378280i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1847.38 | − | 1120.67i | −1.97581 | − | 1.19858i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 246.887i | − | 0.263486i | −0.991284 | − | 0.131743i | \(-0.957943\pi\) | ||
0.991284 | − | 0.131743i | \(-0.0420574\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 171.579i | 0.182726i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1658.64 | −1.76264 | −0.881318 | − | 0.472525i | \(-0.843343\pi\) | ||||
−0.881318 | + | 0.472525i | \(0.843343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 254.145 | 0.269507 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.5980 | + | 11.2820i | 0.0196804 | + | 0.0119387i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00750 | 0.00634372 | 0.00317186 | − | 0.999995i | \(-0.498990\pi\) | ||||
0.00317186 | + | 0.999995i | \(0.498990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 283.794 | 0.299045 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 816.129i | − | 0.858180i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1089.55i | − | 1.14329i | −0.820503 | − | 0.571643i | \(-0.806306\pi\) | ||
0.820503 | − | 0.571643i | \(-0.193694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 361.481 | − | 595.887i | 0.378514 | − | 0.623966i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1248.91i | 1.30502i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 45.0512i | − | 0.0469773i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 775.379 | 0.806846 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 313.150 | 0.325182 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 472.096 | − | 778.233i | 0.489219 | − | 0.806459i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1699.27 | −1.75726 | −0.878630 | − | 0.477502i | \(-0.841542\pi\) | ||||
−0.878630 | + | 0.477502i | \(0.841542\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −851.382 | −0.878619 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 197.851i | − | 0.203760i | −0.994797 | − | 0.101880i | \(-0.967514\pi\) | ||
0.994797 | − | 0.101880i | \(-0.0324857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.4070i | 0.0117235i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −199.180 | + | 103.756i | −0.204287 | + | 0.106417i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 847.868i | − | 0.867828i | −0.900954 | − | 0.433914i | \(-0.857132\pi\) | ||
0.900954 | − | 0.433914i | \(-0.142868\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 628.672i | 0.642157i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.50497 | 0.00153412 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −96.0512 | −0.0977123 | −0.0488562 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488562 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 669.135 | − | 1103.04i | 0.679324 | − | 1.11984i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −80.7101 | −0.0817732 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 533.993 | 0.539933 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1184.45i | 1.19520i | 0.801793 | + | 0.597602i | \(0.203880\pi\) | ||||
−0.801793 | + | 0.597602i | \(0.796120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 468.858i | − | 0.472163i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −665.108 | + | 1096.40i | −0.668450 | + | 1.10191i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1887.35i | 1.89303i | 0.322655 | + | 0.946517i | \(0.395425\pi\) | ||||
−0.322655 | + | 0.946517i | \(0.604575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 80.8504i | − | 0.0809313i |
(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 | 960.3.j.e.319.5 | 8 | ||
4.3 | odd | 2 | inner | 960.3.j.e.319.1 | 8 | ||
5.4 | even | 2 | inner | 960.3.j.e.319.2 | 8 | ||
8.3 | odd | 2 | 60.3.f.b.19.2 | yes | 8 | ||
8.5 | even | 2 | 60.3.f.b.19.8 | yes | 8 | ||
20.19 | odd | 2 | inner | 960.3.j.e.319.6 | 8 | ||
24.5 | odd | 2 | 180.3.f.h.19.1 | 8 | |||
24.11 | even | 2 | 180.3.f.h.19.7 | 8 | |||
40.3 | even | 4 | 300.3.c.f.151.6 | 8 | |||
40.13 | odd | 4 | 300.3.c.f.151.5 | 8 | |||
40.19 | odd | 2 | 60.3.f.b.19.7 | yes | 8 | ||
40.27 | even | 4 | 300.3.c.f.151.3 | 8 | |||
40.29 | even | 2 | 60.3.f.b.19.1 | ✓ | 8 | ||
40.37 | odd | 4 | 300.3.c.f.151.4 | 8 | |||
120.29 | odd | 2 | 180.3.f.h.19.8 | 8 | |||
120.53 | even | 4 | 900.3.c.r.451.4 | 8 | |||
120.59 | even | 2 | 180.3.f.h.19.2 | 8 | |||
120.77 | even | 4 | 900.3.c.r.451.5 | 8 | |||
120.83 | odd | 4 | 900.3.c.r.451.3 | 8 | |||
120.107 | odd | 4 | 900.3.c.r.451.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.b.19.1 | ✓ | 8 | 40.29 | even | 2 | ||
60.3.f.b.19.2 | yes | 8 | 8.3 | odd | 2 | ||
60.3.f.b.19.7 | yes | 8 | 40.19 | odd | 2 | ||
60.3.f.b.19.8 | yes | 8 | 8.5 | even | 2 | ||
180.3.f.h.19.1 | 8 | 24.5 | odd | 2 | |||
180.3.f.h.19.2 | 8 | 120.59 | even | 2 | |||
180.3.f.h.19.7 | 8 | 24.11 | even | 2 | |||
180.3.f.h.19.8 | 8 | 120.29 | odd | 2 | |||
300.3.c.f.151.3 | 8 | 40.27 | even | 4 | |||
300.3.c.f.151.4 | 8 | 40.37 | odd | 4 | |||
300.3.c.f.151.5 | 8 | 40.13 | odd | 4 | |||
300.3.c.f.151.6 | 8 | 40.3 | even | 4 | |||
900.3.c.r.451.3 | 8 | 120.83 | odd | 4 | |||
900.3.c.r.451.4 | 8 | 120.53 | even | 4 | |||
900.3.c.r.451.5 | 8 | 120.77 | even | 4 | |||
900.3.c.r.451.6 | 8 | 120.107 | odd | 4 | |||
960.3.j.e.319.1 | 8 | 4.3 | odd | 2 | inner | ||
960.3.j.e.319.2 | 8 | 5.4 | even | 2 | inner | ||
960.3.j.e.319.5 | 8 | 1.1 | even | 1 | trivial | ||
960.3.j.e.319.6 | 8 | 20.19 | odd | 2 | inner |