Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90192 | −1.34486 | −0.672432 | − | 0.740159i | \(-0.734750\pi\) | ||||
−0.672432 | + | 0.740159i | \(0.734750\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.61732 | 0.808658 | ||||||||
\(5\) | 0.767188 | 0.343097 | 0.171548 | − | 0.985176i | \(-0.445123\pi\) | ||||
0.171548 | + | 0.985176i | \(0.445123\pi\) | |||||||
\(6\) | 1.90192 | 0.776457 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.727834 | 0.257328 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.45913 | −0.461418 | ||||||||
\(11\) | 0.295463 | 0.0890855 | 0.0445427 | − | 0.999007i | \(-0.485817\pi\) | ||||
0.0445427 | + | 0.999007i | \(0.485817\pi\) | |||||||
\(12\) | −1.61732 | −0.466879 | ||||||||
\(13\) | 3.77953 | 1.04825 | 0.524127 | − | 0.851640i | \(-0.324392\pi\) | ||||
0.524127 | + | 0.851640i | \(0.324392\pi\) | |||||||
\(14\) | −1.90192 | −0.508311 | ||||||||
\(15\) | −0.767188 | −0.198087 | ||||||||
\(16\) | −4.61892 | −1.15473 | ||||||||
\(17\) | 5.24425 | 1.27192 | 0.635959 | − | 0.771723i | \(-0.280605\pi\) | ||||
0.635959 | + | 0.771723i | \(0.280605\pi\) | |||||||
\(18\) | −1.90192 | −0.448288 | ||||||||
\(19\) | −3.76509 | −0.863771 | −0.431885 | − | 0.901929i | \(-0.642151\pi\) | ||||
−0.431885 | + | 0.901929i | \(0.642151\pi\) | |||||||
\(20\) | 1.24079 | 0.277448 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.561948 | −0.119808 | ||||||||
\(23\) | −1.71339 | −0.357267 | −0.178634 | − | 0.983916i | \(-0.557168\pi\) | ||||
−0.178634 | + | 0.983916i | \(0.557168\pi\) | |||||||
\(24\) | −0.727834 | −0.148569 | ||||||||
\(25\) | −4.41142 | −0.882285 | ||||||||
\(26\) | −7.18839 | −1.40976 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.61732 | 0.305644 | ||||||||
\(29\) | −7.83095 | −1.45417 | −0.727086 | − | 0.686547i | \(-0.759126\pi\) | ||||
−0.727086 | + | 0.686547i | \(0.759126\pi\) | |||||||
\(30\) | 1.45913 | 0.266400 | ||||||||
\(31\) | 0.600616 | 0.107874 | 0.0539369 | − | 0.998544i | \(-0.482823\pi\) | ||||
0.0539369 | + | 0.998544i | \(0.482823\pi\) | |||||||
\(32\) | 7.32917 | 1.29563 | ||||||||
\(33\) | −0.295463 | −0.0514335 | ||||||||
\(34\) | −9.97417 | −1.71056 | ||||||||
\(35\) | 0.767188 | 0.129678 | ||||||||
\(36\) | 1.61732 | 0.269553 | ||||||||
\(37\) | −3.78080 | −0.621560 | −0.310780 | − | 0.950482i | \(-0.600590\pi\) | ||||
−0.310780 | + | 0.950482i | \(0.600590\pi\) | |||||||
\(38\) | 7.16091 | 1.16165 | ||||||||
\(39\) | −3.77953 | −0.605210 | ||||||||
\(40\) | 0.558386 | 0.0882885 | ||||||||
\(41\) | 8.68124 | 1.35578 | 0.677891 | − | 0.735162i | \(-0.262894\pi\) | ||||
0.677891 | + | 0.735162i | \(0.262894\pi\) | |||||||
\(42\) | 1.90192 | 0.293473 | ||||||||
\(43\) | 2.68115 | 0.408871 | 0.204435 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204435 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(44\) | 0.477857 | 0.0720397 | ||||||||
\(45\) | 0.767188 | 0.114366 | ||||||||
\(46\) | 3.25875 | 0.480476 | ||||||||
\(47\) | −10.2548 | −1.49582 | −0.747910 | − | 0.663800i | \(-0.768943\pi\) | ||||
−0.747910 | + | 0.663800i | \(0.768943\pi\) | |||||||
\(48\) | 4.61892 | 0.666684 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.39019 | 1.18655 | ||||||||
\(51\) | −5.24425 | −0.734342 | ||||||||
\(52\) | 6.11270 | 0.847679 | ||||||||
\(53\) | −7.17506 | −0.985570 | −0.492785 | − | 0.870151i | \(-0.664021\pi\) | ||||
−0.492785 | + | 0.870151i | \(0.664021\pi\) | |||||||
\(54\) | 1.90192 | 0.258819 | ||||||||
\(55\) | 0.226676 | 0.0305649 | ||||||||
\(56\) | 0.727834 | 0.0972610 | ||||||||
\(57\) | 3.76509 | 0.498698 | ||||||||
\(58\) | 14.8939 | 1.95566 | ||||||||
\(59\) | 9.38143 | 1.22136 | 0.610679 | − | 0.791878i | \(-0.290897\pi\) | ||||
0.610679 | + | 0.791878i | \(0.290897\pi\) | |||||||
\(60\) | −1.24079 | −0.160185 | ||||||||
\(61\) | 10.0051 | 1.28103 | 0.640514 | − | 0.767947i | \(-0.278721\pi\) | ||||
0.640514 | + | 0.767947i | \(0.278721\pi\) | |||||||
\(62\) | −1.14233 | −0.145075 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −4.70168 | −0.587711 | ||||||||
\(65\) | 2.89961 | 0.359653 | ||||||||
\(66\) | 0.561948 | 0.0691711 | ||||||||
\(67\) | 0.510569 | 0.0623759 | 0.0311880 | − | 0.999514i | \(-0.490071\pi\) | ||||
0.0311880 | + | 0.999514i | \(0.490071\pi\) | |||||||
\(68\) | 8.48161 | 1.02855 | ||||||||
\(69\) | 1.71339 | 0.206268 | ||||||||
\(70\) | −1.45913 | −0.174400 | ||||||||
\(71\) | 7.64336 | 0.907100 | 0.453550 | − | 0.891231i | \(-0.350157\pi\) | ||||
0.453550 | + | 0.891231i | \(0.350157\pi\) | |||||||
\(72\) | 0.727834 | 0.0857761 | ||||||||
\(73\) | 6.16649 | 0.721734 | 0.360867 | − | 0.932617i | \(-0.382481\pi\) | ||||
0.360867 | + | 0.932617i | \(0.382481\pi\) | |||||||
\(74\) | 7.19080 | 0.835914 | ||||||||
\(75\) | 4.41142 | 0.509387 | ||||||||
\(76\) | −6.08934 | −0.698495 | ||||||||
\(77\) | 0.295463 | 0.0336711 | ||||||||
\(78\) | 7.18839 | 0.813925 | ||||||||
\(79\) | −1.92887 | −0.217015 | −0.108507 | − | 0.994096i | \(-0.534607\pi\) | ||||
−0.108507 | + | 0.994096i | \(0.534607\pi\) | |||||||
\(80\) | −3.54358 | −0.396184 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.5111 | −1.82334 | ||||||||
\(83\) | −4.65688 | −0.511159 | −0.255580 | − | 0.966788i | \(-0.582266\pi\) | ||||
−0.255580 | + | 0.966788i | \(0.582266\pi\) | |||||||
\(84\) | −1.61732 | −0.176464 | ||||||||
\(85\) | 4.02332 | 0.436391 | ||||||||
\(86\) | −5.09934 | −0.549876 | ||||||||
\(87\) | 7.83095 | 0.839566 | ||||||||
\(88\) | 0.215048 | 0.0229242 | ||||||||
\(89\) | 5.88295 | 0.623591 | 0.311796 | − | 0.950149i | \(-0.399070\pi\) | ||||
0.311796 | + | 0.950149i | \(0.399070\pi\) | |||||||
\(90\) | −1.45913 | −0.153806 | ||||||||
\(91\) | 3.77953 | 0.396203 | ||||||||
\(92\) | −2.77110 | −0.288907 | ||||||||
\(93\) | −0.600616 | −0.0622809 | ||||||||
\(94\) | 19.5039 | 2.01167 | ||||||||
\(95\) | −2.88853 | −0.296357 | ||||||||
\(96\) | −7.32917 | −0.748030 | ||||||||
\(97\) | 18.0326 | 1.83094 | 0.915468 | − | 0.402390i | \(-0.131820\pi\) | ||||
0.915468 | + | 0.402390i | \(0.131820\pi\) | |||||||
\(98\) | −1.90192 | −0.192123 | ||||||||
\(99\) | 0.295463 | 0.0296952 | ||||||||
\(100\) | −7.13467 | −0.713467 | ||||||||
\(101\) | −14.1510 | −1.40807 | −0.704037 | − | 0.710163i | \(-0.748621\pi\) | ||||
−0.704037 | + | 0.710163i | \(0.748621\pi\) | |||||||
\(102\) | 9.97417 | 0.987590 | ||||||||
\(103\) | −1.46581 | −0.144430 | −0.0722151 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722151 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(104\) | 2.75087 | 0.269745 | ||||||||
\(105\) | −0.767188 | −0.0748699 | ||||||||
\(106\) | 13.6464 | 1.32546 | ||||||||
\(107\) | −7.15713 | −0.691906 | −0.345953 | − | 0.938252i | \(-0.612444\pi\) | ||||
−0.345953 | + | 0.938252i | \(0.612444\pi\) | |||||||
\(108\) | −1.61732 | −0.155626 | ||||||||
\(109\) | 9.55398 | 0.915106 | 0.457553 | − | 0.889182i | \(-0.348726\pi\) | ||||
0.457553 | + | 0.889182i | \(0.348726\pi\) | |||||||
\(110\) | −0.431120 | −0.0411057 | ||||||||
\(111\) | 3.78080 | 0.358858 | ||||||||
\(112\) | −4.61892 | −0.436447 | ||||||||
\(113\) | 3.35560 | 0.315668 | 0.157834 | − | 0.987466i | \(-0.449549\pi\) | ||||
0.157834 | + | 0.987466i | \(0.449549\pi\) | |||||||
\(114\) | −7.16091 | −0.670681 | ||||||||
\(115\) | −1.31449 | −0.122577 | ||||||||
\(116\) | −12.6651 | −1.17593 | ||||||||
\(117\) | 3.77953 | 0.349418 | ||||||||
\(118\) | −17.8428 | −1.64256 | ||||||||
\(119\) | 5.24425 | 0.480740 | ||||||||
\(120\) | −0.558386 | −0.0509734 | ||||||||
\(121\) | −10.9127 | −0.992064 | ||||||||
\(122\) | −19.0290 | −1.72281 | ||||||||
\(123\) | −8.68124 | −0.782761 | ||||||||
\(124\) | 0.971386 | 0.0872330 | ||||||||
\(125\) | −7.22033 | −0.645806 | ||||||||
\(126\) | −1.90192 | −0.169437 | ||||||||
\(127\) | −13.4223 | −1.19104 | −0.595518 | − | 0.803342i | \(-0.703053\pi\) | ||||
−0.595518 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(128\) | −5.71609 | −0.505235 | ||||||||
\(129\) | −2.68115 | −0.236062 | ||||||||
\(130\) | −5.51484 | −0.483684 | ||||||||
\(131\) | 8.26951 | 0.722510 | 0.361255 | − | 0.932467i | \(-0.382348\pi\) | ||||
0.361255 | + | 0.932467i | \(0.382348\pi\) | |||||||
\(132\) | −0.477857 | −0.0415921 | ||||||||
\(133\) | −3.76509 | −0.326475 | ||||||||
\(134\) | −0.971064 | −0.0838871 | ||||||||
\(135\) | −0.767188 | −0.0660290 | ||||||||
\(136\) | 3.81695 | 0.327300 | ||||||||
\(137\) | 3.75976 | 0.321218 | 0.160609 | − | 0.987018i | \(-0.448654\pi\) | ||||
0.160609 | + | 0.987018i | \(0.448654\pi\) | |||||||
\(138\) | −3.25875 | −0.277403 | ||||||||
\(139\) | 19.7004 | 1.67096 | 0.835482 | − | 0.549518i | \(-0.185189\pi\) | ||||
0.835482 | + | 0.549518i | \(0.185189\pi\) | |||||||
\(140\) | 1.24079 | 0.104866 | ||||||||
\(141\) | 10.2548 | 0.863612 | ||||||||
\(142\) | −14.5371 | −1.21993 | ||||||||
\(143\) | 1.11671 | 0.0933842 | ||||||||
\(144\) | −4.61892 | −0.384910 | ||||||||
\(145\) | −6.00781 | −0.498922 | ||||||||
\(146\) | −11.7282 | −0.970633 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −6.11476 | −0.502630 | ||||||||
\(149\) | 17.0164 | 1.39404 | 0.697019 | − | 0.717053i | \(-0.254510\pi\) | ||||
0.697019 | + | 0.717053i | \(0.254510\pi\) | |||||||
\(150\) | −8.39019 | −0.685056 | ||||||||
\(151\) | 22.3002 | 1.81476 | 0.907382 | − | 0.420307i | \(-0.138078\pi\) | ||||
0.907382 | + | 0.420307i | \(0.138078\pi\) | |||||||
\(152\) | −2.74036 | −0.222273 | ||||||||
\(153\) | 5.24425 | 0.423972 | ||||||||
\(154\) | −0.561948 | −0.0452831 | ||||||||
\(155\) | 0.460785 | 0.0370111 | ||||||||
\(156\) | −6.11270 | −0.489408 | ||||||||
\(157\) | 5.94616 | 0.474555 | 0.237277 | − | 0.971442i | \(-0.423745\pi\) | ||||
0.237277 | + | 0.971442i | \(0.423745\pi\) | |||||||
\(158\) | 3.66857 | 0.291855 | ||||||||
\(159\) | 7.17506 | 0.569019 | ||||||||
\(160\) | 5.62285 | 0.444525 | ||||||||
\(161\) | −1.71339 | −0.135034 | ||||||||
\(162\) | −1.90192 | −0.149429 | ||||||||
\(163\) | 8.03189 | 0.629106 | 0.314553 | − | 0.949240i | \(-0.398145\pi\) | ||||
0.314553 | + | 0.949240i | \(0.398145\pi\) | |||||||
\(164\) | 14.0403 | 1.09636 | ||||||||
\(165\) | −0.226676 | −0.0176467 | ||||||||
\(166\) | 8.85704 | 0.687440 | ||||||||
\(167\) | −3.00437 | −0.232486 | −0.116243 | − | 0.993221i | \(-0.537085\pi\) | ||||
−0.116243 | + | 0.993221i | \(0.537085\pi\) | |||||||
\(168\) | −0.727834 | −0.0561536 | ||||||||
\(169\) | 1.28487 | 0.0988363 | ||||||||
\(170\) | −7.65206 | −0.586886 | ||||||||
\(171\) | −3.76509 | −0.287924 | ||||||||
\(172\) | 4.33626 | 0.330637 | ||||||||
\(173\) | 14.1731 | 1.07756 | 0.538779 | − | 0.842447i | \(-0.318886\pi\) | ||||
0.538779 | + | 0.842447i | \(0.318886\pi\) | |||||||
\(174\) | −14.8939 | −1.12910 | ||||||||
\(175\) | −4.41142 | −0.333472 | ||||||||
\(176\) | −1.36472 | −0.102870 | ||||||||
\(177\) | −9.38143 | −0.705152 | ||||||||
\(178\) | −11.1889 | −0.838645 | ||||||||
\(179\) | −16.6373 | −1.24353 | −0.621764 | − | 0.783205i | \(-0.713583\pi\) | ||||
−0.621764 | + | 0.783205i | \(0.713583\pi\) | |||||||
\(180\) | 1.24079 | 0.0924827 | ||||||||
\(181\) | 3.39381 | 0.252260 | 0.126130 | − | 0.992014i | \(-0.459744\pi\) | ||||
0.126130 | + | 0.992014i | \(0.459744\pi\) | |||||||
\(182\) | −7.18839 | −0.532839 | ||||||||
\(183\) | −10.0051 | −0.739602 | ||||||||
\(184\) | −1.24707 | −0.0919350 | ||||||||
\(185\) | −2.90059 | −0.213255 | ||||||||
\(186\) | 1.14233 | 0.0837594 | ||||||||
\(187\) | 1.54948 | 0.113309 | ||||||||
\(188\) | −16.5853 | −1.20961 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 5.49377 | 0.398560 | ||||||||
\(191\) | −24.8240 | −1.79620 | −0.898101 | − | 0.439789i | \(-0.855053\pi\) | ||||
−0.898101 | + | 0.439789i | \(0.855053\pi\) | |||||||
\(192\) | 4.70168 | 0.339315 | ||||||||
\(193\) | 1.89762 | 0.136594 | 0.0682969 | − | 0.997665i | \(-0.478243\pi\) | ||||
0.0682969 | + | 0.997665i | \(0.478243\pi\) | |||||||
\(194\) | −34.2967 | −2.46236 | ||||||||
\(195\) | −2.89961 | −0.207645 | ||||||||
\(196\) | 1.61732 | 0.115523 | ||||||||
\(197\) | −15.6176 | −1.11271 | −0.556353 | − | 0.830946i | \(-0.687800\pi\) | ||||
−0.556353 | + | 0.830946i | \(0.687800\pi\) | |||||||
\(198\) | −0.561948 | −0.0399359 | ||||||||
\(199\) | 6.07308 | 0.430509 | 0.215254 | − | 0.976558i | \(-0.430942\pi\) | ||||
0.215254 | + | 0.976558i | \(0.430942\pi\) | |||||||
\(200\) | −3.21079 | −0.227037 | ||||||||
\(201\) | −0.510569 | −0.0360128 | ||||||||
\(202\) | 26.9141 | 1.89367 | ||||||||
\(203\) | −7.83095 | −0.549625 | ||||||||
\(204\) | −8.48161 | −0.593832 | ||||||||
\(205\) | 6.66014 | 0.465164 | ||||||||
\(206\) | 2.78785 | 0.194239 | ||||||||
\(207\) | −1.71339 | −0.119089 | ||||||||
\(208\) | −17.4574 | −1.21045 | ||||||||
\(209\) | −1.11244 | −0.0769494 | ||||||||
\(210\) | 1.45913 | 0.100690 | ||||||||
\(211\) | −0.221019 | −0.0152156 | −0.00760779 | − | 0.999971i | \(-0.502422\pi\) | ||||
−0.00760779 | + | 0.999971i | \(0.502422\pi\) | |||||||
\(212\) | −11.6043 | −0.796990 | ||||||||
\(213\) | −7.64336 | −0.523714 | ||||||||
\(214\) | 13.6123 | 0.930519 | ||||||||
\(215\) | 2.05694 | 0.140282 | ||||||||
\(216\) | −0.727834 | −0.0495229 | ||||||||
\(217\) | 0.600616 | 0.0407724 | ||||||||
\(218\) | −18.1710 | −1.23069 | ||||||||
\(219\) | −6.16649 | −0.416693 | ||||||||
\(220\) | 0.366606 | 0.0247166 | ||||||||
\(221\) | 19.8208 | 1.33329 | ||||||||
\(222\) | −7.19080 | −0.482615 | ||||||||
\(223\) | 2.40462 | 0.161025 | 0.0805125 | − | 0.996754i | \(-0.474344\pi\) | ||||
0.0805125 | + | 0.996754i | \(0.474344\pi\) | |||||||
\(224\) | 7.32917 | 0.489701 | ||||||||
\(225\) | −4.41142 | −0.294095 | ||||||||
\(226\) | −6.38210 | −0.424531 | ||||||||
\(227\) | 19.0248 | 1.26272 | 0.631361 | − | 0.775489i | \(-0.282497\pi\) | ||||
0.631361 | + | 0.775489i | \(0.282497\pi\) | |||||||
\(228\) | 6.08934 | 0.403277 | ||||||||
\(229\) | 23.2092 | 1.53371 | 0.766855 | − | 0.641821i | \(-0.221821\pi\) | ||||
0.766855 | + | 0.641821i | \(0.221821\pi\) | |||||||
\(230\) | 2.50007 | 0.164850 | ||||||||
\(231\) | −0.295463 | −0.0194400 | ||||||||
\(232\) | −5.69964 | −0.374200 | ||||||||
\(233\) | 5.31731 | 0.348349 | 0.174174 | − | 0.984715i | \(-0.444274\pi\) | ||||
0.174174 | + | 0.984715i | \(0.444274\pi\) | |||||||
\(234\) | −7.18839 | −0.469920 | ||||||||
\(235\) | −7.86738 | −0.513211 | ||||||||
\(236\) | 15.1727 | 0.987662 | ||||||||
\(237\) | 1.92887 | 0.125294 | ||||||||
\(238\) | −9.97417 | −0.646529 | ||||||||
\(239\) | 9.26093 | 0.599039 | 0.299520 | − | 0.954090i | \(-0.403174\pi\) | ||||
0.299520 | + | 0.954090i | \(0.403174\pi\) | |||||||
\(240\) | 3.54358 | 0.228737 | ||||||||
\(241\) | −22.2302 | −1.43198 | −0.715988 | − | 0.698113i | \(-0.754023\pi\) | ||||
−0.715988 | + | 0.698113i | \(0.754023\pi\) | |||||||
\(242\) | 20.7551 | 1.33419 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 16.1815 | 1.03591 | ||||||||
\(245\) | 0.767188 | 0.0490138 | ||||||||
\(246\) | 16.5111 | 1.05271 | ||||||||
\(247\) | −14.2303 | −0.905451 | ||||||||
\(248\) | 0.437149 | 0.0277590 | ||||||||
\(249\) | 4.65688 | 0.295118 | ||||||||
\(250\) | 13.7325 | 0.868521 | ||||||||
\(251\) | −27.8959 | −1.76078 | −0.880388 | − | 0.474255i | \(-0.842717\pi\) | ||||
−0.880388 | + | 0.474255i | \(0.842717\pi\) | |||||||
\(252\) | 1.61732 | 0.101881 | ||||||||
\(253\) | −0.506245 | −0.0318273 | ||||||||
\(254\) | 25.5282 | 1.60178 | ||||||||
\(255\) | −4.02332 | −0.251950 | ||||||||
\(256\) | 20.2749 | 1.26718 | ||||||||
\(257\) | −7.42797 | −0.463344 | −0.231672 | − | 0.972794i | \(-0.574420\pi\) | ||||
−0.231672 | + | 0.972794i | \(0.574420\pi\) | |||||||
\(258\) | 5.09934 | 0.317471 | ||||||||
\(259\) | −3.78080 | −0.234928 | ||||||||
\(260\) | 4.68959 | 0.290836 | ||||||||
\(261\) | −7.83095 | −0.484724 | ||||||||
\(262\) | −15.7280 | −0.971678 | ||||||||
\(263\) | 17.8180 | 1.09871 | 0.549354 | − | 0.835590i | \(-0.314874\pi\) | ||||
0.549354 | + | 0.835590i | \(0.314874\pi\) | |||||||
\(264\) | −0.215048 | −0.0132353 | ||||||||
\(265\) | −5.50462 | −0.338146 | ||||||||
\(266\) | 7.16091 | 0.439064 | ||||||||
\(267\) | −5.88295 | −0.360031 | ||||||||
\(268\) | 0.825752 | 0.0504408 | ||||||||
\(269\) | 12.2074 | 0.744298 | 0.372149 | − | 0.928173i | \(-0.378621\pi\) | ||||
0.372149 | + | 0.928173i | \(0.378621\pi\) | |||||||
\(270\) | 1.45913 | 0.0888000 | ||||||||
\(271\) | 6.36680 | 0.386755 | 0.193378 | − | 0.981124i | \(-0.438056\pi\) | ||||
0.193378 | + | 0.981124i | \(0.438056\pi\) | |||||||
\(272\) | −24.2228 | −1.46872 | ||||||||
\(273\) | −3.77953 | −0.228748 | ||||||||
\(274\) | −7.15077 | −0.431994 | ||||||||
\(275\) | −1.30341 | −0.0785987 | ||||||||
\(276\) | 2.77110 | 0.166801 | ||||||||
\(277\) | 23.3907 | 1.40541 | 0.702706 | − | 0.711481i | \(-0.251975\pi\) | ||||
0.702706 | + | 0.711481i | \(0.251975\pi\) | |||||||
\(278\) | −37.4686 | −2.24722 | ||||||||
\(279\) | 0.600616 | 0.0359579 | ||||||||
\(280\) | 0.558386 | 0.0333699 | ||||||||
\(281\) | −13.8862 | −0.828381 | −0.414191 | − | 0.910190i | \(-0.635935\pi\) | ||||
−0.414191 | + | 0.910190i | \(0.635935\pi\) | |||||||
\(282\) | −19.5039 | −1.16144 | ||||||||
\(283\) | 15.0386 | 0.893954 | 0.446977 | − | 0.894546i | \(-0.352501\pi\) | ||||
0.446977 | + | 0.894546i | \(0.352501\pi\) | |||||||
\(284\) | 12.3617 | 0.733534 | ||||||||
\(285\) | 2.88853 | 0.171102 | ||||||||
\(286\) | −2.12390 | −0.125589 | ||||||||
\(287\) | 8.68124 | 0.512438 | ||||||||
\(288\) | 7.32917 | 0.431875 | ||||||||
\(289\) | 10.5022 | 0.617774 | ||||||||
\(290\) | 11.4264 | 0.670982 | ||||||||
\(291\) | −18.0326 | −1.05709 | ||||||||
\(292\) | 9.97317 | 0.583636 | ||||||||
\(293\) | 7.98940 | 0.466746 | 0.233373 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(294\) | 1.90192 | 0.110922 | ||||||||
\(295\) | 7.19732 | 0.419044 | ||||||||
\(296\) | −2.75180 | −0.159945 | ||||||||
\(297\) | −0.295463 | −0.0171445 | ||||||||
\(298\) | −32.3639 | −1.87479 | ||||||||
\(299\) | −6.47583 | −0.374507 | ||||||||
\(300\) | 7.13467 | 0.411920 | ||||||||
\(301\) | 2.68115 | 0.154539 | ||||||||
\(302\) | −42.4133 | −2.44061 | ||||||||
\(303\) | 14.1510 | 0.812952 | ||||||||
\(304\) | 17.3906 | 0.997422 | ||||||||
\(305\) | 7.67582 | 0.439516 | ||||||||
\(306\) | −9.97417 | −0.570185 | ||||||||
\(307\) | 7.17730 | 0.409630 | 0.204815 | − | 0.978801i | \(-0.434341\pi\) | ||||
0.204815 | + | 0.978801i | \(0.434341\pi\) | |||||||
\(308\) | 0.477857 | 0.0272285 | ||||||||
\(309\) | 1.46581 | 0.0833869 | ||||||||
\(310\) | −0.876378 | −0.0497749 | ||||||||
\(311\) | −9.33978 | −0.529611 | −0.264805 | − | 0.964302i | \(-0.585308\pi\) | ||||
−0.264805 | + | 0.964302i | \(0.585308\pi\) | |||||||
\(312\) | −2.75087 | −0.155738 | ||||||||
\(313\) | 8.57535 | 0.484707 | 0.242354 | − | 0.970188i | \(-0.422081\pi\) | ||||
0.242354 | + | 0.970188i | \(0.422081\pi\) | |||||||
\(314\) | −11.3091 | −0.638212 | ||||||||
\(315\) | 0.767188 | 0.0432261 | ||||||||
\(316\) | −3.11959 | −0.175491 | ||||||||
\(317\) | −21.1175 | −1.18608 | −0.593039 | − | 0.805174i | \(-0.702072\pi\) | ||||
−0.593039 | + | 0.805174i | \(0.702072\pi\) | |||||||
\(318\) | −13.6464 | −0.765253 | ||||||||
\(319\) | −2.31376 | −0.129546 | ||||||||
\(320\) | −3.60707 | −0.201642 | ||||||||
\(321\) | 7.15713 | 0.399472 | ||||||||
\(322\) | 3.25875 | 0.181603 | ||||||||
\(323\) | −19.7451 | −1.09864 | ||||||||
\(324\) | 1.61732 | 0.0898509 | ||||||||
\(325\) | −16.6731 | −0.924858 | ||||||||
\(326\) | −15.2761 | −0.846062 | ||||||||
\(327\) | −9.55398 | −0.528337 | ||||||||
\(328\) | 6.31851 | 0.348881 | ||||||||
\(329\) | −10.2548 | −0.565367 | ||||||||
\(330\) | 0.431120 | 0.0237324 | ||||||||
\(331\) | −11.9243 | −0.655419 | −0.327709 | − | 0.944779i | \(-0.606277\pi\) | ||||
−0.327709 | + | 0.944779i | \(0.606277\pi\) | |||||||
\(332\) | −7.53166 | −0.413353 | ||||||||
\(333\) | −3.78080 | −0.207187 | ||||||||
\(334\) | 5.71409 | 0.312661 | ||||||||
\(335\) | 0.391702 | 0.0214010 | ||||||||
\(336\) | 4.61892 | 0.251983 | ||||||||
\(337\) | −20.7509 | −1.13037 | −0.565186 | − | 0.824964i | \(-0.691195\pi\) | ||||
−0.565186 | + | 0.824964i | \(0.691195\pi\) | |||||||
\(338\) | −2.44373 | −0.132921 | ||||||||
\(339\) | −3.35560 | −0.182251 | ||||||||
\(340\) | 6.50699 | 0.352891 | ||||||||
\(341\) | 0.177460 | 0.00960998 | ||||||||
\(342\) | 7.16091 | 0.387218 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.95143 | 0.105214 | ||||||||
\(345\) | 1.31449 | 0.0707700 | ||||||||
\(346\) | −26.9561 | −1.44917 | ||||||||
\(347\) | 23.7950 | 1.27738 | 0.638691 | − | 0.769463i | \(-0.279476\pi\) | ||||
0.638691 | + | 0.769463i | \(0.279476\pi\) | |||||||
\(348\) | 12.6651 | 0.678922 | ||||||||
\(349\) | 27.5842 | 1.47655 | 0.738274 | − | 0.674501i | \(-0.235641\pi\) | ||||
0.738274 | + | 0.674501i | \(0.235641\pi\) | |||||||
\(350\) | 8.39019 | 0.448475 | ||||||||
\(351\) | −3.77953 | −0.201737 | ||||||||
\(352\) | 2.16550 | 0.115421 | ||||||||
\(353\) | 21.1141 | 1.12379 | 0.561895 | − | 0.827208i | \(-0.310072\pi\) | ||||
0.561895 | + | 0.827208i | \(0.310072\pi\) | |||||||
\(354\) | 17.8428 | 0.948333 | ||||||||
\(355\) | 5.86389 | 0.311223 | ||||||||
\(356\) | 9.51459 | 0.504272 | ||||||||
\(357\) | −5.24425 | −0.277555 | ||||||||
\(358\) | 31.6428 | 1.67237 | ||||||||
\(359\) | −5.18095 | −0.273440 | −0.136720 | − | 0.990610i | \(-0.543656\pi\) | ||||
−0.136720 | + | 0.990610i | \(0.543656\pi\) | |||||||
\(360\) | 0.558386 | 0.0294295 | ||||||||
\(361\) | −4.82411 | −0.253900 | ||||||||
\(362\) | −6.45476 | −0.339255 | ||||||||
\(363\) | 10.9127 | 0.572768 | ||||||||
\(364\) | 6.11270 | 0.320393 | ||||||||
\(365\) | 4.73086 | 0.247624 | ||||||||
\(366\) | 19.0290 | 0.994663 | ||||||||
\(367\) | −32.1695 | −1.67923 | −0.839616 | − | 0.543180i | \(-0.817220\pi\) | ||||
−0.839616 | + | 0.543180i | \(0.817220\pi\) | |||||||
\(368\) | 7.91403 | 0.412547 | ||||||||
\(369\) | 8.68124 | 0.451927 | ||||||||
\(370\) | 5.51670 | 0.286799 | ||||||||
\(371\) | −7.17506 | −0.372511 | ||||||||
\(372\) | −0.971386 | −0.0503640 | ||||||||
\(373\) | −13.6941 | −0.709055 | −0.354527 | − | 0.935046i | \(-0.615358\pi\) | ||||
−0.354527 | + | 0.935046i | \(0.615358\pi\) | |||||||
\(374\) | −2.94700 | −0.152386 | ||||||||
\(375\) | 7.22033 | 0.372856 | ||||||||
\(376\) | −7.46382 | −0.384917 | ||||||||
\(377\) | −29.5974 | −1.52434 | ||||||||
\(378\) | 1.90192 | 0.0978244 | ||||||||
\(379\) | 13.6856 | 0.702981 | 0.351490 | − | 0.936191i | \(-0.385675\pi\) | ||||
0.351490 | + | 0.936191i | \(0.385675\pi\) | |||||||
\(380\) | −4.67167 | −0.239652 | ||||||||
\(381\) | 13.4223 | 0.687645 | ||||||||
\(382\) | 47.2134 | 2.41565 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 5.71609 | 0.291698 | ||||||||
\(385\) | 0.226676 | 0.0115525 | ||||||||
\(386\) | −3.60913 | −0.183700 | ||||||||
\(387\) | 2.68115 | 0.136290 | ||||||||
\(388\) | 29.1645 | 1.48060 | ||||||||
\(389\) | 7.83762 | 0.397383 | 0.198692 | − | 0.980062i | \(-0.436331\pi\) | ||||
0.198692 | + | 0.980062i | \(0.436331\pi\) | |||||||
\(390\) | 5.51484 | 0.279255 | ||||||||
\(391\) | −8.98547 | −0.454415 | ||||||||
\(392\) | 0.727834 | 0.0367612 | ||||||||
\(393\) | −8.26951 | −0.417142 | ||||||||
\(394\) | 29.7035 | 1.49644 | ||||||||
\(395\) | −1.47981 | −0.0744571 | ||||||||
\(396\) | 0.477857 | 0.0240132 | ||||||||
\(397\) | 25.5653 | 1.28309 | 0.641543 | − | 0.767087i | \(-0.278294\pi\) | ||||
0.641543 | + | 0.767087i | \(0.278294\pi\) | |||||||
\(398\) | −11.5505 | −0.578976 | ||||||||
\(399\) | 3.76509 | 0.188490 | ||||||||
\(400\) | 20.3760 | 1.01880 | ||||||||
\(401\) | −5.32713 | −0.266024 | −0.133012 | − | 0.991114i | \(-0.542465\pi\) | ||||
−0.133012 | + | 0.991114i | \(0.542465\pi\) | |||||||
\(402\) | 0.971064 | 0.0484323 | ||||||||
\(403\) | 2.27005 | 0.113079 | ||||||||
\(404\) | −22.8866 | −1.13865 | ||||||||
\(405\) | 0.767188 | 0.0381219 | ||||||||
\(406\) | 14.8939 | 0.739171 | ||||||||
\(407\) | −1.11709 | −0.0553720 | ||||||||
\(408\) | −3.81695 | −0.188967 | ||||||||
\(409\) | 1.46525 | 0.0724517 | 0.0362259 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362259 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(410\) | −12.6671 | −0.625583 | ||||||||
\(411\) | −3.75976 | −0.185455 | ||||||||
\(412\) | −2.37067 | −0.116795 | ||||||||
\(413\) | 9.38143 | 0.461630 | ||||||||
\(414\) | 3.25875 | 0.160159 | ||||||||
\(415\) | −3.57270 | −0.175377 | ||||||||
\(416\) | 27.7008 | 1.35815 | ||||||||
\(417\) | −19.7004 | −0.964731 | ||||||||
\(418\) | 2.11579 | 0.103486 | ||||||||
\(419\) | −23.1847 | −1.13265 | −0.566325 | − | 0.824182i | \(-0.691635\pi\) | ||||
−0.566325 | + | 0.824182i | \(0.691635\pi\) | |||||||
\(420\) | −1.24079 | −0.0605441 | ||||||||
\(421\) | 33.2782 | 1.62188 | 0.810941 | − | 0.585128i | \(-0.198956\pi\) | ||||
0.810941 | + | 0.585128i | \(0.198956\pi\) | |||||||
\(422\) | 0.420361 | 0.0204629 | ||||||||
\(423\) | −10.2548 | −0.498607 | ||||||||
\(424\) | −5.22226 | −0.253615 | ||||||||
\(425\) | −23.1346 | −1.12219 | ||||||||
\(426\) | 14.5371 | 0.704324 | ||||||||
\(427\) | 10.0051 | 0.484183 | ||||||||
\(428\) | −11.5753 | −0.559516 | ||||||||
\(429\) | −1.11671 | −0.0539154 | ||||||||
\(430\) | −3.91215 | −0.188661 | ||||||||
\(431\) | −3.59405 | −0.173119 | −0.0865596 | − | 0.996247i | \(-0.527587\pi\) | ||||
−0.0865596 | + | 0.996247i | \(0.527587\pi\) | |||||||
\(432\) | 4.61892 | 0.222228 | ||||||||
\(433\) | −11.5775 | −0.556379 | −0.278190 | − | 0.960526i | \(-0.589734\pi\) | ||||
−0.278190 | + | 0.960526i | \(0.589734\pi\) | |||||||
\(434\) | −1.14233 | −0.0548334 | ||||||||
\(435\) | 6.00781 | 0.288053 | ||||||||
\(436\) | 15.4518 | 0.740008 | ||||||||
\(437\) | 6.45108 | 0.308597 | ||||||||
\(438\) | 11.7282 | 0.560395 | ||||||||
\(439\) | −17.9531 | −0.856853 | −0.428426 | − | 0.903577i | \(-0.640932\pi\) | ||||
−0.428426 | + | 0.903577i | \(0.640932\pi\) | |||||||
\(440\) | 0.164982 | 0.00786522 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −37.6977 | −1.79310 | ||||||||
\(443\) | −16.7634 | −0.796454 | −0.398227 | − | 0.917287i | \(-0.630374\pi\) | ||||
−0.398227 | + | 0.917287i | \(0.630374\pi\) | |||||||
\(444\) | 6.11476 | 0.290194 | ||||||||
\(445\) | 4.51333 | 0.213952 | ||||||||
\(446\) | −4.57340 | −0.216557 | ||||||||
\(447\) | −17.0164 | −0.804848 | ||||||||
\(448\) | −4.70168 | −0.222134 | ||||||||
\(449\) | −27.0944 | −1.27866 | −0.639332 | − | 0.768931i | \(-0.720789\pi\) | ||||
−0.639332 | + | 0.768931i | \(0.720789\pi\) | |||||||
\(450\) | 8.39019 | 0.395518 | ||||||||
\(451\) | 2.56499 | 0.120780 | ||||||||
\(452\) | 5.42707 | 0.255268 | ||||||||
\(453\) | −22.3002 | −1.04775 | ||||||||
\(454\) | −36.1838 | −1.69819 | ||||||||
\(455\) | 2.89961 | 0.135936 | ||||||||
\(456\) | 2.74036 | 0.128329 | ||||||||
\(457\) | 6.62146 | 0.309739 | 0.154869 | − | 0.987935i | \(-0.450504\pi\) | ||||
0.154869 | + | 0.987935i | \(0.450504\pi\) | |||||||
\(458\) | −44.1422 | −2.06263 | ||||||||
\(459\) | −5.24425 | −0.244781 | ||||||||
\(460\) | −2.12595 | −0.0991231 | ||||||||
\(461\) | 32.5390 | 1.51549 | 0.757747 | − | 0.652549i | \(-0.226300\pi\) | ||||
0.757747 | + | 0.652549i | \(0.226300\pi\) | |||||||
\(462\) | 0.561948 | 0.0261442 | ||||||||
\(463\) | −19.9036 | −0.924997 | −0.462498 | − | 0.886620i | \(-0.653047\pi\) | ||||
−0.462498 | + | 0.886620i | \(0.653047\pi\) | |||||||
\(464\) | 36.1706 | 1.67918 | ||||||||
\(465\) | −0.460785 | −0.0213684 | ||||||||
\(466\) | −10.1131 | −0.468481 | ||||||||
\(467\) | −19.0186 | −0.880074 | −0.440037 | − | 0.897980i | \(-0.645035\pi\) | ||||
−0.440037 | + | 0.897980i | \(0.645035\pi\) | |||||||
\(468\) | 6.11270 | 0.282560 | ||||||||
\(469\) | 0.510569 | 0.0235759 | ||||||||
\(470\) | 14.9632 | 0.690199 | ||||||||
\(471\) | −5.94616 | −0.273984 | ||||||||
\(472\) | 6.82813 | 0.314290 | ||||||||
\(473\) | 0.792179 | 0.0364245 | ||||||||
\(474\) | −3.66857 | −0.168503 | ||||||||
\(475\) | 16.6094 | 0.762092 | ||||||||
\(476\) | 8.48161 | 0.388754 | ||||||||
\(477\) | −7.17506 | −0.328523 | ||||||||
\(478\) | −17.6136 | −0.805626 | ||||||||
\(479\) | 31.6118 | 1.44438 | 0.722191 | − | 0.691694i | \(-0.243135\pi\) | ||||
0.722191 | + | 0.691694i | \(0.243135\pi\) | |||||||
\(480\) | −5.62285 | −0.256647 | ||||||||
\(481\) | −14.2897 | −0.651553 | ||||||||
\(482\) | 42.2802 | 1.92581 | ||||||||
\(483\) | 1.71339 | 0.0779621 | ||||||||
\(484\) | −17.6493 | −0.802241 | ||||||||
\(485\) | 13.8344 | 0.628188 | ||||||||
\(486\) | 1.90192 | 0.0862730 | ||||||||
\(487\) | 12.0818 | 0.547479 | 0.273740 | − | 0.961804i | \(-0.411739\pi\) | ||||
0.273740 | + | 0.961804i | \(0.411739\pi\) | |||||||
\(488\) | 7.28209 | 0.329645 | ||||||||
\(489\) | −8.03189 | −0.363215 | ||||||||
\(490\) | −1.45913 | −0.0659169 | ||||||||
\(491\) | −5.55174 | −0.250547 | −0.125273 | − | 0.992122i | \(-0.539981\pi\) | ||||
−0.125273 | + | 0.992122i | \(0.539981\pi\) | |||||||
\(492\) | −14.0403 | −0.632986 | ||||||||
\(493\) | −41.0675 | −1.84959 | ||||||||
\(494\) | 27.0649 | 1.21771 | ||||||||
\(495\) | 0.226676 | 0.0101883 | ||||||||
\(496\) | −2.77420 | −0.124565 | ||||||||
\(497\) | 7.64336 | 0.342851 | ||||||||
\(498\) | −8.85704 | −0.396893 | ||||||||
\(499\) | −18.8268 | −0.842804 | −0.421402 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421402 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(500\) | −11.6776 | −0.522236 | ||||||||
\(501\) | 3.00437 | 0.134226 | ||||||||
\(502\) | 53.0559 | 2.36800 | ||||||||
\(503\) | 2.85168 | 0.127150 | 0.0635751 | − | 0.997977i | \(-0.479750\pi\) | ||||
0.0635751 | + | 0.997977i | \(0.479750\pi\) | |||||||
\(504\) | 0.727834 | 0.0324203 | ||||||||
\(505\) | −10.8564 | −0.483106 | ||||||||
\(506\) | 0.962839 | 0.0428034 | ||||||||
\(507\) | −1.28487 | −0.0570632 | ||||||||
\(508\) | −21.7081 | −0.963141 | ||||||||
\(509\) | 1.44698 | 0.0641361 | 0.0320681 | − | 0.999486i | \(-0.489791\pi\) | ||||
0.0320681 | + | 0.999486i | \(0.489791\pi\) | |||||||
\(510\) | 7.65206 | 0.338839 | ||||||||
\(511\) | 6.16649 | 0.272790 | ||||||||
\(512\) | −27.1292 | −1.19895 | ||||||||
\(513\) | 3.76509 | 0.166233 | ||||||||
\(514\) | 14.1274 | 0.623135 | ||||||||
\(515\) | −1.12455 | −0.0495536 | ||||||||
\(516\) | −4.33626 | −0.190893 | ||||||||
\(517\) | −3.02992 | −0.133256 | ||||||||
\(518\) | 7.19080 | 0.315946 | ||||||||
\(519\) | −14.1731 | −0.622128 | ||||||||
\(520\) | 2.11044 | 0.0925488 | ||||||||
\(521\) | −13.0860 | −0.573309 | −0.286654 | − | 0.958034i | \(-0.592543\pi\) | ||||
−0.286654 | + | 0.958034i | \(0.592543\pi\) | |||||||
\(522\) | 14.8939 | 0.651888 | ||||||||
\(523\) | 11.6582 | 0.509777 | 0.254888 | − | 0.966971i | \(-0.417961\pi\) | ||||
0.254888 | + | 0.966971i | \(0.417961\pi\) | |||||||
\(524\) | 13.3744 | 0.584264 | ||||||||
\(525\) | 4.41142 | 0.192530 | ||||||||
\(526\) | −33.8886 | −1.47761 | ||||||||
\(527\) | 3.14978 | 0.137206 | ||||||||
\(528\) | 1.36472 | 0.0593918 | ||||||||
\(529\) | −20.0643 | −0.872360 | ||||||||
\(530\) | 10.4694 | 0.454760 | ||||||||
\(531\) | 9.38143 | 0.407119 | ||||||||
\(532\) | −6.08934 | −0.264006 | ||||||||
\(533\) | 32.8110 | 1.42120 | ||||||||
\(534\) | 11.1889 | 0.484192 | ||||||||
\(535\) | −5.49086 | −0.237391 | ||||||||
\(536\) | 0.371610 | 0.0160511 | ||||||||
\(537\) | 16.6373 | 0.717951 | ||||||||
\(538\) | −23.2175 | −1.00098 | ||||||||
\(539\) | 0.295463 | 0.0127265 | ||||||||
\(540\) | −1.24079 | −0.0533949 | ||||||||
\(541\) | 10.5262 | 0.452556 | 0.226278 | − | 0.974063i | \(-0.427344\pi\) | ||||
0.226278 | + | 0.974063i | \(0.427344\pi\) | |||||||
\(542\) | −12.1092 | −0.520133 | ||||||||
\(543\) | −3.39381 | −0.145642 | ||||||||
\(544\) | 38.4360 | 1.64793 | ||||||||
\(545\) | 7.32970 | 0.313970 | ||||||||
\(546\) | 7.18839 | 0.307635 | ||||||||
\(547\) | 15.0590 | 0.643877 | 0.321938 | − | 0.946761i | \(-0.395666\pi\) | ||||
0.321938 | + | 0.946761i | \(0.395666\pi\) | |||||||
\(548\) | 6.08072 | 0.259755 | ||||||||
\(549\) | 10.0051 | 0.427009 | ||||||||
\(550\) | 2.47899 | 0.105705 | ||||||||
\(551\) | 29.4842 | 1.25607 | ||||||||
\(552\) | 1.24707 | 0.0530787 | ||||||||
\(553\) | −1.92887 | −0.0820239 | ||||||||
\(554\) | −44.4874 | −1.89009 | ||||||||
\(555\) | 2.90059 | 0.123123 | ||||||||
\(556\) | 31.8617 | 1.35124 | ||||||||
\(557\) | 12.1681 | 0.515579 | 0.257790 | − | 0.966201i | \(-0.417006\pi\) | ||||
0.257790 | + | 0.966201i | \(0.417006\pi\) | |||||||
\(558\) | −1.14233 | −0.0483585 | ||||||||
\(559\) | 10.1335 | 0.428600 | ||||||||
\(560\) | −3.54358 | −0.149744 | ||||||||
\(561\) | −1.54948 | −0.0654192 | ||||||||
\(562\) | 26.4105 | 1.11406 | ||||||||
\(563\) | −9.57859 | −0.403689 | −0.201845 | − | 0.979418i | \(-0.564694\pi\) | ||||
−0.201845 | + | 0.979418i | \(0.564694\pi\) | |||||||
\(564\) | 16.5853 | 0.698367 | ||||||||
\(565\) | 2.57438 | 0.108305 | ||||||||
\(566\) | −28.6023 | −1.20225 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 5.56310 | 0.233422 | ||||||||
\(569\) | 12.8056 | 0.536840 | 0.268420 | − | 0.963302i | \(-0.413498\pi\) | ||||
0.268420 | + | 0.963302i | \(0.413498\pi\) | |||||||
\(570\) | −5.49377 | −0.230109 | ||||||||
\(571\) | 14.6512 | 0.613134 | 0.306567 | − | 0.951849i | \(-0.400820\pi\) | ||||
0.306567 | + | 0.951849i | \(0.400820\pi\) | |||||||
\(572\) | 1.80608 | 0.0755159 | ||||||||
\(573\) | 24.8240 | 1.03704 | ||||||||
\(574\) | −16.5111 | −0.689159 | ||||||||
\(575\) | 7.55851 | 0.315211 | ||||||||
\(576\) | −4.70168 | −0.195904 | ||||||||
\(577\) | 38.7768 | 1.61430 | 0.807150 | − | 0.590346i | \(-0.201009\pi\) | ||||
0.807150 | + | 0.590346i | \(0.201009\pi\) | |||||||
\(578\) | −19.9743 | −0.830821 | ||||||||
\(579\) | −1.89762 | −0.0788625 | ||||||||
\(580\) | −9.71654 | −0.403457 | ||||||||
\(581\) | −4.65688 | −0.193200 | ||||||||
\(582\) | 34.2967 | 1.42164 | ||||||||
\(583\) | −2.11997 | −0.0878000 | ||||||||
\(584\) | 4.48819 | 0.185722 | ||||||||
\(585\) | 2.89961 | 0.119884 | ||||||||
\(586\) | −15.1952 | −0.627709 | ||||||||
\(587\) | −14.9209 | −0.615853 | −0.307926 | − | 0.951410i | \(-0.599635\pi\) | ||||
−0.307926 | + | 0.951410i | \(0.599635\pi\) | |||||||
\(588\) | −1.61732 | −0.0666970 | ||||||||
\(589\) | −2.26137 | −0.0931782 | ||||||||
\(590\) | −13.6888 | −0.563557 | ||||||||
\(591\) | 15.6176 | 0.642421 | ||||||||
\(592\) | 17.4632 | 0.717734 | ||||||||
\(593\) | 9.73014 | 0.399569 | 0.199784 | − | 0.979840i | \(-0.435976\pi\) | ||||
0.199784 | + | 0.979840i | \(0.435976\pi\) | |||||||
\(594\) | 0.561948 | 0.0230570 | ||||||||
\(595\) | 4.02332 | 0.164940 | ||||||||
\(596\) | 27.5209 | 1.12730 | ||||||||
\(597\) | −6.07308 | −0.248554 | ||||||||
\(598\) | 12.3165 | 0.503661 | ||||||||
\(599\) | 25.5990 | 1.04595 | 0.522974 | − | 0.852349i | \(-0.324823\pi\) | ||||
0.522974 | + | 0.852349i | \(0.324823\pi\) | |||||||
\(600\) | 3.21079 | 0.131080 | ||||||||
\(601\) | 25.3901 | 1.03569 | 0.517843 | − | 0.855476i | \(-0.326735\pi\) | ||||
0.517843 | + | 0.855476i | \(0.326735\pi\) | |||||||
\(602\) | −5.09934 | −0.207833 | ||||||||
\(603\) | 0.510569 | 0.0207920 | ||||||||
\(604\) | 36.0665 | 1.46752 | ||||||||
\(605\) | −8.37209 | −0.340374 | ||||||||
\(606\) | −26.9141 | −1.09331 | ||||||||
\(607\) | 29.1121 | 1.18163 | 0.590813 | − | 0.806809i | \(-0.298807\pi\) | ||||
0.590813 | + | 0.806809i | \(0.298807\pi\) | |||||||
\(608\) | −27.5950 | −1.11912 | ||||||||
\(609\) | 7.83095 | 0.317326 | ||||||||
\(610\) | −14.5988 | −0.591090 | ||||||||
\(611\) | −38.7585 | −1.56800 | ||||||||
\(612\) | 8.48161 | 0.342849 | ||||||||
\(613\) | 40.4891 | 1.63534 | 0.817670 | − | 0.575688i | \(-0.195266\pi\) | ||||
0.817670 | + | 0.575688i | \(0.195266\pi\) | |||||||
\(614\) | −13.6507 | −0.550897 | ||||||||
\(615\) | −6.66014 | −0.268563 | ||||||||
\(616\) | 0.215048 | 0.00866454 | ||||||||
\(617\) | 4.43962 | 0.178732 | 0.0893661 | − | 0.995999i | \(-0.471516\pi\) | ||||
0.0893661 | + | 0.995999i | \(0.471516\pi\) | |||||||
\(618\) | −2.78785 | −0.112144 | ||||||||
\(619\) | 12.2384 | 0.491903 | 0.245951 | − | 0.969282i | \(-0.420900\pi\) | ||||
0.245951 | + | 0.969282i | \(0.420900\pi\) | |||||||
\(620\) | 0.745235 | 0.0299294 | ||||||||
\(621\) | 1.71339 | 0.0687561 | ||||||||
\(622\) | 17.7636 | 0.712254 | ||||||||
\(623\) | 5.88295 | 0.235695 | ||||||||
\(624\) | 17.4574 | 0.698854 | ||||||||
\(625\) | 16.5178 | 0.660711 | ||||||||
\(626\) | −16.3097 | −0.651865 | ||||||||
\(627\) | 1.11244 | 0.0444268 | ||||||||
\(628\) | 9.61682 | 0.383753 | ||||||||
\(629\) | −19.8275 | −0.790573 | ||||||||
\(630\) | −1.45913 | −0.0581333 | ||||||||
\(631\) | 37.9108 | 1.50921 | 0.754603 | − | 0.656182i | \(-0.227830\pi\) | ||||
0.754603 | + | 0.656182i | \(0.227830\pi\) | |||||||
\(632\) | −1.40390 | −0.0558441 | ||||||||
\(633\) | 0.221019 | 0.00878472 | ||||||||
\(634\) | 40.1639 | 1.59511 | ||||||||
\(635\) | −10.2974 | −0.408641 | ||||||||
\(636\) | 11.6043 | 0.460142 | ||||||||
\(637\) | 3.77953 | 0.149751 | ||||||||
\(638\) | 4.40059 | 0.174221 | ||||||||
\(639\) | 7.64336 | 0.302367 | ||||||||
\(640\) | −4.38531 | −0.173345 | ||||||||
\(641\) | −4.08103 | −0.161191 | −0.0805955 | − | 0.996747i | \(-0.525682\pi\) | ||||
−0.0805955 | + | 0.996747i | \(0.525682\pi\) | |||||||
\(642\) | −13.6123 | −0.537236 | ||||||||
\(643\) | 23.8611 | 0.940991 | 0.470496 | − | 0.882402i | \(-0.344075\pi\) | ||||
0.470496 | + | 0.882402i | \(0.344075\pi\) | |||||||
\(644\) | −2.77110 | −0.109197 | ||||||||
\(645\) | −2.05694 | −0.0809920 | ||||||||
\(646\) | 37.5536 | 1.47753 | ||||||||
\(647\) | −34.4655 | −1.35498 | −0.677489 | − | 0.735533i | \(-0.736932\pi\) | ||||
−0.677489 | + | 0.735533i | \(0.736932\pi\) | |||||||
\(648\) | 0.727834 | 0.0285920 | ||||||||
\(649\) | 2.77187 | 0.108805 | ||||||||
\(650\) | 31.7110 | 1.24381 | ||||||||
\(651\) | −0.600616 | −0.0235400 | ||||||||
\(652\) | 12.9901 | 0.508732 | ||||||||
\(653\) | 31.9447 | 1.25009 | 0.625046 | − | 0.780588i | \(-0.285080\pi\) | ||||
0.625046 | + | 0.780588i | \(0.285080\pi\) | |||||||
\(654\) | 18.1710 | 0.710541 | ||||||||
\(655\) | 6.34427 | 0.247891 | ||||||||
\(656\) | −40.0980 | −1.56556 | ||||||||
\(657\) | 6.16649 | 0.240578 | ||||||||
\(658\) | 19.5039 | 0.760341 | ||||||||
\(659\) | −11.1976 | −0.436196 | −0.218098 | − | 0.975927i | \(-0.569985\pi\) | ||||
−0.218098 | + | 0.975927i | \(0.569985\pi\) | |||||||
\(660\) | −0.366606 | −0.0142701 | ||||||||
\(661\) | −31.5028 | −1.22532 | −0.612658 | − | 0.790348i | \(-0.709900\pi\) | ||||
−0.612658 | + | 0.790348i | \(0.709900\pi\) | |||||||
\(662\) | 22.6791 | 0.881449 | ||||||||
\(663\) | −19.8208 | −0.769777 | ||||||||
\(664\) | −3.38944 | −0.131536 | ||||||||
\(665\) | −2.88853 | −0.112012 | ||||||||
\(666\) | 7.19080 | 0.278638 | ||||||||
\(667\) | 13.4175 | 0.519528 | ||||||||
\(668\) | −4.85903 | −0.188001 | ||||||||
\(669\) | −2.40462 | −0.0929679 | ||||||||
\(670\) | −0.744988 | −0.0287814 | ||||||||
\(671\) | 2.95615 | 0.114121 | ||||||||
\(672\) | −7.32917 | −0.282729 | ||||||||
\(673\) | 6.63070 | 0.255595 | 0.127797 | − | 0.991800i | \(-0.459209\pi\) | ||||
0.127797 | + | 0.991800i | \(0.459209\pi\) | |||||||
\(674\) | 39.4666 | 1.52020 | ||||||||
\(675\) | 4.41142 | 0.169796 | ||||||||
\(676\) | 2.07804 | 0.0799248 | ||||||||
\(677\) | −6.09030 | −0.234069 | −0.117035 | − | 0.993128i | \(-0.537339\pi\) | ||||
−0.117035 | + | 0.993128i | \(0.537339\pi\) | |||||||
\(678\) | 6.38210 | 0.245103 | ||||||||
\(679\) | 18.0326 | 0.692029 | ||||||||
\(680\) | 2.92831 | 0.112296 | ||||||||
\(681\) | −19.0248 | −0.729033 | ||||||||
\(682\) | −0.337515 | −0.0129241 | ||||||||
\(683\) | 26.4849 | 1.01342 | 0.506709 | − | 0.862117i | \(-0.330862\pi\) | ||||
0.506709 | + | 0.862117i | \(0.330862\pi\) | |||||||
\(684\) | −6.08934 | −0.232832 | ||||||||
\(685\) | 2.88444 | 0.110209 | ||||||||
\(686\) | −1.90192 | −0.0726158 | ||||||||
\(687\) | −23.2092 | −0.885488 | ||||||||
\(688\) | −12.3840 | −0.472135 | ||||||||
\(689\) | −27.1184 | −1.03313 | ||||||||
\(690\) | −2.50007 | −0.0951760 | ||||||||
\(691\) | −26.3606 | −1.00281 | −0.501403 | − | 0.865214i | \(-0.667183\pi\) | ||||
−0.501403 | + | 0.865214i | \(0.667183\pi\) | |||||||
\(692\) | 22.9223 | 0.871376 | ||||||||
\(693\) | 0.295463 | 0.0112237 | ||||||||
\(694\) | −45.2563 | −1.71790 | ||||||||
\(695\) | 15.1139 | 0.573302 | ||||||||
\(696\) | 5.69964 | 0.216044 | ||||||||
\(697\) | 45.5266 | 1.72444 | ||||||||
\(698\) | −52.4631 | −1.98576 | ||||||||
\(699\) | −5.31731 | −0.201119 | ||||||||
\(700\) | −7.13467 | −0.269665 | ||||||||
\(701\) | 0.142946 | 0.00539901 | 0.00269951 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269951 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(702\) | 7.18839 | 0.271308 | ||||||||
\(703\) | 14.2351 | 0.536886 | ||||||||
\(704\) | −1.38917 | −0.0523565 | ||||||||
\(705\) | 7.86738 | 0.296303 | ||||||||
\(706\) | −40.1575 | −1.51135 | ||||||||
\(707\) | −14.1510 | −0.532202 | ||||||||
\(708\) | −15.1727 | −0.570227 | ||||||||
\(709\) | 12.7183 | 0.477644 | 0.238822 | − | 0.971063i | \(-0.423239\pi\) | ||||
0.238822 | + | 0.971063i | \(0.423239\pi\) | |||||||
\(710\) | −11.1527 | −0.418552 | ||||||||
\(711\) | −1.92887 | −0.0723383 | ||||||||
\(712\) | 4.28181 | 0.160468 | ||||||||
\(713\) | −1.02909 | −0.0385398 | ||||||||
\(714\) | 9.97417 | 0.373274 | ||||||||
\(715\) | 0.856728 | 0.0320398 | ||||||||
\(716\) | −26.9077 | −1.00559 | ||||||||
\(717\) | −9.26093 | −0.345856 | ||||||||
\(718\) | 9.85377 | 0.367739 | ||||||||
\(719\) | 1.48639 | 0.0554329 | 0.0277164 | − | 0.999616i | \(-0.491176\pi\) | ||||
0.0277164 | + | 0.999616i | \(0.491176\pi\) | |||||||
\(720\) | −3.54358 | −0.132061 | ||||||||
\(721\) | −1.46581 | −0.0545895 | ||||||||
\(722\) | 9.17508 | 0.341461 | ||||||||
\(723\) | 22.2302 | 0.826751 | ||||||||
\(724\) | 5.48886 | 0.203992 | ||||||||
\(725\) | 34.5457 | 1.28299 | ||||||||
\(726\) | −20.7551 | −0.770295 | ||||||||
\(727\) | 35.5619 | 1.31892 | 0.659458 | − | 0.751741i | \(-0.270786\pi\) | ||||
0.659458 | + | 0.751741i | \(0.270786\pi\) | |||||||
\(728\) | 2.75087 | 0.101954 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.99774 | −0.333021 | ||||||||
\(731\) | 14.0606 | 0.520050 | ||||||||
\(732\) | −16.1815 | −0.598085 | ||||||||
\(733\) | 24.3035 | 0.897671 | 0.448835 | − | 0.893615i | \(-0.351839\pi\) | ||||
0.448835 | + | 0.893615i | \(0.351839\pi\) | |||||||
\(734\) | 61.1839 | 2.25834 | ||||||||
\(735\) | −0.767188 | −0.0282981 | ||||||||
\(736\) | −12.5578 | −0.462885 | ||||||||
\(737\) | 0.150854 | 0.00555679 | ||||||||
\(738\) | −16.5111 | −0.607781 | ||||||||
\(739\) | −5.99935 | −0.220690 | −0.110345 | − | 0.993893i | \(-0.535196\pi\) | ||||
−0.110345 | + | 0.993893i | \(0.535196\pi\) | |||||||
\(740\) | −4.69117 | −0.172451 | ||||||||
\(741\) | 14.2303 | 0.522762 | ||||||||
\(742\) | 13.6464 | 0.500976 | ||||||||
\(743\) | −5.87179 | −0.215415 | −0.107708 | − | 0.994183i | \(-0.534351\pi\) | ||||
−0.107708 | + | 0.994183i | \(0.534351\pi\) | |||||||
\(744\) | −0.437149 | −0.0160266 | ||||||||
\(745\) | 13.0548 | 0.478290 | ||||||||
\(746\) | 26.0452 | 0.953582 | ||||||||
\(747\) | −4.65688 | −0.170386 | ||||||||
\(748\) | 2.50600 | 0.0916286 | ||||||||
\(749\) | −7.15713 | −0.261516 | ||||||||
\(750\) | −13.7325 | −0.501441 | ||||||||
\(751\) | −29.3366 | −1.07051 | −0.535254 | − | 0.844691i | \(-0.679784\pi\) | ||||
−0.535254 | + | 0.844691i | \(0.679784\pi\) | |||||||
\(752\) | 47.3662 | 1.72727 | ||||||||
\(753\) | 27.8959 | 1.01658 | ||||||||
\(754\) | 56.2919 | 2.05003 | ||||||||
\(755\) | 17.1084 | 0.622640 | ||||||||
\(756\) | −1.61732 | −0.0588212 | ||||||||
\(757\) | 24.4811 | 0.889780 | 0.444890 | − | 0.895585i | \(-0.353243\pi\) | ||||
0.444890 | + | 0.895585i | \(0.353243\pi\) | |||||||
\(758\) | −26.0289 | −0.945414 | ||||||||
\(759\) | 0.506245 | 0.0183755 | ||||||||
\(760\) | −2.10237 | −0.0762610 | ||||||||
\(761\) | 50.0059 | 1.81271 | 0.906356 | − | 0.422515i | \(-0.138853\pi\) | ||||
0.906356 | + | 0.422515i | \(0.138853\pi\) | |||||||
\(762\) | −25.5282 | −0.924789 | ||||||||
\(763\) | 9.55398 | 0.345877 | ||||||||
\(764\) | −40.1483 | −1.45251 | ||||||||
\(765\) | 4.02332 | 0.145464 | ||||||||
\(766\) | 1.90192 | 0.0687193 | ||||||||
\(767\) | 35.4574 | 1.28029 | ||||||||
\(768\) | −20.2749 | −0.731609 | ||||||||
\(769\) | −35.6544 | −1.28573 | −0.642866 | − | 0.765979i | \(-0.722255\pi\) | ||||
−0.642866 | + | 0.765979i | \(0.722255\pi\) | |||||||
\(770\) | −0.431120 | −0.0155365 | ||||||||
\(771\) | 7.42797 | 0.267512 | ||||||||
\(772\) | 3.06906 | 0.110458 | ||||||||
\(773\) | −14.7306 | −0.529821 | −0.264911 | − | 0.964273i | \(-0.585342\pi\) | ||||
−0.264911 | + | 0.964273i | \(0.585342\pi\) | |||||||
\(774\) | −5.09934 | −0.183292 | ||||||||
\(775\) | −2.64957 | −0.0951753 | ||||||||
\(776\) | 13.1248 | 0.471152 | ||||||||
\(777\) | 3.78080 | 0.135636 | ||||||||
\(778\) | −14.9066 | −0.534426 | ||||||||
\(779\) | −32.6856 | −1.17108 | ||||||||
\(780\) | −4.68959 | −0.167914 | ||||||||
\(781\) | 2.25833 | 0.0808094 | ||||||||
\(782\) | 17.0897 | 0.611126 | ||||||||
\(783\) | 7.83095 | 0.279855 | ||||||||
\(784\) | −4.61892 | −0.164961 | ||||||||
\(785\) | 4.56182 | 0.162818 | ||||||||
\(786\) | 15.7280 | 0.560998 | ||||||||
\(787\) | −3.71374 | −0.132381 | −0.0661903 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661903 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(788\) | −25.2586 | −0.899800 | ||||||||
\(789\) | −17.8180 | −0.634339 | ||||||||
\(790\) | 2.81448 | 0.100135 | ||||||||
\(791\) | 3.35560 | 0.119311 | ||||||||
\(792\) | 0.215048 | 0.00764141 | ||||||||
\(793\) | 37.8148 | 1.34284 | ||||||||
\(794\) | −48.6233 | −1.72558 | ||||||||
\(795\) | 5.50462 | 0.195229 | ||||||||
\(796\) | 9.82209 | 0.348135 | ||||||||
\(797\) | 21.3671 | 0.756860 | 0.378430 | − | 0.925630i | \(-0.376464\pi\) | ||||
0.378430 | + | 0.925630i | \(0.376464\pi\) | |||||||
\(798\) | −7.16091 | −0.253494 | ||||||||
\(799\) | −53.7789 | −1.90256 | ||||||||
\(800\) | −32.3321 | −1.14311 | ||||||||
\(801\) | 5.88295 | 0.207864 | ||||||||
\(802\) | 10.1318 | 0.357766 | ||||||||
\(803\) | 1.82197 | 0.0642960 | ||||||||
\(804\) | −0.825752 | −0.0291220 | ||||||||
\(805\) | −1.31449 | −0.0463299 | ||||||||
\(806\) | −4.31746 | −0.152076 | ||||||||
\(807\) | −12.2074 | −0.429721 | ||||||||
\(808\) | −10.2996 | −0.362337 | ||||||||
\(809\) | −2.55237 | −0.0897365 | −0.0448683 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448683 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(810\) | −1.45913 | −0.0512687 | ||||||||
\(811\) | 7.37838 | 0.259090 | 0.129545 | − | 0.991574i | \(-0.458648\pi\) | ||||
0.129545 | + | 0.991574i | \(0.458648\pi\) | |||||||
\(812\) | −12.6651 | −0.444459 | ||||||||
\(813\) | −6.36680 | −0.223293 | ||||||||
\(814\) | 2.12462 | 0.0744678 | ||||||||
\(815\) | 6.16197 | 0.215844 | ||||||||
\(816\) | 24.2228 | 0.847967 | ||||||||
\(817\) | −10.0948 | −0.353171 | ||||||||
\(818\) | −2.78679 | −0.0974377 | ||||||||
\(819\) | 3.77953 | 0.132068 | ||||||||
\(820\) | 10.7716 | 0.376159 | ||||||||
\(821\) | 8.86130 | 0.309262 | 0.154631 | − | 0.987972i | \(-0.450581\pi\) | ||||
0.154631 | + | 0.987972i | \(0.450581\pi\) | |||||||
\(822\) | 7.15077 | 0.249412 | ||||||||
\(823\) | 26.1096 | 0.910122 | 0.455061 | − | 0.890460i | \(-0.349617\pi\) | ||||
0.455061 | + | 0.890460i | \(0.349617\pi\) | |||||||
\(824\) | −1.06687 | −0.0371660 | ||||||||
\(825\) | 1.30341 | 0.0453790 | ||||||||
\(826\) | −17.8428 | −0.620829 | ||||||||
\(827\) | 39.7746 | 1.38310 | 0.691549 | − | 0.722329i | \(-0.256928\pi\) | ||||
0.691549 | + | 0.722329i | \(0.256928\pi\) | |||||||
\(828\) | −2.77110 | −0.0963024 | ||||||||
\(829\) | 12.4044 | 0.430822 | 0.215411 | − | 0.976523i | \(-0.430891\pi\) | ||||
0.215411 | + | 0.976523i | \(0.430891\pi\) | |||||||
\(830\) | 6.79501 | 0.235858 | ||||||||
\(831\) | −23.3907 | −0.811415 | ||||||||
\(832\) | −17.7702 | −0.616070 | ||||||||
\(833\) | 5.24425 | 0.181702 | ||||||||
\(834\) | 37.4686 | 1.29743 | ||||||||
\(835\) | −2.30492 | −0.0797650 | ||||||||
\(836\) | −1.79918 | −0.0622258 | ||||||||
\(837\) | −0.600616 | −0.0207603 | ||||||||
\(838\) | 44.0956 | 1.52326 | ||||||||
\(839\) | 24.7912 | 0.855888 | 0.427944 | − | 0.903805i | \(-0.359238\pi\) | ||||
0.427944 | + | 0.903805i | \(0.359238\pi\) | |||||||
\(840\) | −0.558386 | −0.0192661 | ||||||||
\(841\) | 32.3238 | 1.11462 | ||||||||
\(842\) | −63.2927 | −2.18121 | ||||||||
\(843\) | 13.8862 | 0.478266 | ||||||||
\(844\) | −0.357458 | −0.0123042 | ||||||||
\(845\) | 0.985738 | 0.0339104 | ||||||||
\(846\) | 19.5039 | 0.670558 | ||||||||
\(847\) | −10.9127 | −0.374965 | ||||||||
\(848\) | 33.1410 | 1.13807 | ||||||||
\(849\) | −15.0386 | −0.516124 | ||||||||
\(850\) | 44.0003 | 1.50920 | ||||||||
\(851\) | 6.47801 | 0.222063 | ||||||||
\(852\) | −12.3617 | −0.423506 | ||||||||
\(853\) | 19.6021 | 0.671161 | 0.335581 | − | 0.942011i | \(-0.391067\pi\) | ||||
0.335581 | + | 0.942011i | \(0.391067\pi\) | |||||||
\(854\) | −19.0290 | −0.651160 | ||||||||
\(855\) | −2.88853 | −0.0987856 | ||||||||
\(856\) | −5.20921 | −0.178047 | ||||||||
\(857\) | −53.8625 | −1.83991 | −0.919954 | − | 0.392027i | \(-0.871774\pi\) | ||||
−0.919954 | + | 0.392027i | \(0.871774\pi\) | |||||||
\(858\) | 2.12390 | 0.0725088 | ||||||||
\(859\) | −30.7683 | −1.04980 | −0.524900 | − | 0.851164i | \(-0.675897\pi\) | ||||
−0.524900 | + | 0.851164i | \(0.675897\pi\) | |||||||
\(860\) | 3.32673 | 0.113440 | ||||||||
\(861\) | −8.68124 | −0.295856 | ||||||||
\(862\) | 6.83561 | 0.232822 | ||||||||
\(863\) | −26.2585 | −0.893851 | −0.446926 | − | 0.894571i | \(-0.647481\pi\) | ||||
−0.446926 | + | 0.894571i | \(0.647481\pi\) | |||||||
\(864\) | −7.32917 | −0.249343 | ||||||||
\(865\) | 10.8734 | 0.369707 | ||||||||
\(866\) | 22.0195 | 0.748254 | ||||||||
\(867\) | −10.5022 | −0.356672 | ||||||||
\(868\) | 0.971386 | 0.0329710 | ||||||||
\(869\) | −0.569910 | −0.0193329 | ||||||||
\(870\) | −11.4264 | −0.387391 | ||||||||
\(871\) | 1.92971 | 0.0653858 | ||||||||
\(872\) | 6.95372 | 0.235483 | ||||||||
\(873\) | 18.0326 | 0.610312 | ||||||||
\(874\) | −12.2695 | −0.415021 | ||||||||
\(875\) | −7.22033 | −0.244092 | ||||||||
\(876\) | −9.97317 | −0.336962 | ||||||||
\(877\) | −9.51226 | −0.321206 | −0.160603 | − | 0.987019i | \(-0.551344\pi\) | ||||
−0.160603 | + | 0.987019i | \(0.551344\pi\) | |||||||
\(878\) | 34.1454 | 1.15235 | ||||||||
\(879\) | −7.98940 | −0.269476 | ||||||||
\(880\) | −1.04700 | −0.0352942 | ||||||||
\(881\) | 25.2562 | 0.850901 | 0.425451 | − | 0.904982i | \(-0.360116\pi\) | ||||
0.425451 | + | 0.904982i | \(0.360116\pi\) | |||||||
\(882\) | −1.90192 | −0.0640411 | ||||||||
\(883\) | 5.80893 | 0.195486 | 0.0977431 | − | 0.995212i | \(-0.468838\pi\) | ||||
0.0977431 | + | 0.995212i | \(0.468838\pi\) | |||||||
\(884\) | 32.0565 | 1.07818 | ||||||||
\(885\) | −7.19732 | −0.241935 | ||||||||
\(886\) | 31.8827 | 1.07112 | ||||||||
\(887\) | 22.1020 | 0.742113 | 0.371057 | − | 0.928610i | \(-0.378996\pi\) | ||||
0.371057 | + | 0.928610i | \(0.378996\pi\) | |||||||
\(888\) | 2.75180 | 0.0923444 | ||||||||
\(889\) | −13.4223 | −0.450169 | ||||||||
\(890\) | −8.58401 | −0.287737 | ||||||||
\(891\) | 0.295463 | 0.00989839 | ||||||||
\(892\) | 3.88903 | 0.130214 | ||||||||
\(893\) | 38.6103 | 1.29205 | ||||||||
\(894\) | 32.3639 | 1.08241 | ||||||||
\(895\) | −12.7639 | −0.426650 | ||||||||
\(896\) | −5.71609 | −0.190961 | ||||||||
\(897\) | 6.47583 | 0.216222 | ||||||||
\(898\) | 51.5315 | 1.71963 | ||||||||
\(899\) | −4.70339 | −0.156867 | ||||||||
\(900\) | −7.13467 | −0.237822 | ||||||||
\(901\) | −37.6278 | −1.25356 | ||||||||
\(902\) | −4.87841 | −0.162433 | ||||||||
\(903\) | −2.68115 | −0.0892229 | ||||||||
\(904\) | 2.44232 | 0.0812305 | ||||||||
\(905\) | 2.60369 | 0.0865495 | ||||||||
\(906\) | 42.4133 | 1.40909 | ||||||||
\(907\) | −11.3382 | −0.376478 | −0.188239 | − | 0.982123i | \(-0.560278\pi\) | ||||
−0.188239 | + | 0.982123i | \(0.560278\pi\) | |||||||
\(908\) | 30.7692 | 1.02111 | ||||||||
\(909\) | −14.1510 | −0.469358 | ||||||||
\(910\) | −5.51484 | −0.182815 | ||||||||
\(911\) | 0.809435 | 0.0268178 | 0.0134089 | − | 0.999910i | \(-0.495732\pi\) | ||||
0.0134089 | + | 0.999910i | \(0.495732\pi\) | |||||||
\(912\) | −17.3906 | −0.575862 | ||||||||
\(913\) | −1.37594 | −0.0455369 | ||||||||
\(914\) | −12.5935 | −0.416557 | ||||||||
\(915\) | −7.67582 | −0.253755 | ||||||||
\(916\) | 37.5367 | 1.24025 | ||||||||
\(917\) | 8.26951 | 0.273083 | ||||||||
\(918\) | 9.97417 | 0.329197 | ||||||||
\(919\) | −12.4541 | −0.410821 | −0.205411 | − | 0.978676i | \(-0.565853\pi\) | ||||
−0.205411 | + | 0.978676i | \(0.565853\pi\) | |||||||
\(920\) | −0.956735 | −0.0315426 | ||||||||
\(921\) | −7.17730 | −0.236500 | ||||||||
\(922\) | −61.8868 | −2.03813 | ||||||||
\(923\) | 28.8883 | 0.950871 | ||||||||
\(924\) | −0.477857 | −0.0157204 | ||||||||
\(925\) | 16.6787 | 0.548393 | ||||||||
\(926\) | 37.8551 | 1.24399 | ||||||||
\(927\) | −1.46581 | −0.0481434 | ||||||||
\(928\) | −57.3944 | −1.88406 | ||||||||
\(929\) | −42.2794 | −1.38714 | −0.693571 | − | 0.720389i | \(-0.743963\pi\) | ||||
−0.693571 | + | 0.720389i | \(0.743963\pi\) | |||||||
\(930\) | 0.876378 | 0.0287376 | ||||||||
\(931\) | −3.76509 | −0.123396 | ||||||||
\(932\) | 8.59978 | 0.281695 | ||||||||
\(933\) | 9.33978 | 0.305771 | ||||||||
\(934\) | 36.1719 | 1.18358 | ||||||||
\(935\) | 1.18874 | 0.0388761 | ||||||||
\(936\) | 2.75087 | 0.0899151 | ||||||||
\(937\) | −16.6054 | −0.542474 | −0.271237 | − | 0.962513i | \(-0.587433\pi\) | ||||
−0.271237 | + | 0.962513i | \(0.587433\pi\) | |||||||
\(938\) | −0.971064 | −0.0317064 | ||||||||
\(939\) | −8.57535 | −0.279846 | ||||||||
\(940\) | −12.7240 | −0.415012 | ||||||||
\(941\) | 19.4063 | 0.632626 | 0.316313 | − | 0.948655i | \(-0.397555\pi\) | ||||
0.316313 | + | 0.948655i | \(0.397555\pi\) | |||||||
\(942\) | 11.3091 | 0.368472 | ||||||||
\(943\) | −14.8744 | −0.484377 | ||||||||
\(944\) | −43.3321 | −1.41034 | ||||||||
\(945\) | −0.767188 | −0.0249566 | ||||||||
\(946\) | −1.50667 | −0.0489859 | ||||||||
\(947\) | −46.2388 | −1.50256 | −0.751280 | − | 0.659984i | \(-0.770563\pi\) | ||||
−0.751280 | + | 0.659984i | \(0.770563\pi\) | |||||||
\(948\) | 3.11959 | 0.101320 | ||||||||
\(949\) | 23.3065 | 0.756560 | ||||||||
\(950\) | −31.5898 | −1.02491 | ||||||||
\(951\) | 21.1175 | 0.684783 | ||||||||
\(952\) | 3.81695 | 0.123708 | ||||||||
\(953\) | 38.1796 | 1.23676 | 0.618379 | − | 0.785880i | \(-0.287790\pi\) | ||||
0.618379 | + | 0.785880i | \(0.287790\pi\) | |||||||
\(954\) | 13.6464 | 0.441819 | ||||||||
\(955\) | −19.0447 | −0.616271 | ||||||||
\(956\) | 14.9779 | 0.484418 | ||||||||
\(957\) | 2.31376 | 0.0747932 | ||||||||
\(958\) | −60.1233 | −1.94250 | ||||||||
\(959\) | 3.75976 | 0.121409 | ||||||||
\(960\) | 3.60707 | 0.116418 | ||||||||
\(961\) | −30.6393 | −0.988363 | ||||||||
\(962\) | 27.1779 | 0.876250 | ||||||||
\(963\) | −7.15713 | −0.230635 | ||||||||
\(964\) | −35.9533 | −1.15798 | ||||||||
\(965\) | 1.45583 | 0.0468649 | ||||||||
\(966\) | −3.25875 | −0.104848 | ||||||||
\(967\) | −49.8459 | −1.60293 | −0.801467 | − | 0.598038i | \(-0.795947\pi\) | ||||
−0.801467 | + | 0.598038i | \(0.795947\pi\) | |||||||
\(968\) | −7.94264 | −0.255286 | ||||||||
\(969\) | 19.7451 | 0.634303 | ||||||||
\(970\) | −26.3120 | −0.844828 | ||||||||
\(971\) | −35.2170 | −1.13017 | −0.565084 | − | 0.825033i | \(-0.691156\pi\) | ||||
−0.565084 | + | 0.825033i | \(0.691156\pi\) | |||||||
\(972\) | −1.61732 | −0.0518755 | ||||||||
\(973\) | 19.7004 | 0.631565 | ||||||||
\(974\) | −22.9787 | −0.736285 | ||||||||
\(975\) | 16.6731 | 0.533967 | ||||||||
\(976\) | −46.2130 | −1.47924 | ||||||||
\(977\) | −14.0709 | −0.450166 | −0.225083 | − | 0.974340i | \(-0.572265\pi\) | ||||
−0.225083 | + | 0.974340i | \(0.572265\pi\) | |||||||
\(978\) | 15.2761 | 0.488474 | ||||||||
\(979\) | 1.73819 | 0.0555529 | ||||||||
\(980\) | 1.24079 | 0.0396354 | ||||||||
\(981\) | 9.55398 | 0.305035 | ||||||||
\(982\) | 10.5590 | 0.336951 | ||||||||
\(983\) | −23.1123 | −0.737168 | −0.368584 | − | 0.929595i | \(-0.620157\pi\) | ||||
−0.368584 | + | 0.929595i | \(0.620157\pi\) | |||||||
\(984\) | −6.31851 | −0.201427 | ||||||||
\(985\) | −11.9816 | −0.381766 | ||||||||
\(986\) | 78.1072 | 2.48744 | ||||||||
\(987\) | 10.2548 | 0.326415 | ||||||||
\(988\) | −23.0149 | −0.732201 | ||||||||
\(989\) | −4.59386 | −0.146076 | ||||||||
\(990\) | −0.431120 | −0.0137019 | ||||||||
\(991\) | −40.0720 | −1.27293 | −0.636465 | − | 0.771306i | \(-0.719604\pi\) | ||||
−0.636465 | + | 0.771306i | \(0.719604\pi\) | |||||||
\(992\) | 4.40201 | 0.139764 | ||||||||
\(993\) | 11.9243 | 0.378406 | ||||||||
\(994\) | −14.5371 | −0.461088 | ||||||||
\(995\) | 4.65919 | 0.147706 | ||||||||
\(996\) | 7.53166 | 0.238650 | ||||||||
\(997\) | 7.16819 | 0.227019 | 0.113509 | − | 0.993537i | \(-0.463791\pi\) | ||||
0.113509 | + | 0.993537i | \(0.463791\pi\) | |||||||
\(998\) | 35.8072 | 1.13346 | ||||||||
\(999\) | 3.78080 | 0.119619 |
(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 | 8043.2.a.t.1.10 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.10 | ✓ | 52 | 1.1 | even | 1 | trivial |