Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −0.345669 | −0.199572 | −0.0997861 | − | 0.995009i | \(-0.531816\pi\) | ||||
−0.0997861 | + | 0.995009i | \(0.531816\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.40831 | 1.07703 | 0.538515 | − | 0.842616i | \(-0.318985\pi\) | ||||
0.538515 | + | 0.842616i | \(0.318985\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.76498 | −0.667099 | −0.333550 | − | 0.942733i | \(-0.608247\pi\) | ||||
−0.333550 | + | 0.942733i | \(0.608247\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.88051 | −0.960171 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.38392 | −0.718780 | −0.359390 | − | 0.933187i | \(-0.617015\pi\) | ||||
−0.359390 | + | 0.933187i | \(0.617015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.86705 | 1.34988 | 0.674939 | − | 0.737874i | \(-0.264170\pi\) | ||||
0.674939 | + | 0.737874i | \(0.264170\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.832480 | −0.214945 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.36266 | 1.05810 | 0.529050 | − | 0.848590i | \(-0.322548\pi\) | ||||
0.529050 | + | 0.848590i | \(0.322548\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.69953 | −1.07815 | −0.539073 | − | 0.842259i | \(-0.681225\pi\) | ||||
−0.539073 | + | 0.842259i | \(0.681225\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.610099 | 0.133134 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.71079 | −0.356724 | −0.178362 | − | 0.983965i | \(-0.557080\pi\) | ||||
−0.178362 | + | 0.983965i | \(0.557080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.799972 | 0.159994 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.03271 | 0.391196 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.59945 | 0.482706 | 0.241353 | − | 0.970437i | \(-0.422409\pi\) | ||||
0.241353 | + | 0.970437i | \(0.422409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.727592 | −0.130679 | −0.0653397 | − | 0.997863i | \(-0.520813\pi\) | ||||
−0.0653397 | + | 0.997863i | \(0.520813\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.824049 | 0.143448 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.25062 | −0.718486 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.06065 | −1.16076 | −0.580382 | − | 0.814344i | \(-0.697097\pi\) | ||||
−0.580382 | + | 0.814344i | \(0.697097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.68239 | −0.269398 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.505625 | −0.0789653 | −0.0394827 | − | 0.999220i | \(-0.512571\pi\) | ||||
−0.0394827 | + | 0.999220i | \(0.512571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.98623 | 0.912891 | 0.456445 | − | 0.889751i | \(-0.349122\pi\) | ||||
0.456445 | + | 0.889751i | \(0.349122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.93718 | −1.03413 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.49724 | −1.23945 | −0.619725 | − | 0.784819i | \(-0.712756\pi\) | ||||
−0.619725 | + | 0.784819i | \(0.712756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.88485 | −0.554978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50804 | −0.211167 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.93839 | 0.678341 | 0.339170 | − | 0.940725i | \(-0.389854\pi\) | ||||
0.339170 | + | 0.940725i | \(0.389854\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.74123 | −0.774148 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.62448 | 0.215168 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.80350 | −1.01593 | −0.507965 | − | 0.861378i | \(-0.669602\pi\) | ||||
−0.507965 | + | 0.861378i | \(0.669602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.09511 | 0.780399 | 0.390200 | − | 0.920730i | \(-0.372406\pi\) | ||||
0.390200 | + | 0.920730i | \(0.372406\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.08405 | 0.640530 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.7214 | 1.45386 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.910535 | −0.111240 | −0.0556198 | − | 0.998452i | \(-0.517713\pi\) | ||||
−0.0556198 | + | 0.998452i | \(0.517713\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.591367 | 0.0711922 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5995 | 1.49529 | 0.747643 | − | 0.664101i | \(-0.231185\pi\) | ||||
0.747643 | + | 0.664101i | \(0.231185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.63460 | 0.893563 | 0.446781 | − | 0.894643i | \(-0.352570\pi\) | ||||
0.446781 | + | 0.894643i | \(0.352570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.276526 | −0.0319304 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.20758 | 0.479498 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0523 | −1.35599 | −0.677993 | − | 0.735069i | \(-0.737150\pi\) | ||||
−0.677993 | + | 0.735069i | \(0.737150\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.93889 | 0.882099 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.9712 | −1.75307 | −0.876534 | − | 0.481340i | \(-0.840150\pi\) | ||||
−0.876534 | + | 0.481340i | \(0.840150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5067 | 1.13961 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.898550 | −0.0963347 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.5797 | −1.43945 | −0.719725 | − | 0.694259i | \(-0.755732\pi\) | ||||
−0.719725 | + | 0.694259i | \(0.755732\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.59025 | −0.900503 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.251506 | 0.0260800 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3179 | −1.16120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4638 | 1.16398 | 0.581989 | − | 0.813197i | \(-0.302275\pi\) | ||||
0.581989 | + | 0.813197i | \(0.302275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.86692 | 0.690152 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4579 | −1.04060 | −0.520298 | − | 0.853985i | \(-0.674179\pi\) | ||||
−0.520298 | + | 0.853985i | \(0.674179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.52747 | 0.347572 | 0.173786 | − | 0.984783i | \(-0.444400\pi\) | ||||
0.173786 | + | 0.984783i | \(0.444400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46931 | 0.143390 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3428 | 1.57992 | 0.789960 | − | 0.613159i | \(-0.210101\pi\) | ||||
0.789960 | + | 0.613159i | \(0.210101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.9336 | −1.04725 | −0.523623 | − | 0.851950i | \(-0.675420\pi\) | ||||
−0.523623 | + | 0.851950i | \(0.675420\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.44065 | 0.231656 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.74781 | −0.728853 | −0.364426 | − | 0.931232i | \(-0.618735\pi\) | ||||
−0.364426 | + | 0.931232i | \(0.618735\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.12012 | −0.384203 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.0196 | −1.29611 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.70001 | −0.705858 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.31691 | −0.483355 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.174779 | 0.0157593 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1150 | −0.904711 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8641 | −1.23024 | −0.615122 | − | 0.788432i | \(-0.710893\pi\) | ||||
−0.615122 | + | 0.788432i | \(0.710893\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.06925 | −0.182188 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.2082 | −0.979261 | −0.489631 | − | 0.871930i | \(-0.662868\pi\) | ||||
−0.489631 | + | 0.871930i | \(0.662868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.29457 | 0.719230 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.89541 | 0.421330 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.43734 | 0.122801 | 0.0614003 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614003 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.34126 | −0.537858 | −0.268929 | − | 0.963160i | \(-0.586670\pi\) | ||||
−0.268929 | + | 0.963160i | \(0.586670\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.93724 | 0.247360 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.6027 | −0.970265 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.26029 | 0.519889 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.34287 | 0.110758 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0181 | −1.80380 | −0.901898 | − | 0.431950i | \(-0.857826\pi\) | ||||
−0.901898 | + | 0.431950i | \(0.857826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.489202 | −0.0398107 | −0.0199053 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199053 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.5667 | −1.01596 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.75227 | −0.140746 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.78075 | −0.700781 | −0.350390 | − | 0.936604i | \(-0.613951\pi\) | ||||
−0.350390 | + | 0.936604i | \(0.613951\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.70705 | −0.135378 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.01951 | 0.237970 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.90187 | 0.462270 | 0.231135 | − | 0.972922i | \(-0.425756\pi\) | ||||
0.231135 | + | 0.972922i | \(0.425756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.98457 | 0.154498 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.2549 | 1.33522 | 0.667612 | − | 0.744509i | \(-0.267316\pi\) | ||||
0.667612 | + | 0.744509i | \(0.267316\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6882 | 0.822170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.5371 | 1.03520 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.5820 | −1.64085 | −0.820425 | − | 0.571754i | \(-0.806263\pi\) | ||||
−0.820425 | + | 0.571754i | \(0.806263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41193 | −0.106732 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.69743 | 0.202751 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.90335 | 0.441237 | 0.220619 | − | 0.975360i | \(-0.429192\pi\) | ||||
0.220619 | + | 0.975360i | \(0.429192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0844297 | −0.00627561 | −0.00313780 | − | 0.999995i | \(-0.500999\pi\) | ||||
−0.00313780 | + | 0.999995i | \(0.500999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.10689 | −0.155746 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.0043 | −1.25018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4003 | −0.760542 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.58769 | −0.260966 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.02592 | 0.580735 | 0.290368 | − | 0.956915i | \(-0.406222\pi\) | ||||
0.290368 | + | 0.956915i | \(0.406222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.57717 | −0.617398 | −0.308699 | − | 0.951160i | \(-0.599894\pi\) | ||||
−0.308699 | + | 0.951160i | \(0.599894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.05172 | −0.290150 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.4701 | 1.67217 | 0.836087 | − | 0.548597i | \(-0.184838\pi\) | ||||
0.836087 | + | 0.548597i | \(0.184838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.3839 | −0.877872 | −0.438936 | − | 0.898518i | \(-0.644645\pi\) | ||||
−0.438936 | + | 0.898518i | \(0.644645\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.314744 | 0.0222003 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.58798 | −0.322013 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.21770 | −0.0850480 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.92795 | 0.342516 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2033 | 0.774950 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6398 | −0.801314 | −0.400657 | − | 0.916228i | \(-0.631218\pi\) | ||||
−0.400657 | + | 0.916228i | \(0.631218\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.35526 | −0.298417 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.4167 | 0.983211 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.28418 | 0.0871761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.63905 | −0.178330 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.2333 | 1.42831 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.8154 | 1.12604 | 0.563022 | − | 0.826442i | \(-0.309639\pi\) | ||||
0.563022 | + | 0.826442i | \(0.309639\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.30433 | −0.153622 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.84706 | 0.520828 | 0.260414 | − | 0.965497i | \(-0.416141\pi\) | ||||
0.260414 | + | 0.965497i | \(0.416141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8878 | 0.719488 | 0.359744 | − | 0.933051i | \(-0.382864\pi\) | ||||
0.359744 | + | 0.933051i | \(0.382864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.45443 | −0.0956944 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.41401 | 0.354684 | 0.177342 | − | 0.984149i | \(-0.443250\pi\) | ||||
0.177342 | + | 0.984149i | \(0.443250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.4640 | −1.33493 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.16609 | 0.270617 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.0408 | −1.81381 | −0.906904 | − | 0.421338i | \(-0.861561\pi\) | ||||
−0.906904 | + | 0.421338i | \(0.861561\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.82891 | −0.633136 | −0.316568 | − | 0.948570i | \(-0.602530\pi\) | ||||
−0.316568 | + | 0.948570i | \(0.602530\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.84237 | −0.567238 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.35593 | −0.597729 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.8729 | −1.45537 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.52076 | 0.349864 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.51782 | −0.474521 | −0.237260 | − | 0.971446i | \(-0.576249\pi\) | ||||
−0.237260 | + | 0.971446i | \(0.576249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.07839 | 0.256406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.63183 | −0.227434 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.7198 | 1.60436 | 0.802180 | − | 0.597083i | \(-0.203674\pi\) | ||||
0.802180 | + | 0.597083i | \(0.203674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4619 | 0.774345 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.48775 | −0.463480 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6598 | −0.657312 | −0.328656 | − | 0.944450i | \(-0.606596\pi\) | ||||
−0.328656 | + | 0.944450i | \(0.606596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.8932 | 0.730594 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.69410 | 0.287274 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.6684 | −1.93086 | −0.965430 | − | 0.260664i | \(-0.916058\pi\) | ||||
−0.965430 | + | 0.260664i | \(0.916058\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9165 | −0.663131 | −0.331566 | − | 0.943432i | \(-0.607577\pi\) | ||||
−0.331566 | + | 0.943432i | \(0.607577\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.96938 | 0.179715 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.90707 | −0.115001 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.4127 | −0.745805 | −0.372903 | − | 0.927871i | \(-0.621637\pi\) | ||||
−0.372903 | + | 0.927871i | \(0.621637\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.09584 | 0.125475 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.24750 | −0.492004 | −0.246002 | − | 0.969269i | \(-0.579117\pi\) | ||||
−0.246002 | + | 0.969269i | \(0.579117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3593 | −1.38857 | −0.694283 | − | 0.719702i | \(-0.744278\pi\) | ||||
−0.694283 | + | 0.719702i | \(0.744278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.91226 | 0.231742 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.892417 | 0.0526777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03281 | 0.119577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.96270 | −0.232298 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.5343 | 1.60857 | 0.804286 | − | 0.594242i | \(-0.202548\pi\) | ||||
0.804286 | + | 0.594242i | \(0.202548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.7933 | −1.09419 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.84583 | −0.281184 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.32650 | −0.481534 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5656 | −0.608989 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.61496 | 0.207674 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.6789 | 0.840514 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.65984 | 0.551316 | 0.275658 | − | 0.961256i | \(-0.411104\pi\) | ||||
0.275658 | + | 0.961256i | \(0.411104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.21934 | −0.0693656 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.58513 | −0.430113 | −0.215057 | − | 0.976602i | \(-0.568994\pi\) | ||||
−0.215057 | + | 0.976602i | \(0.568994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.4572 | 1.21283 | 0.606415 | − | 0.795148i | \(-0.292607\pi\) | ||||
0.606415 | + | 0.795148i | \(0.292607\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.2440 | 0.689870 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.8585 | −1.39619 | −0.698096 | − | 0.716004i | \(-0.745969\pi\) | ||||
−0.698096 | + | 0.716004i | \(0.745969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.19689 | −0.346959 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.64921 | −0.315308 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.5025 | −1.14079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.89351 | 0.215973 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.77940 | 0.209001 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.9975 | 0.826837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.8366 | 1.80487 | 0.902433 | − | 0.430831i | \(-0.141780\pi\) | ||||
0.902433 | + | 0.430831i | \(0.141780\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.3383 | 1.11453 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.19285 | −0.119808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.38650 | 0.184474 | 0.0922372 | − | 0.995737i | \(-0.470598\pi\) | ||||
0.0922372 | + | 0.995737i | \(0.470598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.67818 | 0.145459 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.73452 | 0.0939297 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2115 | 1.03733 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.42420 | 0.0766762 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.6622 | 1.86077 | 0.930383 | − | 0.366588i | \(-0.119474\pi\) | ||||
0.930383 | + | 0.366588i | \(0.119474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7339 | −0.842215 | −0.421108 | − | 0.907011i | \(-0.638359\pi\) | ||||
−0.421108 | + | 0.907011i | \(0.638359\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.89332 | 0.528066 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0604 | −0.695133 | −0.347567 | − | 0.937655i | \(-0.612992\pi\) | ||||
−0.347567 | + | 0.937655i | \(0.612992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.3435 | 1.61047 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.66165 | 0.140870 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.98010 | −0.210062 | −0.105031 | − | 0.994469i | \(-0.533494\pi\) | ||||
−0.105031 | + | 0.994469i | \(0.533494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.08557 | 0.162398 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.83789 | 0.0964643 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.3865 | 0.962394 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0076 | −0.574595 | −0.287297 | − | 0.957841i | \(-0.592757\pi\) | ||||
−0.287297 | + | 0.957841i | \(0.592757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.45646 | 0.0758202 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.71616 | −0.452521 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2570 | −0.945313 | −0.472656 | − | 0.881247i | \(-0.656705\pi\) | ||||
−0.472656 | + | 0.881247i | \(0.656705\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.49644 | 0.180555 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.6517 | 0.651594 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.83252 | 0.350963 | 0.175481 | − | 0.984483i | \(-0.443852\pi\) | ||||
0.175481 | + | 0.984483i | \(0.443852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.79241 | 0.245522 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.6179 | −1.25792 | −0.628958 | − | 0.777439i | \(-0.716518\pi\) | ||||
−0.628958 | + | 0.777439i | \(0.716518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.1332 | 0.516434 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.2434 | −0.876531 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6918 | −0.947714 | −0.473857 | − | 0.880602i | \(-0.657139\pi\) | ||||
−0.473857 | + | 0.880602i | \(0.657139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.46359 | −0.377450 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.87432 | 0.195433 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.0256 | −1.46044 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.74016 | −0.187713 | −0.0938566 | − | 0.995586i | \(-0.529920\pi\) | ||||
−0.0938566 | + | 0.995586i | \(0.529920\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.86718 | −0.143538 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.02949 | 0.301098 | 0.150549 | − | 0.988603i | \(-0.451896\pi\) | ||||
0.150549 | + | 0.988603i | \(0.451896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.54123 | −0.176401 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.1193 | 0.950048 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.8321 | 0.834334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.6504 | 0.922202 | 0.461101 | − | 0.887348i | \(-0.347455\pi\) | ||||
0.461101 | + | 0.887348i | \(0.347455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.496846 | −0.0245076 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7730 | 0.677726 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.4637 | −1.88811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.19198 | 0.107342 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.12097 | −0.250176 | −0.125088 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125088 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6013 | 1.10152 | 0.550759 | − | 0.834664i | \(-0.314338\pi\) | ||||
0.550759 | + | 0.834664i | \(0.314338\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.4764 | 1.19008 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.49001 | 0.169290 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7578 | −0.520604 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.01069 | 0.193638 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.5884 | −1.42522 | −0.712612 | − | 0.701558i | \(-0.752488\pi\) | ||||
−0.712612 | + | 0.701558i | \(0.752488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.9988 | −0.768852 | −0.384426 | − | 0.923156i | \(-0.625601\pi\) | ||||
−0.384426 | + | 0.923156i | \(0.625601\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.16399 | −0.103755 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.03990 | 0.384601 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8720 | 1.28253 | 0.641266 | − | 0.767319i | \(-0.278410\pi\) | ||||
0.641266 | + | 0.767319i | \(0.278410\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.1904 | 0.532874 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.4164 | −1.20757 | −0.603786 | − | 0.797146i | \(-0.706342\pi\) | ||||
−0.603786 | + | 0.797146i | \(0.706342\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.7043 | −1.55033 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.61099 | 0.359987 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.13787 | 0.289664 | 0.144832 | − | 0.989456i | \(-0.453736\pi\) | ||||
0.144832 | + | 0.989456i | \(0.453736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20537 | 0.0567587 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.169102 | 0.00794510 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.6880 | −0.969869 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9094 | 0.884543 | 0.442272 | − | 0.896881i | \(-0.354173\pi\) | ||||
0.442272 | + | 0.896881i | \(0.354173\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.86803 | 0.413924 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.4986 | −1.00129 | −0.500646 | − | 0.865652i | \(-0.666904\pi\) | ||||
−0.500646 | + | 0.865652i | \(0.666904\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.7435 | 0.964031 | 0.482016 | − | 0.876163i | \(-0.339905\pi\) | ||||
0.482016 | + | 0.876163i | \(0.339905\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.605705 | 0.0280889 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.7390 | −0.635765 | −0.317883 | − | 0.948130i | \(-0.602972\pi\) | ||||
−0.317883 | + | 0.948130i | \(0.602972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.60708 | 0.0742079 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.03524 | 0.139856 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.2707 | −0.656168 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.75949 | −0.172497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.2251 | −0.651323 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.2040 | 1.42575 | 0.712873 | − | 0.701294i | \(-0.247394\pi\) | ||||
0.712873 | + | 0.701294i | \(0.247394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.3646 | −1.56689 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.04375 | −0.0474923 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.6085 | 1.25364 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.8122 | −1.80406 | −0.902031 | − | 0.431671i | \(-0.857924\pi\) | ||||
−0.902031 | + | 0.431671i | \(0.857924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.04009 | −0.0922563 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.16131 | 0.232927 | 0.116463 | − | 0.993195i | \(-0.462844\pi\) | ||||
0.116463 | + | 0.993195i | \(0.462844\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3405 | 0.510752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.5377 | 0.743314 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.2379 | −0.997504 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.9568 | −0.893391 | −0.446696 | − | 0.894686i | \(-0.647399\pi\) | ||||
−0.446696 | + | 0.894686i | \(0.647399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.96449 | −0.266474 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.6423 | 0.742044 | 0.371022 | − | 0.928624i | \(-0.379007\pi\) | ||||
0.371022 | + | 0.928624i | \(0.379007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.1858 | −1.12075 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.69459 | −0.164082 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.6290 | 0.870039 | 0.435019 | − | 0.900421i | \(-0.356742\pi\) | ||||
0.435019 | + | 0.900421i | \(0.356742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4749 | −0.596095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.55279 | −0.421766 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.49524 | 0.374345 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2568 | 0.890892 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.46023 | 0.327468 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.8899 | 1.52855 | 0.764277 | − | 0.644889i | \(-0.223096\pi\) | ||||
0.764277 | + | 0.644889i | \(0.223096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.51450 | 0.416040 | 0.208020 | − | 0.978125i | \(-0.433298\pi\) | ||||
0.208020 | + | 0.978125i | \(0.433298\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.488062 | 0.0213008 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.17424 | −0.138272 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0732 | −0.872748 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.4781 | 0.975466 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.46090 | −0.106594 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.3586 | 1.70162 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.04061 | −0.0880587 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.26118 | 0.398907 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.90299 | −0.0818158 | −0.0409079 | − | 0.999163i | \(-0.513025\pi\) | ||||
−0.0409079 | + | 0.999163i | \(0.513025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0291847 | 0.00125244 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.3315 | −1.12792 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.14465 | 0.0489416 | 0.0244708 | − | 0.999701i | \(-0.492210\pi\) | ||||
0.0244708 | + | 0.999701i | \(0.492210\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.5571 | −0.749317 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.2162 | −0.520427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.2720 | 0.904577 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.87785 | 0.249501 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.16627 | −0.176531 | −0.0882653 | − | 0.996097i | \(-0.528132\pi\) | ||||
−0.0882653 | + | 0.996097i | \(0.528132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.1353 | 1.23229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.59505 | 0.151783 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.1721 | −1.27160 | −0.635801 | − | 0.771853i | \(-0.719330\pi\) | ||||
−0.635801 | + | 0.771853i | \(0.719330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.6592 | −0.784997 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.0120 | −0.588448 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0112 | −0.461614 | −0.230807 | − | 0.973000i | \(-0.574137\pi\) | ||||
−0.230807 | + | 0.973000i | \(0.574137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.87520 | −0.120323 | −0.0601617 | − | 0.998189i | \(-0.519162\pi\) | ||||
−0.0601617 | + | 0.998189i | \(0.519162\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.77431 | −0.115899 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.36858 | −0.0570739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.04004 | −0.0849280 | −0.0424640 | − | 0.999098i | \(-0.513521\pi\) | ||||
−0.0424640 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.96486 | 0.123215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.1889 | 1.16947 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7728 | −0.487578 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.7636 | −1.39595 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.9834 | −0.783531 | −0.391765 | − | 0.920065i | \(-0.628135\pi\) | ||||
−0.391765 | + | 0.920065i | \(0.628135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.41934 | 0.140891 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.11288 | −0.333719 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.28178 | 0.299027 | 0.149513 | − | 0.988760i | \(-0.452229\pi\) | ||||
0.149513 | + | 0.988760i | \(0.452229\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.5440 | −0.760231 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.28074 | 0.175199 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.89664 | −0.404366 | −0.202183 | − | 0.979348i | \(-0.564804\pi\) | ||||
−0.202183 | + | 0.979348i | \(0.564804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.7579 | −1.70334 | −0.851669 | − | 0.524080i | \(-0.824409\pi\) | ||||
−0.851669 | + | 0.524080i | \(0.824409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.62281 | 0.106809 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.8048 | −0.520588 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5724 | 0.429121 | 0.214560 | − | 0.976711i | \(-0.431168\pi\) | ||||
0.214560 | + | 0.976711i | \(0.431168\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.58592 | 0.0642648 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41.3565 | −1.67311 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.4068 | −1.02617 | −0.513085 | − | 0.858338i | \(-0.671497\pi\) | ||||
−0.513085 | + | 0.858338i | \(0.671497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.420922 | 0.0169732 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1154 | −0.528007 | −0.264003 | − | 0.964522i | \(-0.585043\pi\) | ||||
−0.264003 | + | 0.964522i | \(0.585043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.6281 | −1.03008 | −0.515041 | − | 0.857166i | \(-0.672223\pi\) | ||||
−0.515041 | + | 0.857166i | \(0.672223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.47754 | −0.139549 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.9680 | 0.960257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.3599 | −1.13440 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.87264 | −0.154658 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.8032 | −1.22821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.0099 | −0.438299 | −0.219149 | − | 0.975691i | \(-0.570328\pi\) | ||||
−0.219149 | + | 0.975691i | \(0.570328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.02351 | 0.159920 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.3892 | −1.32501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.9078 | −0.749153 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.2930 | −1.43573 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.74422 | 0.147888 | 0.0739439 | − | 0.997262i | \(-0.476441\pi\) | ||||
0.0739439 | + | 0.997262i | \(0.476441\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.38602 | 0.212404 | 0.106202 | − | 0.994345i | \(-0.466131\pi\) | ||||
0.106202 | + | 0.994345i | \(0.466131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.98341 | −0.196222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.2176 | 0.637579 | 0.318790 | − | 0.947825i | \(-0.396724\pi\) | ||||
0.318790 | + | 0.947825i | \(0.396724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6030 | 0.730230 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.443903 | −0.0173979 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0560 | 0.823986 | 0.411993 | − | 0.911187i | \(-0.364833\pi\) | ||||
0.411993 | + | 0.911187i | \(0.364833\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.9928 | −1.05469 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.9916 | −0.857973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.7317 | −1.39191 | −0.695954 | − | 0.718086i | \(-0.745018\pi\) | ||||
−0.695954 | + | 0.718086i | \(0.745018\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.06191 | 0.235781 | 0.117890 | − | 0.993027i | \(-0.462387\pi\) | ||||
0.117890 | + | 0.993027i | \(0.462387\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.33970 | −0.285050 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.9759 | 0.774633 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.44711 | −0.172193 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.81257 | −0.224727 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.5303 | −0.560936 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.8548 | 1.92176 | 0.960881 | − | 0.276960i | \(-0.0893271\pi\) | ||||
0.960881 | + | 0.276960i | \(0.0893271\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.62611 | 0.0625891 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.4365 | 1.32350 | 0.661750 | − | 0.749724i | \(-0.269814\pi\) | ||||
0.661750 | + | 0.749724i | \(0.269814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.2335 | −0.776489 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.71249 | −0.103943 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.65122 | −0.369294 | −0.184647 | − | 0.982805i | \(-0.559114\pi\) | ||||
−0.184647 | + | 0.982805i | \(0.559114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.46158 | 0.132260 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.76359 | −0.143590 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0354 | 0.915677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.5886 | −0.745184 | −0.372592 | − | 0.927995i | \(-0.621531\pi\) | ||||
−0.372592 | + | 0.927995i | \(0.621531\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.1200 | −0.460400 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.2717 | −0.579290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20587 | −0.0835533 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.87146 | −0.0707850 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.2854 | 0.992788 | 0.496394 | − | 0.868097i | \(-0.334657\pi\) | ||||
0.496394 | + | 0.868097i | \(0.334657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.1817 | 1.25147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.07378 | 0.266414 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.4579 | 0.694181 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.38546 | −0.0520321 | −0.0260161 | − | 0.999662i | \(-0.508282\pi\) | ||||
−0.0260161 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.7167 | 1.30198 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.24476 | 0.0466165 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.9429 | −1.04501 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.69284 | 0.361986 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.0270462 | 0.00100865 | 0.000504326 | − | 1.00000i | \(-0.499839\pi\) | ||||
0.000504326 | 1.00000i | \(0.499839\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.22590 | −0.231865 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.39755 | 0.126356 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.07949 | 0.0772303 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6126 | 1.02409 | 0.512047 | − | 0.858957i | \(-0.328887\pi\) | ||||
0.512047 | + | 0.858957i | \(0.328887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7601 | −0.768894 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.1159 | 0.965930 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5920 | 0.871390 | 0.435695 | − | 0.900094i | \(-0.356503\pi\) | ||||
0.435695 | + | 0.900094i | \(0.356503\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.23406 | 0.119290 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.17065 | 0.0799568 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.67759 | −0.245639 | −0.122820 | − | 0.992429i | \(-0.539194\pi\) | ||||
−0.122820 | + | 0.992429i | \(0.539194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.90644 | 0.290450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0827 | 0.883509 | 0.441754 | − | 0.897136i | \(-0.354356\pi\) | ||||
0.441754 | + | 0.897136i | \(0.354356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.0266 | −1.94274 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.0053 | 1.68325 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.8447 | −1.05396 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.59868 | 0.0947011 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.17815 | −0.0428773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.7801 | 0.573536 | 0.286768 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286768 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.40977 | −0.0511715 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.4764 | −1.64852 | −0.824260 | − | 0.566212i | \(-0.808408\pi\) | ||||
−0.824260 | + | 0.566212i | \(0.808408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.2975 | 0.698618 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.2646 | −1.09422 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.9801 | −1.37138 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.00267693 | 9.65325e−5 0 | 4.82663e−5 | − | 1.00000i | \(-0.499985\pi\) | ||||
4.82663e−5 | 1.00000i | \(0.499985\pi\) | ||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.89055 | −0.320185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −55.0852 | −1.98128 | −0.990639 | − | 0.136506i | \(-0.956413\pi\) | ||||
−0.990639 | + | 0.136506i | \(0.956413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.582053 | −0.0209080 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.30770 | −0.154538 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.37620 | 0.0851361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.0363 | −1.07478 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.28394 | 0.188832 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.1468 | −0.754762 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0275 | 0.500025 | 0.250012 | − | 0.968243i | \(-0.419565\pi\) | ||||
0.250012 | + | 0.968243i | \(0.419565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.68477 | 0.131181 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6747 | 0.486217 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.6653 | 1.05344 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.11111 | −0.145806 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.8671 | 1.62469 | 0.812347 | − | 0.583174i | \(-0.198189\pi\) | ||||
0.812347 | + | 0.583174i | \(0.198189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.0706 | −1.31146 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.1166 | 1.38212 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.2003 | −0.642275 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.27192 | 0.256301 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.9468 | 0.385346 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.8037 | 0.907209 | 0.453605 | − | 0.891203i | \(-0.350138\pi\) | ||||
0.453605 | + | 0.891203i | \(0.350138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6603 | 0.901055 | 0.450527 | − | 0.892763i | \(-0.351236\pi\) | ||||
0.450527 | + | 0.892763i | \(0.351236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.77350 | 0.132343 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.2136 | 0.497879 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.1324 | −0.984229 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.7443 | 0.864637 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1493 | 0.424013 | 0.212006 | − | 0.977268i | \(-0.432000\pi\) | ||||
0.212006 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6280 | 0.963050 | 0.481525 | − | 0.876432i | \(-0.340083\pi\) | ||||
0.481525 | + | 0.876432i | \(0.340083\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.659216 | 0.0229510 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.328324 | −0.0114169 | −0.00570847 | − | 0.999984i | \(-0.501817\pi\) | ||||
−0.00570847 | + | 0.999984i | \(0.501817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0126 | 0.590872 | 0.295436 | − | 0.955363i | \(-0.404535\pi\) | ||||
0.295436 | + | 0.955363i | \(0.404535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.29068 | 0.148842 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.9483 | −0.587223 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.5552 | 1.43808 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.47898 | −0.0511212 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.7710 | 0.440903 | 0.220452 | − | 0.975398i | \(-0.429247\pi\) | ||||
0.220452 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2429 | −0.766995 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.85091 | 0.0981904 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.7406 | 0.885502 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.38423 | 0.322446 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.07459 | 0.277119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0793 | 0.414072 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.0843 | 0.687673 | 0.343837 | − | 0.939030i | \(-0.388273\pi\) | ||||
0.343837 | + | 0.939030i | \(0.388273\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.6015 | 1.11495 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.9693 | −1.67276 | −0.836380 | − | 0.548149i | \(-0.815333\pi\) | ||||
−0.836380 | + | 0.548149i | \(0.815333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0865 | 1.50421 | 0.752106 | − | 0.659042i | \(-0.229038\pi\) | ||||
0.752106 | + | 0.659042i | \(0.229038\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.308481 | −0.0105130 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.68309 | −0.295576 | −0.147788 | − | 0.989019i | \(-0.547215\pi\) | ||||
−0.147788 | + | 0.989019i | \(0.547215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −51.9762 | −1.76724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.702680 | −0.0238643 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.7317 | 0.974655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.43162 | −0.150160 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.0218 | −1.11762 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.8527 | 0.603533 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.9696 | 1.38344 | 0.691722 | − | 0.722163i | \(-0.256852\pi\) | ||||
0.691722 | + | 0.722163i | \(0.256852\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.51776 | −0.321026 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.3948 | 1.56308 | 0.781540 | − | 0.623856i | \(-0.214435\pi\) | ||||
0.781540 | + | 0.623856i | \(0.214435\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.8034 | −1.50776 | −0.753878 | − | 0.657014i | \(-0.771819\pi\) | ||||
−0.753878 | + | 0.657014i | \(0.771819\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.49626 | 0.218369 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.1769 | 0.375283 | 0.187641 | − | 0.982238i | \(-0.439916\pi\) | ||||
0.187641 | + | 0.982238i | \(0.439916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.4699 | 0.820695 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.9257 | −0.634035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.9330 | 1.33631 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2171 | 0.475226 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.87821 | 0.0961008 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.89134 | −0.0630797 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.5445 | 0.717753 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.65219 | 0.121537 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.203333 | −0.00675902 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.6769 | −0.520542 | −0.260271 | − | 0.965536i | \(-0.583812\pi\) | ||||
−0.260271 | + | 0.965536i | \(0.583812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.1240 | 0.999151 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.9282 | 0.892171 | 0.446085 | − | 0.894990i | \(-0.352818\pi\) | ||||
0.446085 | + | 0.894990i | \(0.352818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.0742 | 1.26007 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.07406 | −0.167743 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.7822 | 0.653265 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.5863 | −1.27284 | −0.636422 | − | 0.771341i | \(-0.719586\pi\) | ||||
−0.636422 | + | 0.771341i | \(0.719586\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.33911 | −0.110027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.3225 | 2.01845 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.64832 | −0.185716 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.1609 | −0.333728 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.6751 | 0.448665 | 0.224333 | − | 0.974513i | \(-0.427980\pi\) | ||||
0.224333 | + | 0.974513i | \(0.427980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.2570 | 0.598348 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.62195 | 0.0858387 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.0471 | −0.819126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2200 | 0.693228 | 0.346614 | − | 0.938008i | \(-0.387331\pi\) | ||||
0.346614 | + | 0.938008i | \(0.387331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.41708 | −0.242047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.5181 | −1.25565 | −0.627827 | − | 0.778353i | \(-0.716056\pi\) | ||||
−0.627827 | + | 0.778353i | \(0.716056\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.865017 | 0.0281688 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.64029 | −0.281069 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.2716 | 1.11368 | 0.556838 | − | 0.830621i | \(-0.312014\pi\) | ||||
0.556838 | + | 0.830621i | \(0.312014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.1580 | 1.20620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.59281 | 0.278641 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.72208 | 0.185356 | 0.0926782 | − | 0.995696i | \(-0.470457\pi\) | ||||
0.0926782 | + | 0.995696i | \(0.470457\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3289 | 0.625470 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.14207 | 0.0692434 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.53688 | −0.0819202 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4706 | −0.982923 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −47.0757 | −1.51699 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.6565 | −0.664956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.58868 | 0.0510885 | 0.0255442 | − | 0.999674i | \(-0.491868\pi\) | ||||
0.0255442 | + | 0.999674i | \(0.491868\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.08706 | 0.227669 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7801 | 0.731049 | 0.365524 | − | 0.930802i | \(-0.380890\pi\) | ||||
0.365524 | + | 0.930802i | \(0.380890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1922 | 0.358805 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.34587 | −0.0431022 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.62553 | 0.307948 | 0.153974 | − | 0.988075i | \(-0.450793\pi\) | ||||
0.153974 | + | 0.988075i | \(0.450793\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.3731 | 1.03465 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.4943 | 1.00554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.5987 | 1.86901 | 0.934504 | − | 0.355953i | \(-0.115844\pi\) | ||||
0.934504 | + | 0.355953i | \(0.115844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 56.5233 | 1.80098 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.18416 | −0.165014 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.2412 | −0.325650 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1018 | −0.670322 | −0.335161 | − | 0.942161i | \(-0.608791\pi\) | ||||
−0.335161 | + | 0.942161i | \(0.608791\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.3506 | −0.360201 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.8243 | −0.945495 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.70858 | −0.275803 | −0.137902 | − | 0.990446i | \(-0.544036\pi\) | ||||
−0.137902 | + | 0.990446i | \(0.544036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.3523 | −0.454086 |
(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 | 6008.2.a.b.1.23 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.23 | ✓ | 44 | 1.1 | even | 1 | trivial |