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: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.5 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.d.2591.4 |
$q$-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 | ||||||||
\(5\) | 0.317837i | 0.142141i | 0.997471 | + | 0.0710706i | \(0.0226416\pi\) | ||||
−0.997471 | + | 0.0710706i | \(0.977358\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.87832 | −1.47087 | −0.735434 | − | 0.677597i | \(-0.763022\pi\) | ||||
−0.735434 | + | 0.677597i | \(0.763022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.317837i | 0.0770869i | 0.999257 | + | 0.0385434i | \(0.0122718\pi\) | ||||
−0.999257 | + | 0.0385434i | \(0.987728\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.449490i | 0.103120i | 0.998670 | + | 0.0515600i | \(0.0164193\pi\) | ||||
−0.998670 | + | 0.0515600i | \(0.983581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | 0.979796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.70674i | − 1.43111i | −0.698558 | − | 0.715553i | \(-0.746175\pi\) | ||||
0.698558 | − | 0.715553i | \(-0.253825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.44949i | 0.799152i | 0.916700 | + | 0.399576i | \(0.130843\pi\) | ||||
−0.916700 | + | 0.399576i | \(0.869157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.317837 | 0.0537243 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 5.97469i | − 0.933090i | −0.884497 | − | 0.466545i | \(-0.845499\pi\) | ||||
0.884497 | − | 0.466545i | \(-0.154501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3485i | 1.57813i | 0.614312 | + | 0.789063i | \(0.289434\pi\) | ||||
−0.614312 | + | 0.789063i | \(0.710566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.92480 | 0.572491 | 0.286246 | − | 0.958156i | \(-0.407593\pi\) | ||||
0.286246 | + | 0.958156i | \(0.407593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.635674i | 0.0873166i | 0.999047 | + | 0.0436583i | \(0.0139013\pi\) | ||||
−0.999047 | + | 0.0436583i | \(0.986099\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.55051i | − 0.209071i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.4887 | −1.49570 | −0.747849 | − | 0.663868i | \(-0.768914\pi\) | ||||
−0.747849 | + | 0.663868i | \(0.768914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.34847 | 1.19695 | 0.598474 | − | 0.801142i | \(-0.295774\pi\) | ||||
0.598474 | + | 0.801142i | \(0.295774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.778539i | − 0.0965659i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.10102 | 0.362947 | 0.181473 | − | 0.983396i | \(-0.441913\pi\) | ||||
0.181473 | + | 0.983396i | \(0.441913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.87832i | 0.555936i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.55051i | 0.962008i | 0.876719 | + | 0.481004i | \(0.159728\pi\) | ||||
−0.876719 | + | 0.481004i | \(0.840272\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2173 | 1.12150 | 0.560749 | − | 0.827986i | \(-0.310513\pi\) | ||||
0.560749 | + | 0.827986i | \(0.310513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.101021 | −0.0109572 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1421i | 1.49906i | 0.661968 | + | 0.749532i | \(0.269721\pi\) | ||||
−0.661968 | + | 0.749532i | \(0.730279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.44949i | 0.256776i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.142865 | −0.0146576 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2474 | 1.24354 | 0.621770 | − | 0.783200i | \(-0.286414\pi\) | ||||
0.621770 | + | 0.783200i | \(0.286414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.38551i | 0.436374i | 0.975907 | + | 0.218187i | \(0.0700143\pi\) | ||||
−0.975907 | + | 0.218187i | \(0.929986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.10102i | 0.305553i | 0.988261 | + | 0.152776i | \(0.0488214\pi\) | ||||
−0.988261 | + | 0.152776i | \(0.951179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1421 | 1.36717 | 0.683586 | − | 0.729870i | \(-0.260419\pi\) | ||||
0.683586 | + | 0.729870i | \(0.260419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.68556i | 0.252636i | 0.991990 | + | 0.126318i | \(0.0403160\pi\) | ||||
−0.991990 | + | 0.126318i | \(0.959684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.898979i | 0.0838303i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.317837 | 0.0291361 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.7980 | 1.16345 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.14626i | 0.281410i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2474i | 1.35299i | 0.736446 | + | 0.676496i | \(0.236502\pi\) | ||||
−0.736446 | + | 0.676496i | \(0.763498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0492 | −1.40222 | −0.701111 | − | 0.713052i | \(-0.747312\pi\) | ||||
−0.701111 | + | 0.713052i | \(0.747312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.449490 | 0.0389757 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.97809i | 0.767050i | 0.923530 | + | 0.383525i | \(0.125290\pi\) | ||||
−0.923530 | + | 0.383525i | \(0.874710\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2474i | 1.03882i | 0.854527 | + | 0.519408i | \(0.173847\pi\) | ||||
−0.854527 | + | 0.519408i | \(0.826153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.9494 | 0.999258 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.44949 | 0.203419 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 16.8277i | − 1.37858i | −0.724486 | − | 0.689289i | \(-0.757923\pi\) | ||||
0.724486 | − | 0.689289i | \(-0.242077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2474i | 1.40358i | 0.712385 | + | 0.701789i | \(0.247615\pi\) | ||||
−0.712385 | + | 0.701789i | \(0.752385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.41421 | −0.113592 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3485 | 1.22494 | 0.612471 | − | 0.790493i | \(-0.290176\pi\) | ||||
0.612471 | + | 0.790493i | \(0.290176\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2.82843i | − 0.222911i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2474i | 0.880968i | 0.897760 | + | 0.440484i | \(0.145193\pi\) | ||||
−0.897760 | + | 0.440484i | \(0.854807\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.93160 | 0.768531 | 0.384265 | − | 0.923223i | \(-0.374455\pi\) | ||||
0.384265 | + | 0.923223i | \(0.374455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.12096i | 0.693453i | 0.937966 | + | 0.346727i | \(0.112707\pi\) | ||||
−0.937966 | + | 0.346727i | \(0.887293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.89898i | − 0.370328i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.87832 | −0.364622 | −0.182311 | − | 0.983241i | \(-0.558358\pi\) | ||||
−0.182311 | + | 0.983241i | \(0.558358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6969 | 1.83571 | 0.917854 | − | 0.396917i | \(-0.129920\pi\) | ||||
0.917854 | + | 0.396917i | \(0.129920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2.22486i | − 0.163575i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.55051i | − 0.113385i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0492 | 1.16128 | 0.580638 | − | 0.814162i | \(-0.302803\pi\) | ||||
0.580638 | + | 0.814162i | \(0.302803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | −0.791797 | −0.395899 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395899 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.778539i | 0.0554686i | 0.999615 | + | 0.0277343i | \(0.00882924\pi\) | ||||
−0.999615 | + | 0.0277343i | \(0.991171\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 10.0000i | − 0.708881i | −0.935079 | − | 0.354441i | \(-0.884671\pi\) | ||||
0.935079 | − | 0.354441i | \(-0.115329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.70674 | −0.540907 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.89898 | 0.132630 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 2.19275i | − 0.151676i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 6.00000i | − 0.413057i | −0.978441 | − | 0.206529i | \(-0.933783\pi\) | ||||
0.978441 | − | 0.206529i | \(-0.0662166\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.28913 | −0.224317 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.44949 | 0.302051 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.778539i | − 0.0523702i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 18.2474i | − 1.22194i | −0.791654 | − | 0.610970i | \(-0.790780\pi\) | ||||
0.791654 | − | 0.610970i | \(-0.209220\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.09978 | −0.272112 | −0.136056 | − | 0.990701i | \(-0.543443\pi\) | ||||
−0.136056 | + | 0.990701i | \(0.543443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6969 | 0.839037 | 0.419519 | − | 0.907747i | \(-0.362199\pi\) | ||||
0.419519 | + | 0.907747i | \(0.362199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 18.7347i | − 1.22735i | −0.789558 | − | 0.613676i | \(-0.789690\pi\) | ||||
0.789558 | − | 0.613676i | \(-0.210310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.24745i | 0.0813746i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.32124 | 0.214833 | 0.107416 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107416 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.75255 | −0.241723 | −0.120862 | − | 0.992669i | \(-0.538566\pi\) | ||||
−0.120862 | + | 0.992669i | \(0.538566\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 0.317837i | − 0.0203059i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.10102i | − 0.0700563i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4169 | −1.16246 | −0.581232 | − | 0.813738i | \(-0.697429\pi\) | ||||
−0.581232 | + | 0.813738i | \(0.697429\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.7980 | −0.867470 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 11.0280i | − 0.687906i | −0.938987 | − | 0.343953i | \(-0.888234\pi\) | ||||
0.938987 | − | 0.343953i | \(-0.111766\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.00000i | 0.434959i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.07107 | −0.436021 | −0.218010 | − | 0.975946i | \(-0.569957\pi\) | ||||
−0.218010 | + | 0.975946i | \(0.569957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.202041 | −0.0124113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.0450i | 1.64896i | 0.565888 | + | 0.824482i | \(0.308534\pi\) | ||||
−0.565888 | + | 0.824482i | \(0.691466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.6969i | 1.01427i | 0.861868 | + | 0.507133i | \(0.169295\pi\) | ||||
−0.861868 | + | 0.507133i | \(0.830705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.8988 | −1.44115 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.79796 | 0.528618 | 0.264309 | − | 0.964438i | \(-0.414856\pi\) | ||||
0.264309 | + | 0.964438i | \(0.414856\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 8.48528i | − 0.506189i | −0.967442 | − | 0.253095i | \(-0.918552\pi\) | ||||
0.967442 | − | 0.253095i | \(-0.0814484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.2474i | 1.91691i | 0.285241 | + | 0.958456i | \(0.407926\pi\) | ||||
−0.285241 | + | 0.958456i | \(0.592074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.97469 | −0.352675 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8990 | 0.994058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 20.7525i | − 1.21237i | −0.795322 | − | 0.606187i | \(-0.792698\pi\) | ||||
0.795322 | − | 0.606187i | \(-0.207302\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 3.65153i | − 0.212600i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.92820 | −0.400668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3485 | 0.596476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.97129i | 0.170136i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.89898i | − 0.279600i | −0.990180 | − | 0.139800i | \(-0.955354\pi\) | ||||
0.990180 | − | 0.139800i | \(-0.0446459\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.58166 | −0.543326 | −0.271663 | − | 0.962392i | \(-0.587574\pi\) | ||||
−0.271663 | + | 0.962392i | \(0.587574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.89898 | 0.389953 | 0.194977 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194977 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.285729i | 0.0160481i | 0.999968 | + | 0.00802407i | \(0.00255417\pi\) | ||||
−0.999968 | + | 0.00802407i | \(0.997446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.5959i | 2.10497i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.142865 | −0.00794920 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | −0.665640 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.92480i | − 0.216381i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7.24745i | − 0.398356i | −0.979963 | − | 0.199178i | \(-0.936173\pi\) | ||||
0.979963 | − | 0.199178i | \(-0.0638272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.54270 | 0.138922 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.00000 | 0.163420 | 0.0817102 | − | 0.996656i | \(-0.473962\pi\) | ||||
0.0817102 | + | 0.996656i | \(0.473962\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 21.7060i | − 1.17545i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.69994 | −0.0912577 | −0.0456289 | − | 0.998958i | \(-0.514529\pi\) | ||||
−0.0456289 | + | 0.998958i | \(0.514529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.2020 | 0.760218 | 0.380109 | − | 0.924942i | \(-0.375887\pi\) | ||||
0.380109 | + | 0.924942i | \(0.375887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3602i | 0.551418i | 0.961241 | + | 0.275709i | \(0.0889126\pi\) | ||||
−0.961241 | + | 0.275709i | \(0.911087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1633 | 1.01140 | 0.505701 | − | 0.862709i | \(-0.331234\pi\) | ||||
0.505701 | + | 0.862709i | \(0.331234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7980 | 0.989366 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.985620i | 0.0515897i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.6969i | 0.662775i | 0.943495 | + | 0.331387i | \(0.107517\pi\) | ||||
−0.943495 | + | 0.331387i | \(0.892483\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.635674 | 0.0330026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.2929 | 1.72384 | 0.861919 | − | 0.507045i | \(-0.169262\pi\) | ||||
0.861919 | + | 0.507045i | \(0.169262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.8776i | 0.972245i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.0454i | 1.69743i | 0.528852 | + | 0.848714i | \(0.322623\pi\) | ||||
−0.528852 | + | 0.848714i | \(0.677377\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.83183 | 0.297992 | 0.148996 | − | 0.988838i | \(-0.452396\pi\) | ||||
0.148996 | + | 0.988838i | \(0.452396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.55051 | −0.0790213 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07107i | 0.358517i | 0.983802 | + | 0.179259i | \(0.0573699\pi\) | ||||
−0.983802 | + | 0.179259i | \(0.942630\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.898979i | 0.0454633i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.71767 | −0.136741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.1010 | −0.757898 | −0.378949 | − | 0.925417i | \(-0.623715\pi\) | ||||
−0.378949 | + | 0.925417i | \(0.623715\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6637i | 0.582455i | 0.956654 | + | 0.291228i | \(0.0940637\pi\) | ||||
−0.956654 | + | 0.291228i | \(0.905936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 10.8990i | − 0.542917i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.1482 | 1.69266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.79796 | −0.286691 | −0.143345 | − | 0.989673i | \(-0.545786\pi\) | ||||
−0.143345 | + | 0.989673i | \(0.545786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4887i | 0.565321i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.24745i | 0.159411i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.6096 | −1.00685 | −0.503423 | − | 0.864040i | \(-0.667926\pi\) | ||||
−0.503423 | + | 0.864040i | \(0.667926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.10102 | 0.346083 | 0.173041 | − | 0.984915i | \(-0.444641\pi\) | ||||
0.173041 | + | 0.984915i | \(0.444641\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.55708i | 0.0755294i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 9.34847i | − 0.452404i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.9842 | 1.39612 | 0.698059 | − | 0.716040i | \(-0.254047\pi\) | ||||
0.698059 | + | 0.716040i | \(0.254047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.8434 | 1.24195 | 0.620976 | − | 0.783829i | \(-0.286736\pi\) | ||||
0.620976 | + | 0.783829i | \(0.286736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.27135i | 0.0608169i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 2.00000i | − 0.0954548i | −0.998860 | − | 0.0477274i | \(-0.984802\pi\) | ||||
0.998860 | − | 0.0477274i | \(-0.0151979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8851 | −0.517167 | −0.258584 | − | 0.965989i | \(-0.583256\pi\) | ||||
−0.258584 | + | 0.965989i | \(0.583256\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.49490 | −0.213079 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.6055i | 1.49156i | 0.666194 | + | 0.745778i | \(0.267922\pi\) | ||||
−0.666194 | + | 0.745778i | \(0.732078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.1464i | 1.37245i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.778539 | −0.0364985 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.3939 | −1.00076 | −0.500382 | − | 0.865805i | \(-0.666807\pi\) | ||||
−0.500382 | + | 0.865805i | \(0.666807\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 9.43879i | − 0.439608i | −0.975544 | − | 0.219804i | \(-0.929458\pi\) | ||||
0.975544 | − | 0.219804i | \(-0.0705419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8434i | 1.34046i | 0.742151 | + | 0.670232i | \(0.233806\pi\) | ||||
−0.742151 | + | 0.670232i | \(0.766194\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.8708 | 0.595589 | 0.297794 | − | 0.954630i | \(-0.403749\pi\) | ||||
0.297794 | + | 0.954630i | \(0.403749\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 50.4831i | − 2.32122i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.20204i | 0.101037i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.48188 | 0.250474 | 0.125237 | − | 0.992127i | \(-0.460031\pi\) | ||||
0.125237 | + | 0.992127i | \(0.460031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.1464 | 0.781810 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.89270i | 0.176758i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.20204i | 0.281041i | 0.990078 | + | 0.140521i | \(0.0448776\pi\) | ||||
−0.990078 | + | 0.140521i | \(0.955122\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.6841 | −1.38475 | −0.692377 | − | 0.721536i | \(-0.743437\pi\) | ||||
−0.692377 | + | 0.721536i | \(0.743437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.44949 | 0.110319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 21.4495i | − 0.960211i | −0.877211 | − | 0.480106i | \(-0.840598\pi\) | ||||
0.877211 | − | 0.480106i | \(-0.159402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.1161 | 1.52116 | 0.760581 | − | 0.649243i | \(-0.224914\pi\) | ||||
0.760581 | + | 0.649243i | \(0.224914\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.39388 | −0.0620267 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.79632i | − 0.123945i | −0.998078 | − | 0.0619723i | \(-0.980261\pi\) | ||||
0.998078 | − | 0.0619723i | \(-0.0197391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 3.10102i | − 0.137181i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.985620 | −0.0434316 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.1464 | −0.842059 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 33.0518i | − 1.44803i | −0.689786 | − | 0.724013i | \(-0.742295\pi\) | ||||
0.689786 | − | 0.724013i | \(-0.257705\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 32.7423i | − 1.43172i | −0.698242 | − | 0.715861i | \(-0.746034\pi\) | ||||
0.698242 | − | 0.715861i | \(-0.253966\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.41421 | −0.0616041 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.6349i | 0.633910i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.49490i | 0.194331i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.87832 | 0.210124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.59592 | 0.111607 | 0.0558036 | − | 0.998442i | \(-0.482228\pi\) | ||||
0.0558036 | + | 0.998442i | \(0.482228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.22486i | 0.0953026i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.0454i | 1.75497i | 0.479600 | + | 0.877487i | \(0.340782\pi\) | ||||
−0.479600 | + | 0.877487i | \(0.659218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.46410 | 0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.55051 | 0.363605 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.0265i | 1.65361i | 0.562491 | + | 0.826803i | \(0.309843\pi\) | ||||
−0.562491 | + | 0.826803i | \(0.690157\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 25.3485i | − 1.07213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.77101 | 0.369654 | 0.184827 | − | 0.982771i | \(-0.440828\pi\) | ||||
0.184827 | + | 0.982771i | \(0.440828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.853572 | −0.0359100 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.8549i | 1.75465i | 0.479896 | + | 0.877325i | \(0.340674\pi\) | ||||
−0.479896 | + | 0.877325i | \(0.659326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.55051i | 0.106736i | 0.998575 | + | 0.0533678i | \(0.0169956\pi\) | ||||
−0.998575 | + | 0.0533678i | \(0.983004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.8564 | 0.577852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.89898 | 0.287208 | 0.143604 | − | 0.989635i | \(-0.454131\pi\) | ||||
0.143604 | + | 0.989635i | \(0.454131\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 10.2173i | − 0.423886i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3.10102i | − 0.128431i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.48528 | −0.350225 | −0.175113 | − | 0.984548i | \(-0.556029\pi\) | ||||
−0.175113 | + | 0.984548i | \(0.556029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0813i | 0.660378i | 0.943915 | + | 0.330189i | \(0.107113\pi\) | ||||
−0.943915 | + | 0.330189i | \(0.892887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.101021i | 0.00414144i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.43539 | 0.262943 | 0.131472 | − | 0.991320i | \(-0.458030\pi\) | ||||
0.131472 | + | 0.991320i | \(0.458030\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7526 | −0.479397 | −0.239698 | − | 0.970847i | \(-0.577049\pi\) | ||||
−0.239698 | + | 0.970847i | \(0.577049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.06767i | 0.165374i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 39.8434i | − 1.61719i | −0.588364 | − | 0.808596i | \(-0.700228\pi\) | ||||
0.588364 | − | 0.808596i | \(-0.299772\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.61377 | −0.388931 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0000 | −0.807792 | −0.403896 | − | 0.914805i | \(-0.632344\pi\) | ||||
−0.403896 | + | 0.914805i | \(0.632344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 39.3123i | − 1.58265i | −0.611395 | − | 0.791326i | \(-0.709391\pi\) | ||||
0.611395 | − | 0.791326i | \(-0.290609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.14643i | 0.126466i | 0.997999 | + | 0.0632328i | \(0.0201411\pi\) | ||||
−0.997999 | + | 0.0632328i | \(0.979859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.1421 | 0.566593 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4949 | 0.939796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 2.22486i | − 0.0887110i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.550510i | 0.0219155i | 0.999940 | + | 0.0109577i | \(0.00348802\pi\) | ||||
−0.999940 | + | 0.0109577i | \(0.996512\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.84621 | −0.192316 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44949 | 0.0970523 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1.69994i | − 0.0671437i | −0.999436 | − | 0.0335719i | \(-0.989312\pi\) | ||||
0.999436 | − | 0.0335719i | \(-0.0106883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.6969i | 1.76268i | 0.472487 | + | 0.881338i | \(0.343356\pi\) | ||||
−0.472487 | + | 0.881338i | \(0.656644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.1845 | 0.950791 | 0.475395 | − | 0.879772i | \(-0.342305\pi\) | ||||
0.475395 | + | 0.879772i | \(0.342305\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.0454 | 2.19997 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.51399i | − 0.215779i | −0.994163 | − | 0.107890i | \(-0.965591\pi\) | ||||
0.994163 | − | 0.107890i | \(-0.0344093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 5.10102i | − 0.199313i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8776 | −0.735366 | −0.367683 | − | 0.929951i | \(-0.619849\pi\) | ||||
−0.367683 | + | 0.929951i | \(0.619849\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.7423 | −1.81807 | −0.909033 | − | 0.416724i | \(-0.863178\pi\) | ||||
−0.909033 | + | 0.416724i | \(0.863178\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.142865i | 0.00554005i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 21.7980i | − 0.844020i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.6048 | −1.76055 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.2929 | −0.859326 | −0.429663 | − | 0.902989i | \(-0.641368\pi\) | ||||
−0.429663 | + | 0.902989i | \(0.641368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.6554i | 1.29348i | 0.762710 | + | 0.646741i | \(0.223869\pi\) | ||||
−0.762710 | + | 0.646741i | \(0.776131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 12.2474i | − 0.470014i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.1270 | −1.11451 | −0.557257 | − | 0.830340i | \(-0.688146\pi\) | ||||
−0.557257 | + | 0.830340i | \(0.688146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.85357 | −0.109029 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1.55708i | − 0.0593200i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 3.75255i | − 0.142754i | −0.997449 | − | 0.0713769i | \(-0.977261\pi\) | ||||
0.997449 | − | 0.0713769i | \(-0.0227393\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.89270 | −0.147658 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.89898 | 0.0719290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 15.5563i | − 0.587555i | −0.955874 | − | 0.293778i | \(-0.905087\pi\) | ||||
0.955874 | − | 0.293778i | \(-0.0949125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.14643i | − 0.118670i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.38551 | 0.164934 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0000 | 1.31445 | 0.657226 | − | 0.753693i | \(-0.271730\pi\) | ||||
0.657226 | + | 0.753693i | \(0.271730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.5851i | 0.471314i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.79796i | 0.142036i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.3368 | 1.76537 | 0.882683 | − | 0.469969i | \(-0.155735\pi\) | ||||
0.882683 | + | 0.469969i | \(0.155735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.10102 | 0.115488 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 37.7552i | − 1.40219i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7526i | 0.658406i | 0.944259 | + | 0.329203i | \(0.106780\pi\) | ||||
−0.944259 | + | 0.329203i | \(0.893220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.28913 | −0.121653 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.1010 | 1.22261 | 0.611307 | − | 0.791394i | \(-0.290644\pi\) | ||||
0.611307 | + | 0.791394i | \(0.290644\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.0265i | 1.43756i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.404082i | 0.0148644i | 0.999972 | + | 0.00743220i | \(0.00236576\pi\) | ||||
−0.999972 | + | 0.00743220i | \(0.997634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.1120 | −1.65500 | −0.827499 | − | 0.561467i | \(-0.810237\pi\) | ||||
−0.827499 | + | 0.561467i | \(0.810237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.34847 | 0.195953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 14.1421i | − 0.516742i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 25.3939i | − 0.926636i | −0.886192 | − | 0.463318i | \(-0.846659\pi\) | ||||
0.886192 | − | 0.463318i | \(-0.153341\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.48188 | −0.199506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.6969 | −1.95165 | −0.975824 | − | 0.218557i | \(-0.929865\pi\) | ||||
−0.975824 | + | 0.218557i | \(0.929865\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 33.9732i | − 1.23153i | −0.787930 | − | 0.615764i | \(-0.788847\pi\) | ||||
0.787930 | − | 0.615764i | \(-0.211153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.00000i | − 0.253417i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.1414 | 1.01613 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.8990 | −1.25849 | −0.629245 | − | 0.777207i | \(-0.716636\pi\) | ||||
−0.629245 | + | 0.777207i | \(0.716636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 21.6739i | − 0.779556i | −0.920909 | − | 0.389778i | \(-0.872552\pi\) | ||||
0.920909 | − | 0.389778i | \(-0.127448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.7980i | 0.783006i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.68556 | 0.0962203 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.87832i | 0.174115i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 44.4949i | − 1.58607i | −0.609175 | − | 0.793036i | \(-0.708499\pi\) | ||||
0.609175 | − | 0.793036i | \(-0.291501\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.68556 | 0.0954876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.8990 | −0.813167 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.2275i | 0.681074i | 0.940231 | + | 0.340537i | \(0.110609\pi\) | ||||
−0.940231 | + | 0.340537i | \(0.889391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24745i | 0.0441316i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.1278 | −0.533847 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.898979 | 0.0316849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 27.0771i | − 0.951981i | −0.879450 | − | 0.475991i | \(-0.842090\pi\) | ||||
0.879450 | − | 0.475991i | \(-0.157910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 36.7423i | − 1.29020i | −0.764099 | − | 0.645099i | \(-0.776816\pi\) | ||||
0.764099 | − | 0.645099i | \(-0.223184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.57486 | −0.125222 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.65153 | −0.162736 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 33.3697i | − 1.16461i | −0.812971 | − | 0.582305i | \(-0.802151\pi\) | ||||
0.812971 | − | 0.582305i | \(-0.197849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 9.65153i | − 0.336431i | −0.985750 | − | 0.168216i | \(-0.946200\pi\) | ||||
0.985750 | − | 0.168216i | \(-0.0538005\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.5208 | −0.400617 | −0.200309 | − | 0.979733i | \(-0.564194\pi\) | ||||
−0.200309 | + | 0.979733i | \(0.564194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.04541 | −0.209966 | −0.104983 | − | 0.994474i | \(-0.533479\pi\) | ||||
−0.104983 | + | 0.994474i | \(0.533479\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.317837i | − 0.0110124i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.15663i | 0.109240i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1879 | 0.938630 | 0.469315 | − | 0.883031i | \(-0.344501\pi\) | ||||
0.469315 | + | 0.883031i | \(0.344501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.3939 | −1.04806 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.22486i | − 0.0765375i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 12.7980i | − 0.439743i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.7990 | −0.678701 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.8990 | 1.60579 | 0.802895 | − | 0.596120i | \(-0.203292\pi\) | ||||
0.802895 | + | 0.596120i | \(0.203292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 23.0095i | − 0.785989i | −0.919541 | − | 0.392994i | \(-0.871439\pi\) | ||||
0.919541 | − | 0.392994i | \(-0.128561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 26.4949i | − 0.903994i | −0.892019 | − | 0.451997i | \(-0.850712\pi\) | ||||
0.892019 | − | 0.451997i | \(-0.149288\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.1633 | −0.652327 | −0.326163 | − | 0.945313i | \(-0.605756\pi\) | ||||
−0.326163 | + | 0.945313i | \(0.605756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.89898 | −0.0985683 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 41.7121i | − 1.41499i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5959i | 0.663982i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.14626 | 0.106363 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7980 | −1.31011 | −0.655057 | − | 0.755579i | \(-0.727355\pi\) | ||||
−0.655057 | + | 0.755579i | \(0.727355\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.0689i | 1.65317i | 0.562810 | + | 0.826586i | \(0.309720\pi\) | ||||
−0.562810 | + | 0.826586i | \(0.690280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.04541i | 0.237097i | 0.992948 | + | 0.118548i | \(0.0378241\pi\) | ||||
−0.992948 | + | 0.118548i | \(0.962176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.58166 | −0.321721 | −0.160860 | − | 0.986977i | \(-0.551427\pi\) | ||||
−0.160860 | + | 0.986977i | \(0.551427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.2474 | 0.511383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.76416i | 0.0590353i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.55051i | − 0.0518278i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.2911 | 1.14367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.202041 | −0.00673096 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.84961i | 0.260930i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.05561i | − 0.0682555i | −0.999417 | − | 0.0341278i | \(-0.989135\pi\) | ||||
0.999417 | − | 0.0341278i | \(-0.0108653\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.778539 | 0.0257942 | 0.0128971 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128971 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.8434 | −1.64957 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0492i | 0.529990i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.7526i | 0.420668i | 0.977630 | + | 0.210334i | \(0.0674551\pi\) | ||||
−0.977630 | + | 0.210334i | \(0.932545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.2929 | −1.12754 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 45.0012i | − 1.47644i | −0.674559 | − | 0.738221i | \(-0.735666\pi\) | ||||
0.674559 | − | 0.738221i | \(-0.264334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 0.449490i | − 0.0147314i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.492810 | 0.0161166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.3485 | 0.501413 | 0.250706 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250706 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 25.7737i | − 0.840198i | −0.907478 | − | 0.420099i | \(-0.861995\pi\) | ||||
0.907478 | − | 0.420099i | \(-0.138005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 16.8990i | − 0.550306i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.2979 | −1.30950 | −0.654752 | − | 0.755843i | \(-0.727227\pi\) | ||||
−0.654752 | + | 0.755843i | \(0.727227\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.59592 | −0.246574 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.1687i | 1.72230i | 0.508349 | + | 0.861151i | \(0.330256\pi\) | ||||
−0.508349 | + | 0.861151i | \(0.669744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.10102i | 0.165065i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.97809 | 0.289918 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.2020 | 0.361356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3.49621i | − 0.112547i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.89898i | − 0.157541i | −0.996893 | − | 0.0787703i | \(-0.974901\pi\) | ||||
0.996893 | − | 0.0787703i | \(-0.0250994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.7170 | 0.568565 | 0.284283 | − | 0.958741i | \(-0.408245\pi\) | ||||
0.284283 | + | 0.958741i | \(0.408245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.2474 | 0.392635 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.4483i | 1.03811i | 0.854740 | + | 0.519056i | \(0.173716\pi\) | ||||
−0.854740 | + | 0.519056i | \(0.826284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 68.9898i | − 2.20492i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.8598 | 0.537744 | 0.268872 | − | 0.963176i | \(-0.413349\pi\) | ||||
0.268872 | + | 0.963176i | \(0.413349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.247449 | −0.00788437 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.2699i | 0.930728i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 19.4495i | − 0.617833i | −0.951089 | − | 0.308917i | \(-0.900034\pi\) | ||||
0.951089 | − | 0.308917i | \(-0.0999664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.17837 | 0.100761 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.75255 | 0.245526 | 0.122763 | − | 0.992436i | \(-0.460825\pi\) | ||||
0.122763 | + | 0.992436i | \(0.460825\pi\) | |||||||
\(998\) | 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.d.2591.5 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.d.2591.3 | ✓ | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.d.2591.6 | yes | 8 | |
12.11 | even | 2 | inner | 6048.2.h.d.2591.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.d.2591.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
6048.2.h.d.2591.4 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.d.2591.5 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.d.2591.6 | yes | 8 | 4.3 | odd | 2 | inner |