Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38861 | −0.981899 | −0.490950 | − | 0.871188i | \(-0.663350\pi\) | ||||
−0.490950 | + | 0.871188i | \(0.663350\pi\) | |||||||
\(3\) | −0.0366779 | −0.0211760 | −0.0105880 | − | 0.999944i | \(-0.503370\pi\) | ||||
−0.0105880 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(4\) | −0.0717484 | −0.0358742 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0509315 | 0.0207927 | ||||||||
\(7\) | 3.69082 | 1.39500 | 0.697499 | − | 0.716586i | \(-0.254296\pi\) | ||||
0.697499 | + | 0.716586i | \(0.254296\pi\) | |||||||
\(8\) | 2.87686 | 1.01712 | ||||||||
\(9\) | −2.99865 | −0.999552 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.61704 | 0.789067 | 0.394533 | − | 0.918882i | \(-0.370906\pi\) | ||||
0.394533 | + | 0.918882i | \(0.370906\pi\) | |||||||
\(12\) | 0.00263158 | 0.000759672 0 | ||||||||
\(13\) | 5.39014 | 1.49496 | 0.747478 | − | 0.664286i | \(-0.231264\pi\) | ||||
0.747478 | + | 0.664286i | \(0.231264\pi\) | |||||||
\(14\) | −5.12512 | −1.36975 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.85136 | −0.962839 | ||||||||
\(17\) | 5.52357 | 1.33966 | 0.669832 | − | 0.742513i | \(-0.266366\pi\) | ||||
0.669832 | + | 0.742513i | \(0.266366\pi\) | |||||||
\(18\) | 4.16398 | 0.981459 | ||||||||
\(19\) | −8.11267 | −1.86117 | −0.930587 | − | 0.366071i | \(-0.880703\pi\) | ||||
−0.930587 | + | 0.366071i | \(0.880703\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.135371 | −0.0295404 | ||||||||
\(22\) | −3.63406 | −0.774784 | ||||||||
\(23\) | −7.71557 | −1.60881 | −0.804404 | − | 0.594082i | \(-0.797515\pi\) | ||||
−0.804404 | + | 0.594082i | \(0.797515\pi\) | |||||||
\(24\) | −0.105517 | −0.0215386 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.48483 | −1.46790 | ||||||||
\(27\) | 0.220018 | 0.0423425 | ||||||||
\(28\) | −0.264810 | −0.0500444 | ||||||||
\(29\) | 7.36101 | 1.36690 | 0.683452 | − | 0.729995i | \(-0.260478\pi\) | ||||
0.683452 | + | 0.729995i | \(0.260478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.97766 | 1.07362 | 0.536809 | − | 0.843704i | \(-0.319629\pi\) | ||||
0.536809 | + | 0.843704i | \(0.319629\pi\) | |||||||
\(32\) | −0.405672 | −0.0717133 | ||||||||
\(33\) | −0.0959874 | −0.0167093 | ||||||||
\(34\) | −7.67012 | −1.31541 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.215149 | 0.0358581 | ||||||||
\(37\) | −2.83895 | −0.466720 | −0.233360 | − | 0.972390i | \(-0.574972\pi\) | ||||
−0.233360 | + | 0.972390i | \(0.574972\pi\) | |||||||
\(38\) | 11.2654 | 1.82748 | ||||||||
\(39\) | −0.197699 | −0.0316572 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.56023 | 0.243667 | 0.121833 | − | 0.992551i | \(-0.461123\pi\) | ||||
0.121833 | + | 0.992551i | \(0.461123\pi\) | |||||||
\(42\) | 0.187979 | 0.0290057 | ||||||||
\(43\) | 9.68988 | 1.47769 | 0.738846 | − | 0.673874i | \(-0.235371\pi\) | ||||
0.738846 | + | 0.673874i | \(0.235371\pi\) | |||||||
\(44\) | −0.187768 | −0.0283071 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.7140 | 1.57969 | ||||||||
\(47\) | −0.834859 | −0.121777 | −0.0608884 | − | 0.998145i | \(-0.519393\pi\) | ||||
−0.0608884 | + | 0.998145i | \(0.519393\pi\) | |||||||
\(48\) | 0.141260 | 0.0203891 | ||||||||
\(49\) | 6.62212 | 0.946017 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.202593 | −0.0283687 | ||||||||
\(52\) | −0.386734 | −0.0536304 | ||||||||
\(53\) | 8.02986 | 1.10299 | 0.551493 | − | 0.834179i | \(-0.314058\pi\) | ||||
0.551493 | + | 0.834179i | \(0.314058\pi\) | |||||||
\(54\) | −0.305520 | −0.0415760 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.6180 | 1.41888 | ||||||||
\(57\) | 0.297556 | 0.0394122 | ||||||||
\(58\) | −10.2216 | −1.34216 | ||||||||
\(59\) | 6.01249 | 0.782759 | 0.391380 | − | 0.920229i | \(-0.371998\pi\) | ||||
0.391380 | + | 0.920229i | \(0.371998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.78566 | 0.612741 | 0.306371 | − | 0.951912i | \(-0.400885\pi\) | ||||
0.306371 | + | 0.951912i | \(0.400885\pi\) | |||||||
\(62\) | −8.30066 | −1.05419 | ||||||||
\(63\) | −11.0675 | −1.39437 | ||||||||
\(64\) | 8.26603 | 1.03325 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.133290 | 0.0164068 | ||||||||
\(67\) | 5.31555 | 0.649398 | 0.324699 | − | 0.945817i | \(-0.394737\pi\) | ||||
0.324699 | + | 0.945817i | \(0.394737\pi\) | |||||||
\(68\) | −0.396308 | −0.0480594 | ||||||||
\(69\) | 0.282991 | 0.0340681 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.61386 | −0.547565 | −0.273782 | − | 0.961792i | \(-0.588275\pi\) | ||||
−0.273782 | + | 0.961792i | \(0.588275\pi\) | |||||||
\(72\) | −8.62671 | −1.01667 | ||||||||
\(73\) | −5.51666 | −0.645676 | −0.322838 | − | 0.946454i | \(-0.604637\pi\) | ||||
−0.322838 | + | 0.946454i | \(0.604637\pi\) | |||||||
\(74\) | 3.94221 | 0.458272 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.582071 | 0.0667681 | ||||||||
\(77\) | 9.65901 | 1.10075 | ||||||||
\(78\) | 0.274528 | 0.0310842 | ||||||||
\(79\) | 5.27223 | 0.593172 | 0.296586 | − | 0.955006i | \(-0.404152\pi\) | ||||
0.296586 | + | 0.955006i | \(0.404152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.98789 | 0.998655 | ||||||||
\(82\) | −2.16656 | −0.239256 | ||||||||
\(83\) | −2.54694 | −0.279563 | −0.139782 | − | 0.990182i | \(-0.544640\pi\) | ||||
−0.139782 | + | 0.990182i | \(0.544640\pi\) | |||||||
\(84\) | 0.00971267 | 0.00105974 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −13.4555 | −1.45094 | ||||||||
\(87\) | −0.269986 | −0.0289456 | ||||||||
\(88\) | 7.52886 | 0.802579 | ||||||||
\(89\) | 12.7951 | 1.35627 | 0.678137 | − | 0.734936i | \(-0.262788\pi\) | ||||
0.678137 | + | 0.734936i | \(0.262788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.8940 | 2.08546 | ||||||||
\(92\) | 0.553580 | 0.0577147 | ||||||||
\(93\) | −0.219248 | −0.0227349 | ||||||||
\(94\) | 1.15930 | 0.119572 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0148792 | 0.00151860 | ||||||||
\(97\) | −10.9674 | −1.11357 | −0.556787 | − | 0.830656i | \(-0.687966\pi\) | ||||
−0.556787 | + | 0.830656i | \(0.687966\pi\) | |||||||
\(98\) | −9.19557 | −0.928893 | ||||||||
\(99\) | −7.84759 | −0.788713 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.4616 | −1.63800 | −0.818998 | − | 0.573797i | \(-0.805470\pi\) | ||||
−0.818998 | + | 0.573797i | \(0.805470\pi\) | |||||||
\(102\) | 0.281324 | 0.0278552 | ||||||||
\(103\) | 14.6984 | 1.44827 | 0.724136 | − | 0.689657i | \(-0.242239\pi\) | ||||
0.724136 | + | 0.689657i | \(0.242239\pi\) | |||||||
\(104\) | 15.5067 | 1.52056 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.1504 | −1.08302 | ||||||||
\(107\) | −0.783974 | −0.0757896 | −0.0378948 | − | 0.999282i | \(-0.512065\pi\) | ||||
−0.0378948 | + | 0.999282i | \(0.512065\pi\) | |||||||
\(108\) | −0.0157859 | −0.00151900 | ||||||||
\(109\) | −12.3667 | −1.18451 | −0.592256 | − | 0.805750i | \(-0.701763\pi\) | ||||
−0.592256 | + | 0.805750i | \(0.701763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.104127 | 0.00988327 | ||||||||
\(112\) | −14.2146 | −1.34316 | ||||||||
\(113\) | −20.2824 | −1.90801 | −0.954003 | − | 0.299796i | \(-0.903081\pi\) | ||||
−0.954003 | + | 0.299796i | \(0.903081\pi\) | |||||||
\(114\) | −0.413190 | −0.0386988 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.528141 | −0.0490366 | ||||||||
\(117\) | −16.1632 | −1.49429 | ||||||||
\(118\) | −8.34903 | −0.768590 | ||||||||
\(119\) | 20.3865 | 1.86883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.15111 | −0.377374 | ||||||||
\(122\) | −6.64544 | −0.601650 | ||||||||
\(123\) | −0.0572259 | −0.00515988 | ||||||||
\(124\) | −0.428887 | −0.0385152 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.3685 | 1.36913 | ||||||||
\(127\) | −5.27769 | −0.468319 | −0.234160 | − | 0.972198i | \(-0.575234\pi\) | ||||
−0.234160 | + | 0.972198i | \(0.575234\pi\) | |||||||
\(128\) | −10.6670 | −0.942838 | ||||||||
\(129\) | −0.355404 | −0.0312916 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.74621 | −0.152567 | −0.0762835 | − | 0.997086i | \(-0.524305\pi\) | ||||
−0.0762835 | + | 0.997086i | \(0.524305\pi\) | |||||||
\(132\) | 0.00688695 | 0.000599432 0 | ||||||||
\(133\) | −29.9424 | −2.59633 | ||||||||
\(134\) | −7.38126 | −0.637643 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.8906 | 1.36260 | ||||||||
\(137\) | −2.84655 | −0.243197 | −0.121599 | − | 0.992579i | \(-0.538802\pi\) | ||||
−0.121599 | + | 0.992579i | \(0.538802\pi\) | |||||||
\(138\) | −0.392965 | −0.0334514 | ||||||||
\(139\) | 3.73442 | 0.316749 | 0.158375 | − | 0.987379i | \(-0.449375\pi\) | ||||
0.158375 | + | 0.987379i | \(0.449375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0306209 | 0.00257874 | ||||||||
\(142\) | 6.40688 | 0.537653 | ||||||||
\(143\) | 14.1062 | 1.17962 | ||||||||
\(144\) | 11.5489 | 0.962407 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.66051 | 0.633988 | ||||||||
\(147\) | −0.242885 | −0.0200328 | ||||||||
\(148\) | 0.203690 | 0.0167432 | ||||||||
\(149\) | −10.3087 | −0.844520 | −0.422260 | − | 0.906475i | \(-0.638763\pi\) | ||||
−0.422260 | + | 0.906475i | \(0.638763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.96022 | −0.240899 | −0.120450 | − | 0.992719i | \(-0.538434\pi\) | ||||
−0.120450 | + | 0.992719i | \(0.538434\pi\) | |||||||
\(152\) | −23.3390 | −1.89304 | ||||||||
\(153\) | −16.5633 | −1.33906 | ||||||||
\(154\) | −13.4126 | −1.08082 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0141846 | 0.00113568 | ||||||||
\(157\) | 4.61712 | 0.368486 | 0.184243 | − | 0.982881i | \(-0.441017\pi\) | ||||
0.184243 | + | 0.982881i | \(0.441017\pi\) | |||||||
\(158\) | −7.32109 | −0.582435 | ||||||||
\(159\) | −0.294518 | −0.0233568 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.4768 | −2.24428 | ||||||||
\(162\) | −12.4807 | −0.980578 | ||||||||
\(163\) | −4.19155 | −0.328307 | −0.164154 | − | 0.986435i | \(-0.552489\pi\) | ||||
−0.164154 | + | 0.986435i | \(0.552489\pi\) | |||||||
\(164\) | −0.111944 | −0.00874135 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.53672 | 0.274503 | ||||||||
\(167\) | 15.1804 | 1.17469 | 0.587346 | − | 0.809336i | \(-0.300173\pi\) | ||||
0.587346 | + | 0.809336i | \(0.300173\pi\) | |||||||
\(168\) | −0.389444 | −0.0300463 | ||||||||
\(169\) | 16.0536 | 1.23490 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.3271 | 1.86034 | ||||||||
\(172\) | −0.695233 | −0.0530110 | ||||||||
\(173\) | 11.5652 | 0.879284 | 0.439642 | − | 0.898173i | \(-0.355105\pi\) | ||||
0.439642 | + | 0.898173i | \(0.355105\pi\) | |||||||
\(174\) | 0.374907 | 0.0284216 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.0791 | −0.759744 | ||||||||
\(177\) | −0.220525 | −0.0165757 | ||||||||
\(178\) | −17.7674 | −1.33172 | ||||||||
\(179\) | −10.9935 | −0.821694 | −0.410847 | − | 0.911704i | \(-0.634767\pi\) | ||||
−0.410847 | + | 0.911704i | \(0.634767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.352647 | −0.0262120 | −0.0131060 | − | 0.999914i | \(-0.504172\pi\) | ||||
−0.0131060 | + | 0.999914i | \(0.504172\pi\) | |||||||
\(182\) | −27.6251 | −2.04771 | ||||||||
\(183\) | −0.175528 | −0.0129754 | ||||||||
\(184\) | −22.1966 | −1.63636 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.304451 | 0.0223234 | ||||||||
\(187\) | 14.4554 | 1.05708 | ||||||||
\(188\) | 0.0598998 | 0.00436864 | ||||||||
\(189\) | 0.812046 | 0.0590676 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1867 | 1.09887 | 0.549437 | − | 0.835535i | \(-0.314842\pi\) | ||||
0.549437 | + | 0.835535i | \(0.314842\pi\) | |||||||
\(192\) | −0.303181 | −0.0218802 | ||||||||
\(193\) | 0.151159 | 0.0108807 | 0.00544033 | − | 0.999985i | \(-0.498268\pi\) | ||||
0.00544033 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(194\) | 15.2295 | 1.09342 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.475126 | −0.0339376 | ||||||||
\(197\) | 26.5412 | 1.89098 | 0.945490 | − | 0.325653i | \(-0.105584\pi\) | ||||
0.945490 | + | 0.325653i | \(0.105584\pi\) | |||||||
\(198\) | 10.8973 | 0.774437 | ||||||||
\(199\) | 17.6403 | 1.25048 | 0.625242 | − | 0.780431i | \(-0.285000\pi\) | ||||
0.625242 | + | 0.780431i | \(0.285000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.194963 | −0.0137516 | ||||||||
\(202\) | 22.8589 | 1.60835 | ||||||||
\(203\) | 27.1681 | 1.90683 | ||||||||
\(204\) | 0.0145357 | 0.00101770 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.4104 | −1.42206 | ||||||||
\(207\) | 23.1363 | 1.60809 | ||||||||
\(208\) | −20.7594 | −1.43940 | ||||||||
\(209\) | −21.2312 | −1.46859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.78020 | −0.260240 | −0.130120 | − | 0.991498i | \(-0.541536\pi\) | ||||
−0.130120 | + | 0.991498i | \(0.541536\pi\) | |||||||
\(212\) | −0.576130 | −0.0395688 | ||||||||
\(213\) | 0.169227 | 0.0115952 | ||||||||
\(214\) | 1.08864 | 0.0744177 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.632961 | 0.0430676 | ||||||||
\(217\) | 22.0624 | 1.49769 | ||||||||
\(218\) | 17.1725 | 1.16307 | ||||||||
\(219\) | 0.202339 | 0.0136728 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.7729 | 2.00274 | ||||||||
\(222\) | −0.144592 | −0.00970437 | ||||||||
\(223\) | −16.3491 | −1.09482 | −0.547410 | − | 0.836865i | \(-0.684386\pi\) | ||||
−0.547410 | + | 0.836865i | \(0.684386\pi\) | |||||||
\(224\) | −1.49726 | −0.100040 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28.1644 | 1.87347 | ||||||||
\(227\) | 20.9681 | 1.39170 | 0.695851 | − | 0.718186i | \(-0.255027\pi\) | ||||
0.695851 | + | 0.718186i | \(0.255027\pi\) | |||||||
\(228\) | −0.0213491 | −0.00141388 | ||||||||
\(229\) | −15.2467 | −1.00753 | −0.503764 | − | 0.863841i | \(-0.668052\pi\) | ||||
−0.503764 | + | 0.863841i | \(0.668052\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.354272 | −0.0233094 | ||||||||
\(232\) | 21.1766 | 1.39031 | ||||||||
\(233\) | −17.5288 | −1.14835 | −0.574175 | − | 0.818732i | \(-0.694677\pi\) | ||||
−0.574175 | + | 0.818732i | \(0.694677\pi\) | |||||||
\(234\) | 22.4444 | 1.46724 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.431386 | −0.0280809 | ||||||||
\(237\) | −0.193374 | −0.0125610 | ||||||||
\(238\) | −28.3090 | −1.83500 | ||||||||
\(239\) | 0.809356 | 0.0523529 | 0.0261764 | − | 0.999657i | \(-0.491667\pi\) | ||||
0.0261764 | + | 0.999657i | \(0.491667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 5.76429 | 0.370543 | ||||||||
\(243\) | −0.989711 | −0.0634900 | ||||||||
\(244\) | −0.343364 | −0.0219816 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0794647 | 0.00506648 | ||||||||
\(247\) | −43.7284 | −2.78237 | ||||||||
\(248\) | 17.1969 | 1.09200 | ||||||||
\(249\) | 0.0934164 | 0.00592003 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.0352 | −1.20149 | −0.600745 | − | 0.799441i | \(-0.705129\pi\) | ||||
−0.600745 | + | 0.799441i | \(0.705129\pi\) | |||||||
\(252\) | 0.794074 | 0.0500220 | ||||||||
\(253\) | −20.1920 | −1.26946 | ||||||||
\(254\) | 7.32868 | 0.459842 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.71972 | −0.107482 | ||||||||
\(257\) | 19.3841 | 1.20915 | 0.604573 | − | 0.796550i | \(-0.293344\pi\) | ||||
0.604573 | + | 0.796550i | \(0.293344\pi\) | |||||||
\(258\) | 0.493520 | 0.0307252 | ||||||||
\(259\) | −10.4780 | −0.651074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.0731 | −1.36629 | ||||||||
\(262\) | 2.42481 | 0.149805 | ||||||||
\(263\) | 8.35304 | 0.515071 | 0.257535 | − | 0.966269i | \(-0.417090\pi\) | ||||
0.257535 | + | 0.966269i | \(0.417090\pi\) | |||||||
\(264\) | −0.276143 | −0.0169954 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 41.5784 | 2.54934 | ||||||||
\(267\) | −0.469296 | −0.0287204 | ||||||||
\(268\) | −0.381382 | −0.0232966 | ||||||||
\(269\) | 7.93093 | 0.483557 | 0.241779 | − | 0.970331i | \(-0.422269\pi\) | ||||
0.241779 | + | 0.970331i | \(0.422269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.54415 | −0.579766 | −0.289883 | − | 0.957062i | \(-0.593616\pi\) | ||||
−0.289883 | + | 0.957062i | \(0.593616\pi\) | |||||||
\(272\) | −21.2732 | −1.28988 | ||||||||
\(273\) | −0.729671 | −0.0441617 | ||||||||
\(274\) | 3.95277 | 0.238795 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.0203041 | −0.00122217 | ||||||||
\(277\) | −27.9456 | −1.67909 | −0.839544 | − | 0.543291i | \(-0.817178\pi\) | ||||
−0.839544 | + | 0.543291i | \(0.817178\pi\) | |||||||
\(278\) | −5.18567 | −0.311016 | ||||||||
\(279\) | −17.9249 | −1.07314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6875 | 1.71135 | 0.855676 | − | 0.517512i | \(-0.173142\pi\) | ||||
0.855676 | + | 0.517512i | \(0.173142\pi\) | |||||||
\(282\) | −0.0425206 | −0.00253207 | ||||||||
\(283\) | −14.4245 | −0.857449 | −0.428725 | − | 0.903435i | \(-0.641037\pi\) | ||||
−0.428725 | + | 0.903435i | \(0.641037\pi\) | |||||||
\(284\) | 0.331037 | 0.0196435 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.5881 | −1.15827 | ||||||||
\(287\) | 5.75851 | 0.339914 | ||||||||
\(288\) | 1.21647 | 0.0716812 | ||||||||
\(289\) | 13.5099 | 0.794698 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.402262 | 0.0235810 | ||||||||
\(292\) | 0.395811 | 0.0231631 | ||||||||
\(293\) | 28.2391 | 1.64975 | 0.824874 | − | 0.565316i | \(-0.191246\pi\) | ||||
0.824874 | + | 0.565316i | \(0.191246\pi\) | |||||||
\(294\) | 0.337274 | 0.0196702 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.16726 | −0.474712 | ||||||||
\(297\) | 0.575796 | 0.0334110 | ||||||||
\(298\) | 14.3148 | 0.829234 | ||||||||
\(299\) | −41.5880 | −2.40510 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.7635 | 2.06138 | ||||||||
\(302\) | 4.11060 | 0.236539 | ||||||||
\(303\) | 0.603778 | 0.0346862 | ||||||||
\(304\) | 31.2448 | 1.79201 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 23.0000 | 1.31482 | ||||||||
\(307\) | 29.8363 | 1.70285 | 0.851423 | − | 0.524479i | \(-0.175740\pi\) | ||||
0.851423 | + | 0.524479i | \(0.175740\pi\) | |||||||
\(308\) | −0.693018 | −0.0394884 | ||||||||
\(309\) | −0.539105 | −0.0306686 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0603 | 1.13752 | 0.568759 | − | 0.822504i | \(-0.307424\pi\) | ||||
0.568759 | + | 0.822504i | \(0.307424\pi\) | |||||||
\(312\) | −0.568753 | −0.0321993 | ||||||||
\(313\) | −11.9865 | −0.677516 | −0.338758 | − | 0.940874i | \(-0.610007\pi\) | ||||
−0.338758 | + | 0.940874i | \(0.610007\pi\) | |||||||
\(314\) | −6.41140 | −0.361816 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.378274 | −0.0212796 | ||||||||
\(317\) | −27.2280 | −1.52928 | −0.764639 | − | 0.644459i | \(-0.777083\pi\) | ||||
−0.764639 | + | 0.644459i | \(0.777083\pi\) | |||||||
\(318\) | 0.408973 | 0.0229341 | ||||||||
\(319\) | 19.2640 | 1.07858 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0287545 | 0.00160492 | ||||||||
\(322\) | 39.5432 | 2.20366 | ||||||||
\(323\) | −44.8109 | −2.49335 | ||||||||
\(324\) | −0.644867 | −0.0358259 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.82044 | 0.322365 | ||||||||
\(327\) | 0.453583 | 0.0250832 | ||||||||
\(328\) | 4.48856 | 0.247839 | ||||||||
\(329\) | −3.08131 | −0.169878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1507 | 0.942688 | 0.471344 | − | 0.881950i | \(-0.343769\pi\) | ||||
0.471344 | + | 0.881950i | \(0.343769\pi\) | |||||||
\(332\) | 0.182739 | 0.0100291 | ||||||||
\(333\) | 8.51303 | 0.466511 | ||||||||
\(334\) | −21.0797 | −1.15343 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.521363 | 0.0284427 | ||||||||
\(337\) | 4.40209 | 0.239797 | 0.119899 | − | 0.992786i | \(-0.461743\pi\) | ||||
0.119899 | + | 0.992786i | \(0.461743\pi\) | |||||||
\(338\) | −22.2923 | −1.21254 | ||||||||
\(339\) | 0.743915 | 0.0404039 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.6438 | 0.847157 | ||||||||
\(342\) | −33.7810 | −1.82667 | ||||||||
\(343\) | −1.39470 | −0.0753065 | ||||||||
\(344\) | 27.8764 | 1.50300 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0596 | −0.863368 | ||||||||
\(347\) | 4.06906 | 0.218438 | 0.109219 | − | 0.994018i | \(-0.465165\pi\) | ||||
0.109219 | + | 0.994018i | \(0.465165\pi\) | |||||||
\(348\) | 0.0193711 | 0.00103840 | ||||||||
\(349\) | 34.5033 | 1.84692 | 0.923459 | − | 0.383697i | \(-0.125349\pi\) | ||||
0.923459 | + | 0.383697i | \(0.125349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.18593 | 0.0633002 | ||||||||
\(352\) | −1.06166 | −0.0565866 | ||||||||
\(353\) | −8.89963 | −0.473679 | −0.236840 | − | 0.971549i | \(-0.576112\pi\) | ||||
−0.236840 | + | 0.971549i | \(0.576112\pi\) | |||||||
\(354\) | 0.306225 | 0.0162757 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.918025 | −0.0486552 | ||||||||
\(357\) | −0.747733 | −0.0395743 | ||||||||
\(358\) | 15.2658 | 0.806820 | ||||||||
\(359\) | 10.9527 | 0.578060 | 0.289030 | − | 0.957320i | \(-0.406667\pi\) | ||||
0.289030 | + | 0.957320i | \(0.406667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.8154 | 2.46397 | ||||||||
\(362\) | 0.489691 | 0.0257376 | ||||||||
\(363\) | 0.152254 | 0.00799126 | ||||||||
\(364\) | −1.42736 | −0.0748142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.243741 | 0.0127405 | ||||||||
\(367\) | −9.11480 | −0.475789 | −0.237894 | − | 0.971291i | \(-0.576457\pi\) | ||||
−0.237894 | + | 0.971291i | \(0.576457\pi\) | |||||||
\(368\) | 29.7154 | 1.54902 | ||||||||
\(369\) | −4.67859 | −0.243557 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.6367 | 1.53866 | ||||||||
\(372\) | 0.0157307 | 0.000815598 0 | ||||||||
\(373\) | 6.33820 | 0.328180 | 0.164090 | − | 0.986445i | \(-0.447531\pi\) | ||||
0.164090 | + | 0.986445i | \(0.447531\pi\) | |||||||
\(374\) | −20.0730 | −1.03795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.40177 | −0.123862 | ||||||||
\(377\) | 39.6769 | 2.04346 | ||||||||
\(378\) | −1.12762 | −0.0579985 | ||||||||
\(379\) | 20.0791 | 1.03139 | 0.515696 | − | 0.856772i | \(-0.327533\pi\) | ||||
0.515696 | + | 0.856772i | \(0.327533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.193575 | 0.00991712 | ||||||||
\(382\) | −21.0885 | −1.07898 | ||||||||
\(383\) | −13.2925 | −0.679214 | −0.339607 | − | 0.940567i | \(-0.610294\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(384\) | 0.391243 | 0.0199655 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.209901 | −0.0106837 | ||||||||
\(387\) | −29.0566 | −1.47703 | ||||||||
\(388\) | 0.786895 | 0.0399486 | ||||||||
\(389\) | −3.03200 | −0.153729 | −0.0768644 | − | 0.997042i | \(-0.524491\pi\) | ||||
−0.0768644 | + | 0.997042i | \(0.524491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.6175 | −2.15526 | ||||||||
\(392\) | 19.0509 | 0.962216 | ||||||||
\(393\) | 0.0640473 | 0.00323076 | ||||||||
\(394\) | −36.8554 | −1.85675 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.563052 | 0.0282944 | ||||||||
\(397\) | −2.31275 | −0.116073 | −0.0580367 | − | 0.998314i | \(-0.518484\pi\) | ||||
−0.0580367 | + | 0.998314i | \(0.518484\pi\) | |||||||
\(398\) | −24.4955 | −1.22785 | ||||||||
\(399\) | 1.09822 | 0.0549799 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0279 | 0.900269 | 0.450134 | − | 0.892961i | \(-0.351376\pi\) | ||||
0.450134 | + | 0.892961i | \(0.351376\pi\) | |||||||
\(402\) | 0.270729 | 0.0135027 | ||||||||
\(403\) | 32.2204 | 1.60501 | ||||||||
\(404\) | 1.18110 | 0.0587618 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −37.7261 | −1.87231 | ||||||||
\(407\) | −7.42964 | −0.368274 | ||||||||
\(408\) | −0.582832 | −0.0288545 | ||||||||
\(409\) | −14.6411 | −0.723956 | −0.361978 | − | 0.932187i | \(-0.617899\pi\) | ||||
−0.361978 | + | 0.932187i | \(0.617899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.104406 | 0.00514995 | ||||||||
\(412\) | −1.05458 | −0.0519556 | ||||||||
\(413\) | 22.1910 | 1.09195 | ||||||||
\(414\) | −32.1275 | −1.57898 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.18663 | −0.107208 | ||||||||
\(417\) | −0.136971 | −0.00670748 | ||||||||
\(418\) | 29.4819 | 1.44201 | ||||||||
\(419\) | 11.8773 | 0.580242 | 0.290121 | − | 0.956990i | \(-0.406304\pi\) | ||||
0.290121 | + | 0.956990i | \(0.406304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8898 | −0.676945 | −0.338473 | − | 0.940976i | \(-0.609910\pi\) | ||||
−0.338473 | + | 0.940976i | \(0.609910\pi\) | |||||||
\(422\) | 5.24924 | 0.255529 | ||||||||
\(423\) | 2.50346 | 0.121722 | ||||||||
\(424\) | 23.1008 | 1.12187 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.234991 | −0.0113853 | ||||||||
\(427\) | 17.6630 | 0.854772 | ||||||||
\(428\) | 0.0562489 | 0.00271889 | ||||||||
\(429\) | −0.517386 | −0.0249796 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5438 | 0.700551 | 0.350276 | − | 0.936647i | \(-0.386088\pi\) | ||||
0.350276 | + | 0.936647i | \(0.386088\pi\) | |||||||
\(432\) | −0.847367 | −0.0407690 | ||||||||
\(433\) | −34.3657 | −1.65151 | −0.825754 | − | 0.564030i | \(-0.809250\pi\) | ||||
−0.825754 | + | 0.564030i | \(0.809250\pi\) | |||||||
\(434\) | −30.6362 | −1.47059 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.887288 | 0.0424934 | ||||||||
\(437\) | 62.5939 | 2.99427 | ||||||||
\(438\) | −0.280971 | −0.0134253 | ||||||||
\(439\) | −9.72345 | −0.464075 | −0.232037 | − | 0.972707i | \(-0.574539\pi\) | ||||
−0.232037 | + | 0.972707i | \(0.574539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.8574 | −0.945593 | ||||||||
\(442\) | −41.3430 | −1.96649 | ||||||||
\(443\) | 23.9451 | 1.13767 | 0.568833 | − | 0.822453i | \(-0.307395\pi\) | ||||
0.568833 | + | 0.822453i | \(0.307395\pi\) | |||||||
\(444\) | −0.00747092 | −0.000354554 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.7027 | 1.07500 | ||||||||
\(447\) | 0.378101 | 0.0178836 | ||||||||
\(448\) | 30.5084 | 1.44139 | ||||||||
\(449\) | 14.7162 | 0.694499 | 0.347250 | − | 0.937773i | \(-0.387116\pi\) | ||||
0.347250 | + | 0.937773i | \(0.387116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.08318 | 0.192269 | ||||||||
\(452\) | 1.45523 | 0.0684482 | ||||||||
\(453\) | 0.108575 | 0.00510128 | ||||||||
\(454\) | −29.1166 | −1.36651 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.856026 | 0.0400871 | ||||||||
\(457\) | −24.2946 | −1.13646 | −0.568228 | − | 0.822871i | \(-0.692371\pi\) | ||||
−0.568228 | + | 0.822871i | \(0.692371\pi\) | |||||||
\(458\) | 21.1717 | 0.989291 | ||||||||
\(459\) | 1.21529 | 0.0567247 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.5144 | 0.536281 | 0.268140 | − | 0.963380i | \(-0.413591\pi\) | ||||
0.268140 | + | 0.963380i | \(0.413591\pi\) | |||||||
\(462\) | 0.491947 | 0.0228875 | ||||||||
\(463\) | 5.82777 | 0.270840 | 0.135420 | − | 0.990788i | \(-0.456762\pi\) | ||||
0.135420 | + | 0.990788i | \(0.456762\pi\) | |||||||
\(464\) | −28.3499 | −1.31611 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.3408 | 1.12756 | ||||||||
\(467\) | −10.0402 | −0.464605 | −0.232302 | − | 0.972644i | \(-0.574626\pi\) | ||||
−0.232302 | + | 0.972644i | \(0.574626\pi\) | |||||||
\(468\) | 1.15968 | 0.0536063 | ||||||||
\(469\) | 19.6187 | 0.905909 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.169346 | −0.00780306 | ||||||||
\(472\) | 17.2971 | 0.796163 | ||||||||
\(473\) | 25.3588 | 1.16600 | ||||||||
\(474\) | 0.268522 | 0.0123336 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.46270 | −0.0670427 | ||||||||
\(477\) | −24.0788 | −1.10249 | ||||||||
\(478\) | −1.12388 | −0.0514053 | ||||||||
\(479\) | 7.83576 | 0.358025 | 0.179012 | − | 0.983847i | \(-0.442710\pi\) | ||||
0.179012 | + | 0.983847i | \(0.442710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.3023 | −0.697727 | ||||||||
\(482\) | 1.38861 | 0.0632497 | ||||||||
\(483\) | 1.04447 | 0.0475249 | ||||||||
\(484\) | 0.297835 | 0.0135380 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.37433 | 0.0623408 | ||||||||
\(487\) | −42.5597 | −1.92856 | −0.964281 | − | 0.264880i | \(-0.914668\pi\) | ||||
−0.964281 | + | 0.264880i | \(0.914668\pi\) | |||||||
\(488\) | 13.7677 | 0.623234 | ||||||||
\(489\) | 0.153737 | 0.00695223 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8949 | −0.581938 | −0.290969 | − | 0.956732i | \(-0.593978\pi\) | ||||
−0.290969 | + | 0.956732i | \(0.593978\pi\) | |||||||
\(492\) | 0.00410587 | 0.000185107 0 | ||||||||
\(493\) | 40.6591 | 1.83119 | ||||||||
\(494\) | 60.7220 | 2.73201 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.0221 | −1.03372 | ||||||||
\(497\) | −17.0289 | −0.763851 | ||||||||
\(498\) | −0.129719 | −0.00581287 | ||||||||
\(499\) | −3.36405 | −0.150595 | −0.0752977 | − | 0.997161i | \(-0.523991\pi\) | ||||
−0.0752977 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.556784 | −0.0248753 | ||||||||
\(502\) | 26.4325 | 1.17974 | ||||||||
\(503\) | −34.4241 | −1.53489 | −0.767447 | − | 0.641113i | \(-0.778473\pi\) | ||||
−0.767447 | + | 0.641113i | \(0.778473\pi\) | |||||||
\(504\) | −31.8396 | −1.41825 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28.0388 | 1.24648 | ||||||||
\(507\) | −0.588813 | −0.0261501 | ||||||||
\(508\) | 0.378666 | 0.0168006 | ||||||||
\(509\) | 37.5965 | 1.66643 | 0.833217 | − | 0.552947i | \(-0.186497\pi\) | ||||
0.833217 | + | 0.552947i | \(0.186497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.3610 | −0.900716 | ||||||||
\(512\) | 23.7220 | 1.04837 | ||||||||
\(513\) | −1.78493 | −0.0788067 | ||||||||
\(514\) | −26.9170 | −1.18726 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0254997 | 0.00112256 | ||||||||
\(517\) | −2.18486 | −0.0960900 | ||||||||
\(518\) | 14.5500 | 0.639289 | ||||||||
\(519\) | −0.424186 | −0.0186197 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.9298 | −1.70555 | −0.852774 | − | 0.522281i | \(-0.825081\pi\) | ||||
−0.852774 | + | 0.522281i | \(0.825081\pi\) | |||||||
\(522\) | 30.6511 | 1.34156 | ||||||||
\(523\) | −0.192415 | −0.00841374 | −0.00420687 | − | 0.999991i | \(-0.501339\pi\) | ||||
−0.00420687 | + | 0.999991i | \(0.501339\pi\) | |||||||
\(524\) | 0.125288 | 0.00547322 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.5992 | −0.505747 | ||||||||
\(527\) | 33.0180 | 1.43829 | ||||||||
\(528\) | 0.369682 | 0.0160883 | ||||||||
\(529\) | 36.5301 | 1.58826 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.0294 | −0.782408 | ||||||||
\(532\) | 2.14832 | 0.0931413 | ||||||||
\(533\) | 8.40985 | 0.364271 | ||||||||
\(534\) | 0.651671 | 0.0282006 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.2921 | 0.660518 | ||||||||
\(537\) | 0.403219 | 0.0174002 | ||||||||
\(538\) | −11.0130 | −0.474805 | ||||||||
\(539\) | 17.3303 | 0.746470 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9233 | −0.985548 | −0.492774 | − | 0.870157i | \(-0.664017\pi\) | ||||
−0.492774 | + | 0.870157i | \(0.664017\pi\) | |||||||
\(542\) | 13.2532 | 0.569272 | ||||||||
\(543\) | 0.0129343 | 0.000555066 0 | ||||||||
\(544\) | −2.24076 | −0.0960718 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.01323 | 0.0433623 | ||||||||
\(547\) | 18.0310 | 0.770950 | 0.385475 | − | 0.922718i | \(-0.374038\pi\) | ||||
0.385475 | + | 0.922718i | \(0.374038\pi\) | |||||||
\(548\) | 0.204236 | 0.00872452 | ||||||||
\(549\) | −14.3506 | −0.612467 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.7174 | −2.54405 | ||||||||
\(552\) | 0.814126 | 0.0346515 | ||||||||
\(553\) | 19.4588 | 0.827473 | ||||||||
\(554\) | 38.8057 | 1.64870 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.267939 | −0.0113631 | ||||||||
\(557\) | 23.7519 | 1.00640 | 0.503201 | − | 0.864170i | \(-0.332156\pi\) | ||||
0.503201 | + | 0.864170i | \(0.332156\pi\) | |||||||
\(558\) | 24.8908 | 1.05371 | ||||||||
\(559\) | 52.2298 | 2.20909 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.530194 | −0.0223848 | ||||||||
\(562\) | −39.8359 | −1.68038 | ||||||||
\(563\) | 6.47734 | 0.272987 | 0.136494 | − | 0.990641i | \(-0.456417\pi\) | ||||
0.136494 | + | 0.990641i | \(0.456417\pi\) | |||||||
\(564\) | −0.00219700 | −9.25104e−5 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.0301 | 0.841929 | ||||||||
\(567\) | 33.1727 | 1.39312 | ||||||||
\(568\) | −13.2734 | −0.556941 | ||||||||
\(569\) | 16.7745 | 0.703223 | 0.351611 | − | 0.936146i | \(-0.385634\pi\) | ||||
0.351611 | + | 0.936146i | \(0.385634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.8775 | 1.20849 | 0.604243 | − | 0.796800i | \(-0.293476\pi\) | ||||
0.604243 | + | 0.796800i | \(0.293476\pi\) | |||||||
\(572\) | −1.01210 | −0.0423179 | ||||||||
\(573\) | −0.557017 | −0.0232697 | ||||||||
\(574\) | −7.99636 | −0.333762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.7870 | −1.03279 | ||||||||
\(577\) | −15.4881 | −0.644779 | −0.322390 | − | 0.946607i | \(-0.604486\pi\) | ||||
−0.322390 | + | 0.946607i | \(0.604486\pi\) | |||||||
\(578\) | −18.7600 | −0.780313 | ||||||||
\(579\) | −0.00554419 | −0.000230409 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.40029 | −0.389990 | ||||||||
\(582\) | −0.558587 | −0.0231542 | ||||||||
\(583\) | 21.0145 | 0.870330 | ||||||||
\(584\) | −15.8707 | −0.656732 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.2133 | −1.61989 | ||||||||
\(587\) | −10.7554 | −0.443922 | −0.221961 | − | 0.975056i | \(-0.571246\pi\) | ||||
−0.221961 | + | 0.975056i | \(0.571246\pi\) | |||||||
\(588\) | 0.0174266 | 0.000718662 0 | ||||||||
\(589\) | −48.4947 | −1.99819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.973474 | −0.0400434 | ||||||||
\(592\) | 10.9338 | 0.449377 | ||||||||
\(593\) | 11.9957 | 0.492604 | 0.246302 | − | 0.969193i | \(-0.420785\pi\) | ||||
0.246302 | + | 0.969193i | \(0.420785\pi\) | |||||||
\(594\) | −0.799558 | −0.0328063 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.739632 | 0.0302965 | ||||||||
\(597\) | −0.647007 | −0.0264803 | ||||||||
\(598\) | 57.7498 | 2.36156 | ||||||||
\(599\) | 26.0997 | 1.06641 | 0.533203 | − | 0.845987i | \(-0.320988\pi\) | ||||
0.533203 | + | 0.845987i | \(0.320988\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1996 | 0.987124 | 0.493562 | − | 0.869711i | \(-0.335695\pi\) | ||||
0.493562 | + | 0.869711i | \(0.335695\pi\) | |||||||
\(602\) | −49.6618 | −2.02406 | ||||||||
\(603\) | −15.9395 | −0.649107 | ||||||||
\(604\) | 0.212391 | 0.00864206 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.838416 | −0.0340583 | ||||||||
\(607\) | 38.7637 | 1.57337 | 0.786685 | − | 0.617355i | \(-0.211796\pi\) | ||||
0.786685 | + | 0.617355i | \(0.211796\pi\) | |||||||
\(608\) | 3.29108 | 0.133471 | ||||||||
\(609\) | −0.996469 | −0.0403790 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.50001 | −0.182051 | ||||||||
\(612\) | 1.18839 | 0.0480378 | ||||||||
\(613\) | −0.0930290 | −0.00375741 | −0.00187870 | − | 0.999998i | \(-0.500598\pi\) | ||||
−0.00187870 | + | 0.999998i | \(0.500598\pi\) | |||||||
\(614\) | −41.4311 | −1.67202 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.7876 | 1.11959 | ||||||||
\(617\) | −21.3227 | −0.858419 | −0.429209 | − | 0.903205i | \(-0.641208\pi\) | ||||
−0.429209 | + | 0.903205i | \(0.641208\pi\) | |||||||
\(618\) | 0.748609 | 0.0301135 | ||||||||
\(619\) | 25.9696 | 1.04381 | 0.521904 | − | 0.853004i | \(-0.325222\pi\) | ||||
0.521904 | + | 0.853004i | \(0.325222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.69756 | −0.0681209 | ||||||||
\(622\) | −27.8561 | −1.11693 | ||||||||
\(623\) | 47.2242 | 1.89200 | ||||||||
\(624\) | 0.761409 | 0.0304808 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.6446 | 0.665252 | ||||||||
\(627\) | 0.778714 | 0.0310989 | ||||||||
\(628\) | −0.331271 | −0.0132192 | ||||||||
\(629\) | −15.6811 | −0.625248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6418 | −0.742120 | −0.371060 | − | 0.928609i | \(-0.621006\pi\) | ||||
−0.371060 | + | 0.928609i | \(0.621006\pi\) | |||||||
\(632\) | 15.1675 | 0.603329 | ||||||||
\(633\) | 0.138650 | 0.00551083 | ||||||||
\(634\) | 37.8092 | 1.50160 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0211312 | 0.000837908 0 | ||||||||
\(637\) | 35.6942 | 1.41425 | ||||||||
\(638\) | −26.7503 | −1.05906 | ||||||||
\(639\) | 13.8354 | 0.547319 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4174 | −0.885432 | −0.442716 | − | 0.896662i | \(-0.645985\pi\) | ||||
−0.442716 | + | 0.896662i | \(0.645985\pi\) | |||||||
\(642\) | −0.0399289 | −0.00157587 | ||||||||
\(643\) | 35.0341 | 1.38161 | 0.690805 | − | 0.723041i | \(-0.257256\pi\) | ||||
0.690805 | + | 0.723041i | \(0.257256\pi\) | |||||||
\(644\) | 2.04316 | 0.0805118 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 62.2251 | 2.44821 | ||||||||
\(647\) | −13.4824 | −0.530047 | −0.265023 | − | 0.964242i | \(-0.585380\pi\) | ||||
−0.265023 | + | 0.964242i | \(0.585380\pi\) | |||||||
\(648\) | 25.8569 | 1.01576 | ||||||||
\(649\) | 15.7349 | 0.617649 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.809203 | −0.0317152 | ||||||||
\(652\) | 0.300737 | 0.0117778 | ||||||||
\(653\) | 38.6066 | 1.51079 | 0.755397 | − | 0.655268i | \(-0.227444\pi\) | ||||
0.755397 | + | 0.655268i | \(0.227444\pi\) | |||||||
\(654\) | −0.629852 | −0.0246292 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.00899 | −0.234612 | ||||||||
\(657\) | 16.5425 | 0.645386 | ||||||||
\(658\) | 4.27876 | 0.166803 | ||||||||
\(659\) | −10.6663 | −0.415501 | −0.207750 | − | 0.978182i | \(-0.566614\pi\) | ||||
−0.207750 | + | 0.978182i | \(0.566614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.68886 | −0.182376 | −0.0911878 | − | 0.995834i | \(-0.529066\pi\) | ||||
−0.0911878 | + | 0.995834i | \(0.529066\pi\) | |||||||
\(662\) | −23.8157 | −0.925624 | ||||||||
\(663\) | −1.09201 | −0.0424100 | ||||||||
\(664\) | −7.32720 | −0.284350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.8213 | −0.458067 | ||||||||
\(667\) | −56.7944 | −2.19909 | ||||||||
\(668\) | −1.08917 | −0.0421412 | ||||||||
\(669\) | 0.599652 | 0.0231839 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.5243 | 0.483494 | ||||||||
\(672\) | 0.0549163 | 0.00211844 | ||||||||
\(673\) | −19.9709 | −0.769820 | −0.384910 | − | 0.922954i | \(-0.625768\pi\) | ||||
−0.384910 | + | 0.922954i | \(0.625768\pi\) | |||||||
\(674\) | −6.11281 | −0.235457 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.15182 | −0.0443009 | ||||||||
\(677\) | −10.1509 | −0.390132 | −0.195066 | − | 0.980790i | \(-0.562492\pi\) | ||||
−0.195066 | + | 0.980790i | \(0.562492\pi\) | |||||||
\(678\) | −1.03301 | −0.0396726 | ||||||||
\(679\) | −40.4787 | −1.55343 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.769066 | −0.0294707 | ||||||||
\(682\) | −21.7232 | −0.831823 | ||||||||
\(683\) | 34.4938 | 1.31987 | 0.659934 | − | 0.751324i | \(-0.270584\pi\) | ||||
0.659934 | + | 0.751324i | \(0.270584\pi\) | |||||||
\(684\) | −1.74543 | −0.0667382 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.93669 | 0.0739433 | ||||||||
\(687\) | 0.559216 | 0.0213354 | ||||||||
\(688\) | −37.3192 | −1.42278 | ||||||||
\(689\) | 43.2821 | 1.64892 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.0773 | −0.992027 | −0.496013 | − | 0.868315i | \(-0.665203\pi\) | ||||
−0.496013 | + | 0.868315i | \(0.665203\pi\) | |||||||
\(692\) | −0.829782 | −0.0315436 | ||||||||
\(693\) | −28.9640 | −1.10025 | ||||||||
\(694\) | −5.65035 | −0.214484 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.776713 | −0.0294412 | ||||||||
\(697\) | 8.61804 | 0.326431 | ||||||||
\(698\) | −47.9118 | −1.81349 | ||||||||
\(699\) | 0.642920 | 0.0243175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.3525 | 1.07086 | 0.535430 | − | 0.844579i | \(-0.320149\pi\) | ||||
0.535430 | + | 0.844579i | \(0.320149\pi\) | |||||||
\(702\) | −1.64680 | −0.0621544 | ||||||||
\(703\) | 23.0315 | 0.868648 | ||||||||
\(704\) | 21.6325 | 0.815307 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.3582 | 0.465105 | ||||||||
\(707\) | −60.7569 | −2.28500 | ||||||||
\(708\) | 0.0158223 | 0.000594640 0 | ||||||||
\(709\) | −4.52985 | −0.170122 | −0.0850610 | − | 0.996376i | \(-0.527109\pi\) | ||||
−0.0850610 | + | 0.996376i | \(0.527109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.8096 | −0.592906 | ||||||||
\(712\) | 36.8096 | 1.37950 | ||||||||
\(713\) | −46.1210 | −1.72725 | ||||||||
\(714\) | 1.03831 | 0.0388579 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.788767 | 0.0294776 | ||||||||
\(717\) | −0.0296855 | −0.00110862 | ||||||||
\(718\) | −15.2091 | −0.567597 | ||||||||
\(719\) | −32.1437 | −1.19876 | −0.599379 | − | 0.800466i | \(-0.704586\pi\) | ||||
−0.599379 | + | 0.800466i | \(0.704586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 54.2489 | 2.02033 | ||||||||
\(722\) | −65.0085 | −2.41937 | ||||||||
\(723\) | 0.0366779 | 0.00136407 | ||||||||
\(724\) | 0.0253018 | 0.000940336 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.211422 | −0.00784661 | ||||||||
\(727\) | 1.21358 | 0.0450090 | 0.0225045 | − | 0.999747i | \(-0.492836\pi\) | ||||
0.0225045 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(728\) | 57.2323 | 2.12117 | ||||||||
\(729\) | −26.9274 | −0.997310 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 53.5227 | 1.97961 | ||||||||
\(732\) | 0.0125939 | 0.000465482 0 | ||||||||
\(733\) | −15.9118 | −0.587715 | −0.293858 | − | 0.955849i | \(-0.594939\pi\) | ||||
−0.293858 | + | 0.955849i | \(0.594939\pi\) | |||||||
\(734\) | 12.6570 | 0.467177 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.12999 | 0.115373 | ||||||||
\(737\) | 13.9110 | 0.512419 | ||||||||
\(738\) | 6.49675 | 0.239149 | ||||||||
\(739\) | 38.0619 | 1.40013 | 0.700066 | − | 0.714079i | \(-0.253154\pi\) | ||||
0.700066 | + | 0.714079i | \(0.253154\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.60387 | 0.0589195 | ||||||||
\(742\) | −41.1540 | −1.51081 | ||||||||
\(743\) | 19.2213 | 0.705161 | 0.352581 | − | 0.935781i | \(-0.385304\pi\) | ||||
0.352581 | + | 0.935781i | \(0.385304\pi\) | |||||||
\(744\) | −0.630745 | −0.0231242 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.80132 | −0.322239 | ||||||||
\(747\) | 7.63740 | 0.279438 | ||||||||
\(748\) | −1.03715 | −0.0379220 | ||||||||
\(749\) | −2.89350 | −0.105726 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.13459 | −0.187364 | −0.0936820 | − | 0.995602i | \(-0.529864\pi\) | ||||
−0.0936820 | + | 0.995602i | \(0.529864\pi\) | |||||||
\(752\) | 3.21534 | 0.117251 | ||||||||
\(753\) | 0.698170 | 0.0254427 | ||||||||
\(754\) | −55.0959 | −2.00647 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.0582630 | −0.00211900 | ||||||||
\(757\) | −9.04957 | −0.328912 | −0.164456 | − | 0.986384i | \(-0.552587\pi\) | ||||
−0.164456 | + | 0.986384i | \(0.552587\pi\) | |||||||
\(758\) | −27.8821 | −1.01272 | ||||||||
\(759\) | 0.740598 | 0.0268820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.1984 | 0.877193 | 0.438596 | − | 0.898684i | \(-0.355476\pi\) | ||||
0.438596 | + | 0.898684i | \(0.355476\pi\) | |||||||
\(762\) | −0.268800 | −0.00973761 | ||||||||
\(763\) | −45.6431 | −1.65239 | ||||||||
\(764\) | −1.08962 | −0.0394212 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4581 | 0.666919 | ||||||||
\(767\) | 32.4082 | 1.17019 | ||||||||
\(768\) | 0.0630757 | 0.00227605 | ||||||||
\(769\) | −18.9691 | −0.684042 | −0.342021 | − | 0.939692i | \(-0.611111\pi\) | ||||
−0.342021 | + | 0.939692i | \(0.611111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.710967 | −0.0256048 | ||||||||
\(772\) | −0.0108454 | −0.000390335 0 | ||||||||
\(773\) | −7.02815 | −0.252785 | −0.126393 | − | 0.991980i | \(-0.540340\pi\) | ||||
−0.126393 | + | 0.991980i | \(0.540340\pi\) | |||||||
\(774\) | 40.3484 | 1.45029 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31.5518 | −1.13264 | ||||||||
\(777\) | 0.384312 | 0.0137871 | ||||||||
\(778\) | 4.21029 | 0.150946 | ||||||||
\(779\) | −12.6576 | −0.453506 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0747 | −0.432065 | ||||||||
\(782\) | 59.1794 | 2.11625 | ||||||||
\(783\) | 1.61955 | 0.0578781 | ||||||||
\(784\) | −25.5041 | −0.910862 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.0889370 | −0.00317228 | ||||||||
\(787\) | 36.9565 | 1.31736 | 0.658678 | − | 0.752425i | \(-0.271116\pi\) | ||||
0.658678 | + | 0.752425i | \(0.271116\pi\) | |||||||
\(788\) | −1.90429 | −0.0678374 | ||||||||
\(789\) | −0.306372 | −0.0109071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −74.8585 | −2.66166 | ||||||||
\(792\) | −22.5764 | −0.802219 | ||||||||
\(793\) | 25.7954 | 0.916022 | ||||||||
\(794\) | 3.21152 | 0.113972 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.26566 | −0.0448601 | ||||||||
\(797\) | 32.9379 | 1.16672 | 0.583359 | − | 0.812214i | \(-0.301738\pi\) | ||||
0.583359 | + | 0.812214i | \(0.301738\pi\) | |||||||
\(798\) | −1.52501 | −0.0539847 | ||||||||
\(799\) | −4.61141 | −0.163140 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.3680 | −1.35567 | ||||||||
\(802\) | −25.0338 | −0.883973 | ||||||||
\(803\) | −14.4373 | −0.509481 | ||||||||
\(804\) | 0.0139883 | 0.000493329 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44.7418 | −1.57596 | ||||||||
\(807\) | −0.290890 | −0.0102398 | ||||||||
\(808\) | −47.3579 | −1.66604 | ||||||||
\(809\) | 34.4463 | 1.21107 | 0.605534 | − | 0.795819i | \(-0.292959\pi\) | ||||
0.605534 | + | 0.795819i | \(0.292959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.2181 | 1.72828 | 0.864140 | − | 0.503251i | \(-0.167863\pi\) | ||||
0.864140 | + | 0.503251i | \(0.167863\pi\) | |||||||
\(812\) | −1.94927 | −0.0684059 | ||||||||
\(813\) | 0.350059 | 0.0122771 | ||||||||
\(814\) | 10.3169 | 0.361607 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.780258 | 0.0273145 | ||||||||
\(817\) | −78.6107 | −2.75024 | ||||||||
\(818\) | 20.3309 | 0.710852 | ||||||||
\(819\) | −59.6553 | −2.08452 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0723 | −0.421328 | −0.210664 | − | 0.977559i | \(-0.567563\pi\) | ||||
−0.210664 | + | 0.977559i | \(0.567563\pi\) | |||||||
\(822\) | −0.144979 | −0.00505673 | ||||||||
\(823\) | −27.1896 | −0.947770 | −0.473885 | − | 0.880587i | \(-0.657149\pi\) | ||||
−0.473885 | + | 0.880587i | \(0.657149\pi\) | |||||||
\(824\) | 42.2851 | 1.47307 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.8147 | −1.07218 | ||||||||
\(827\) | −25.6452 | −0.891772 | −0.445886 | − | 0.895090i | \(-0.647111\pi\) | ||||
−0.445886 | + | 0.895090i | \(0.647111\pi\) | |||||||
\(828\) | −1.66000 | −0.0576888 | ||||||||
\(829\) | −21.3080 | −0.740057 | −0.370029 | − | 0.929020i | \(-0.620652\pi\) | ||||
−0.370029 | + | 0.929020i | \(0.620652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.02499 | 0.0355564 | ||||||||
\(832\) | 44.5551 | 1.54467 | ||||||||
\(833\) | 36.5778 | 1.26734 | ||||||||
\(834\) | 0.190199 | 0.00658607 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.52330 | 0.0526845 | ||||||||
\(837\) | 1.31519 | 0.0454597 | ||||||||
\(838\) | −16.4929 | −0.569739 | ||||||||
\(839\) | 16.2665 | 0.561582 | 0.280791 | − | 0.959769i | \(-0.409403\pi\) | ||||
0.280791 | + | 0.959769i | \(0.409403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.1844 | 0.868429 | ||||||||
\(842\) | 19.2875 | 0.664692 | ||||||||
\(843\) | −1.05220 | −0.0362396 | ||||||||
\(844\) | 0.271223 | 0.00933589 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.47634 | −0.119519 | ||||||||
\(847\) | −15.3210 | −0.526435 | ||||||||
\(848\) | −30.9259 | −1.06200 | ||||||||
\(849\) | 0.529061 | 0.0181573 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.9041 | 0.750864 | ||||||||
\(852\) | −0.0121418 | −0.000415970 0 | ||||||||
\(853\) | −30.7507 | −1.05288 | −0.526442 | − | 0.850211i | \(-0.676474\pi\) | ||||
−0.526442 | + | 0.850211i | \(0.676474\pi\) | |||||||
\(854\) | −24.5271 | −0.839300 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.25538 | −0.0770874 | ||||||||
\(857\) | 7.02517 | 0.239975 | 0.119988 | − | 0.992775i | \(-0.461715\pi\) | ||||
0.119988 | + | 0.992775i | \(0.461715\pi\) | |||||||
\(858\) | 0.718450 | 0.0245275 | ||||||||
\(859\) | −2.64135 | −0.0901215 | −0.0450608 | − | 0.998984i | \(-0.514348\pi\) | ||||
−0.0450608 | + | 0.998984i | \(0.514348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.211210 | −0.00719802 | ||||||||
\(862\) | −20.1958 | −0.687871 | ||||||||
\(863\) | −0.483719 | −0.0164660 | −0.00823299 | − | 0.999966i | \(-0.502621\pi\) | ||||
−0.00823299 | + | 0.999966i | \(0.502621\pi\) | |||||||
\(864\) | −0.0892551 | −0.00303652 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 47.7207 | 1.62162 | ||||||||
\(867\) | −0.495513 | −0.0168285 | ||||||||
\(868\) | −1.58294 | −0.0537286 | ||||||||
\(869\) | 13.7976 | 0.468052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6516 | 0.970822 | ||||||||
\(872\) | −35.5772 | −1.20480 | ||||||||
\(873\) | 32.8875 | 1.11307 | ||||||||
\(874\) | −86.9188 | −2.94007 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0145175 | −0.000490502 0 | ||||||||
\(877\) | −12.5713 | −0.424501 | −0.212251 | − | 0.977215i | \(-0.568079\pi\) | ||||
−0.212251 | + | 0.977215i | \(0.568079\pi\) | |||||||
\(878\) | 13.5021 | 0.455675 | ||||||||
\(879\) | −1.03575 | −0.0349351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.5085 | −0.623567 | −0.311784 | − | 0.950153i | \(-0.600926\pi\) | ||||
−0.311784 | + | 0.950153i | \(0.600926\pi\) | |||||||
\(882\) | 27.5743 | 0.928476 | ||||||||
\(883\) | 4.07979 | 0.137296 | 0.0686479 | − | 0.997641i | \(-0.478132\pi\) | ||||
0.0686479 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(884\) | −2.13615 | −0.0718466 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.2505 | −1.11707 | ||||||||
\(887\) | −6.49890 | −0.218212 | −0.109106 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109106 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(888\) | 0.299558 | 0.0100525 | ||||||||
\(889\) | −19.4790 | −0.653304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.5217 | 0.788005 | ||||||||
\(892\) | 1.17302 | 0.0392758 | ||||||||
\(893\) | 6.77294 | 0.226648 | ||||||||
\(894\) | −0.525036 | −0.0175598 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −39.3699 | −1.31526 | ||||||||
\(897\) | 1.52536 | 0.0509303 | ||||||||
\(898\) | −20.4351 | −0.681928 | ||||||||
\(899\) | 44.0016 | 1.46753 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.3535 | 1.47763 | ||||||||
\(902\) | −5.66996 | −0.188789 | ||||||||
\(903\) | −1.31173 | −0.0436517 | ||||||||
\(904\) | −58.3496 | −1.94068 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.150768 | −0.00500894 | ||||||||
\(907\) | 4.17469 | 0.138618 | 0.0693091 | − | 0.997595i | \(-0.477921\pi\) | ||||
0.0693091 | + | 0.997595i | \(0.477921\pi\) | |||||||
\(908\) | −1.50443 | −0.0499262 | ||||||||
\(909\) | 49.3628 | 1.63726 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.0766 | 1.82477 | 0.912385 | − | 0.409333i | \(-0.134239\pi\) | ||||
0.912385 | + | 0.409333i | \(0.134239\pi\) | |||||||
\(912\) | −1.14599 | −0.0379476 | ||||||||
\(913\) | −6.66544 | −0.220594 | ||||||||
\(914\) | 33.7359 | 1.11588 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.09392 | 0.0361443 | ||||||||
\(917\) | −6.44494 | −0.212831 | ||||||||
\(918\) | −1.68756 | −0.0556979 | ||||||||
\(919\) | −29.2769 | −0.965755 | −0.482877 | − | 0.875688i | \(-0.660408\pi\) | ||||
−0.482877 | + | 0.875688i | \(0.660408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.09433 | −0.0360595 | ||||||||
\(922\) | −15.9891 | −0.526574 | ||||||||
\(923\) | −24.8694 | −0.818586 | ||||||||
\(924\) | 0.0254184 | 0.000836205 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.09253 | −0.265937 | ||||||||
\(927\) | −44.0753 | −1.44762 | ||||||||
\(928\) | −2.98615 | −0.0980253 | ||||||||
\(929\) | 24.0911 | 0.790403 | 0.395201 | − | 0.918595i | \(-0.370675\pi\) | ||||
0.395201 | + | 0.918595i | \(0.370675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.7230 | −1.76070 | ||||||||
\(932\) | 1.25766 | 0.0411962 | ||||||||
\(933\) | −0.735771 | −0.0240881 | ||||||||
\(934\) | 13.9420 | 0.456195 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −46.4992 | −1.51987 | ||||||||
\(937\) | 44.1001 | 1.44069 | 0.720344 | − | 0.693617i | \(-0.243984\pi\) | ||||
0.720344 | + | 0.693617i | \(0.243984\pi\) | |||||||
\(938\) | −27.2429 | −0.889511 | ||||||||
\(939\) | 0.439639 | 0.0143471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.9838 | −1.10784 | −0.553921 | − | 0.832569i | \(-0.686869\pi\) | ||||
−0.553921 | + | 0.832569i | \(0.686869\pi\) | |||||||
\(942\) | 0.235157 | 0.00766182 | ||||||||
\(943\) | −12.0381 | −0.392013 | ||||||||
\(944\) | −23.1562 | −0.753671 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.2136 | −1.14489 | ||||||||
\(947\) | 6.98838 | 0.227092 | 0.113546 | − | 0.993533i | \(-0.463779\pi\) | ||||
0.113546 | + | 0.993533i | \(0.463779\pi\) | |||||||
\(948\) | 0.0138743 | 0.000450616 0 | ||||||||
\(949\) | −29.7356 | −0.965257 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.998666 | 0.0323840 | ||||||||
\(952\) | 58.6491 | 1.90083 | ||||||||
\(953\) | 51.8095 | 1.67828 | 0.839138 | − | 0.543919i | \(-0.183060\pi\) | ||||
0.839138 | + | 0.543919i | \(0.183060\pi\) | |||||||
\(954\) | 33.4362 | 1.08254 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.0580700 | −0.00187812 | ||||||||
\(957\) | −0.706564 | −0.0228400 | ||||||||
\(958\) | −10.8809 | −0.351544 | ||||||||
\(959\) | −10.5061 | −0.339260 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.73237 | 0.152657 | ||||||||
\(962\) | 21.2491 | 0.685097 | ||||||||
\(963\) | 2.35087 | 0.0757556 | ||||||||
\(964\) | 0.0717484 | 0.00231086 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.45036 | −0.0466647 | ||||||||
\(967\) | 19.3056 | 0.620826 | 0.310413 | − | 0.950602i | \(-0.399533\pi\) | ||||
0.310413 | + | 0.950602i | \(0.399533\pi\) | |||||||
\(968\) | −11.9422 | −0.383836 | ||||||||
\(969\) | 1.64357 | 0.0527991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.7263 | 1.56370 | 0.781851 | − | 0.623465i | \(-0.214276\pi\) | ||||
0.781851 | + | 0.623465i | \(0.214276\pi\) | |||||||
\(972\) | 0.0710102 | 0.00227765 | ||||||||
\(973\) | 13.7831 | 0.441864 | ||||||||
\(974\) | 59.0990 | 1.89365 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.4313 | −0.589971 | ||||||||
\(977\) | 13.0658 | 0.418012 | 0.209006 | − | 0.977914i | \(-0.432977\pi\) | ||||
0.209006 | + | 0.977914i | \(0.432977\pi\) | |||||||
\(978\) | −0.213482 | −0.00682639 | ||||||||
\(979\) | 33.4852 | 1.07019 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.0834 | 1.18398 | ||||||||
\(982\) | 17.9060 | 0.571405 | ||||||||
\(983\) | 8.81862 | 0.281270 | 0.140635 | − | 0.990061i | \(-0.455086\pi\) | ||||
0.140635 | + | 0.990061i | \(0.455086\pi\) | |||||||
\(984\) | −0.164631 | −0.00524824 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −56.4598 | −1.79805 | ||||||||
\(987\) | 0.113016 | 0.00359734 | ||||||||
\(988\) | 3.13745 | 0.0998154 | ||||||||
\(989\) | −74.7630 | −2.37732 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8928 | 1.45783 | 0.728916 | − | 0.684603i | \(-0.240024\pi\) | ||||
0.728916 | + | 0.684603i | \(0.240024\pi\) | |||||||
\(992\) | −2.42497 | −0.0769928 | ||||||||
\(993\) | −0.629051 | −0.0199623 | ||||||||
\(994\) | 23.6466 | 0.750025 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.00670248 | −0.000212376 0 | ||||||||
\(997\) | −42.5992 | −1.34913 | −0.674565 | − | 0.738215i | \(-0.735669\pi\) | ||||
−0.674565 | + | 0.738215i | \(0.735669\pi\) | |||||||
\(998\) | 4.67136 | 0.147869 | ||||||||
\(999\) | −0.624620 | −0.0197621 |
(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 | 6025.2.a.q.1.20 | 66 | ||
5.2 | odd | 4 | 1205.2.b.d.724.20 | ✓ | 66 | ||
5.3 | odd | 4 | 1205.2.b.d.724.47 | yes | 66 | ||
5.4 | even | 2 | inner | 6025.2.a.q.1.47 | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.d.724.20 | ✓ | 66 | 5.2 | odd | 4 | ||
1205.2.b.d.724.47 | yes | 66 | 5.3 | odd | 4 | ||
6025.2.a.q.1.20 | 66 | 1.1 | even | 1 | trivial | ||
6025.2.a.q.1.47 | 66 | 5.4 | even | 2 | inner |