Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.3 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.a.2591.6 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.21441i | − 0.990315i | −0.868803 | − | 0.495158i | \(-0.835110\pi\) | ||||
0.868803 | − | 0.495158i | \(-0.164890\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.614014 | 0.185132 | 0.0925662 | − | 0.995707i | \(-0.470493\pi\) | ||||
0.0925662 | + | 0.995707i | \(0.470493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.56048 | −1.54220 | −0.771100 | − | 0.636715i | \(-0.780293\pi\) | ||||
−0.771100 | + | 0.636715i | \(0.780293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.585786i | 0.142074i | 0.997474 | + | 0.0710370i | \(0.0226309\pi\) | ||||
−0.997474 | + | 0.0710370i | \(0.977369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.89898i | − 0.894487i | −0.894412 | − | 0.447244i | \(-0.852406\pi\) | ||||
0.894412 | − | 0.447244i | \(-0.147594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.850087 | 0.177255 | 0.0886277 | − | 0.996065i | \(-0.471752\pi\) | ||||
0.0886277 | + | 0.996065i | \(0.471752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0963763 | 0.0192753 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.74202i | 0.880571i | 0.897858 | + | 0.440285i | \(0.145123\pi\) | ||||
−0.897858 | + | 0.440285i | \(0.854877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.07055i | 0.551487i | 0.961231 | + | 0.275744i | \(0.0889241\pi\) | ||||
−0.961231 | + | 0.275744i | \(0.911076\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.21441 | 0.374304 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.17157 | 0.357004 | 0.178502 | − | 0.983940i | \(-0.442875\pi\) | ||||
0.178502 | + | 0.983940i | \(0.442875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 6.07812i | − 0.949242i | −0.880190 | − | 0.474621i | \(-0.842585\pi\) | ||||
0.880190 | − | 0.474621i | \(-0.157415\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.21733i | − 1.40563i | −0.711373 | − | 0.702815i | \(-0.751926\pi\) | ||||
0.711373 | − | 0.702815i | \(-0.248074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.41421 | 0.498014 | 0.249007 | − | 0.968502i | \(-0.419896\pi\) | ||||
0.249007 | + | 0.968502i | \(0.419896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.47015i | 0.614023i | 0.951706 | + | 0.307011i | \(0.0993290\pi\) | ||||
−0.951706 | + | 0.307011i | \(0.900671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.35968i | − 0.183339i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.9136 | −1.81140 | −0.905698 | − | 0.423924i | \(-0.860652\pi\) | ||||
−0.905698 | + | 0.423924i | \(0.860652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.92820 | −1.14314 | −0.571570 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.3132i | 1.52726i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.83183i | − 0.590302i | −0.955451 | − | 0.295151i | \(-0.904630\pi\) | ||||
0.955451 | − | 0.295151i | \(-0.0953699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.33610 | 0.633278 | 0.316639 | − | 0.948546i | \(-0.397446\pi\) | ||||
0.316639 | + | 0.948546i | \(0.397446\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.28788 | −1.08706 | −0.543532 | − | 0.839388i | \(-0.682913\pi\) | ||||
−0.543532 | + | 0.839388i | \(0.682913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.614014i | 0.0699734i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.29717i | 0.145943i | 0.997334 | + | 0.0729717i | \(0.0232483\pi\) | ||||
−0.997334 | + | 0.0729717i | \(0.976752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.5400 | −1.59597 | −0.797985 | − | 0.602677i | \(-0.794101\pi\) | ||||
−0.797985 | + | 0.602677i | \(0.794101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.29717 | 0.140698 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4059i | 1.20903i | 0.796596 | + | 0.604513i | \(0.206632\pi\) | ||||
−0.796596 | + | 0.604513i | \(0.793368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 5.56048i | − 0.582896i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.63395 | −0.885825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.27135 | 0.738294 | 0.369147 | − | 0.929371i | \(-0.379650\pi\) | ||||
0.369147 | + | 0.929371i | \(0.379650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.1416i | 1.90466i | 0.305066 | + | 0.952331i | \(0.401321\pi\) | ||||
−0.305066 | + | 0.952331i | \(0.598679\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3843i | 1.02319i | 0.859226 | + | 0.511596i | \(0.170945\pi\) | ||||
−0.859226 | + | 0.511596i | \(0.829055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.65634 | −0.643493 | −0.321746 | − | 0.946826i | \(-0.604270\pi\) | ||||
−0.321746 | + | 0.946826i | \(0.604270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.31835 | 0.509406 | 0.254703 | − | 0.967019i | \(-0.418022\pi\) | ||||
0.254703 | + | 0.967019i | \(0.418022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8977i | 1.30739i | 0.756759 | + | 0.653694i | \(0.226782\pi\) | ||||
−0.756759 | + | 0.653694i | \(0.773218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.88244i | − 0.175539i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.585786 | −0.0536990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6230 | −0.965726 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.2855i | − 1.00940i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.16693i | − 0.192284i | −0.995368 | − | 0.0961419i | \(-0.969350\pi\) | ||||
0.995368 | − | 0.0961419i | \(-0.0306503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.98414 | −0.697578 | −0.348789 | − | 0.937201i | \(-0.613407\pi\) | ||||
−0.348789 | + | 0.937201i | \(0.613407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.89898 | 0.338084 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 10.1862i | − 0.870264i | −0.900367 | − | 0.435132i | \(-0.856702\pi\) | ||||
0.900367 | − | 0.435132i | \(-0.143298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.53590i | 0.215092i | 0.994200 | + | 0.107546i | \(0.0342993\pi\) | ||||
−0.994200 | + | 0.107546i | \(0.965701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41421 | −0.285511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.5008 | 0.872043 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.02798i | 0.575755i | 0.957667 | + | 0.287877i | \(0.0929495\pi\) | ||||
−0.957667 | + | 0.287877i | \(0.907050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.79947 | 0.546147 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.21733 | −0.256771 | −0.128386 | − | 0.991724i | \(-0.540979\pi\) | ||||
−0.128386 | + | 0.991724i | \(0.540979\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.850087i | 0.0669963i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.23748i | 0.645209i | 0.946534 | + | 0.322605i | \(0.104558\pi\) | ||||
−0.946534 | + | 0.322605i | \(0.895442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.8836 | −1.53864 | −0.769321 | − | 0.638862i | \(-0.779405\pi\) | ||||
−0.769321 | + | 0.638862i | \(0.779405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.9189 | 1.37838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2855i | 0.858019i | 0.903300 | + | 0.429010i | \(0.141137\pi\) | ||||
−0.903300 | + | 0.429010i | \(0.858863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0963763i | 0.00728536i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8126 | −1.40612 | −0.703059 | − | 0.711132i | \(-0.748183\pi\) | ||||
−0.703059 | + | 0.711132i | \(0.748183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4548 | 0.851430 | 0.425715 | − | 0.904857i | \(-0.360023\pi\) | ||||
0.425715 | + | 0.904857i | \(0.360023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 4.80876i | − 0.353547i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.359681i | 0.0263025i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.336613 | 0.0243565 | 0.0121782 | − | 0.999926i | \(-0.496123\pi\) | ||||
0.0121782 | + | 0.999926i | \(0.496123\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.80725 | −0.705941 | −0.352971 | − | 0.935634i | \(-0.614828\pi\) | ||||
−0.352971 | + | 0.935634i | \(0.614828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.38750i | − 0.312596i | −0.987710 | − | 0.156298i | \(-0.950044\pi\) | ||||
0.987710 | − | 0.156298i | \(-0.0499561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.21609i | 0.369759i | 0.982761 | + | 0.184879i | \(0.0591894\pi\) | ||||
−0.982761 | + | 0.184879i | \(0.940811\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.74202 | −0.332824 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4595 | −0.940049 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 2.39403i | − 0.165598i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.12096i | − 0.214855i | −0.994213 | − | 0.107428i | \(-0.965739\pi\) | ||||
0.994213 | − | 0.107428i | \(-0.0342614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.4110 | −1.39202 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.07055 | −0.208443 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.25725i | − 0.219107i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.21858i | − 0.483392i | −0.970352 | − | 0.241696i | \(-0.922296\pi\) | ||||
0.970352 | − | 0.241696i | \(-0.0777036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.85765 | 0.587903 | 0.293951 | − | 0.955820i | \(-0.405030\pi\) | ||||
0.293951 | + | 0.955820i | \(0.405030\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.677003 | −0.0447376 | −0.0223688 | − | 0.999750i | \(-0.507121\pi\) | ||||
−0.0223688 | + | 0.999750i | \(0.507121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.89898i | 0.582992i | 0.956572 | + | 0.291496i | \(0.0941529\pi\) | ||||
−0.956572 | + | 0.291496i | \(0.905847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.56048i | − 0.493191i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0134 | 0.647711 | 0.323855 | − | 0.946107i | \(-0.395021\pi\) | ||||
0.323855 | + | 0.946107i | \(0.395021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.8306 | −0.890906 | −0.445453 | − | 0.895305i | \(-0.646957\pi\) | ||||
−0.445453 | + | 0.895305i | \(0.646957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.21441i | 0.141474i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.6802i | 1.37948i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5546 | −0.729319 | −0.364660 | − | 0.931141i | \(-0.618815\pi\) | ||||
−0.364660 | + | 0.931141i | \(0.618815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.521966 | 0.0328157 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 8.80604i | − 0.549306i | −0.961543 | − | 0.274653i | \(-0.911437\pi\) | ||||
0.961543 | − | 0.274653i | \(-0.0885629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17157i | 0.134935i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9662 | 0.984520 | 0.492260 | − | 0.870448i | \(-0.336171\pi\) | ||||
0.492260 | + | 0.870448i | \(0.336171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.89877 | 0.608076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.05870i | − 0.308434i | −0.988037 | − | 0.154217i | \(-0.950714\pi\) | ||||
0.988037 | − | 0.154217i | \(-0.0492855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.05845i | 0.125042i | 0.998044 | + | 0.0625209i | \(0.0199140\pi\) | ||||
−0.998044 | + | 0.0625209i | \(0.980086\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0591764 | 0.00356847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.1598 | 1.69196 | 0.845979 | − | 0.533216i | \(-0.179017\pi\) | ||||
0.845979 | + | 0.533216i | \(0.179017\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.1676i | 1.79965i | 0.436252 | + | 0.899824i | \(0.356305\pi\) | ||||
−0.436252 | + | 0.899824i | \(0.643695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3044i | 1.38530i | 0.721272 | + | 0.692652i | \(0.243558\pi\) | ||||
−0.721272 | + | 0.692652i | \(0.756442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.07812 | 0.358780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6569 | 0.979815 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.3273i | 1.30437i | 0.758058 | + | 0.652187i | \(0.226148\pi\) | ||||
−0.758058 | + | 0.652187i | \(0.773852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.8104i | 1.79385i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.72689 | −0.273363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.21733 | 0.531278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.7707i | 1.13207i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.0985i | − 0.918792i | −0.888232 | − | 0.459396i | \(-0.848066\pi\) | ||||
0.888232 | − | 0.459396i | \(-0.151934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.486010 | 0.0275591 | 0.0137796 | − | 0.999905i | \(-0.495614\pi\) | ||||
0.0137796 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4899 | 0.649449 | 0.324724 | − | 0.945809i | \(-0.394728\pi\) | ||||
0.324724 | + | 0.945809i | \(0.394728\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.77021i | − 0.492584i | −0.969196 | − | 0.246292i | \(-0.920788\pi\) | ||||
0.969196 | − | 0.246292i | \(-0.0792122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.91167i | 0.163022i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.28397 | 0.127083 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.535898 | −0.0297263 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.41421i | 0.188232i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 22.3246i | − 1.22707i | −0.789668 | − | 0.613535i | \(-0.789747\pi\) | ||||
0.789668 | − | 0.613535i | \(-0.210253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.6997 | −0.584585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.19275 | −0.391814 | −0.195907 | − | 0.980622i | \(-0.562765\pi\) | ||||
−0.195907 | + | 0.980622i | \(0.562765\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.88536i | 0.102098i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.99776 | 0.375659 | 0.187830 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187830 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.47496 | −0.346597 | −0.173298 | − | 0.984869i | \(-0.555442\pi\) | ||||
−0.173298 | + | 0.984869i | \(0.555442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.9605i | 1.22206i | 0.791606 | + | 0.611032i | \(0.209245\pi\) | ||||
−0.791606 | + | 0.611032i | \(0.790755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 11.8163i | − 0.627145i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.7819 | −1.51905 | −0.759525 | − | 0.650478i | \(-0.774569\pi\) | ||||
−0.759525 | + | 0.650478i | \(0.774569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.79796 | 0.199893 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.5672i | 1.07654i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.1867i | 1.78453i | 0.451513 | + | 0.892264i | \(0.350884\pi\) | ||||
−0.451513 | + | 0.892264i | \(0.649116\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.47015 | −0.232079 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1457 | 0.835995 | 0.417998 | − | 0.908448i | \(-0.362732\pi\) | ||||
0.417998 | + | 0.908448i | \(0.362732\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 26.3679i | − 1.35802i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 14.4370i | − 0.741581i | −0.928717 | − | 0.370790i | \(-0.879087\pi\) | ||||
0.928717 | − | 0.370790i | \(-0.120913\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.5546 | −0.999193 | −0.499596 | − | 0.866258i | \(-0.666518\pi\) | ||||
−0.499596 | + | 0.866258i | \(0.666518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.35968 | 0.0692958 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.9116i | 1.36447i | 0.731131 | + | 0.682237i | \(0.238993\pi\) | ||||
−0.731131 | + | 0.682237i | \(0.761007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.497970i | 0.0251834i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.87248 | 0.144530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.6383 | −1.98939 | −0.994694 | − | 0.102877i | \(-0.967195\pi\) | ||||
−0.994694 | + | 0.102877i | \(0.967195\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.79744i | 0.139698i | 0.997558 | + | 0.0698488i | \(0.0222517\pi\) | ||||
−0.997558 | + | 0.0698488i | \(0.977748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 17.0737i | − 0.850504i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.33338 | 0.0660930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.7318 | −1.17346 | −0.586732 | − | 0.809781i | \(-0.699586\pi\) | ||||
−0.586732 | + | 0.809781i | \(0.699586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 13.9136i | − 0.684643i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.1975i | 1.58051i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.4268 | −0.802503 | −0.401252 | − | 0.915968i | \(-0.631425\pi\) | ||||
−0.401252 | + | 0.915968i | \(0.631425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9695 | −0.973255 | −0.486628 | − | 0.873609i | \(-0.661773\pi\) | ||||
−0.486628 | + | 0.873609i | \(0.661773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0564559i | 0.00273852i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8.92820i | − 0.432066i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.4332 | −1.41775 | −0.708873 | − | 0.705337i | \(-0.750796\pi\) | ||||
−0.708873 | + | 0.705337i | \(0.750796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.23873 | 0.155643 | 0.0778216 | − | 0.996967i | \(-0.475204\pi\) | ||||
0.0778216 | + | 0.996967i | \(0.475204\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.31447i | − 0.158553i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.94835i | 0.379354i | 0.981847 | + | 0.189677i | \(0.0607441\pi\) | ||||
−0.981847 | + | 0.189677i | \(0.939256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.67171 | 0.174448 | 0.0872242 | − | 0.996189i | \(-0.472200\pi\) | ||||
0.0872242 | + | 0.996189i | \(0.472200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.2574 | 1.19732 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.6392i | 1.11560i | 0.829974 | + | 0.557802i | \(0.188355\pi\) | ||||
−0.829974 | + | 0.557802i | \(0.811645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3.73205i | − 0.175735i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.3132 | −0.577251 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.57826 | −0.448052 | −0.224026 | − | 0.974583i | \(-0.571920\pi\) | ||||
−0.224026 | + | 0.974583i | \(0.571920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.7836i | 1.80633i | 0.429290 | + | 0.903166i | \(0.358764\pi\) | ||||
−0.429290 | + | 0.903166i | \(0.641236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 25.7060i | − 1.19466i | −0.801996 | − | 0.597330i | \(-0.796228\pi\) | ||||
0.801996 | − | 0.597330i | \(-0.203772\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0983 | −0.513568 | −0.256784 | − | 0.966469i | \(-0.582663\pi\) | ||||
−0.256784 | + | 0.966469i | \(0.582663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.83183 | 0.223113 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5.65957i | − 0.260228i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.375769i | − 0.0172415i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.2713 | −0.606383 | −0.303192 | − | 0.952930i | \(-0.598052\pi\) | ||||
−0.303192 | + | 0.952930i | \(0.598052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0750 | −0.550572 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 16.1018i | − 0.731144i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.20929i | − 0.371998i | −0.982550 | − | 0.185999i | \(-0.940448\pi\) | ||||
0.982550 | − | 0.185999i | \(-0.0595522\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.7413 | −1.29708 | −0.648539 | − | 0.761182i | \(-0.724620\pi\) | ||||
−0.648539 | + | 0.761182i | \(0.724620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.77781 | −0.125106 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.33610i | 0.239357i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 29.7600i | − 1.33224i | −0.745844 | − | 0.666121i | \(-0.767953\pi\) | ||||
0.745844 | − | 0.666121i | \(-0.232047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.75715 | 0.390462 | 0.195231 | − | 0.980757i | \(-0.437454\pi\) | ||||
0.195231 | + | 0.980757i | \(0.437454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.3874 | 1.88622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 29.6843i | − 1.31573i | −0.753134 | − | 0.657867i | \(-0.771459\pi\) | ||||
0.753134 | − | 0.657867i | \(-0.228541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 9.28788i | − 0.410872i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.9950 | 1.01328 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.09638 | 0.0921985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.8766i | 0.476512i | 0.971202 | + | 0.238256i | \(0.0765757\pi\) | ||||
−0.971202 | + | 0.238256i | \(0.923424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17.7812i | − 0.777518i | −0.921339 | − | 0.388759i | \(-0.872904\pi\) | ||||
0.921339 | − | 0.388759i | \(-0.127096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.79869 | −0.0783521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2774 | −0.968581 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.7972i | 1.46392i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7399i | 0.637261i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.614014 | −0.0264475 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7433 | −0.676857 | −0.338428 | − | 0.940992i | \(-0.609895\pi\) | ||||
−0.338428 | + | 0.940992i | \(0.609895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 11.7770i | − 0.504472i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 41.8963i | − 1.79136i | −0.444704 | − | 0.895678i | \(-0.646691\pi\) | ||||
0.444704 | − | 0.895678i | \(-0.353309\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.4890 | 0.787659 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.29717 | −0.0551614 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.2681i | 1.28250i | 0.767332 | + | 0.641251i | \(0.221584\pi\) | ||||
−0.767332 | + | 0.641251i | \(0.778416\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.2528i | 2.16776i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.8126 | 1.29860 | 0.649298 | − | 0.760535i | \(-0.275063\pi\) | ||||
0.649298 | + | 0.760535i | \(0.275063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.7753 | 1.29473 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 15.8252i | − 0.663427i | −0.943380 | − | 0.331713i | \(-0.892373\pi\) | ||||
0.943380 | − | 0.331713i | \(-0.107627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00929i | 0.251481i | 0.992063 | + | 0.125740i | \(0.0401307\pi\) | ||||
−0.992063 | + | 0.125740i | \(0.959869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0819283 | 0.00341665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.5148 | −1.10383 | −0.551913 | − | 0.833901i | \(-0.686102\pi\) | ||||
−0.551913 | + | 0.833901i | \(0.686102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 14.5400i | − 0.603220i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.74474i | 0.113675i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.9572 | 1.64921 | 0.824605 | − | 0.565708i | \(-0.191397\pi\) | ||||
0.824605 | + | 0.565708i | \(0.191397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9720 | 0.493299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.10931i | 0.127684i | 0.997960 | + | 0.0638421i | \(0.0203354\pi\) | ||||
−0.997960 | + | 0.0638421i | \(0.979665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.29717i | 0.0531789i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.1517 | −1.23196 | −0.615982 | − | 0.787760i | \(-0.711241\pi\) | ||||
−0.615982 | + | 0.787760i | \(0.711241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9024 | 0.607881 | 0.303940 | − | 0.952691i | \(-0.401698\pi\) | ||||
0.303940 | + | 0.952691i | \(0.401698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.5237i | 0.956373i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.7060i | 0.881020i | 0.897748 | + | 0.440510i | \(0.145202\pi\) | ||||
−0.897748 | + | 0.440510i | \(0.854798\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.9847 | −0.768037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.5127 | −1.71707 | −0.858535 | − | 0.512754i | \(-0.828625\pi\) | ||||
−0.858535 | + | 0.512754i | \(0.828625\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 2.68460i | − 0.108078i | −0.998539 | − | 0.0540390i | \(-0.982790\pi\) | ||||
0.998539 | − | 0.0540390i | \(-0.0172095\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 20.9631i | − 0.842578i | −0.906926 | − | 0.421289i | \(-0.861578\pi\) | ||||
0.906926 | − | 0.421289i | \(-0.138422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.4059 | −0.456969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.5088 | −0.980353 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.27208i | 0.0507211i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.458427i | 0.0182497i | 0.999958 | + | 0.00912484i | \(0.00290457\pi\) | ||||
−0.999958 | + | 0.00912484i | \(0.997095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.79847 | −0.190422 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.56048 | 0.220314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4573i | 0.531531i | 0.964038 | + | 0.265766i | \(0.0856248\pi\) | ||||
−0.964038 | + | 0.265766i | \(0.914375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 44.4655i | − 1.75355i | −0.480904 | − | 0.876773i | \(-0.659691\pi\) | ||||
0.480904 | − | 0.876773i | \(-0.340309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.4377 | 1.58977 | 0.794885 | − | 0.606760i | \(-0.207531\pi\) | ||||
0.794885 | + | 0.606760i | \(0.207531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.54315 | −0.335348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 50.2226i | − 1.96536i | −0.185304 | − | 0.982681i | \(-0.559327\pi\) | ||||
0.185304 | − | 0.982681i | \(-0.440673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.6802i | 0.690822i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.3533 | 1.92253 | 0.961266 | − | 0.275622i | \(-0.0888839\pi\) | ||||
0.961266 | + | 0.275622i | \(0.0888839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3476 | 1.18038 | 0.590192 | − | 0.807263i | \(-0.299052\pi\) | ||||
0.590192 | + | 0.807263i | \(0.299052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 8.63395i | − 0.334810i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.03113i | 0.156086i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.48205 | −0.211632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 34.2805i | − 1.31751i | −0.752359 | − | 0.658753i | \(-0.771084\pi\) | ||||
0.752359 | − | 0.658753i | \(-0.228916\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.27135i | 0.279049i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.5843 | 0.787636 | 0.393818 | − | 0.919188i | \(-0.371154\pi\) | ||||
0.393818 | + | 0.919188i | \(0.371154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5564 | −0.861836 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 24.8562i | − 0.946946i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7778i | 1.39909i | 0.714587 | + | 0.699547i | \(0.246615\pi\) | ||||
−0.714587 | + | 0.699547i | \(0.753385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.61553 | 0.213009 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.56048 | 0.134863 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 29.0711i | − 1.09800i | −0.835823 | − | 0.549000i | \(-0.815009\pi\) | ||||
0.835823 | − | 0.549000i | \(-0.184991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 8.46692i | − 0.319336i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.1416 | −0.719895 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4663 | −1.40707 | −0.703537 | − | 0.710658i | \(-0.748397\pi\) | ||||
−0.703537 | + | 0.710658i | \(0.748397\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.61024i | 0.0977542i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.56048i | 0.282746i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.0552 | −0.971696 | −0.485848 | − | 0.874043i | \(-0.661489\pi\) | ||||
−0.485848 | + | 0.874043i | \(0.661489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3843 | −0.386730 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.457018i | 0.0169732i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 41.9975i | − 1.55760i | −0.627271 | − | 0.778801i | \(-0.715828\pi\) | ||||
0.627271 | − | 0.778801i | \(-0.284172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.39939 | 0.199704 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.2375 | 1.19072 | 0.595359 | − | 0.803460i | \(-0.297010\pi\) | ||||
0.595359 | + | 0.803460i | \(0.297010\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.96681i | − 0.109284i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 36.1810i | − 1.33094i | −0.746425 | − | 0.665469i | \(-0.768231\pi\) | ||||
0.746425 | − | 0.665469i | \(-0.231769\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0113 | −0.660771 | −0.330386 | − | 0.943846i | \(-0.607179\pi\) | ||||
−0.330386 | + | 0.943846i | \(0.607179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.5628 | 0.570179 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 6.65634i | − 0.243217i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 32.1484i | − 1.17311i | −0.809909 | − | 0.586555i | \(-0.800484\pi\) | ||||
0.809909 | − | 0.586555i | \(-0.199516\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.40159 | 0.159979 | 0.0799893 | − | 0.996796i | \(-0.474511\pi\) | ||||
0.0799893 | + | 0.996796i | \(0.474511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 35.7247i | − 1.29502i | −0.762057 | − | 0.647509i | \(-0.775811\pi\) | ||||
0.762057 | − | 0.647509i | \(-0.224189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31835i | 0.192537i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 77.3662 | 2.79353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.1561 | −0.762907 | −0.381454 | − | 0.924388i | \(-0.624576\pi\) | ||||
−0.381454 | + | 0.924388i | \(0.624576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.9557i | 1.11340i | 0.830714 | + | 0.556700i | \(0.187933\pi\) | ||||
−0.830714 | + | 0.556700i | \(0.812067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.295929i | 0.0106301i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.6984 | −0.849085 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.27644 | 0.117240 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.12450i | 0.254284i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 32.2326i | − 1.14897i | −0.818515 | − | 0.574484i | \(-0.805203\pi\) | ||||
0.818515 | − | 0.574484i | \(-0.194797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8977 | −0.494147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.6451 | 1.76295 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 11.4686i | − 0.406240i | −0.979154 | − | 0.203120i | \(-0.934892\pi\) | ||||
0.979154 | − | 0.203120i | \(-0.0651082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000i | 0.0707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.70289 | −0.201251 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.88244 | 0.0663474 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.12628i | 0.215389i | 0.994184 | + | 0.107694i | \(0.0343468\pi\) | ||||
−0.994184 | + | 0.107694i | \(0.965653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23645i | 0.113647i | 0.998384 | + | 0.0568236i | \(0.0180973\pi\) | ||||
−0.998384 | + | 0.0568236i | \(0.981903\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.2412 | 0.638961 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.9382 | −1.25732 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.7411i | 0.793668i | 0.917890 | + | 0.396834i | \(0.129891\pi\) | ||||
−0.917890 | + | 0.396834i | \(0.870109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 16.9282i | − 0.590080i | −0.955485 | − | 0.295040i | \(-0.904667\pi\) | ||||
0.955485 | − | 0.295040i | \(-0.0953330\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0092 | 1.87808 | 0.939041 | − | 0.343805i | \(-0.111716\pi\) | ||||
0.939041 | + | 0.343805i | \(0.111716\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.8581 | −1.28013 | −0.640067 | − | 0.768319i | \(-0.721094\pi\) | ||||
−0.640067 | + | 0.768319i | \(0.721094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.585786i | − 0.0202963i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.0306i | 1.52374i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.700690 | 0.0241905 | 0.0120953 | − | 0.999927i | \(-0.496150\pi\) | ||||
0.0120953 | + | 0.999927i | \(0.496150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.51326 | 0.224595 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 39.6799i | − 1.36503i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10.6230i | − 0.365010i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.84603 | 0.0632810 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.2951 | −1.41392 | −0.706959 | − | 0.707254i | \(-0.749934\pi\) | ||||
−0.706959 | + | 0.707254i | \(0.749934\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.9935i | 0.614645i | 0.951605 | + | 0.307323i | \(0.0994331\pi\) | ||||
−0.951605 | + | 0.307323i | \(0.900567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21.6877i | − 0.739973i | −0.929037 | − | 0.369987i | \(-0.879362\pi\) | ||||
0.929037 | − | 0.369987i | \(-0.120638\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.6116 | −0.769706 | −0.384853 | − | 0.922978i | \(-0.625748\pi\) | ||||
−0.384853 | + | 0.922978i | \(0.625748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.9907 | 0.849710 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.796483i | 0.0270188i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.8673i | 0.910363i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.2855 | 0.381519 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.7821 | −1.17451 | −0.587254 | − | 0.809402i | \(-0.699791\pi\) | ||||
−0.587254 | + | 0.809402i | \(0.699791\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 33.6493i | − 1.13367i | −0.823830 | − | 0.566837i | \(-0.808167\pi\) | ||||
0.823830 | − | 0.566837i | \(-0.191833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.1132i | 1.88836i | 0.329429 | + | 0.944180i | \(0.393144\pi\) | ||||
−0.329429 | + | 0.944180i | \(0.606856\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.7126 | −0.863344 | −0.431672 | − | 0.902031i | \(-0.642076\pi\) | ||||
−0.431672 | + | 0.902031i | \(0.642076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.16693 | 0.0726765 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 13.3119i | − 0.445467i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.6588i | 1.39250i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.5606 | −0.485624 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.61856 | −0.0872367 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 25.3657i | − 0.843184i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.05322i | 0.234198i | 0.993120 | + | 0.117099i | \(0.0373595\pi\) | ||||
−0.993120 | + | 0.117099i | \(0.962640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1805 | 1.09932 | 0.549659 | − | 0.835389i | \(-0.314758\pi\) | ||||
0.549659 | + | 0.835389i | \(0.314758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.92776 | −0.295466 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 7.98414i | − 0.263660i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7710i | 0.487251i | 0.969869 | + | 0.243625i | \(0.0783367\pi\) | ||||
−0.969869 | + | 0.243625i | \(0.921663\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.6713 | −0.976641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.209288 | 0.00688135 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.9025i | 0.718598i | 0.933222 | + | 0.359299i | \(0.116984\pi\) | ||||
−0.933222 | + | 0.359299i | \(0.883016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.89898i | 0.127784i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.796483 | 0.0260478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.8854 | 1.72769 | 0.863846 | − | 0.503757i | \(-0.168049\pi\) | ||||
0.863846 | + | 0.503757i | \(0.168049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 0.929998i | − 0.0303171i | −0.999885 | − | 0.0151585i | \(-0.995175\pi\) | ||||
0.999885 | − | 0.0151585i | \(-0.00482530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.16693i | − 0.168258i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.7277 | −0.413593 | −0.206797 | − | 0.978384i | \(-0.566304\pi\) | ||||
−0.206797 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.6451 | 1.67647 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.98965i | − 0.129238i | −0.997910 | − | 0.0646188i | \(-0.979417\pi\) | ||||
0.997910 | − | 0.0646188i | \(-0.0205831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 0.745400i | − 0.0241206i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.1862 | 0.328929 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.5717 | 0.695862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.7173i | 0.699104i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.37871i | − 0.0764940i | −0.999268 | − | 0.0382470i | \(-0.987823\pi\) | ||||
0.999268 | − | 0.0382470i | \(-0.0121774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.5224 | −1.30042 | −0.650212 | − | 0.759753i | \(-0.725320\pi\) | ||||
−0.650212 | + | 0.759753i | \(0.725320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.53590 | −0.0812972 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 14.2117i | − 0.454671i | −0.973816 | − | 0.227336i | \(-0.926999\pi\) | ||||
0.973816 | − | 0.227336i | \(-0.0730014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.00340i | 0.223830i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.6919 | 1.07461 | 0.537303 | − | 0.843389i | \(-0.319443\pi\) | ||||
0.537303 | + | 0.843389i | \(0.319443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.71573 | −0.309569 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 7.83554i | − 0.249156i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9339i | 0.823817i | 0.911225 | + | 0.411908i | \(0.135138\pi\) | ||||
−0.911225 | + | 0.411908i | \(0.864862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.5506 | 0.366178 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3697 | 0.993487 | 0.496744 | − | 0.867897i | \(-0.334529\pi\) | ||||
0.496744 | + | 0.867897i | \(0.334529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 6048.2.h.a.2591.3 | ✓ | 8 | |
3.2 | odd | 2 | 6048.2.h.g.2591.6 | yes | 8 | ||
4.3 | odd | 2 | 6048.2.h.g.2591.3 | yes | 8 | ||
12.11 | even | 2 | inner | 6048.2.h.a.2591.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.a.2591.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.a.2591.6 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.g.2591.3 | yes | 8 | 4.3 | odd | 2 | ||
6048.2.h.g.2591.6 | yes | 8 | 3.2 | odd | 2 |