Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15921 | −1.52680 | −0.763398 | − | 0.645929i | \(-0.776470\pi\) | ||||
−0.763398 | + | 0.645929i | \(0.776470\pi\) | |||||||
\(3\) | −0.135675 | −0.0783319 | −0.0391659 | − | 0.999233i | \(-0.512470\pi\) | ||||
−0.0391659 | + | 0.999233i | \(0.512470\pi\) | |||||||
\(4\) | 2.66221 | 1.33110 | ||||||||
\(5\) | −3.14294 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(6\) | 0.292951 | 0.119597 | ||||||||
\(7\) | 0.215452 | 0.0814333 | 0.0407167 | − | 0.999171i | \(-0.487036\pi\) | ||||
0.0407167 | + | 0.999171i | \(0.487036\pi\) | |||||||
\(8\) | −1.42985 | −0.505527 | ||||||||
\(9\) | −2.98159 | −0.993864 | ||||||||
\(10\) | 6.78628 | 2.14601 | ||||||||
\(11\) | 6.40909 | 1.93241 | 0.966206 | − | 0.257770i | \(-0.0829877\pi\) | ||||
0.966206 | + | 0.257770i | \(0.0829877\pi\) | |||||||
\(12\) | −0.361194 | −0.104268 | ||||||||
\(13\) | 6.09951 | 1.69170 | 0.845849 | − | 0.533422i | \(-0.179094\pi\) | ||||
0.845849 | + | 0.533422i | \(0.179094\pi\) | |||||||
\(14\) | −0.465208 | −0.124332 | ||||||||
\(15\) | 0.426417 | 0.110101 | ||||||||
\(16\) | −2.23707 | −0.559268 | ||||||||
\(17\) | −1.51328 | −0.367023 | −0.183512 | − | 0.983018i | \(-0.558746\pi\) | ||||
−0.183512 | + | 0.983018i | \(0.558746\pi\) | |||||||
\(18\) | 6.43790 | 1.51743 | ||||||||
\(19\) | 0.941921 | 0.216092 | 0.108046 | − | 0.994146i | \(-0.465541\pi\) | ||||
0.108046 | + | 0.994146i | \(0.465541\pi\) | |||||||
\(20\) | −8.36715 | −1.87095 | ||||||||
\(21\) | −0.0292314 | −0.00637882 | ||||||||
\(22\) | −13.8386 | −2.95040 | ||||||||
\(23\) | 5.61733 | 1.17129 | 0.585647 | − | 0.810566i | \(-0.300841\pi\) | ||||
0.585647 | + | 0.810566i | \(0.300841\pi\) | |||||||
\(24\) | 0.193994 | 0.0395988 | ||||||||
\(25\) | 4.87806 | 0.975613 | ||||||||
\(26\) | −13.1701 | −2.58288 | ||||||||
\(27\) | 0.811551 | 0.156183 | ||||||||
\(28\) | 0.573579 | 0.108396 | ||||||||
\(29\) | 0.309118 | 0.0574017 | 0.0287008 | − | 0.999588i | \(-0.490863\pi\) | ||||
0.0287008 | + | 0.999588i | \(0.490863\pi\) | |||||||
\(30\) | −0.920727 | −0.168101 | ||||||||
\(31\) | 3.60497 | 0.647471 | 0.323736 | − | 0.946148i | \(-0.395061\pi\) | ||||
0.323736 | + | 0.946148i | \(0.395061\pi\) | |||||||
\(32\) | 7.69000 | 1.35941 | ||||||||
\(33\) | −0.869551 | −0.151369 | ||||||||
\(34\) | 3.26749 | 0.560369 | ||||||||
\(35\) | −0.677153 | −0.114460 | ||||||||
\(36\) | −7.93761 | −1.32294 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −2.03381 | −0.329928 | ||||||||
\(39\) | −0.827549 | −0.132514 | ||||||||
\(40\) | 4.49392 | 0.710551 | ||||||||
\(41\) | 11.4789 | 1.79271 | 0.896353 | − | 0.443342i | \(-0.146207\pi\) | ||||
0.896353 | + | 0.443342i | \(0.146207\pi\) | |||||||
\(42\) | 0.0631169 | 0.00973916 | ||||||||
\(43\) | −3.97805 | −0.606646 | −0.303323 | − | 0.952888i | \(-0.598096\pi\) | ||||
−0.303323 | + | 0.952888i | \(0.598096\pi\) | |||||||
\(44\) | 17.0623 | 2.57224 | ||||||||
\(45\) | 9.37096 | 1.39694 | ||||||||
\(46\) | −12.1290 | −1.78833 | ||||||||
\(47\) | 0.788927 | 0.115077 | 0.0575384 | − | 0.998343i | \(-0.481675\pi\) | ||||
0.0575384 | + | 0.998343i | \(0.481675\pi\) | |||||||
\(48\) | 0.303514 | 0.0438085 | ||||||||
\(49\) | −6.95358 | −0.993369 | ||||||||
\(50\) | −10.5328 | −1.48956 | ||||||||
\(51\) | 0.205313 | 0.0287496 | ||||||||
\(52\) | 16.2381 | 2.25183 | ||||||||
\(53\) | 8.30370 | 1.14060 | 0.570300 | − | 0.821436i | \(-0.306827\pi\) | ||||
0.570300 | + | 0.821436i | \(0.306827\pi\) | |||||||
\(54\) | −1.75231 | −0.238460 | ||||||||
\(55\) | −20.1434 | −2.71613 | ||||||||
\(56\) | −0.308063 | −0.0411667 | ||||||||
\(57\) | −0.127795 | −0.0169269 | ||||||||
\(58\) | −0.667451 | −0.0876406 | ||||||||
\(59\) | 13.6028 | 1.77093 | 0.885467 | − | 0.464703i | \(-0.153839\pi\) | ||||
0.885467 | + | 0.464703i | \(0.153839\pi\) | |||||||
\(60\) | 1.13521 | 0.146555 | ||||||||
\(61\) | −7.36806 | −0.943383 | −0.471692 | − | 0.881764i | \(-0.656356\pi\) | ||||
−0.471692 | + | 0.881764i | \(0.656356\pi\) | |||||||
\(62\) | −7.78390 | −0.988556 | ||||||||
\(63\) | −0.642391 | −0.0809337 | ||||||||
\(64\) | −12.1302 | −1.51628 | ||||||||
\(65\) | −19.1704 | −2.37779 | ||||||||
\(66\) | 1.87755 | 0.231110 | ||||||||
\(67\) | 8.94172 | 1.09241 | 0.546203 | − | 0.837653i | \(-0.316073\pi\) | ||||
0.546203 | + | 0.837653i | \(0.316073\pi\) | |||||||
\(68\) | −4.02865 | −0.488546 | ||||||||
\(69\) | −0.762129 | −0.0917496 | ||||||||
\(70\) | 1.46212 | 0.174757 | ||||||||
\(71\) | −1.27963 | −0.151864 | −0.0759320 | − | 0.997113i | \(-0.524193\pi\) | ||||
−0.0759320 | + | 0.997113i | \(0.524193\pi\) | |||||||
\(72\) | 4.26322 | 0.502425 | ||||||||
\(73\) | −10.6218 | −1.24319 | −0.621594 | − | 0.783339i | \(-0.713515\pi\) | ||||
−0.621594 | + | 0.783339i | \(0.713515\pi\) | |||||||
\(74\) | −2.15921 | −0.251004 | ||||||||
\(75\) | −0.661830 | −0.0764216 | ||||||||
\(76\) | 2.50759 | 0.287640 | ||||||||
\(77\) | 1.38085 | 0.157363 | ||||||||
\(78\) | 1.78686 | 0.202322 | ||||||||
\(79\) | −7.77543 | −0.874804 | −0.437402 | − | 0.899266i | \(-0.644101\pi\) | ||||
−0.437402 | + | 0.899266i | \(0.644101\pi\) | |||||||
\(80\) | 7.03097 | 0.786087 | ||||||||
\(81\) | 8.83467 | 0.981630 | ||||||||
\(82\) | −24.7854 | −2.73709 | ||||||||
\(83\) | −5.35637 | −0.587938 | −0.293969 | − | 0.955815i | \(-0.594976\pi\) | ||||
−0.293969 | + | 0.955815i | \(0.594976\pi\) | |||||||
\(84\) | −0.0778201 | −0.00849087 | ||||||||
\(85\) | 4.75613 | 0.515875 | ||||||||
\(86\) | 8.58945 | 0.926224 | ||||||||
\(87\) | −0.0419394 | −0.00449638 | ||||||||
\(88\) | −9.16400 | −0.976886 | ||||||||
\(89\) | 5.06343 | 0.536723 | 0.268361 | − | 0.963318i | \(-0.413518\pi\) | ||||
0.268361 | + | 0.963318i | \(0.413518\pi\) | |||||||
\(90\) | −20.2339 | −2.13284 | ||||||||
\(91\) | 1.31415 | 0.137761 | ||||||||
\(92\) | 14.9545 | 1.55911 | ||||||||
\(93\) | −0.489103 | −0.0507176 | ||||||||
\(94\) | −1.70346 | −0.175699 | ||||||||
\(95\) | −2.96040 | −0.303731 | ||||||||
\(96\) | −1.04334 | −0.106485 | ||||||||
\(97\) | −9.73558 | −0.988498 | −0.494249 | − | 0.869320i | \(-0.664557\pi\) | ||||
−0.494249 | + | 0.869320i | \(0.664557\pi\) | |||||||
\(98\) | 15.0143 | 1.51667 | ||||||||
\(99\) | −19.1093 | −1.92056 | ||||||||
\(100\) | 12.9864 | 1.29864 | ||||||||
\(101\) | −13.3935 | −1.33270 | −0.666350 | − | 0.745639i | \(-0.732144\pi\) | ||||
−0.666350 | + | 0.745639i | \(0.732144\pi\) | |||||||
\(102\) | −0.443315 | −0.0438948 | ||||||||
\(103\) | −16.2053 | −1.59675 | −0.798376 | − | 0.602159i | \(-0.794307\pi\) | ||||
−0.798376 | + | 0.602159i | \(0.794307\pi\) | |||||||
\(104\) | −8.72135 | −0.855199 | ||||||||
\(105\) | 0.0918726 | 0.00896585 | ||||||||
\(106\) | −17.9295 | −1.74146 | ||||||||
\(107\) | −4.96272 | −0.479764 | −0.239882 | − | 0.970802i | \(-0.577109\pi\) | ||||
−0.239882 | + | 0.970802i | \(0.577109\pi\) | |||||||
\(108\) | 2.16052 | 0.207896 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 43.4938 | 4.14698 | ||||||||
\(111\) | −0.135675 | −0.0128777 | ||||||||
\(112\) | −0.481982 | −0.0455430 | ||||||||
\(113\) | −11.4705 | −1.07905 | −0.539525 | − | 0.841970i | \(-0.681396\pi\) | ||||
−0.539525 | + | 0.841970i | \(0.681396\pi\) | |||||||
\(114\) | 0.275937 | 0.0258438 | ||||||||
\(115\) | −17.6549 | −1.64633 | ||||||||
\(116\) | 0.822935 | 0.0764076 | ||||||||
\(117\) | −18.1862 | −1.68132 | ||||||||
\(118\) | −29.3714 | −2.70385 | ||||||||
\(119\) | −0.326039 | −0.0298879 | ||||||||
\(120\) | −0.609711 | −0.0556587 | ||||||||
\(121\) | 30.0764 | 2.73422 | ||||||||
\(122\) | 15.9092 | 1.44035 | ||||||||
\(123\) | −1.55740 | −0.140426 | ||||||||
\(124\) | 9.59717 | 0.861851 | ||||||||
\(125\) | 0.383238 | 0.0342779 | ||||||||
\(126\) | 1.38706 | 0.123569 | ||||||||
\(127\) | −7.87326 | −0.698639 | −0.349319 | − | 0.937004i | \(-0.613587\pi\) | ||||
−0.349319 | + | 0.937004i | \(0.613587\pi\) | |||||||
\(128\) | 10.8118 | 0.955633 | ||||||||
\(129\) | 0.539720 | 0.0475197 | ||||||||
\(130\) | 41.3929 | 3.63040 | ||||||||
\(131\) | 20.5299 | 1.79371 | 0.896853 | − | 0.442329i | \(-0.145848\pi\) | ||||
0.896853 | + | 0.442329i | \(0.145848\pi\) | |||||||
\(132\) | −2.31492 | −0.201488 | ||||||||
\(133\) | 0.202939 | 0.0175971 | ||||||||
\(134\) | −19.3071 | −1.66788 | ||||||||
\(135\) | −2.55066 | −0.219525 | ||||||||
\(136\) | 2.16375 | 0.185540 | ||||||||
\(137\) | 7.14762 | 0.610662 | 0.305331 | − | 0.952246i | \(-0.401233\pi\) | ||||
0.305331 | + | 0.952246i | \(0.401233\pi\) | |||||||
\(138\) | 1.64560 | 0.140083 | ||||||||
\(139\) | −9.77207 | −0.828856 | −0.414428 | − | 0.910082i | \(-0.636018\pi\) | ||||
−0.414428 | + | 0.910082i | \(0.636018\pi\) | |||||||
\(140\) | −1.80272 | −0.152358 | ||||||||
\(141\) | −0.107038 | −0.00901419 | ||||||||
\(142\) | 2.76299 | 0.231865 | ||||||||
\(143\) | 39.0923 | 3.26906 | ||||||||
\(144\) | 6.67003 | 0.555836 | ||||||||
\(145\) | −0.971538 | −0.0806818 | ||||||||
\(146\) | 22.9348 | 1.89809 | ||||||||
\(147\) | 0.943425 | 0.0778124 | ||||||||
\(148\) | 2.66221 | 0.218832 | ||||||||
\(149\) | 4.31774 | 0.353723 | 0.176861 | − | 0.984236i | \(-0.443406\pi\) | ||||
0.176861 | + | 0.984236i | \(0.443406\pi\) | |||||||
\(150\) | 1.42903 | 0.116680 | ||||||||
\(151\) | 13.3709 | 1.08811 | 0.544053 | − | 0.839051i | \(-0.316889\pi\) | ||||
0.544053 | + | 0.839051i | \(0.316889\pi\) | |||||||
\(152\) | −1.34680 | −0.109240 | ||||||||
\(153\) | 4.51197 | 0.364771 | ||||||||
\(154\) | −2.98156 | −0.240261 | ||||||||
\(155\) | −11.3302 | −0.910063 | ||||||||
\(156\) | −2.20311 | −0.176390 | ||||||||
\(157\) | 4.04462 | 0.322796 | 0.161398 | − | 0.986889i | \(-0.448400\pi\) | ||||
0.161398 | + | 0.986889i | \(0.448400\pi\) | |||||||
\(158\) | 16.7888 | 1.33565 | ||||||||
\(159\) | −1.12660 | −0.0893454 | ||||||||
\(160\) | −24.1692 | −1.91074 | ||||||||
\(161\) | 1.21027 | 0.0953823 | ||||||||
\(162\) | −19.0759 | −1.49875 | ||||||||
\(163\) | 16.6323 | 1.30274 | 0.651372 | − | 0.758758i | \(-0.274194\pi\) | ||||
0.651372 | + | 0.758758i | \(0.274194\pi\) | |||||||
\(164\) | 30.5592 | 2.38628 | ||||||||
\(165\) | 2.73295 | 0.212760 | ||||||||
\(166\) | 11.5656 | 0.897661 | ||||||||
\(167\) | 8.54871 | 0.661519 | 0.330760 | − | 0.943715i | \(-0.392695\pi\) | ||||
0.330760 | + | 0.943715i | \(0.392695\pi\) | |||||||
\(168\) | 0.0417964 | 0.00322467 | ||||||||
\(169\) | 24.2040 | 1.86184 | ||||||||
\(170\) | −10.2695 | −0.787635 | ||||||||
\(171\) | −2.80843 | −0.214766 | ||||||||
\(172\) | −10.5904 | −0.807509 | ||||||||
\(173\) | 13.1635 | 1.00080 | 0.500401 | − | 0.865794i | \(-0.333186\pi\) | ||||
0.500401 | + | 0.865794i | \(0.333186\pi\) | |||||||
\(174\) | 0.0905563 | 0.00686505 | ||||||||
\(175\) | 1.05099 | 0.0794474 | ||||||||
\(176\) | −14.3376 | −1.08074 | ||||||||
\(177\) | −1.84556 | −0.138720 | ||||||||
\(178\) | −10.9330 | −0.819466 | ||||||||
\(179\) | −4.68878 | −0.350456 | −0.175228 | − | 0.984528i | \(-0.556066\pi\) | ||||
−0.175228 | + | 0.984528i | \(0.556066\pi\) | |||||||
\(180\) | 24.9474 | 1.85947 | ||||||||
\(181\) | 17.4209 | 1.29488 | 0.647441 | − | 0.762116i | \(-0.275839\pi\) | ||||
0.647441 | + | 0.762116i | \(0.275839\pi\) | |||||||
\(182\) | −2.83754 | −0.210332 | ||||||||
\(183\) | 0.999660 | 0.0738970 | ||||||||
\(184\) | −8.03191 | −0.592120 | ||||||||
\(185\) | −3.14294 | −0.231073 | ||||||||
\(186\) | 1.05608 | 0.0774354 | ||||||||
\(187\) | −9.69871 | −0.709240 | ||||||||
\(188\) | 2.10029 | 0.153179 | ||||||||
\(189\) | 0.174851 | 0.0127185 | ||||||||
\(190\) | 6.39214 | 0.463735 | ||||||||
\(191\) | −25.7363 | −1.86221 | −0.931106 | − | 0.364748i | \(-0.881155\pi\) | ||||
−0.931106 | + | 0.364748i | \(0.881155\pi\) | |||||||
\(192\) | 1.64577 | 0.118773 | ||||||||
\(193\) | 5.43046 | 0.390893 | 0.195447 | − | 0.980714i | \(-0.437384\pi\) | ||||
0.195447 | + | 0.980714i | \(0.437384\pi\) | |||||||
\(194\) | 21.0212 | 1.50923 | ||||||||
\(195\) | 2.60094 | 0.186257 | ||||||||
\(196\) | −18.5119 | −1.32228 | ||||||||
\(197\) | −7.00772 | −0.499279 | −0.249640 | − | 0.968339i | \(-0.580312\pi\) | ||||
−0.249640 | + | 0.968339i | \(0.580312\pi\) | |||||||
\(198\) | 41.2610 | 2.93229 | ||||||||
\(199\) | −13.3484 | −0.946242 | −0.473121 | − | 0.880997i | \(-0.656873\pi\) | ||||
−0.473121 | + | 0.880997i | \(0.656873\pi\) | |||||||
\(200\) | −6.97488 | −0.493198 | ||||||||
\(201\) | −1.21317 | −0.0855701 | ||||||||
\(202\) | 28.9194 | 2.03476 | ||||||||
\(203\) | 0.0666001 | 0.00467441 | ||||||||
\(204\) | 0.546586 | 0.0382687 | ||||||||
\(205\) | −36.0775 | −2.51976 | ||||||||
\(206\) | 34.9906 | 2.43791 | ||||||||
\(207\) | −16.7486 | −1.16411 | ||||||||
\(208\) | −13.6450 | −0.946112 | ||||||||
\(209\) | 6.03686 | 0.417578 | ||||||||
\(210\) | −0.198373 | −0.0136890 | ||||||||
\(211\) | −22.5515 | −1.55251 | −0.776254 | − | 0.630420i | \(-0.782883\pi\) | ||||
−0.776254 | + | 0.630420i | \(0.782883\pi\) | |||||||
\(212\) | 22.1062 | 1.51826 | ||||||||
\(213\) | 0.173613 | 0.0118958 | ||||||||
\(214\) | 10.7156 | 0.732502 | ||||||||
\(215\) | 12.5028 | 0.852681 | ||||||||
\(216\) | −1.16039 | −0.0789547 | ||||||||
\(217\) | 0.776699 | 0.0527257 | ||||||||
\(218\) | 2.15921 | 0.146240 | ||||||||
\(219\) | 1.44111 | 0.0973813 | ||||||||
\(220\) | −53.6258 | −3.61545 | ||||||||
\(221\) | −9.23023 | −0.620893 | ||||||||
\(222\) | 0.292951 | 0.0196616 | ||||||||
\(223\) | 27.2391 | 1.82406 | 0.912032 | − | 0.410120i | \(-0.134513\pi\) | ||||
0.912032 | + | 0.410120i | \(0.134513\pi\) | |||||||
\(224\) | 1.65683 | 0.110702 | ||||||||
\(225\) | −14.5444 | −0.969627 | ||||||||
\(226\) | 24.7672 | 1.64749 | ||||||||
\(227\) | −25.8073 | −1.71289 | −0.856445 | − | 0.516239i | \(-0.827332\pi\) | ||||
−0.856445 | + | 0.516239i | \(0.827332\pi\) | |||||||
\(228\) | −0.340216 | −0.0225314 | ||||||||
\(229\) | 19.5665 | 1.29299 | 0.646495 | − | 0.762919i | \(-0.276234\pi\) | ||||
0.646495 | + | 0.762919i | \(0.276234\pi\) | |||||||
\(230\) | 38.1207 | 2.51361 | ||||||||
\(231\) | −0.187347 | −0.0123265 | ||||||||
\(232\) | −0.441990 | −0.0290181 | ||||||||
\(233\) | −3.87374 | −0.253777 | −0.126889 | − | 0.991917i | \(-0.540499\pi\) | ||||
−0.126889 | + | 0.991917i | \(0.540499\pi\) | |||||||
\(234\) | 39.2680 | 2.56703 | ||||||||
\(235\) | −2.47955 | −0.161748 | ||||||||
\(236\) | 36.2134 | 2.35729 | ||||||||
\(237\) | 1.05493 | 0.0685250 | ||||||||
\(238\) | 0.703987 | 0.0456327 | ||||||||
\(239\) | −19.7036 | −1.27452 | −0.637259 | − | 0.770650i | \(-0.719932\pi\) | ||||
−0.637259 | + | 0.770650i | \(0.719932\pi\) | |||||||
\(240\) | −0.953926 | −0.0615756 | ||||||||
\(241\) | −3.83368 | −0.246949 | −0.123475 | − | 0.992348i | \(-0.539404\pi\) | ||||
−0.123475 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(242\) | −64.9414 | −4.17459 | ||||||||
\(243\) | −3.63329 | −0.233076 | ||||||||
\(244\) | −19.6153 | −1.25574 | ||||||||
\(245\) | 21.8547 | 1.39624 | ||||||||
\(246\) | 3.36276 | 0.214402 | ||||||||
\(247\) | 5.74525 | 0.365562 | ||||||||
\(248\) | −5.15454 | −0.327314 | ||||||||
\(249\) | 0.726724 | 0.0460543 | ||||||||
\(250\) | −0.827493 | −0.0523353 | ||||||||
\(251\) | 5.12914 | 0.323748 | 0.161874 | − | 0.986811i | \(-0.448246\pi\) | ||||
0.161874 | + | 0.986811i | \(0.448246\pi\) | |||||||
\(252\) | −1.71018 | −0.107731 | ||||||||
\(253\) | 36.0019 | 2.26342 | ||||||||
\(254\) | 17.0001 | 1.06668 | ||||||||
\(255\) | −0.645287 | −0.0404094 | ||||||||
\(256\) | 0.915568 | 0.0572230 | ||||||||
\(257\) | −27.1978 | −1.69655 | −0.848277 | − | 0.529553i | \(-0.822360\pi\) | ||||
−0.848277 | + | 0.529553i | \(0.822360\pi\) | |||||||
\(258\) | −1.16537 | −0.0725529 | ||||||||
\(259\) | 0.215452 | 0.0133876 | ||||||||
\(260\) | −51.0355 | −3.16509 | ||||||||
\(261\) | −0.921663 | −0.0570495 | ||||||||
\(262\) | −44.3285 | −2.73862 | ||||||||
\(263\) | 28.5341 | 1.75949 | 0.879744 | − | 0.475447i | \(-0.157714\pi\) | ||||
0.879744 | + | 0.475447i | \(0.157714\pi\) | |||||||
\(264\) | 1.24332 | 0.0765213 | ||||||||
\(265\) | −26.0980 | −1.60319 | ||||||||
\(266\) | −0.438189 | −0.0268671 | ||||||||
\(267\) | −0.686980 | −0.0420425 | ||||||||
\(268\) | 23.8047 | 1.45410 | ||||||||
\(269\) | −5.56873 | −0.339532 | −0.169766 | − | 0.985484i | \(-0.554301\pi\) | ||||
−0.169766 | + | 0.985484i | \(0.554301\pi\) | |||||||
\(270\) | 5.50741 | 0.335170 | ||||||||
\(271\) | 2.58386 | 0.156958 | 0.0784792 | − | 0.996916i | \(-0.474994\pi\) | ||||
0.0784792 | + | 0.996916i | \(0.474994\pi\) | |||||||
\(272\) | 3.38530 | 0.205264 | ||||||||
\(273\) | −0.178297 | −0.0107910 | ||||||||
\(274\) | −15.4332 | −0.932356 | ||||||||
\(275\) | 31.2639 | 1.88529 | ||||||||
\(276\) | −2.02895 | −0.122128 | ||||||||
\(277\) | 21.9033 | 1.31604 | 0.658022 | − | 0.752999i | \(-0.271393\pi\) | ||||
0.658022 | + | 0.752999i | \(0.271393\pi\) | |||||||
\(278\) | 21.1000 | 1.26549 | ||||||||
\(279\) | −10.7485 | −0.643498 | ||||||||
\(280\) | 0.968225 | 0.0578625 | ||||||||
\(281\) | −6.60437 | −0.393984 | −0.196992 | − | 0.980405i | \(-0.563117\pi\) | ||||
−0.196992 | + | 0.980405i | \(0.563117\pi\) | |||||||
\(282\) | 0.231117 | 0.0137628 | ||||||||
\(283\) | 26.7604 | 1.59074 | 0.795369 | − | 0.606126i | \(-0.207277\pi\) | ||||
0.795369 | + | 0.606126i | \(0.207277\pi\) | |||||||
\(284\) | −3.40664 | −0.202147 | ||||||||
\(285\) | 0.401652 | 0.0237918 | ||||||||
\(286\) | −84.4086 | −4.99118 | ||||||||
\(287\) | 2.47316 | 0.145986 | ||||||||
\(288\) | −22.9285 | −1.35107 | ||||||||
\(289\) | −14.7100 | −0.865294 | ||||||||
\(290\) | 2.09776 | 0.123185 | ||||||||
\(291\) | 1.32087 | 0.0774309 | ||||||||
\(292\) | −28.2774 | −1.65481 | ||||||||
\(293\) | 25.1790 | 1.47097 | 0.735486 | − | 0.677539i | \(-0.236954\pi\) | ||||
0.735486 | + | 0.677539i | \(0.236954\pi\) | |||||||
\(294\) | −2.03706 | −0.118804 | ||||||||
\(295\) | −42.7528 | −2.48916 | ||||||||
\(296\) | −1.42985 | −0.0831081 | ||||||||
\(297\) | 5.20130 | 0.301810 | ||||||||
\(298\) | −9.32292 | −0.540062 | ||||||||
\(299\) | 34.2629 | 1.98148 | ||||||||
\(300\) | −1.76193 | −0.101725 | ||||||||
\(301\) | −0.857079 | −0.0494012 | ||||||||
\(302\) | −28.8706 | −1.66132 | ||||||||
\(303\) | 1.81716 | 0.104393 | ||||||||
\(304\) | −2.10714 | −0.120853 | ||||||||
\(305\) | 23.1574 | 1.32599 | ||||||||
\(306\) | −9.74231 | −0.556931 | ||||||||
\(307\) | 28.5667 | 1.63039 | 0.815193 | − | 0.579189i | \(-0.196631\pi\) | ||||
0.815193 | + | 0.579189i | \(0.196631\pi\) | |||||||
\(308\) | 3.67611 | 0.209466 | ||||||||
\(309\) | 2.19864 | 0.125077 | ||||||||
\(310\) | 24.4643 | 1.38948 | ||||||||
\(311\) | −11.7887 | −0.668478 | −0.334239 | − | 0.942488i | \(-0.608479\pi\) | ||||
−0.334239 | + | 0.942488i | \(0.608479\pi\) | |||||||
\(312\) | 1.18327 | 0.0669893 | ||||||||
\(313\) | 5.54193 | 0.313248 | 0.156624 | − | 0.987658i | \(-0.449939\pi\) | ||||
0.156624 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(314\) | −8.73320 | −0.492843 | ||||||||
\(315\) | 2.01900 | 0.113758 | ||||||||
\(316\) | −20.6998 | −1.16445 | ||||||||
\(317\) | 12.0089 | 0.674486 | 0.337243 | − | 0.941418i | \(-0.390506\pi\) | ||||
0.337243 | + | 0.941418i | \(0.390506\pi\) | |||||||
\(318\) | 2.43258 | 0.136412 | ||||||||
\(319\) | 1.98116 | 0.110924 | ||||||||
\(320\) | 38.1246 | 2.13123 | ||||||||
\(321\) | 0.673316 | 0.0375808 | ||||||||
\(322\) | −2.61322 | −0.145629 | ||||||||
\(323\) | −1.42539 | −0.0793106 | ||||||||
\(324\) | 23.5197 | 1.30665 | ||||||||
\(325\) | 29.7538 | 1.65044 | ||||||||
\(326\) | −35.9128 | −1.98902 | ||||||||
\(327\) | 0.135675 | 0.00750283 | ||||||||
\(328\) | −16.4131 | −0.906260 | ||||||||
\(329\) | 0.169976 | 0.00937109 | ||||||||
\(330\) | −5.90102 | −0.324840 | ||||||||
\(331\) | −32.5550 | −1.78938 | −0.894692 | − | 0.446684i | \(-0.852605\pi\) | ||||
−0.894692 | + | 0.446684i | \(0.852605\pi\) | |||||||
\(332\) | −14.2598 | −0.782606 | ||||||||
\(333\) | −2.98159 | −0.163390 | ||||||||
\(334\) | −18.4585 | −1.01000 | ||||||||
\(335\) | −28.1033 | −1.53545 | ||||||||
\(336\) | 0.0653928 | 0.00356747 | ||||||||
\(337\) | 26.7159 | 1.45531 | 0.727655 | − | 0.685944i | \(-0.240610\pi\) | ||||
0.727655 | + | 0.685944i | \(0.240610\pi\) | |||||||
\(338\) | −52.2616 | −2.84265 | ||||||||
\(339\) | 1.55625 | 0.0845240 | ||||||||
\(340\) | 12.6618 | 0.686683 | ||||||||
\(341\) | 23.1045 | 1.25118 | ||||||||
\(342\) | 6.06399 | 0.327903 | ||||||||
\(343\) | −3.00633 | −0.162327 | ||||||||
\(344\) | 5.68799 | 0.306676 | ||||||||
\(345\) | 2.39533 | 0.128960 | ||||||||
\(346\) | −28.4228 | −1.52802 | ||||||||
\(347\) | −4.95830 | −0.266175 | −0.133088 | − | 0.991104i | \(-0.542489\pi\) | ||||
−0.133088 | + | 0.991104i | \(0.542489\pi\) | |||||||
\(348\) | −0.111651 | −0.00598515 | ||||||||
\(349\) | −4.93248 | −0.264030 | −0.132015 | − | 0.991248i | \(-0.542145\pi\) | ||||
−0.132015 | + | 0.991248i | \(0.542145\pi\) | |||||||
\(350\) | −2.26931 | −0.121300 | ||||||||
\(351\) | 4.95006 | 0.264215 | ||||||||
\(352\) | 49.2859 | 2.62695 | ||||||||
\(353\) | 29.9732 | 1.59531 | 0.797656 | − | 0.603113i | \(-0.206073\pi\) | ||||
0.797656 | + | 0.603113i | \(0.206073\pi\) | |||||||
\(354\) | 3.98495 | 0.211798 | ||||||||
\(355\) | 4.02180 | 0.213455 | ||||||||
\(356\) | 13.4799 | 0.714434 | ||||||||
\(357\) | 0.0442352 | 0.00234118 | ||||||||
\(358\) | 10.1241 | 0.535075 | ||||||||
\(359\) | 23.7562 | 1.25380 | 0.626902 | − | 0.779098i | \(-0.284323\pi\) | ||||
0.626902 | + | 0.779098i | \(0.284323\pi\) | |||||||
\(360\) | −13.3990 | −0.706191 | ||||||||
\(361\) | −18.1128 | −0.953304 | ||||||||
\(362\) | −37.6153 | −1.97702 | ||||||||
\(363\) | −4.08061 | −0.214176 | ||||||||
\(364\) | 3.49855 | 0.183374 | ||||||||
\(365\) | 33.3837 | 1.74738 | ||||||||
\(366\) | −2.15848 | −0.112826 | ||||||||
\(367\) | −11.8751 | −0.619874 | −0.309937 | − | 0.950757i | \(-0.600308\pi\) | ||||
−0.309937 | + | 0.950757i | \(0.600308\pi\) | |||||||
\(368\) | −12.5664 | −0.655066 | ||||||||
\(369\) | −34.2254 | −1.78171 | ||||||||
\(370\) | 6.78628 | 0.352802 | ||||||||
\(371\) | 1.78905 | 0.0928829 | ||||||||
\(372\) | −1.30209 | −0.0675104 | ||||||||
\(373\) | 16.3120 | 0.844601 | 0.422300 | − | 0.906456i | \(-0.361223\pi\) | ||||
0.422300 | + | 0.906456i | \(0.361223\pi\) | |||||||
\(374\) | 20.9416 | 1.08286 | ||||||||
\(375\) | −0.0519957 | −0.00268505 | ||||||||
\(376\) | −1.12804 | −0.0581744 | ||||||||
\(377\) | 1.88546 | 0.0971064 | ||||||||
\(378\) | −0.377540 | −0.0194186 | ||||||||
\(379\) | −31.7353 | −1.63013 | −0.815066 | − | 0.579368i | \(-0.803299\pi\) | ||||
−0.815066 | + | 0.579368i | \(0.803299\pi\) | |||||||
\(380\) | −7.88120 | −0.404297 | ||||||||
\(381\) | 1.06820 | 0.0547257 | ||||||||
\(382\) | 55.5702 | 2.84322 | ||||||||
\(383\) | −5.01688 | −0.256351 | −0.128175 | − | 0.991752i | \(-0.540912\pi\) | ||||
−0.128175 | + | 0.991752i | \(0.540912\pi\) | |||||||
\(384\) | −1.46688 | −0.0748565 | ||||||||
\(385\) | −4.33994 | −0.221184 | ||||||||
\(386\) | −11.7255 | −0.596814 | ||||||||
\(387\) | 11.8609 | 0.602924 | ||||||||
\(388\) | −25.9181 | −1.31579 | ||||||||
\(389\) | 18.8873 | 0.957627 | 0.478813 | − | 0.877917i | \(-0.341067\pi\) | ||||
0.478813 | + | 0.877917i | \(0.341067\pi\) | |||||||
\(390\) | −5.61598 | −0.284376 | ||||||||
\(391\) | −8.50056 | −0.429892 | ||||||||
\(392\) | 9.94254 | 0.502174 | ||||||||
\(393\) | −2.78539 | −0.140504 | ||||||||
\(394\) | 15.1312 | 0.762297 | ||||||||
\(395\) | 24.4377 | 1.22959 | ||||||||
\(396\) | −50.8729 | −2.55646 | ||||||||
\(397\) | 6.38387 | 0.320397 | 0.160199 | − | 0.987085i | \(-0.448787\pi\) | ||||
0.160199 | + | 0.987085i | \(0.448787\pi\) | |||||||
\(398\) | 28.8220 | 1.44472 | ||||||||
\(399\) | −0.0275337 | −0.00137841 | ||||||||
\(400\) | −10.9126 | −0.545629 | ||||||||
\(401\) | −0.364983 | −0.0182264 | −0.00911320 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911320 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(402\) | 2.61949 | 0.130648 | ||||||||
\(403\) | 21.9885 | 1.09533 | ||||||||
\(404\) | −35.6562 | −1.77396 | ||||||||
\(405\) | −27.7668 | −1.37974 | ||||||||
\(406\) | −0.143804 | −0.00713687 | ||||||||
\(407\) | 6.40909 | 0.317687 | ||||||||
\(408\) | −0.293566 | −0.0145337 | ||||||||
\(409\) | 14.4559 | 0.714798 | 0.357399 | − | 0.933952i | \(-0.383664\pi\) | ||||
0.357399 | + | 0.933952i | \(0.383664\pi\) | |||||||
\(410\) | 77.8991 | 3.84716 | ||||||||
\(411\) | −0.969752 | −0.0478343 | ||||||||
\(412\) | −43.1417 | −2.12544 | ||||||||
\(413\) | 2.93075 | 0.144213 | ||||||||
\(414\) | 36.1638 | 1.77735 | ||||||||
\(415\) | 16.8347 | 0.826385 | ||||||||
\(416\) | 46.9052 | 2.29972 | ||||||||
\(417\) | 1.32582 | 0.0649258 | ||||||||
\(418\) | −13.0349 | −0.637556 | ||||||||
\(419\) | −4.79350 | −0.234178 | −0.117089 | − | 0.993121i | \(-0.537356\pi\) | ||||
−0.117089 | + | 0.993121i | \(0.537356\pi\) | |||||||
\(420\) | 0.244584 | 0.0119345 | ||||||||
\(421\) | 17.3069 | 0.843488 | 0.421744 | − | 0.906715i | \(-0.361418\pi\) | ||||
0.421744 | + | 0.906715i | \(0.361418\pi\) | |||||||
\(422\) | 48.6935 | 2.37036 | ||||||||
\(423\) | −2.35226 | −0.114371 | ||||||||
\(424\) | −11.8730 | −0.576604 | ||||||||
\(425\) | −7.38185 | −0.358073 | ||||||||
\(426\) | −0.374869 | −0.0181624 | ||||||||
\(427\) | −1.58747 | −0.0768228 | ||||||||
\(428\) | −13.2118 | −0.638616 | ||||||||
\(429\) | −5.30383 | −0.256071 | ||||||||
\(430\) | −26.9961 | −1.30187 | ||||||||
\(431\) | −16.8484 | −0.811558 | −0.405779 | − | 0.913971i | \(-0.633000\pi\) | ||||
−0.405779 | + | 0.913971i | \(0.633000\pi\) | |||||||
\(432\) | −1.81550 | −0.0873481 | ||||||||
\(433\) | 25.5437 | 1.22755 | 0.613775 | − | 0.789481i | \(-0.289650\pi\) | ||||
0.613775 | + | 0.789481i | \(0.289650\pi\) | |||||||
\(434\) | −1.67706 | −0.0805014 | ||||||||
\(435\) | 0.131813 | 0.00631995 | ||||||||
\(436\) | −2.66221 | −0.127497 | ||||||||
\(437\) | 5.29108 | 0.253107 | ||||||||
\(438\) | −3.11167 | −0.148681 | ||||||||
\(439\) | −36.0917 | −1.72256 | −0.861282 | − | 0.508128i | \(-0.830338\pi\) | ||||
−0.861282 | + | 0.508128i | \(0.830338\pi\) | |||||||
\(440\) | 28.8019 | 1.37308 | ||||||||
\(441\) | 20.7327 | 0.987273 | ||||||||
\(442\) | 19.9300 | 0.947976 | ||||||||
\(443\) | 17.1547 | 0.815043 | 0.407521 | − | 0.913196i | \(-0.366393\pi\) | ||||
0.407521 | + | 0.913196i | \(0.366393\pi\) | |||||||
\(444\) | −0.361194 | −0.0171415 | ||||||||
\(445\) | −15.9141 | −0.754399 | ||||||||
\(446\) | −58.8150 | −2.78497 | ||||||||
\(447\) | −0.585808 | −0.0277077 | ||||||||
\(448\) | −2.61349 | −0.123476 | ||||||||
\(449\) | 34.1085 | 1.60968 | 0.804840 | − | 0.593492i | \(-0.202251\pi\) | ||||
0.804840 | + | 0.593492i | \(0.202251\pi\) | |||||||
\(450\) | 31.4045 | 1.48042 | ||||||||
\(451\) | 73.5694 | 3.46425 | ||||||||
\(452\) | −30.5367 | −1.43633 | ||||||||
\(453\) | −1.81409 | −0.0852334 | ||||||||
\(454\) | 55.7234 | 2.61523 | ||||||||
\(455\) | −4.13030 | −0.193632 | ||||||||
\(456\) | 0.182727 | 0.00855697 | ||||||||
\(457\) | 24.4800 | 1.14513 | 0.572564 | − | 0.819860i | \(-0.305949\pi\) | ||||
0.572564 | + | 0.819860i | \(0.305949\pi\) | |||||||
\(458\) | −42.2482 | −1.97413 | ||||||||
\(459\) | −1.22810 | −0.0573228 | ||||||||
\(460\) | −47.0010 | −2.19143 | ||||||||
\(461\) | 22.2691 | 1.03718 | 0.518589 | − | 0.855024i | \(-0.326458\pi\) | ||||
0.518589 | + | 0.855024i | \(0.326458\pi\) | |||||||
\(462\) | 0.404522 | 0.0188201 | ||||||||
\(463\) | −4.73547 | −0.220076 | −0.110038 | − | 0.993927i | \(-0.535097\pi\) | ||||
−0.110038 | + | 0.993927i | \(0.535097\pi\) | |||||||
\(464\) | −0.691518 | −0.0321029 | ||||||||
\(465\) | 1.53722 | 0.0712869 | ||||||||
\(466\) | 8.36424 | 0.387466 | ||||||||
\(467\) | 29.5509 | 1.36745 | 0.683725 | − | 0.729739i | \(-0.260359\pi\) | ||||
0.683725 | + | 0.729739i | \(0.260359\pi\) | |||||||
\(468\) | −48.4155 | −2.23801 | ||||||||
\(469\) | 1.92652 | 0.0889582 | ||||||||
\(470\) | 5.35388 | 0.246956 | ||||||||
\(471\) | −0.548753 | −0.0252852 | ||||||||
\(472\) | −19.4499 | −0.895254 | ||||||||
\(473\) | −25.4956 | −1.17229 | ||||||||
\(474\) | −2.27782 | −0.104624 | ||||||||
\(475\) | 4.59475 | 0.210822 | ||||||||
\(476\) | −0.867982 | −0.0397839 | ||||||||
\(477\) | −24.7582 | −1.13360 | ||||||||
\(478\) | 42.5442 | 1.94593 | ||||||||
\(479\) | 17.2676 | 0.788976 | 0.394488 | − | 0.918901i | \(-0.370922\pi\) | ||||
0.394488 | + | 0.918901i | \(0.370922\pi\) | |||||||
\(480\) | 3.27915 | 0.149672 | ||||||||
\(481\) | 6.09951 | 0.278114 | ||||||||
\(482\) | 8.27775 | 0.377041 | ||||||||
\(483\) | −0.164203 | −0.00747147 | ||||||||
\(484\) | 80.0696 | 3.63953 | ||||||||
\(485\) | 30.5983 | 1.38940 | ||||||||
\(486\) | 7.84506 | 0.355859 | ||||||||
\(487\) | −33.4329 | −1.51499 | −0.757494 | − | 0.652843i | \(-0.773576\pi\) | ||||
−0.757494 | + | 0.652843i | \(0.773576\pi\) | |||||||
\(488\) | 10.5352 | 0.476905 | ||||||||
\(489\) | −2.25659 | −0.102046 | ||||||||
\(490\) | −47.1889 | −2.13178 | ||||||||
\(491\) | 12.6270 | 0.569849 | 0.284924 | − | 0.958550i | \(-0.408032\pi\) | ||||
0.284924 | + | 0.958550i | \(0.408032\pi\) | |||||||
\(492\) | −4.14612 | −0.186921 | ||||||||
\(493\) | −0.467780 | −0.0210678 | ||||||||
\(494\) | −12.4052 | −0.558138 | ||||||||
\(495\) | 60.0593 | 2.69947 | ||||||||
\(496\) | −8.06456 | −0.362110 | ||||||||
\(497\) | −0.275699 | −0.0123668 | ||||||||
\(498\) | −1.56915 | −0.0703154 | ||||||||
\(499\) | −3.86740 | −0.173128 | −0.0865642 | − | 0.996246i | \(-0.527589\pi\) | ||||
−0.0865642 | + | 0.996246i | \(0.527589\pi\) | |||||||
\(500\) | 1.02026 | 0.0456274 | ||||||||
\(501\) | −1.15984 | −0.0518180 | ||||||||
\(502\) | −11.0749 | −0.494297 | ||||||||
\(503\) | 0.0290584 | 0.00129565 | 0.000647825 | − | 1.00000i | \(-0.499794\pi\) | ||||
0.000647825 | 1.00000i | \(0.499794\pi\) | ||||||||
\(504\) | 0.918520 | 0.0409141 | ||||||||
\(505\) | 42.0949 | 1.87320 | ||||||||
\(506\) | −77.7359 | −3.45578 | ||||||||
\(507\) | −3.28387 | −0.145842 | ||||||||
\(508\) | −20.9602 | −0.929961 | ||||||||
\(509\) | −26.6224 | −1.18002 | −0.590009 | − | 0.807396i | \(-0.700876\pi\) | ||||
−0.590009 | + | 0.807396i | \(0.700876\pi\) | |||||||
\(510\) | 1.39331 | 0.0616969 | ||||||||
\(511\) | −2.28849 | −0.101237 | ||||||||
\(512\) | −23.6004 | −1.04300 | ||||||||
\(513\) | 0.764417 | 0.0337498 | ||||||||
\(514\) | 58.7259 | 2.59029 | ||||||||
\(515\) | 50.9321 | 2.24434 | ||||||||
\(516\) | 1.43685 | 0.0632537 | ||||||||
\(517\) | 5.05630 | 0.222376 | ||||||||
\(518\) | −0.465208 | −0.0204401 | ||||||||
\(519\) | −1.78596 | −0.0783947 | ||||||||
\(520\) | 27.4107 | 1.20204 | ||||||||
\(521\) | −17.0833 | −0.748435 | −0.374217 | − | 0.927341i | \(-0.622089\pi\) | ||||
−0.374217 | + | 0.927341i | \(0.622089\pi\) | |||||||
\(522\) | 1.99007 | 0.0871029 | ||||||||
\(523\) | −26.7360 | −1.16909 | −0.584543 | − | 0.811363i | \(-0.698726\pi\) | ||||
−0.584543 | + | 0.811363i | \(0.698726\pi\) | |||||||
\(524\) | 54.6548 | 2.38761 | ||||||||
\(525\) | −0.142593 | −0.00622326 | ||||||||
\(526\) | −61.6113 | −2.68638 | ||||||||
\(527\) | −5.45531 | −0.237637 | ||||||||
\(528\) | 1.94525 | 0.0846560 | ||||||||
\(529\) | 8.55435 | 0.371928 | ||||||||
\(530\) | 56.3512 | 2.44774 | ||||||||
\(531\) | −40.5580 | −1.76007 | ||||||||
\(532\) | 0.540266 | 0.0234235 | ||||||||
\(533\) | 70.0157 | 3.03272 | ||||||||
\(534\) | 1.48334 | 0.0641903 | ||||||||
\(535\) | 15.5975 | 0.674340 | ||||||||
\(536\) | −12.7853 | −0.552240 | ||||||||
\(537\) | 0.636149 | 0.0274519 | ||||||||
\(538\) | 12.0241 | 0.518395 | ||||||||
\(539\) | −44.5661 | −1.91960 | ||||||||
\(540\) | −6.79037 | −0.292211 | ||||||||
\(541\) | 11.9183 | 0.512409 | 0.256204 | − | 0.966623i | \(-0.417528\pi\) | ||||
0.256204 | + | 0.966623i | \(0.417528\pi\) | |||||||
\(542\) | −5.57911 | −0.239643 | ||||||||
\(543\) | −2.36357 | −0.101430 | ||||||||
\(544\) | −11.6371 | −0.498936 | ||||||||
\(545\) | 3.14294 | 0.134629 | ||||||||
\(546\) | 0.384982 | 0.0164757 | ||||||||
\(547\) | 3.46419 | 0.148118 | 0.0740590 | − | 0.997254i | \(-0.476405\pi\) | ||||
0.0740590 | + | 0.997254i | \(0.476405\pi\) | |||||||
\(548\) | 19.0284 | 0.812855 | ||||||||
\(549\) | 21.9685 | 0.937595 | ||||||||
\(550\) | −67.5055 | −2.87845 | ||||||||
\(551\) | 0.291164 | 0.0124040 | ||||||||
\(552\) | 1.08973 | 0.0463819 | ||||||||
\(553\) | −1.67523 | −0.0712382 | ||||||||
\(554\) | −47.2940 | −2.00933 | ||||||||
\(555\) | 0.426417 | 0.0181004 | ||||||||
\(556\) | −26.0153 | −1.10329 | ||||||||
\(557\) | −13.2451 | −0.561212 | −0.280606 | − | 0.959823i | \(-0.590535\pi\) | ||||
−0.280606 | + | 0.959823i | \(0.590535\pi\) | |||||||
\(558\) | 23.2084 | 0.982490 | ||||||||
\(559\) | −24.2641 | −1.02626 | ||||||||
\(560\) | 1.51484 | 0.0640137 | ||||||||
\(561\) | 1.31587 | 0.0555561 | ||||||||
\(562\) | 14.2603 | 0.601533 | ||||||||
\(563\) | 43.1107 | 1.81690 | 0.908450 | − | 0.417993i | \(-0.137266\pi\) | ||||
0.908450 | + | 0.417993i | \(0.137266\pi\) | |||||||
\(564\) | −0.284956 | −0.0119988 | ||||||||
\(565\) | 36.0509 | 1.51667 | ||||||||
\(566\) | −57.7813 | −2.42873 | ||||||||
\(567\) | 1.90345 | 0.0799374 | ||||||||
\(568\) | 1.82967 | 0.0767713 | ||||||||
\(569\) | −42.3754 | −1.77647 | −0.888235 | − | 0.459390i | \(-0.848068\pi\) | ||||
−0.888235 | + | 0.459390i | \(0.848068\pi\) | |||||||
\(570\) | −0.867252 | −0.0363252 | ||||||||
\(571\) | −0.482562 | −0.0201946 | −0.0100973 | − | 0.999949i | \(-0.503214\pi\) | ||||
−0.0100973 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(572\) | 104.072 | 4.35146 | ||||||||
\(573\) | 3.49176 | 0.145871 | ||||||||
\(574\) | −5.34008 | −0.222891 | ||||||||
\(575\) | 27.4017 | 1.14273 | ||||||||
\(576\) | 36.1674 | 1.50697 | ||||||||
\(577\) | −37.0326 | −1.54169 | −0.770844 | − | 0.637023i | \(-0.780165\pi\) | ||||
−0.770844 | + | 0.637023i | \(0.780165\pi\) | |||||||
\(578\) | 31.7620 | 1.32113 | ||||||||
\(579\) | −0.736777 | −0.0306194 | ||||||||
\(580\) | −2.58643 | −0.107396 | ||||||||
\(581\) | −1.15404 | −0.0478777 | ||||||||
\(582\) | −2.85205 | −0.118221 | ||||||||
\(583\) | 53.2191 | 2.20411 | ||||||||
\(584\) | 15.1875 | 0.628465 | ||||||||
\(585\) | 57.1582 | 2.36320 | ||||||||
\(586\) | −54.3669 | −2.24587 | ||||||||
\(587\) | 21.9665 | 0.906655 | 0.453327 | − | 0.891344i | \(-0.350237\pi\) | ||||
0.453327 | + | 0.891344i | \(0.350237\pi\) | |||||||
\(588\) | 2.51159 | 0.103576 | ||||||||
\(589\) | 3.39559 | 0.139913 | ||||||||
\(590\) | 92.3124 | 3.80044 | ||||||||
\(591\) | 0.950771 | 0.0391095 | ||||||||
\(592\) | −2.23707 | −0.0919430 | ||||||||
\(593\) | −10.9162 | −0.448275 | −0.224137 | − | 0.974558i | \(-0.571956\pi\) | ||||
−0.224137 | + | 0.974558i | \(0.571956\pi\) | |||||||
\(594\) | −11.2307 | −0.460802 | ||||||||
\(595\) | 1.02472 | 0.0420094 | ||||||||
\(596\) | 11.4947 | 0.470841 | ||||||||
\(597\) | 1.81104 | 0.0741209 | ||||||||
\(598\) | −73.9810 | −3.02531 | ||||||||
\(599\) | −5.70872 | −0.233252 | −0.116626 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116626 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(600\) | 0.946315 | 0.0386331 | ||||||||
\(601\) | 14.7194 | 0.600417 | 0.300208 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300208 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(602\) | 1.85062 | 0.0754255 | ||||||||
\(603\) | −26.6606 | −1.08570 | ||||||||
\(604\) | 35.5960 | 1.44838 | ||||||||
\(605\) | −94.5283 | −3.84312 | ||||||||
\(606\) | −3.92363 | −0.159387 | ||||||||
\(607\) | −31.2488 | −1.26835 | −0.634174 | − | 0.773190i | \(-0.718660\pi\) | ||||
−0.634174 | + | 0.773190i | \(0.718660\pi\) | |||||||
\(608\) | 7.24338 | 0.293758 | ||||||||
\(609\) | −0.00903595 | −0.000366155 0 | ||||||||
\(610\) | −50.0017 | −2.02451 | ||||||||
\(611\) | 4.81207 | 0.194675 | ||||||||
\(612\) | 12.0118 | 0.485548 | ||||||||
\(613\) | 21.3293 | 0.861482 | 0.430741 | − | 0.902476i | \(-0.358252\pi\) | ||||
0.430741 | + | 0.902476i | \(0.358252\pi\) | |||||||
\(614\) | −61.6816 | −2.48927 | ||||||||
\(615\) | 4.89481 | 0.197378 | ||||||||
\(616\) | −1.97441 | −0.0795511 | ||||||||
\(617\) | −11.8392 | −0.476626 | −0.238313 | − | 0.971188i | \(-0.576594\pi\) | ||||
−0.238313 | + | 0.971188i | \(0.576594\pi\) | |||||||
\(618\) | −4.74734 | −0.190966 | ||||||||
\(619\) | 22.4949 | 0.904146 | 0.452073 | − | 0.891981i | \(-0.350685\pi\) | ||||
0.452073 | + | 0.891981i | \(0.350685\pi\) | |||||||
\(620\) | −30.1633 | −1.21139 | ||||||||
\(621\) | 4.55875 | 0.182936 | ||||||||
\(622\) | 25.4544 | 1.02063 | ||||||||
\(623\) | 1.09093 | 0.0437071 | ||||||||
\(624\) | 1.85129 | 0.0741107 | ||||||||
\(625\) | −25.5948 | −1.02379 | ||||||||
\(626\) | −11.9662 | −0.478266 | ||||||||
\(627\) | −0.819049 | −0.0327097 | ||||||||
\(628\) | 10.7676 | 0.429674 | ||||||||
\(629\) | −1.51328 | −0.0603382 | ||||||||
\(630\) | −4.35944 | −0.173684 | ||||||||
\(631\) | 26.2358 | 1.04443 | 0.522214 | − | 0.852814i | \(-0.325106\pi\) | ||||
0.522214 | + | 0.852814i | \(0.325106\pi\) | |||||||
\(632\) | 11.1177 | 0.442237 | ||||||||
\(633\) | 3.05967 | 0.121611 | ||||||||
\(634\) | −25.9298 | −1.02980 | ||||||||
\(635\) | 24.7452 | 0.981982 | ||||||||
\(636\) | −2.99925 | −0.118928 | ||||||||
\(637\) | −42.4134 | −1.68048 | ||||||||
\(638\) | −4.27775 | −0.169358 | ||||||||
\(639\) | 3.81533 | 0.150932 | ||||||||
\(640\) | −33.9807 | −1.34320 | ||||||||
\(641\) | −20.8763 | −0.824563 | −0.412282 | − | 0.911056i | \(-0.635268\pi\) | ||||
−0.412282 | + | 0.911056i | \(0.635268\pi\) | |||||||
\(642\) | −1.45383 | −0.0573782 | ||||||||
\(643\) | 25.3355 | 0.999135 | 0.499568 | − | 0.866275i | \(-0.333492\pi\) | ||||
0.499568 | + | 0.866275i | \(0.333492\pi\) | |||||||
\(644\) | 3.22198 | 0.126964 | ||||||||
\(645\) | −1.69631 | −0.0667921 | ||||||||
\(646\) | 3.07771 | 0.121091 | ||||||||
\(647\) | 27.4629 | 1.07968 | 0.539838 | − | 0.841769i | \(-0.318485\pi\) | ||||
0.539838 | + | 0.841769i | \(0.318485\pi\) | |||||||
\(648\) | −12.6322 | −0.496240 | ||||||||
\(649\) | 87.1815 | 3.42217 | ||||||||
\(650\) | −64.2448 | −2.51989 | ||||||||
\(651\) | −0.105378 | −0.00413010 | ||||||||
\(652\) | 44.2787 | 1.73409 | ||||||||
\(653\) | 10.6541 | 0.416927 | 0.208463 | − | 0.978030i | \(-0.433154\pi\) | ||||
0.208463 | + | 0.978030i | \(0.433154\pi\) | |||||||
\(654\) | −0.292951 | −0.0114553 | ||||||||
\(655\) | −64.5242 | −2.52117 | ||||||||
\(656\) | −25.6791 | −1.00260 | ||||||||
\(657\) | 31.6699 | 1.23556 | ||||||||
\(658\) | −0.367015 | −0.0143077 | ||||||||
\(659\) | 11.0960 | 0.432238 | 0.216119 | − | 0.976367i | \(-0.430660\pi\) | ||||
0.216119 | + | 0.976367i | \(0.430660\pi\) | |||||||
\(660\) | 7.27567 | 0.283205 | ||||||||
\(661\) | −0.636140 | −0.0247430 | −0.0123715 | − | 0.999923i | \(-0.503938\pi\) | ||||
−0.0123715 | + | 0.999923i | \(0.503938\pi\) | |||||||
\(662\) | 70.2932 | 2.73202 | ||||||||
\(663\) | 1.25231 | 0.0486357 | ||||||||
\(664\) | 7.65878 | 0.297218 | ||||||||
\(665\) | −0.637825 | −0.0247338 | ||||||||
\(666\) | 6.43790 | 0.249463 | ||||||||
\(667\) | 1.73641 | 0.0672342 | ||||||||
\(668\) | 22.7584 | 0.880550 | ||||||||
\(669\) | −3.69565 | −0.142882 | ||||||||
\(670\) | 60.6810 | 2.34431 | ||||||||
\(671\) | −47.2225 | −1.82301 | ||||||||
\(672\) | −0.224790 | −0.00867146 | ||||||||
\(673\) | 7.63329 | 0.294242 | 0.147121 | − | 0.989119i | \(-0.452999\pi\) | ||||
0.147121 | + | 0.989119i | \(0.452999\pi\) | |||||||
\(674\) | −57.6854 | −2.22196 | ||||||||
\(675\) | 3.95880 | 0.152374 | ||||||||
\(676\) | 64.4360 | 2.47831 | ||||||||
\(677\) | −0.859250 | −0.0330237 | −0.0165118 | − | 0.999864i | \(-0.505256\pi\) | ||||
−0.0165118 | + | 0.999864i | \(0.505256\pi\) | |||||||
\(678\) | −3.36028 | −0.129051 | ||||||||
\(679\) | −2.09755 | −0.0804967 | ||||||||
\(680\) | −6.80053 | −0.260789 | ||||||||
\(681\) | 3.50140 | 0.134174 | ||||||||
\(682\) | −49.8877 | −1.91030 | ||||||||
\(683\) | 1.62253 | 0.0620844 | 0.0310422 | − | 0.999518i | \(-0.490117\pi\) | ||||
0.0310422 | + | 0.999518i | \(0.490117\pi\) | |||||||
\(684\) | −7.47661 | −0.285875 | ||||||||
\(685\) | −22.4645 | −0.858326 | ||||||||
\(686\) | 6.49131 | 0.247840 | ||||||||
\(687\) | −2.65468 | −0.101282 | ||||||||
\(688\) | 8.89917 | 0.339278 | ||||||||
\(689\) | 50.6485 | 1.92955 | ||||||||
\(690\) | −5.17202 | −0.196895 | ||||||||
\(691\) | −0.186189 | −0.00708295 | −0.00354147 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354147 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(692\) | 35.0440 | 1.33217 | ||||||||
\(693\) | −4.11714 | −0.156397 | ||||||||
\(694\) | 10.7060 | 0.406395 | ||||||||
\(695\) | 30.7130 | 1.16501 | ||||||||
\(696\) | 0.0599669 | 0.00227304 | ||||||||
\(697\) | −17.3708 | −0.657964 | ||||||||
\(698\) | 10.6503 | 0.403119 | ||||||||
\(699\) | 0.525569 | 0.0198788 | ||||||||
\(700\) | 2.79795 | 0.105753 | ||||||||
\(701\) | −19.0075 | −0.717903 | −0.358952 | − | 0.933356i | \(-0.616866\pi\) | ||||
−0.358952 | + | 0.933356i | \(0.616866\pi\) | |||||||
\(702\) | −10.6882 | −0.403402 | ||||||||
\(703\) | 0.941921 | 0.0355252 | ||||||||
\(704\) | −77.7437 | −2.93008 | ||||||||
\(705\) | 0.336412 | 0.0126700 | ||||||||
\(706\) | −64.7185 | −2.43571 | ||||||||
\(707\) | −2.88565 | −0.108526 | ||||||||
\(708\) | −4.91325 | −0.184651 | ||||||||
\(709\) | 33.8296 | 1.27050 | 0.635249 | − | 0.772307i | \(-0.280897\pi\) | ||||
0.635249 | + | 0.772307i | \(0.280897\pi\) | |||||||
\(710\) | −8.68392 | −0.325902 | ||||||||
\(711\) | 23.1832 | 0.869436 | ||||||||
\(712\) | −7.23993 | −0.271328 | ||||||||
\(713\) | 20.2503 | 0.758379 | ||||||||
\(714\) | −0.0955133 | −0.00357450 | ||||||||
\(715\) | −122.865 | −4.59488 | ||||||||
\(716\) | −12.4825 | −0.466493 | ||||||||
\(717\) | 2.67328 | 0.0998354 | ||||||||
\(718\) | −51.2947 | −1.91430 | ||||||||
\(719\) | 38.9365 | 1.45209 | 0.726043 | − | 0.687649i | \(-0.241357\pi\) | ||||
0.726043 | + | 0.687649i | \(0.241357\pi\) | |||||||
\(720\) | −20.9635 | −0.781264 | ||||||||
\(721\) | −3.49146 | −0.130029 | ||||||||
\(722\) | 39.1094 | 1.45550 | ||||||||
\(723\) | 0.520134 | 0.0193440 | ||||||||
\(724\) | 46.3779 | 1.72362 | ||||||||
\(725\) | 1.50790 | 0.0560018 | ||||||||
\(726\) | 8.81091 | 0.327003 | ||||||||
\(727\) | −26.4963 | −0.982694 | −0.491347 | − | 0.870964i | \(-0.663495\pi\) | ||||
−0.491347 | + | 0.870964i | \(0.663495\pi\) | |||||||
\(728\) | −1.87904 | −0.0696417 | ||||||||
\(729\) | −26.0111 | −0.963373 | ||||||||
\(730\) | −72.0825 | −2.66789 | ||||||||
\(731\) | 6.01988 | 0.222653 | ||||||||
\(732\) | 2.66130 | 0.0983645 | ||||||||
\(733\) | −40.2879 | −1.48807 | −0.744034 | − | 0.668142i | \(-0.767090\pi\) | ||||
−0.744034 | + | 0.668142i | \(0.767090\pi\) | |||||||
\(734\) | 25.6408 | 0.946421 | ||||||||
\(735\) | −2.96513 | −0.109370 | ||||||||
\(736\) | 43.1973 | 1.59227 | ||||||||
\(737\) | 57.3083 | 2.11098 | ||||||||
\(738\) | 73.9001 | 2.72030 | ||||||||
\(739\) | −26.1948 | −0.963592 | −0.481796 | − | 0.876283i | \(-0.660015\pi\) | ||||
−0.481796 | + | 0.876283i | \(0.660015\pi\) | |||||||
\(740\) | −8.36715 | −0.307583 | ||||||||
\(741\) | −0.779486 | −0.0286351 | ||||||||
\(742\) | −3.86295 | −0.141813 | ||||||||
\(743\) | −7.73748 | −0.283861 | −0.141930 | − | 0.989877i | \(-0.545331\pi\) | ||||
−0.141930 | + | 0.989877i | \(0.545331\pi\) | |||||||
\(744\) | 0.699342 | 0.0256391 | ||||||||
\(745\) | −13.5704 | −0.497180 | ||||||||
\(746\) | −35.2210 | −1.28953 | ||||||||
\(747\) | 15.9705 | 0.584330 | ||||||||
\(748\) | −25.8200 | −0.944072 | ||||||||
\(749\) | −1.06923 | −0.0390688 | ||||||||
\(750\) | 0.112270 | 0.00409952 | ||||||||
\(751\) | −22.5759 | −0.823805 | −0.411903 | − | 0.911228i | \(-0.635136\pi\) | ||||
−0.411903 | + | 0.911228i | \(0.635136\pi\) | |||||||
\(752\) | −1.76489 | −0.0643588 | ||||||||
\(753\) | −0.695895 | −0.0253598 | ||||||||
\(754\) | −4.07112 | −0.148262 | ||||||||
\(755\) | −42.0238 | −1.52940 | ||||||||
\(756\) | 0.465488 | 0.0169296 | ||||||||
\(757\) | −20.8059 | −0.756205 | −0.378102 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378102 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(758\) | 68.5233 | 2.48888 | ||||||||
\(759\) | −4.88455 | −0.177298 | ||||||||
\(760\) | 4.23292 | 0.153544 | ||||||||
\(761\) | 48.4590 | 1.75664 | 0.878319 | − | 0.478074i | \(-0.158665\pi\) | ||||
0.878319 | + | 0.478074i | \(0.158665\pi\) | |||||||
\(762\) | −2.30648 | −0.0835549 | ||||||||
\(763\) | −0.215452 | −0.00779990 | ||||||||
\(764\) | −68.5153 | −2.47880 | ||||||||
\(765\) | −14.1808 | −0.512710 | ||||||||
\(766\) | 10.8325 | 0.391395 | ||||||||
\(767\) | 82.9703 | 2.99589 | ||||||||
\(768\) | −0.124219 | −0.00448238 | ||||||||
\(769\) | −42.3172 | −1.52600 | −0.762998 | − | 0.646401i | \(-0.776274\pi\) | ||||
−0.762998 | + | 0.646401i | \(0.776274\pi\) | |||||||
\(770\) | 9.37085 | 0.337702 | ||||||||
\(771\) | 3.69006 | 0.132894 | ||||||||
\(772\) | 14.4570 | 0.520319 | ||||||||
\(773\) | −10.1730 | −0.365898 | −0.182949 | − | 0.983122i | \(-0.558564\pi\) | ||||
−0.182949 | + | 0.983122i | \(0.558564\pi\) | |||||||
\(774\) | −25.6102 | −0.920541 | ||||||||
\(775\) | 17.5853 | 0.631681 | ||||||||
\(776\) | 13.9204 | 0.499712 | ||||||||
\(777\) | −0.0292314 | −0.00104867 | ||||||||
\(778\) | −40.7818 | −1.46210 | ||||||||
\(779\) | 10.8122 | 0.387388 | ||||||||
\(780\) | 6.92423 | 0.247927 | ||||||||
\(781\) | −8.20126 | −0.293464 | ||||||||
\(782\) | 18.3545 | 0.656357 | ||||||||
\(783\) | 0.250865 | 0.00896517 | ||||||||
\(784\) | 15.5556 | 0.555559 | ||||||||
\(785\) | −12.7120 | −0.453710 | ||||||||
\(786\) | 6.01425 | 0.214521 | ||||||||
\(787\) | 14.4841 | 0.516304 | 0.258152 | − | 0.966104i | \(-0.416887\pi\) | ||||
0.258152 | + | 0.966104i | \(0.416887\pi\) | |||||||
\(788\) | −18.6560 | −0.664592 | ||||||||
\(789\) | −3.87136 | −0.137824 | ||||||||
\(790\) | −52.7662 | −1.87734 | ||||||||
\(791\) | −2.47134 | −0.0878706 | ||||||||
\(792\) | 27.3233 | 0.970892 | ||||||||
\(793\) | −44.9415 | −1.59592 | ||||||||
\(794\) | −13.7841 | −0.489181 | ||||||||
\(795\) | 3.54084 | 0.125581 | ||||||||
\(796\) | −35.5362 | −1.25955 | ||||||||
\(797\) | 34.4304 | 1.21959 | 0.609794 | − | 0.792560i | \(-0.291252\pi\) | ||||
0.609794 | + | 0.792560i | \(0.291252\pi\) | |||||||
\(798\) | 0.0594512 | 0.00210455 | ||||||||
\(799\) | −1.19386 | −0.0422359 | ||||||||
\(800\) | 37.5123 | 1.32626 | ||||||||
\(801\) | −15.0971 | −0.533430 | ||||||||
\(802\) | 0.788078 | 0.0278280 | ||||||||
\(803\) | −68.0761 | −2.40235 | ||||||||
\(804\) | −3.22970 | −0.113903 | ||||||||
\(805\) | −3.80379 | −0.134066 | ||||||||
\(806\) | −47.4779 | −1.67234 | ||||||||
\(807\) | 0.755537 | 0.0265962 | ||||||||
\(808\) | 19.1506 | 0.673715 | ||||||||
\(809\) | 44.0582 | 1.54901 | 0.774503 | − | 0.632571i | \(-0.218000\pi\) | ||||
0.774503 | + | 0.632571i | \(0.218000\pi\) | |||||||
\(810\) | 59.9545 | 2.10659 | ||||||||
\(811\) | −2.20246 | −0.0773388 | −0.0386694 | − | 0.999252i | \(-0.512312\pi\) | ||||
−0.0386694 | + | 0.999252i | \(0.512312\pi\) | |||||||
\(812\) | 0.177303 | 0.00622212 | ||||||||
\(813\) | −0.350565 | −0.0122948 | ||||||||
\(814\) | −13.8386 | −0.485042 | ||||||||
\(815\) | −52.2744 | −1.83109 | ||||||||
\(816\) | −0.459300 | −0.0160787 | ||||||||
\(817\) | −3.74701 | −0.131091 | ||||||||
\(818\) | −31.2134 | −1.09135 | ||||||||
\(819\) | −3.91827 | −0.136915 | ||||||||
\(820\) | −96.0458 | −3.35407 | ||||||||
\(821\) | −6.34252 | −0.221356 | −0.110678 | − | 0.993856i | \(-0.535302\pi\) | ||||
−0.110678 | + | 0.993856i | \(0.535302\pi\) | |||||||
\(822\) | 2.09390 | 0.0730332 | ||||||||
\(823\) | 5.51507 | 0.192243 | 0.0961217 | − | 0.995370i | \(-0.469356\pi\) | ||||
0.0961217 | + | 0.995370i | \(0.469356\pi\) | |||||||
\(824\) | 23.1710 | 0.807201 | ||||||||
\(825\) | −4.24173 | −0.147678 | ||||||||
\(826\) | −6.32813 | −0.220184 | ||||||||
\(827\) | −53.3974 | −1.85681 | −0.928405 | − | 0.371569i | \(-0.878820\pi\) | ||||
−0.928405 | + | 0.371569i | \(0.878820\pi\) | |||||||
\(828\) | −44.5882 | −1.54955 | ||||||||
\(829\) | −39.4903 | −1.37155 | −0.685777 | − | 0.727812i | \(-0.740538\pi\) | ||||
−0.685777 | + | 0.727812i | \(0.740538\pi\) | |||||||
\(830\) | −36.3498 | −1.26172 | ||||||||
\(831\) | −2.97173 | −0.103088 | ||||||||
\(832\) | −73.9884 | −2.56509 | ||||||||
\(833\) | 10.5227 | 0.364589 | ||||||||
\(834\) | −2.86274 | −0.0991284 | ||||||||
\(835\) | −26.8681 | −0.929808 | ||||||||
\(836\) | 16.0714 | 0.555839 | ||||||||
\(837\) | 2.92561 | 0.101124 | ||||||||
\(838\) | 10.3502 | 0.357542 | ||||||||
\(839\) | 37.6281 | 1.29907 | 0.649533 | − | 0.760334i | \(-0.274965\pi\) | ||||
0.649533 | + | 0.760334i | \(0.274965\pi\) | |||||||
\(840\) | −0.131364 | −0.00453248 | ||||||||
\(841\) | −28.9044 | −0.996705 | ||||||||
\(842\) | −37.3694 | −1.28783 | ||||||||
\(843\) | 0.896047 | 0.0308615 | ||||||||
\(844\) | −60.0367 | −2.06655 | ||||||||
\(845\) | −76.0716 | −2.61694 | ||||||||
\(846\) | 5.07903 | 0.174621 | ||||||||
\(847\) | 6.48003 | 0.222656 | ||||||||
\(848\) | −18.5760 | −0.637901 | ||||||||
\(849\) | −3.63070 | −0.124605 | ||||||||
\(850\) | 15.9390 | 0.546703 | ||||||||
\(851\) | 5.61733 | 0.192559 | ||||||||
\(852\) | 0.462195 | 0.0158345 | ||||||||
\(853\) | −16.9514 | −0.580406 | −0.290203 | − | 0.956965i | \(-0.593723\pi\) | ||||
−0.290203 | + | 0.956965i | \(0.593723\pi\) | |||||||
\(854\) | 3.42768 | 0.117293 | ||||||||
\(855\) | 8.82671 | 0.301867 | ||||||||
\(856\) | 7.09592 | 0.242534 | ||||||||
\(857\) | −51.8794 | −1.77217 | −0.886084 | − | 0.463525i | \(-0.846585\pi\) | ||||
−0.886084 | + | 0.463525i | \(0.846585\pi\) | |||||||
\(858\) | 11.4521 | 0.390969 | ||||||||
\(859\) | 27.5784 | 0.940962 | 0.470481 | − | 0.882410i | \(-0.344080\pi\) | ||||
0.470481 | + | 0.882410i | \(0.344080\pi\) | |||||||
\(860\) | 33.2849 | 1.13501 | ||||||||
\(861\) | −0.335545 | −0.0114353 | ||||||||
\(862\) | 36.3793 | 1.23908 | ||||||||
\(863\) | −0.959694 | −0.0326683 | −0.0163342 | − | 0.999867i | \(-0.505200\pi\) | ||||
−0.0163342 | + | 0.999867i | \(0.505200\pi\) | |||||||
\(864\) | 6.24083 | 0.212317 | ||||||||
\(865\) | −41.3721 | −1.40669 | ||||||||
\(866\) | −55.1542 | −1.87422 | ||||||||
\(867\) | 1.99578 | 0.0677801 | ||||||||
\(868\) | 2.06773 | 0.0701834 | ||||||||
\(869\) | −49.8334 | −1.69048 | ||||||||
\(870\) | −0.284613 | −0.00964928 | ||||||||
\(871\) | 54.5401 | 1.84802 | ||||||||
\(872\) | 1.42985 | 0.0484207 | ||||||||
\(873\) | 29.0275 | 0.982433 | ||||||||
\(874\) | −11.4246 | −0.386442 | ||||||||
\(875\) | 0.0825696 | 0.00279136 | ||||||||
\(876\) | 3.83654 | 0.129625 | ||||||||
\(877\) | 24.7586 | 0.836039 | 0.418020 | − | 0.908438i | \(-0.362724\pi\) | ||||
0.418020 | + | 0.908438i | \(0.362724\pi\) | |||||||
\(878\) | 77.9297 | 2.63000 | ||||||||
\(879\) | −3.41615 | −0.115224 | ||||||||
\(880\) | 45.0621 | 1.51904 | ||||||||
\(881\) | 11.3979 | 0.384004 | 0.192002 | − | 0.981395i | \(-0.438502\pi\) | ||||
0.192002 | + | 0.981395i | \(0.438502\pi\) | |||||||
\(882\) | −44.7664 | −1.50736 | ||||||||
\(883\) | −4.91864 | −0.165526 | −0.0827628 | − | 0.996569i | \(-0.526374\pi\) | ||||
−0.0827628 | + | 0.996569i | \(0.526374\pi\) | |||||||
\(884\) | −24.5728 | −0.826472 | ||||||||
\(885\) | 5.80047 | 0.194981 | ||||||||
\(886\) | −37.0406 | −1.24440 | ||||||||
\(887\) | 24.5944 | 0.825799 | 0.412899 | − | 0.910777i | \(-0.364516\pi\) | ||||
0.412899 | + | 0.910777i | \(0.364516\pi\) | |||||||
\(888\) | 0.193994 | 0.00651001 | ||||||||
\(889\) | −1.69631 | −0.0568925 | ||||||||
\(890\) | 34.3619 | 1.15181 | ||||||||
\(891\) | 56.6222 | 1.89691 | ||||||||
\(892\) | 72.5160 | 2.42802 | ||||||||
\(893\) | 0.743108 | 0.0248671 | ||||||||
\(894\) | 1.26488 | 0.0423041 | ||||||||
\(895\) | 14.7366 | 0.492589 | ||||||||
\(896\) | 2.32942 | 0.0778204 | ||||||||
\(897\) | −4.64861 | −0.155213 | ||||||||
\(898\) | −73.6476 | −2.45765 | ||||||||
\(899\) | 1.11436 | 0.0371659 | ||||||||
\(900\) | −38.7202 | −1.29067 | ||||||||
\(901\) | −12.5658 | −0.418627 | ||||||||
\(902\) | −158.852 | −5.28919 | ||||||||
\(903\) | 0.116284 | 0.00386969 | ||||||||
\(904\) | 16.4010 | 0.545488 | ||||||||
\(905\) | −54.7527 | −1.82004 | ||||||||
\(906\) | 3.91701 | 0.130134 | ||||||||
\(907\) | −0.681186 | −0.0226184 | −0.0113092 | − | 0.999936i | \(-0.503600\pi\) | ||||
−0.0113092 | + | 0.999936i | \(0.503600\pi\) | |||||||
\(908\) | −68.7043 | −2.28003 | ||||||||
\(909\) | 39.9339 | 1.32452 | ||||||||
\(910\) | 8.91821 | 0.295636 | ||||||||
\(911\) | −32.0443 | −1.06167 | −0.530837 | − | 0.847474i | \(-0.678123\pi\) | ||||
−0.530837 | + | 0.847474i | \(0.678123\pi\) | |||||||
\(912\) | 0.285886 | 0.00946664 | ||||||||
\(913\) | −34.3294 | −1.13614 | ||||||||
\(914\) | −52.8576 | −1.74837 | ||||||||
\(915\) | −3.14187 | −0.103867 | ||||||||
\(916\) | 52.0900 | 1.72110 | ||||||||
\(917\) | 4.42322 | 0.146067 | ||||||||
\(918\) | 2.65173 | 0.0875202 | ||||||||
\(919\) | −12.7384 | −0.420200 | −0.210100 | − | 0.977680i | \(-0.567379\pi\) | ||||
−0.210100 | + | 0.977680i | \(0.567379\pi\) | |||||||
\(920\) | 25.2438 | 0.832263 | ||||||||
\(921\) | −3.87578 | −0.127711 | ||||||||
\(922\) | −48.0838 | −1.58356 | ||||||||
\(923\) | −7.80511 | −0.256908 | ||||||||
\(924\) | −0.498756 | −0.0164079 | ||||||||
\(925\) | 4.87806 | 0.160390 | ||||||||
\(926\) | 10.2249 | 0.336011 | ||||||||
\(927\) | 48.3175 | 1.58695 | ||||||||
\(928\) | 2.37712 | 0.0780326 | ||||||||
\(929\) | −22.7956 | −0.747899 | −0.373949 | − | 0.927449i | \(-0.621997\pi\) | ||||
−0.373949 | + | 0.927449i | \(0.621997\pi\) | |||||||
\(930\) | −3.31919 | −0.108840 | ||||||||
\(931\) | −6.54972 | −0.214659 | ||||||||
\(932\) | −10.3127 | −0.337804 | ||||||||
\(933\) | 1.59943 | 0.0523631 | ||||||||
\(934\) | −63.8066 | −2.08782 | ||||||||
\(935\) | 30.4825 | 0.996883 | ||||||||
\(936\) | 26.0035 | 0.849951 | ||||||||
\(937\) | 7.34039 | 0.239800 | 0.119900 | − | 0.992786i | \(-0.461743\pi\) | ||||
0.119900 | + | 0.992786i | \(0.461743\pi\) | |||||||
\(938\) | −4.15976 | −0.135821 | ||||||||
\(939\) | −0.751899 | −0.0245373 | ||||||||
\(940\) | −6.60108 | −0.215303 | ||||||||
\(941\) | 60.0308 | 1.95695 | 0.978474 | − | 0.206372i | \(-0.0661656\pi\) | ||||
0.978474 | + | 0.206372i | \(0.0661656\pi\) | |||||||
\(942\) | 1.18487 | 0.0386053 | ||||||||
\(943\) | 64.4808 | 2.09978 | ||||||||
\(944\) | −30.4304 | −0.990425 | ||||||||
\(945\) | −0.549545 | −0.0178767 | ||||||||
\(946\) | 55.0505 | 1.78985 | ||||||||
\(947\) | −1.45653 | −0.0473308 | −0.0236654 | − | 0.999720i | \(-0.507534\pi\) | ||||
−0.0236654 | + | 0.999720i | \(0.507534\pi\) | |||||||
\(948\) | 2.80844 | 0.0912138 | ||||||||
\(949\) | −64.7878 | −2.10310 | ||||||||
\(950\) | −9.92105 | −0.321881 | ||||||||
\(951\) | −1.62930 | −0.0528337 | ||||||||
\(952\) | 0.466185 | 0.0151091 | ||||||||
\(953\) | 26.4407 | 0.856498 | 0.428249 | − | 0.903661i | \(-0.359131\pi\) | ||||
0.428249 | + | 0.903661i | \(0.359131\pi\) | |||||||
\(954\) | 53.4584 | 1.73078 | ||||||||
\(955\) | 80.8876 | 2.61746 | ||||||||
\(956\) | −52.4550 | −1.69652 | ||||||||
\(957\) | −0.268794 | −0.00868886 | ||||||||
\(958\) | −37.2844 | −1.20460 | ||||||||
\(959\) | 1.53997 | 0.0497283 | ||||||||
\(960\) | −5.17254 | −0.166943 | ||||||||
\(961\) | −18.0042 | −0.580781 | ||||||||
\(962\) | −13.1701 | −0.424622 | ||||||||
\(963\) | 14.7968 | 0.476821 | ||||||||
\(964\) | −10.2061 | −0.328715 | ||||||||
\(965\) | −17.0676 | −0.549426 | ||||||||
\(966\) | 0.354548 | 0.0114074 | ||||||||
\(967\) | −29.6811 | −0.954481 | −0.477240 | − | 0.878773i | \(-0.658363\pi\) | ||||
−0.477240 | + | 0.878773i | \(0.658363\pi\) | |||||||
\(968\) | −43.0046 | −1.38222 | ||||||||
\(969\) | 0.193389 | 0.00621255 | ||||||||
\(970\) | −66.0683 | −2.12133 | ||||||||
\(971\) | 23.6579 | 0.759219 | 0.379610 | − | 0.925147i | \(-0.376058\pi\) | ||||
0.379610 | + | 0.925147i | \(0.376058\pi\) | |||||||
\(972\) | −9.67258 | −0.310248 | ||||||||
\(973\) | −2.10541 | −0.0674965 | ||||||||
\(974\) | 72.1887 | 2.31307 | ||||||||
\(975\) | −4.03684 | −0.129282 | ||||||||
\(976\) | 16.4829 | 0.527604 | ||||||||
\(977\) | −7.16926 | −0.229365 | −0.114683 | − | 0.993402i | \(-0.536585\pi\) | ||||
−0.114683 | + | 0.993402i | \(0.536585\pi\) | |||||||
\(978\) | 4.87245 | 0.155804 | ||||||||
\(979\) | 32.4520 | 1.03717 | ||||||||
\(980\) | 58.1817 | 1.85854 | ||||||||
\(981\) | 2.98159 | 0.0951949 | ||||||||
\(982\) | −27.2644 | −0.870042 | ||||||||
\(983\) | 34.9943 | 1.11615 | 0.558073 | − | 0.829792i | \(-0.311541\pi\) | ||||
0.558073 | + | 0.829792i | \(0.311541\pi\) | |||||||
\(984\) | 2.22684 | 0.0709890 | ||||||||
\(985\) | 22.0248 | 0.701769 | ||||||||
\(986\) | 1.01004 | 0.0321661 | ||||||||
\(987\) | −0.0230615 | −0.000734055 0 | ||||||||
\(988\) | 15.2951 | 0.486600 | ||||||||
\(989\) | −22.3460 | −0.710561 | ||||||||
\(990\) | −129.681 | −4.12153 | ||||||||
\(991\) | 40.4662 | 1.28545 | 0.642726 | − | 0.766096i | \(-0.277804\pi\) | ||||
0.642726 | + | 0.766096i | \(0.277804\pi\) | |||||||
\(992\) | 27.7222 | 0.880181 | ||||||||
\(993\) | 4.41689 | 0.140166 | ||||||||
\(994\) | 0.595294 | 0.0188816 | ||||||||
\(995\) | 41.9532 | 1.33000 | ||||||||
\(996\) | 1.93469 | 0.0613030 | ||||||||
\(997\) | −8.77630 | −0.277948 | −0.138974 | − | 0.990296i | \(-0.544380\pi\) | ||||
−0.138974 | + | 0.990296i | \(0.544380\pi\) | |||||||
\(998\) | 8.35054 | 0.264332 | ||||||||
\(999\) | 0.811551 | 0.0256763 |
(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 | 4033.2.a.f.1.11 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.11 | ✓ | 85 | 1.1 | even | 1 | trivial |