Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
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: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.239575536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.10821\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.10821 | −1.21718 | −0.608589 | − | 0.793485i | \(-0.708264\pi\) | ||||
−0.608589 | + | 0.793485i | \(0.708264\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.44457 | 0.481523 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.77465 | 0.535078 | 0.267539 | − | 0.963547i | \(-0.413790\pi\) | ||||
0.267539 | + | 0.963547i | \(0.413790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.44457 | −0.400652 | −0.200326 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200326 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.86806 | −1.42321 | −0.711607 | − | 0.702578i | \(-0.752032\pi\) | ||||
−0.711607 | + | 0.702578i | \(0.752032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.16205 | −1.64309 | −0.821543 | − | 0.570146i | \(-0.806886\pi\) | ||||
−0.821543 | + | 0.570146i | \(0.806886\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.663645 | 0.138380 | 0.0691898 | − | 0.997604i | \(-0.477959\pi\) | ||||
0.0691898 | + | 0.997604i | \(0.477959\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.27918 | 0.631079 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.45763 | 1.19915 | 0.599576 | − | 0.800318i | \(-0.295336\pi\) | ||||
0.599576 | + | 0.800318i | \(0.295336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0732 | 1.80919 | 0.904597 | − | 0.426267i | \(-0.140172\pi\) | ||||
0.904597 | + | 0.426267i | \(0.140172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.74135 | −0.651285 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.01705 | 0.824797 | 0.412399 | − | 0.911004i | \(-0.364691\pi\) | ||||
0.412399 | + | 0.911004i | \(0.364691\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.04546 | 0.487664 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92363 | 0.300421 | 0.150211 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150211 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.81995 | −0.887535 | −0.443767 | − | 0.896142i | \(-0.646358\pi\) | ||||
−0.443767 | + | 0.896142i | \(0.646358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.70322 | −0.540171 | −0.270085 | − | 0.962836i | \(-0.587052\pi\) | ||||
−0.270085 | + | 0.962836i | \(0.587052\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.3711 | 1.73231 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.592363 | 0.0813674 | 0.0406837 | − | 0.999172i | \(-0.487046\pi\) | ||||
0.0406837 | + | 0.999172i | \(0.487046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.0991 | 1.99993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.59076 | 0.988233 | 0.494116 | − | 0.869396i | \(-0.335492\pi\) | ||||
0.494116 | + | 0.869396i | \(0.335492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.72111 | −1.11662 | −0.558312 | − | 0.829631i | \(-0.688551\pi\) | ||||
−0.558312 | + | 0.829631i | \(0.688551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.16832 | 0.264903 | 0.132451 | − | 0.991190i | \(-0.457715\pi\) | ||||
0.132451 | + | 0.991190i | \(0.457715\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.39911 | −0.168433 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.49826 | 0.771201 | 0.385601 | − | 0.922666i | \(-0.373994\pi\) | ||||
0.385601 | + | 0.922666i | \(0.373994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.5320 | 1.81788 | 0.908941 | − | 0.416924i | \(-0.136892\pi\) | ||||
0.908941 | + | 0.416924i | \(0.136892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.70720 | −0.304584 | −0.152292 | − | 0.988336i | \(-0.548665\pi\) | ||||
−0.152292 | + | 0.988336i | \(0.548665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2469 | −1.24966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.35340 | −0.697376 | −0.348688 | − | 0.937239i | \(-0.613373\pi\) | ||||
−0.348688 | + | 0.937239i | \(0.613373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.6141 | −1.45958 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.86157 | −0.621326 | −0.310663 | − | 0.950520i | \(-0.600551\pi\) | ||||
−0.310663 | + | 0.950520i | \(0.600551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.2364 | −2.20211 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7748 | −1.50015 | −0.750076 | − | 0.661351i | \(-0.769983\pi\) | ||||
−0.750076 | + | 0.661351i | \(0.769983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.56361 | 0.257652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.48186 | −0.346458 | −0.173229 | − | 0.984882i | \(-0.555420\pi\) | ||||
−0.173229 | + | 0.984882i | \(0.555420\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.07861 | −0.796009 | −0.398004 | − | 0.917384i | \(-0.630297\pi\) | ||||
−0.398004 | + | 0.917384i | \(0.630297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.129645 | −0.0125333 | −0.00626664 | − | 0.999980i | \(-0.501995\pi\) | ||||
−0.00626664 | + | 0.999980i | \(0.501995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2648 | 1.17476 | 0.587379 | − | 0.809312i | \(-0.300160\pi\) | ||||
0.587379 | + | 0.809312i | \(0.300160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5770 | −1.00393 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.7467 | −1.10503 | −0.552517 | − | 0.833501i | \(-0.686333\pi\) | ||||
−0.552517 | + | 0.833501i | \(0.686333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.08678 | −0.192923 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.85061 | −0.713692 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.05543 | −0.365666 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6983 | 1.12679 | 0.563395 | − | 0.826187i | \(-0.309495\pi\) | ||||
0.563395 | + | 0.826187i | \(0.309495\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.2697 | 1.08029 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.230932 | 0.0201766 | 0.0100883 | − | 0.999949i | \(-0.496789\pi\) | ||||
0.0100883 | + | 0.999949i | \(0.496789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8117 | −1.43632 | −0.718161 | − | 0.695877i | \(-0.755016\pi\) | ||||
−0.718161 | + | 0.695877i | \(0.755016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.5531 | 1.74329 | 0.871644 | − | 0.490139i | \(-0.163054\pi\) | ||||
0.871644 | + | 0.490139i | \(0.163054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.80719 | 0.657484 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.56361 | −0.214380 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.2725 | 1.74271 | 0.871356 | − | 0.490652i | \(-0.163241\pi\) | ||||
0.871356 | + | 0.490652i | \(0.163241\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47990 | 0.527327 | 0.263663 | − | 0.964615i | \(-0.415069\pi\) | ||||
0.263663 | + | 0.964615i | \(0.415069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.47683 | −0.685311 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.44990 | 0.434950 | 0.217475 | − | 0.976066i | \(-0.430218\pi\) | ||||
0.217475 | + | 0.976066i | \(0.430218\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.24883 | −0.0990386 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.26921 | 0.491042 | 0.245521 | − | 0.969391i | \(-0.421041\pi\) | ||||
0.245521 | + | 0.969391i | \(0.421041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.5728 | 1.43720 | 0.718602 | − | 0.695422i | \(-0.244782\pi\) | ||||
0.718602 | + | 0.695422i | \(0.244782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9132 | −0.839478 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3461 | −0.791184 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.9672 | −1.06191 | −0.530954 | − | 0.847401i | \(-0.678166\pi\) | ||||
−0.530954 | + | 0.847401i | \(0.678166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.0030 | −1.20286 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.92539 | 0.592372 | 0.296186 | − | 0.955130i | \(-0.404285\pi\) | ||||
0.296186 | + | 0.955130i | \(0.404285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6887 | 0.868815 | 0.434407 | − | 0.900717i | \(-0.356958\pi\) | ||||
0.434407 | + | 0.900717i | \(0.356958\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.3860 | 1.35913 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4138 | −0.761530 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9782 | −0.939066 | −0.469533 | − | 0.882915i | \(-0.655578\pi\) | ||||
−0.469533 | + | 0.882915i | \(0.655578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4053 | −1.54079 | −0.770393 | − | 0.637570i | \(-0.779940\pi\) | ||||
−0.770393 | + | 0.637570i | \(0.779940\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.42871 | 0.600521 | 0.300261 | − | 0.953857i | \(-0.402926\pi\) | ||||
0.300261 | + | 0.953857i | \(0.402926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.21481 | −0.298780 | −0.149390 | − | 0.988778i | \(-0.547731\pi\) | ||||
−0.149390 | + | 0.988778i | \(0.547731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.57129 | −0.322434 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.958682 | 0.0666330 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.7101 | −0.879179 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.629004 | −0.0433025 | −0.0216512 | − | 0.999766i | \(-0.506892\pi\) | ||||
−0.0216512 | + | 0.999766i | \(0.506892\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.6997 | −0.938689 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.7448 | −2.21269 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.47683 | 0.570213 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4138 | 1.43398 | 0.716988 | − | 0.697086i | \(-0.245520\pi\) | ||||
0.716988 | + | 0.697086i | \(0.245520\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0493 | −1.46346 | −0.731732 | − | 0.681593i | \(-0.761288\pi\) | ||||
−0.731732 | + | 0.681593i | \(0.761288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6359 | −0.768925 | −0.384462 | − | 0.923141i | \(-0.625613\pi\) | ||||
−0.384462 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.2193 | 0.735004 | 0.367502 | − | 0.930023i | \(-0.380213\pi\) | ||||
0.367502 | + | 0.930023i | \(0.380213\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.70737 | 0.370733 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.8279 | 1.47662 | 0.738308 | − | 0.674464i | \(-0.235625\pi\) | ||||
0.738308 | + | 0.674464i | \(0.235625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.20270 | −0.270720 | −0.135360 | − | 0.990796i | \(-0.543219\pi\) | ||||
−0.135360 | + | 0.990796i | \(0.543219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8734 | 0.889979 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3461 | 0.658305 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.3943 | 0.848831 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.9587 | 1.07042 | 0.535211 | − | 0.844718i | \(-0.320232\pi\) | ||||
0.535211 | + | 0.844718i | \(0.320232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.17774 | 0.0740438 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.9303 | −1.67986 | −0.839932 | − | 0.542692i | \(-0.817405\pi\) | ||||
−0.839932 | + | 0.542692i | \(0.817405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.32850 | 0.577420 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.9520 | 1.35362 | 0.676809 | − | 0.736158i | \(-0.263362\pi\) | ||||
0.676809 | + | 0.736158i | \(0.263362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.3575 | 0.756264 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.0854 | −1.46851 | −0.734256 | − | 0.678872i | \(-0.762469\pi\) | ||||
−0.734256 | + | 0.678872i | \(0.762469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.06731 | −0.125580 | −0.0627900 | − | 0.998027i | \(-0.520000\pi\) | ||||
−0.0627900 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.0757 | 1.02598 | 0.512990 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512990 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5514 | 0.871169 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2035 | −0.787655 | −0.393828 | − | 0.919184i | \(-0.628849\pi\) | ||||
−0.393828 | + | 0.919184i | \(0.628849\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.5989 | −1.58114 | −0.790570 | − | 0.612372i | \(-0.790216\pi\) | ||||
−0.790570 | + | 0.612372i | \(0.790216\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.4342 | 1.02554 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.1484 | 1.82595 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.472681 | 0.0276143 | 0.0138071 | − | 0.999905i | \(-0.495605\pi\) | ||||
0.0138071 | + | 0.999905i | \(0.495605\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.81940 | 0.337676 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.958682 | −0.0554420 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.34050 | 0.421701 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2073 | −0.867929 | −0.433965 | − | 0.900930i | \(-0.642886\pi\) | ||||
−0.433965 | + | 0.900930i | \(0.642886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.0314 | 0.968885 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5806 | 0.940200 | 0.470100 | − | 0.882613i | \(-0.344218\pi\) | ||||
0.470100 | + | 0.882613i | \(0.344218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.17950 | 0.0666695 | 0.0333348 | − | 0.999444i | \(-0.489387\pi\) | ||||
0.0333348 | + | 0.999444i | \(0.489387\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.4288 | −1.54056 | −0.770278 | − | 0.637709i | \(-0.779882\pi\) | ||||
−0.770278 | + | 0.637709i | \(0.779882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4600 | 0.641640 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.273320 | 0.0152552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.0273 | 2.33846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.8569 | −1.42989 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.21160 | 0.286455 | 0.143228 | − | 0.989690i | \(-0.454252\pi\) | ||||
0.143228 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.24747 | 0.397159 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.52496 | −0.518858 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.7645 | 1.34502 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8764 | 0.968059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.2781 | −1.46436 | −0.732182 | − | 0.681109i | \(-0.761498\pi\) | ||||
−0.732182 | + | 0.681109i | \(0.761498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.78145 | −0.363003 | −0.181501 | − | 0.983391i | \(-0.558096\pi\) | ||||
−0.181501 | + | 0.983391i | \(0.558096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.73701 | −0.252843 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6791 | 0.834517 | 0.417258 | − | 0.908788i | \(-0.362991\pi\) | ||||
0.417258 | + | 0.908788i | \(0.362991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.33467 | −0.334331 | −0.167165 | − | 0.985929i | \(-0.553461\pi\) | ||||
−0.167165 | + | 0.985929i | \(0.553461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.2949 | 1.69973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5508 | 0.868691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7599 | −0.666059 | −0.333030 | − | 0.942916i | \(-0.608071\pi\) | ||||
−0.333030 | + | 0.942916i | \(0.608071\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.77882 | 0.144660 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.66915 | −0.0864255 | −0.0432127 | − | 0.999066i | \(-0.513759\pi\) | ||||
−0.0432127 | + | 0.999066i | \(0.513759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.32850 | −0.480442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5557 | −1.10724 | −0.553621 | − | 0.832768i | \(-0.686755\pi\) | ||||
−0.553621 | + | 0.832768i | \(0.686755\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.7707 | −1.37151 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.04425 | 0.257749 | 0.128875 | − | 0.991661i | \(-0.458864\pi\) | ||||
0.128875 | + | 0.991661i | \(0.458864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.40733 | −0.427369 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.5195 | −0.634764 | −0.317382 | − | 0.948298i | \(-0.602804\pi\) | ||||
−0.317382 | + | 0.948298i | \(0.602804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.89431 | −0.196944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.486853 | −0.0245585 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3935 | −1.12390 | −0.561950 | − | 0.827171i | \(-0.689949\pi\) | ||||
−0.561950 | + | 0.827171i | \(0.689949\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.3931 | −0.768694 | −0.384347 | − | 0.923189i | \(-0.625573\pi\) | ||||
−0.384347 | + | 0.923189i | \(0.625573\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5514 | −0.724857 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.90351 | 0.441330 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.9701 | −1.53137 | −0.765687 | − | 0.643213i | \(-0.777601\pi\) | ||||
−0.765687 | + | 0.643213i | \(0.777601\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.4427 | 1.74826 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −43.3303 | −2.12189 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.434578 | −0.0212305 | −0.0106153 | − | 0.999944i | \(-0.503379\pi\) | ||||
−0.0106153 | + | 0.999944i | \(0.503379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3152 | −1.33126 | −0.665630 | − | 0.746282i | \(-0.731837\pi\) | ||||
−0.665630 | + | 0.746282i | \(0.731837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.34957 | −0.260105 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.40464 | 0.260938 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.5275 | −0.988773 | −0.494386 | − | 0.869242i | \(-0.664607\pi\) | ||||
−0.494386 | + | 0.869242i | \(0.664607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0082 | −0.769304 | −0.384652 | − | 0.923062i | \(-0.625679\pi\) | ||||
−0.384652 | + | 0.923062i | \(0.625679\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.75306 | −0.227370 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.06958 | −0.385140 | −0.192570 | − | 0.981283i | \(-0.561682\pi\) | ||||
−0.192570 | + | 0.981283i | \(0.561682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.19214 | 0.341709 | 0.170854 | − | 0.985296i | \(-0.445347\pi\) | ||||
0.170854 | + | 0.985296i | \(0.445347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −44.8470 | −2.12119 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.16729 | −0.196667 | −0.0983334 | − | 0.995154i | \(-0.531351\pi\) | ||||
−0.0983334 | + | 0.995154i | \(0.531351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.41378 | 0.160749 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.6610 | −0.641851 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.17950 | 0.429399 | 0.214700 | − | 0.976680i | \(-0.431123\pi\) | ||||
0.214700 | + | 0.976680i | \(0.431123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.2424 | −0.898160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.3537 | −1.27399 | −0.636995 | − | 0.770868i | \(-0.719823\pi\) | ||||
−0.636995 | + | 0.770868i | \(0.719823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8660 | 0.597932 | 0.298966 | − | 0.954264i | \(-0.403358\pi\) | ||||
0.298966 | + | 0.954264i | \(0.403358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.9010 | −0.643260 | −0.321630 | − | 0.946865i | \(-0.604231\pi\) | ||||
−0.321630 | + | 0.946865i | \(0.604231\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.4896 | −0.529411 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3284 | −0.474900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.855710 | 0.0391803 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.371944 | 0.0169946 | 0.00849729 | − | 0.999964i | \(-0.497295\pi\) | ||||
0.00849729 | + | 0.999964i | \(0.497295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.24747 | −0.330456 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.2340 | −0.871577 | −0.435788 | − | 0.900049i | \(-0.643530\pi\) | ||||
−0.435788 | + | 0.900049i | \(0.643530\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.2168 | −0.597686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2267 | 0.687170 | 0.343585 | − | 0.939122i | \(-0.388359\pi\) | ||||
0.343585 | + | 0.939122i | \(0.388359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.8938 | −1.70665 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9430 | 0.624173 | 0.312087 | − | 0.950054i | \(-0.398972\pi\) | ||||
0.312087 | + | 0.950054i | \(0.398972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.1554 | −1.74933 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.6394 | −1.85661 | −0.928305 | − | 0.371821i | \(-0.878734\pi\) | ||||
−0.928305 | + | 0.371821i | \(0.878734\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.0074 | 1.02179 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.1663 | 1.38142 | 0.690712 | − | 0.723130i | \(-0.257297\pi\) | ||||
0.690712 | + | 0.723130i | \(0.257297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.4856 | −1.03692 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.57193 | −0.289033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.4459 | 1.29253 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.91918 | 0.434567 | 0.217284 | − | 0.976109i | \(-0.430280\pi\) | ||||
0.217284 | + | 0.976109i | \(0.430280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2340 | −0.841045 | −0.420523 | − | 0.907282i | \(-0.638153\pi\) | ||||
−0.420523 | + | 0.907282i | \(0.638153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −59.1100 | −2.57487 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5596 | −0.980851 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.9654 | 0.475857 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.77882 | −0.120364 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.7084 | −0.721022 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.60558 | −0.155016 | −0.0775081 | − | 0.996992i | \(-0.524696\pi\) | ||||
−0.0775081 | + | 0.996992i | \(0.524696\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.6423 | −1.05750 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1011 | 0.474647 | 0.237324 | − | 0.971431i | \(-0.423730\pi\) | ||||
0.237324 | + | 0.971431i | \(0.423730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.5982 | −0.537680 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.2499 | −1.97031 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8346 | 1.05228 | 0.526138 | − | 0.850399i | \(-0.323640\pi\) | ||||
0.526138 | + | 0.850399i | \(0.323640\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.40733 | 0.355592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.9545 | 0.926918 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.82819 | −0.119194 | −0.0595970 | − | 0.998223i | \(-0.518982\pi\) | ||||
−0.0595970 | + | 0.998223i | \(0.518982\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.1318 | −1.05358 | −0.526791 | − | 0.849995i | \(-0.676605\pi\) | ||||
−0.526791 | + | 0.849995i | \(0.676605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.2093 | −1.47347 | −0.736733 | − | 0.676184i | \(-0.763632\pi\) | ||||
−0.736733 | + | 0.676184i | \(0.763632\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.3607 | 1.14301 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.8365 | −1.15885 | −0.579424 | − | 0.815027i | \(-0.696722\pi\) | ||||
−0.579424 | + | 0.815027i | \(0.696722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 45.1269 | 1.87541 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.05124 | 0.0435378 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.74640 | 0.195905 | 0.0979524 | − | 0.995191i | \(-0.468771\pi\) | ||||
0.0979524 | + | 0.995191i | \(0.468771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −72.1445 | −2.97266 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7695 | −0.730941 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.48084 | −0.307201 | −0.153601 | − | 0.988133i | \(-0.549087\pi\) | ||||
−0.153601 | + | 0.988133i | \(0.549087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.88573 | 0.363669 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.56165 | −0.186384 | −0.0931920 | − | 0.995648i | \(-0.529707\pi\) | ||||
−0.0931920 | + | 0.995648i | \(0.529707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.96538 | 0.202542 | 0.101271 | − | 0.994859i | \(-0.467709\pi\) | ||||
0.101271 | + | 0.994859i | \(0.467709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.13229 | 0.127557 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.40325 | −0.178722 | −0.0893612 | − | 0.995999i | \(-0.528483\pi\) | ||||
−0.0893612 | + | 0.995999i | \(0.528483\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.34957 | 0.216420 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.6950 | 1.72444 | 0.862218 | − | 0.506538i | \(-0.169075\pi\) | ||||
0.862218 | + | 0.506538i | \(0.169075\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2135 | −0.934541 | −0.467270 | − | 0.884114i | \(-0.654763\pi\) | ||||
−0.467270 | + | 0.884114i | \(0.654763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0134 | 1.12595 | 0.562977 | − | 0.826473i | \(-0.309656\pi\) | ||||
0.562977 | + | 0.826473i | \(0.309656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.17621 | 0.0873284 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.7957 | 1.07012 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.4403 | −1.17386 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8446 | −1.14829 | −0.574144 | − | 0.818755i | \(-0.694665\pi\) | ||||
−0.574144 | + | 0.818755i | \(0.694665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.32608 | 0.0527068 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.38718 | 0.371351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.1854 | −1.62673 | −0.813363 | − | 0.581757i | \(-0.802366\pi\) | ||||
−0.813363 | + | 0.581757i | \(0.802366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.64360 | −0.301434 | −0.150717 | − | 0.988577i | \(-0.548158\pi\) | ||||
−0.150717 | + | 0.988577i | \(0.548158\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.1376 | 0.870318 | 0.435159 | − | 0.900354i | \(-0.356692\pi\) | ||||
0.435159 | + | 0.900354i | \(0.356692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4710 | 0.528781 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.3026 | 0.716238 | 0.358119 | − | 0.933676i | \(-0.383418\pi\) | ||||
0.358119 | + | 0.933676i | \(0.383418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.4370 | 0.875353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.1377 | −1.09609 | −0.548044 | − | 0.836449i | \(-0.684627\pi\) | ||||
−0.548044 | + | 0.836449i | \(0.684627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.2742 | 0.905261 | 0.452630 | − | 0.891698i | \(-0.350486\pi\) | ||||
0.452630 | + | 0.891698i | \(0.350486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8710 | −0.694051 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.28558 | 0.165938 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −45.1449 | −1.74540 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.4769 | −0.597480 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0282 | 0.733484 | 0.366742 | − | 0.930323i | \(-0.380473\pi\) | ||||
0.366742 | + | 0.930323i | \(0.380473\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.7526 | −1.56625 | −0.783124 | − | 0.621866i | \(-0.786375\pi\) | ||||
−0.783124 | + | 0.621866i | \(0.786375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 46.4847 | 1.78130 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.9224 | 1.22148 | 0.610738 | − | 0.791833i | \(-0.290873\pi\) | ||||
0.610738 | + | 0.791833i | \(0.290873\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.5311 | 0.935918 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.855710 | −0.0326000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1124 | 0.460779 | 0.230389 | − | 0.973099i | \(-0.426000\pi\) | ||||
0.230389 | + | 0.973099i | \(0.426000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.2880 | −0.427564 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.6528 | −0.894631 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.83067 | −0.371299 | −0.185650 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185650 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.9323 | −1.35521 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.22203 | −0.346341 | −0.173170 | − | 0.984892i | \(-0.555401\pi\) | ||||
−0.173170 | + | 0.984892i | \(0.555401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.91075 | −0.146664 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.68501 | 0.250356 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.1262 | −1.79731 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5773 | 1.21493 | 0.607464 | − | 0.794347i | \(-0.292187\pi\) | ||||
0.607464 | + | 0.794347i | \(0.292187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.86020 | 0.329515 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4462 | 1.05501 | 0.527505 | − | 0.849552i | \(-0.323128\pi\) | ||||
0.527505 | + | 0.849552i | \(0.323128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.49268 | 0.166396 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.1518 | 1.26315 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.61408 | 0.355104 | 0.177552 | − | 0.984111i | \(-0.443182\pi\) | ||||
0.177552 | + | 0.984111i | \(0.443182\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.84801 | 0.141743 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.88409 | 0.142879 | 0.0714393 | − | 0.997445i | \(-0.477241\pi\) | ||||
0.0714393 | + | 0.997445i | \(0.477241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.8118 | −0.801275 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8174 | −0.616971 | −0.308486 | − | 0.951229i | \(-0.599822\pi\) | ||||
−0.308486 | + | 0.951229i | \(0.599822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.17793 | −0.335803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.3654 | −1.21752 | −0.608760 | − | 0.793354i | \(-0.708333\pi\) | ||||
−0.608760 | + | 0.793354i | \(0.708333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −35.7525 | −1.30290 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2781 | 1.13682 | 0.568412 | − | 0.822744i | \(-0.307558\pi\) | ||||
0.568412 | + | 0.822744i | \(0.307558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.48293 | −0.0901245 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.82448 | −0.102387 | −0.0511937 | − | 0.998689i | \(-0.516303\pi\) | ||||
−0.0511937 | + | 0.998689i | \(0.516303\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.9654 | −0.395937 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.1637 | 1.05167 | 0.525836 | − | 0.850586i | \(-0.323753\pi\) | ||||
0.525836 | + | 0.850586i | \(0.323753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.7748 | 2.04469 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.7784 | 1.46670 | 0.733348 | − | 0.679853i | \(-0.237957\pi\) | ||||
0.733348 | + | 0.679853i | \(0.237957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.7772 | −0.493618 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5321 | 0.412652 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.1758 | 0.756760 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.25206 | −0.294154 | −0.147077 | − | 0.989125i | \(-0.546987\pi\) | ||||
−0.147077 | + | 0.989125i | \(0.546987\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −46.2795 | −1.64760 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.5982 | 0.447377 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.6687 | 1.40514 | 0.702569 | − | 0.711616i | \(-0.252036\pi\) | ||||
0.702569 | + | 0.711616i | \(0.252036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.7307 | 0.768779 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.46745 | −0.299183 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.5639 | 0.972708 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 50.7772 | 1.78744 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.3156 | −1.13616 | −0.568078 | − | 0.822975i | \(-0.692313\pi\) | ||||
−0.568078 | + | 0.822975i | \(0.692313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.67248 | −0.269417 | −0.134709 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134709 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.35833 | 0.152853 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.6828 | 1.45830 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.0562 | 0.595266 | 0.297633 | − | 0.954680i | \(-0.403803\pi\) | ||||
0.297633 | + | 0.954680i | \(0.403803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.1024 | −1.15388 | −0.576939 | − | 0.816787i | \(-0.695753\pi\) | ||||
−0.576939 | + | 0.816787i | \(0.695753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1051 | 0.699123 | 0.349561 | − | 0.936913i | \(-0.386331\pi\) | ||||
0.349561 | + | 0.936913i | \(0.386331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.9667 | −0.658740 | −0.329370 | − | 0.944201i | \(-0.606836\pi\) | ||||
−0.329370 | + | 0.944201i | \(0.606836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.9993 | −1.24880 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 33.0317 | 1.14174 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.15025 | −0.143283 | −0.0716413 | − | 0.997430i | \(-0.522824\pi\) | ||||
−0.0716413 | + | 0.997430i | \(0.522824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7010 | 0.437967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.8358 | 0.958717 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.0762 | 1.92453 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.32954 | 0.114135 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.53140 | −0.0524340 | −0.0262170 | − | 0.999656i | \(-0.508346\pi\) | ||||
−0.0262170 | + | 0.999656i | \(0.508346\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.8235 | −0.813794 | −0.406897 | − | 0.913474i | \(-0.633389\pi\) | ||||
−0.406897 | + | 0.913474i | \(0.633389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6833 | −0.500987 | −0.250494 | − | 0.968118i | \(-0.580593\pi\) | ||||
−0.250494 | + | 0.968118i | \(0.580593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.3325 | −1.44102 | −0.720508 | − | 0.693446i | \(-0.756091\pi\) | ||||
−0.720508 | + | 0.693446i | \(0.756091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.7549 | −1.24826 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.80434 | −0.162976 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.13229 | −0.106134 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.3432 | −0.722359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.5940 | 0.357735 | 0.178868 | − | 0.983873i | \(-0.442757\pi\) | ||||
0.178868 | + | 0.983873i | \(0.442757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.996512 | −0.0336115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.1174 | −0.913609 | −0.456805 | − | 0.889567i | \(-0.651006\pi\) | ||||
−0.456805 | + | 0.889567i | \(0.651006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.7240 | −0.731072 | −0.365536 | − | 0.930797i | \(-0.619114\pi\) | ||||
−0.365536 | + | 0.930797i | \(0.619114\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.1605 | 0.710501 | 0.355251 | − | 0.934771i | \(-0.384396\pi\) | ||||
0.355251 | + | 0.934771i | \(0.384396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.9594 | −0.668664 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.5227 | 0.887547 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.02111 | 0.0674828 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 65.0488 | 2.16950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.47602 | −0.115803 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.8642 | −1.25726 | −0.628630 | − | 0.777705i | \(-0.716384\pi\) | ||||
−0.628630 | + | 0.777705i | \(0.716384\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.02978 | −0.166827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.1221 | −0.997990 | −0.498995 | − | 0.866605i | \(-0.666297\pi\) | ||||
−0.498995 | + | 0.866605i | \(0.666297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2751 | −0.373150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.1132 | −1.52113 | −0.760566 | − | 0.649260i | \(-0.775079\pi\) | ||||
−0.760566 | + | 0.649260i | \(0.775079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.0604 | 1.05642 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.38718 | −0.308983 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.6701 | −0.383297 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.5174 | −0.902816 | −0.451408 | − | 0.892318i | \(-0.649078\pi\) | ||||
−0.451408 | + | 0.892318i | \(0.649078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.9555 | −1.14439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.4704 | −1.64880 | −0.824399 | − | 0.566010i | \(-0.808486\pi\) | ||||
−0.824399 | + | 0.566010i | \(0.808486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.48665 | −0.0811487 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.85663 | −0.0605243 | −0.0302622 | − | 0.999542i | \(-0.509634\pi\) | ||||
−0.0302622 | + | 0.999542i | \(0.509634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.27661 | 0.0415721 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1689 | −1.17533 | −0.587666 | − | 0.809104i | \(-0.699953\pi\) | ||||
−0.587666 | + | 0.809104i | \(0.699953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4370 | −0.728337 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.8258 | 1.87513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3367 | 0.561590 | 0.280795 | − | 0.959768i | \(-0.409402\pi\) | ||||
0.280795 | + | 0.959768i | \(0.409402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.1602 | −0.780990 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.4688 | 2.27319 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.187282 | −0.00603506 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4618 | 0.754480 | 0.377240 | − | 0.926116i | \(-0.376873\pi\) | ||||
0.377240 | + | 0.926116i | \(0.376873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −88.6027 | −2.84633 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.5553 | 1.81495 | 0.907473 | − | 0.420110i | \(-0.138009\pi\) | ||||
0.907473 | + | 0.420110i | \(0.138009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.9783 | −0.927099 | −0.463549 | − | 0.886071i | \(-0.653424\pi\) | ||||
−0.463549 | + | 0.886071i | \(0.653424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.4022 | −0.332457 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.7174 | 0.565673 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.3280 | 1.31816 | 0.659079 | − | 0.752074i | \(-0.270946\pi\) | ||||
0.659079 | + | 0.752074i | \(0.270946\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.86238 | −0.122817 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.0897 | −0.924065 | −0.462032 | − | 0.886863i | \(-0.652880\pi\) | ||||
−0.462032 | + | 0.886863i | \(0.652880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9872 | −0.348667 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.4734 | 0.680069 | 0.340035 | − | 0.940413i | \(-0.389561\pi\) | ||||
0.340035 | + | 0.940413i | \(0.389561\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.4518 | 0.520512 |
(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 | 9800.2.a.cw.1.2 | 6 | ||
5.2 | odd | 4 | 1960.2.g.e.1569.10 | 12 | |||
5.3 | odd | 4 | 1960.2.g.e.1569.3 | 12 | |||
5.4 | even | 2 | 9800.2.a.cy.1.5 | 6 | |||
7.3 | odd | 6 | 1400.2.q.n.401.2 | 12 | |||
7.5 | odd | 6 | 1400.2.q.n.1201.2 | 12 | |||
7.6 | odd | 2 | 9800.2.a.cx.1.5 | 6 | |||
35.3 | even | 12 | 280.2.bg.a.9.10 | yes | 24 | ||
35.12 | even | 12 | 280.2.bg.a.249.10 | yes | 24 | ||
35.13 | even | 4 | 1960.2.g.f.1569.10 | 12 | |||
35.17 | even | 12 | 280.2.bg.a.9.3 | ✓ | 24 | ||
35.19 | odd | 6 | 1400.2.q.o.1201.5 | 12 | |||
35.24 | odd | 6 | 1400.2.q.o.401.5 | 12 | |||
35.27 | even | 4 | 1960.2.g.f.1569.3 | 12 | |||
35.33 | even | 12 | 280.2.bg.a.249.3 | yes | 24 | ||
35.34 | odd | 2 | 9800.2.a.cv.1.2 | 6 | |||
140.3 | odd | 12 | 560.2.bw.f.289.3 | 24 | |||
140.47 | odd | 12 | 560.2.bw.f.529.3 | 24 | |||
140.87 | odd | 12 | 560.2.bw.f.289.10 | 24 | |||
140.103 | odd | 12 | 560.2.bw.f.529.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.3 | ✓ | 24 | 35.17 | even | 12 | ||
280.2.bg.a.9.10 | yes | 24 | 35.3 | even | 12 | ||
280.2.bg.a.249.3 | yes | 24 | 35.33 | even | 12 | ||
280.2.bg.a.249.10 | yes | 24 | 35.12 | even | 12 | ||
560.2.bw.f.289.3 | 24 | 140.3 | odd | 12 | |||
560.2.bw.f.289.10 | 24 | 140.87 | odd | 12 | |||
560.2.bw.f.529.3 | 24 | 140.47 | odd | 12 | |||
560.2.bw.f.529.10 | 24 | 140.103 | odd | 12 | |||
1400.2.q.n.401.2 | 12 | 7.3 | odd | 6 | |||
1400.2.q.n.1201.2 | 12 | 7.5 | odd | 6 | |||
1400.2.q.o.401.5 | 12 | 35.24 | odd | 6 | |||
1400.2.q.o.1201.5 | 12 | 35.19 | odd | 6 | |||
1960.2.g.e.1569.3 | 12 | 5.3 | odd | 4 | |||
1960.2.g.e.1569.10 | 12 | 5.2 | odd | 4 | |||
1960.2.g.f.1569.3 | 12 | 35.27 | even | 4 | |||
1960.2.g.f.1569.10 | 12 | 35.13 | even | 4 | |||
9800.2.a.cv.1.2 | 6 | 35.34 | odd | 2 | |||
9800.2.a.cw.1.2 | 6 | 1.1 | even | 1 | trivial | ||
9800.2.a.cx.1.5 | 6 | 7.6 | odd | 2 | |||
9800.2.a.cy.1.5 | 6 | 5.4 | even | 2 |