Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.07802 | −1.19975 | −0.599873 | − | 0.800096i | \(-0.704782\pi\) | ||||
−0.599873 | + | 0.800096i | \(0.704782\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.66993 | −1.64124 | −0.820622 | − | 0.571471i | \(-0.806373\pi\) | ||||
−0.820622 | + | 0.571471i | \(0.806373\pi\) | |||||||
\(6\) | −2.07802 | −0.848348 | ||||||||
\(7\) | −3.45056 | −1.30419 | −0.652095 | − | 0.758137i | \(-0.726110\pi\) | ||||
−0.652095 | + | 0.758137i | \(0.726110\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.31817 | 0.439389 | ||||||||
\(10\) | −3.66993 | −1.16054 | ||||||||
\(11\) | −0.0411660 | −0.0124120 | −0.00620601 | − | 0.999981i | \(-0.501975\pi\) | ||||
−0.00620601 | + | 0.999981i | \(0.501975\pi\) | |||||||
\(12\) | −2.07802 | −0.599873 | ||||||||
\(13\) | −1.28748 | −0.357084 | −0.178542 | − | 0.983932i | \(-0.557138\pi\) | ||||
−0.178542 | + | 0.983932i | \(0.557138\pi\) | |||||||
\(14\) | −3.45056 | −0.922202 | ||||||||
\(15\) | 7.62619 | 1.96908 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.99294 | −0.968431 | −0.484216 | − | 0.874949i | \(-0.660895\pi\) | ||||
−0.484216 | + | 0.874949i | \(0.660895\pi\) | |||||||
\(18\) | 1.31817 | 0.310695 | ||||||||
\(19\) | 4.34352 | 0.996471 | 0.498235 | − | 0.867042i | \(-0.333982\pi\) | ||||
0.498235 | + | 0.867042i | \(0.333982\pi\) | |||||||
\(20\) | −3.66993 | −0.820622 | ||||||||
\(21\) | 7.17034 | 1.56470 | ||||||||
\(22\) | −0.0411660 | −0.00877662 | ||||||||
\(23\) | −2.81157 | −0.586253 | −0.293127 | − | 0.956074i | \(-0.594696\pi\) | ||||
−0.293127 | + | 0.956074i | \(0.594696\pi\) | |||||||
\(24\) | −2.07802 | −0.424174 | ||||||||
\(25\) | 8.46842 | 1.69368 | ||||||||
\(26\) | −1.28748 | −0.252496 | ||||||||
\(27\) | 3.49488 | 0.672591 | ||||||||
\(28\) | −3.45056 | −0.652095 | ||||||||
\(29\) | −2.72765 | −0.506512 | −0.253256 | − | 0.967399i | \(-0.581501\pi\) | ||||
−0.253256 | + | 0.967399i | \(0.581501\pi\) | |||||||
\(30\) | 7.62619 | 1.39235 | ||||||||
\(31\) | 8.98284 | 1.61337 | 0.806683 | − | 0.590984i | \(-0.201260\pi\) | ||||
0.806683 | + | 0.590984i | \(0.201260\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.0855438 | 0.0148913 | ||||||||
\(34\) | −3.99294 | −0.684784 | ||||||||
\(35\) | 12.6633 | 2.14050 | ||||||||
\(36\) | 1.31817 | 0.219694 | ||||||||
\(37\) | 8.77471 | 1.44255 | 0.721277 | − | 0.692647i | \(-0.243555\pi\) | ||||
0.721277 | + | 0.692647i | \(0.243555\pi\) | |||||||
\(38\) | 4.34352 | 0.704611 | ||||||||
\(39\) | 2.67542 | 0.428410 | ||||||||
\(40\) | −3.66993 | −0.580268 | ||||||||
\(41\) | 0.445901 | 0.0696380 | 0.0348190 | − | 0.999394i | \(-0.488915\pi\) | ||||
0.0348190 | + | 0.999394i | \(0.488915\pi\) | |||||||
\(42\) | 7.17034 | 1.10641 | ||||||||
\(43\) | −9.80961 | −1.49595 | −0.747976 | − | 0.663726i | \(-0.768974\pi\) | ||||
−0.747976 | + | 0.663726i | \(0.768974\pi\) | |||||||
\(44\) | −0.0411660 | −0.00620601 | ||||||||
\(45\) | −4.83758 | −0.721144 | ||||||||
\(46\) | −2.81157 | −0.414544 | ||||||||
\(47\) | 5.77836 | 0.842860 | 0.421430 | − | 0.906861i | \(-0.361528\pi\) | ||||
0.421430 | + | 0.906861i | \(0.361528\pi\) | |||||||
\(48\) | −2.07802 | −0.299936 | ||||||||
\(49\) | 4.90639 | 0.700914 | ||||||||
\(50\) | 8.46842 | 1.19761 | ||||||||
\(51\) | 8.29742 | 1.16187 | ||||||||
\(52\) | −1.28748 | −0.178542 | ||||||||
\(53\) | 7.93141 | 1.08946 | 0.544731 | − | 0.838611i | \(-0.316632\pi\) | ||||
0.544731 | + | 0.838611i | \(0.316632\pi\) | |||||||
\(54\) | 3.49488 | 0.475594 | ||||||||
\(55\) | 0.151077 | 0.0203712 | ||||||||
\(56\) | −3.45056 | −0.461101 | ||||||||
\(57\) | −9.02591 | −1.19551 | ||||||||
\(58\) | −2.72765 | −0.358158 | ||||||||
\(59\) | −4.48136 | −0.583424 | −0.291712 | − | 0.956506i | \(-0.594225\pi\) | ||||
−0.291712 | + | 0.956506i | \(0.594225\pi\) | |||||||
\(60\) | 7.62619 | 0.984538 | ||||||||
\(61\) | 7.09875 | 0.908902 | 0.454451 | − | 0.890772i | \(-0.349836\pi\) | ||||
0.454451 | + | 0.890772i | \(0.349836\pi\) | |||||||
\(62\) | 8.98284 | 1.14082 | ||||||||
\(63\) | −4.54842 | −0.573047 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.72498 | 0.586062 | ||||||||
\(66\) | 0.0855438 | 0.0105297 | ||||||||
\(67\) | −10.4509 | −1.27678 | −0.638391 | − | 0.769713i | \(-0.720400\pi\) | ||||
−0.638391 | + | 0.769713i | \(0.720400\pi\) | |||||||
\(68\) | −3.99294 | −0.484216 | ||||||||
\(69\) | 5.84250 | 0.703354 | ||||||||
\(70\) | 12.6633 | 1.51356 | ||||||||
\(71\) | 7.58055 | 0.899646 | 0.449823 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449823 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(72\) | 1.31817 | 0.155347 | ||||||||
\(73\) | −3.83122 | −0.448410 | −0.224205 | − | 0.974542i | \(-0.571979\pi\) | ||||
−0.224205 | + | 0.974542i | \(0.571979\pi\) | |||||||
\(74\) | 8.77471 | 1.02004 | ||||||||
\(75\) | −17.5975 | −2.03199 | ||||||||
\(76\) | 4.34352 | 0.498235 | ||||||||
\(77\) | 0.142046 | 0.0161876 | ||||||||
\(78\) | 2.67542 | 0.302931 | ||||||||
\(79\) | −1.20276 | −0.135321 | −0.0676604 | − | 0.997708i | \(-0.521553\pi\) | ||||
−0.0676604 | + | 0.997708i | \(0.521553\pi\) | |||||||
\(80\) | −3.66993 | −0.410311 | ||||||||
\(81\) | −11.2169 | −1.24633 | ||||||||
\(82\) | 0.445901 | 0.0492415 | ||||||||
\(83\) | 4.24142 | 0.465556 | 0.232778 | − | 0.972530i | \(-0.425218\pi\) | ||||
0.232778 | + | 0.972530i | \(0.425218\pi\) | |||||||
\(84\) | 7.17034 | 0.782348 | ||||||||
\(85\) | 14.6538 | 1.58943 | ||||||||
\(86\) | −9.80961 | −1.05780 | ||||||||
\(87\) | 5.66811 | 0.607685 | ||||||||
\(88\) | −0.0411660 | −0.00438831 | ||||||||
\(89\) | 7.73181 | 0.819570 | 0.409785 | − | 0.912182i | \(-0.365604\pi\) | ||||
0.409785 | + | 0.912182i | \(0.365604\pi\) | |||||||
\(90\) | −4.83758 | −0.509926 | ||||||||
\(91\) | 4.44255 | 0.465706 | ||||||||
\(92\) | −2.81157 | −0.293127 | ||||||||
\(93\) | −18.6665 | −1.93563 | ||||||||
\(94\) | 5.77836 | 0.595992 | ||||||||
\(95\) | −15.9404 | −1.63545 | ||||||||
\(96\) | −2.07802 | −0.212087 | ||||||||
\(97\) | 12.0758 | 1.22611 | 0.613057 | − | 0.790038i | \(-0.289939\pi\) | ||||
0.613057 | + | 0.790038i | \(0.289939\pi\) | |||||||
\(98\) | 4.90639 | 0.495621 | ||||||||
\(99\) | −0.0542636 | −0.00545370 | ||||||||
\(100\) | 8.46842 | 0.846842 | ||||||||
\(101\) | 5.35286 | 0.532630 | 0.266315 | − | 0.963886i | \(-0.414194\pi\) | ||||
0.266315 | + | 0.963886i | \(0.414194\pi\) | |||||||
\(102\) | 8.29742 | 0.821567 | ||||||||
\(103\) | −17.2376 | −1.69847 | −0.849236 | − | 0.528014i | \(-0.822937\pi\) | ||||
−0.849236 | + | 0.528014i | \(0.822937\pi\) | |||||||
\(104\) | −1.28748 | −0.126248 | ||||||||
\(105\) | −26.3147 | −2.56805 | ||||||||
\(106\) | 7.93141 | 0.770366 | ||||||||
\(107\) | 6.06603 | 0.586425 | 0.293212 | − | 0.956047i | \(-0.405276\pi\) | ||||
0.293212 | + | 0.956047i | \(0.405276\pi\) | |||||||
\(108\) | 3.49488 | 0.336295 | ||||||||
\(109\) | −17.9980 | −1.72390 | −0.861949 | − | 0.506995i | \(-0.830756\pi\) | ||||
−0.861949 | + | 0.506995i | \(0.830756\pi\) | |||||||
\(110\) | 0.151077 | 0.0144046 | ||||||||
\(111\) | −18.2340 | −1.73070 | ||||||||
\(112\) | −3.45056 | −0.326048 | ||||||||
\(113\) | 7.54476 | 0.709751 | 0.354876 | − | 0.934914i | \(-0.384523\pi\) | ||||
0.354876 | + | 0.934914i | \(0.384523\pi\) | |||||||
\(114\) | −9.02591 | −0.845354 | ||||||||
\(115\) | 10.3183 | 0.962185 | ||||||||
\(116\) | −2.72765 | −0.253256 | ||||||||
\(117\) | −1.69712 | −0.156899 | ||||||||
\(118\) | −4.48136 | −0.412543 | ||||||||
\(119\) | 13.7779 | 1.26302 | ||||||||
\(120\) | 7.62619 | 0.696173 | ||||||||
\(121\) | −10.9983 | −0.999846 | ||||||||
\(122\) | 7.09875 | 0.642691 | ||||||||
\(123\) | −0.926591 | −0.0835479 | ||||||||
\(124\) | 8.98284 | 0.806683 | ||||||||
\(125\) | −12.7289 | −1.13850 | ||||||||
\(126\) | −4.54842 | −0.405205 | ||||||||
\(127\) | −14.4684 | −1.28386 | −0.641932 | − | 0.766762i | \(-0.721867\pi\) | ||||
−0.641932 | + | 0.766762i | \(0.721867\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 20.3846 | 1.79476 | ||||||||
\(130\) | 4.72498 | 0.414408 | ||||||||
\(131\) | 13.9591 | 1.21961 | 0.609806 | − | 0.792551i | \(-0.291247\pi\) | ||||
0.609806 | + | 0.792551i | \(0.291247\pi\) | |||||||
\(132\) | 0.0855438 | 0.00744563 | ||||||||
\(133\) | −14.9876 | −1.29959 | ||||||||
\(134\) | −10.4509 | −0.902821 | ||||||||
\(135\) | −12.8260 | −1.10389 | ||||||||
\(136\) | −3.99294 | −0.342392 | ||||||||
\(137\) | 17.7070 | 1.51282 | 0.756408 | − | 0.654101i | \(-0.226953\pi\) | ||||
0.756408 | + | 0.654101i | \(0.226953\pi\) | |||||||
\(138\) | 5.84250 | 0.497347 | ||||||||
\(139\) | −10.8347 | −0.918990 | −0.459495 | − | 0.888180i | \(-0.651970\pi\) | ||||
−0.459495 | + | 0.888180i | \(0.651970\pi\) | |||||||
\(140\) | 12.6633 | 1.07025 | ||||||||
\(141\) | −12.0075 | −1.01122 | ||||||||
\(142\) | 7.58055 | 0.636146 | ||||||||
\(143\) | 0.0530006 | 0.00443213 | ||||||||
\(144\) | 1.31817 | 0.109847 | ||||||||
\(145\) | 10.0103 | 0.831310 | ||||||||
\(146\) | −3.83122 | −0.317074 | ||||||||
\(147\) | −10.1956 | −0.840918 | ||||||||
\(148\) | 8.77471 | 0.721277 | ||||||||
\(149\) | −13.2508 | −1.08555 | −0.542774 | − | 0.839879i | \(-0.682626\pi\) | ||||
−0.542774 | + | 0.839879i | \(0.682626\pi\) | |||||||
\(150\) | −17.5975 | −1.43683 | ||||||||
\(151\) | 10.1082 | 0.822592 | 0.411296 | − | 0.911502i | \(-0.365076\pi\) | ||||
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(152\) | 4.34352 | 0.352306 | ||||||||
\(153\) | −5.26336 | −0.425518 | ||||||||
\(154\) | 0.142046 | 0.0114464 | ||||||||
\(155\) | −32.9664 | −2.64793 | ||||||||
\(156\) | 2.67542 | 0.214205 | ||||||||
\(157\) | 3.55120 | 0.283416 | 0.141708 | − | 0.989908i | \(-0.454741\pi\) | ||||
0.141708 | + | 0.989908i | \(0.454741\pi\) | |||||||
\(158\) | −1.20276 | −0.0956862 | ||||||||
\(159\) | −16.4816 | −1.30708 | ||||||||
\(160\) | −3.66993 | −0.290134 | ||||||||
\(161\) | 9.70151 | 0.764586 | ||||||||
\(162\) | −11.2169 | −0.881286 | ||||||||
\(163\) | 2.35726 | 0.184635 | 0.0923175 | − | 0.995730i | \(-0.470573\pi\) | ||||
0.0923175 | + | 0.995730i | \(0.470573\pi\) | |||||||
\(164\) | 0.445901 | 0.0348190 | ||||||||
\(165\) | −0.313940 | −0.0244402 | ||||||||
\(166\) | 4.24142 | 0.329198 | ||||||||
\(167\) | −1.22613 | −0.0948810 | −0.0474405 | − | 0.998874i | \(-0.515106\pi\) | ||||
−0.0474405 | + | 0.998874i | \(0.515106\pi\) | |||||||
\(168\) | 7.17034 | 0.553204 | ||||||||
\(169\) | −11.3424 | −0.872491 | ||||||||
\(170\) | 14.6538 | 1.12390 | ||||||||
\(171\) | 5.72547 | 0.437838 | ||||||||
\(172\) | −9.80961 | −0.747976 | ||||||||
\(173\) | −13.1214 | −0.997599 | −0.498800 | − | 0.866717i | \(-0.666226\pi\) | ||||
−0.498800 | + | 0.866717i | \(0.666226\pi\) | |||||||
\(174\) | 5.66811 | 0.429698 | ||||||||
\(175\) | −29.2208 | −2.20889 | ||||||||
\(176\) | −0.0411660 | −0.00310300 | ||||||||
\(177\) | 9.31236 | 0.699960 | ||||||||
\(178\) | 7.73181 | 0.579523 | ||||||||
\(179\) | −3.60509 | −0.269457 | −0.134729 | − | 0.990883i | \(-0.543016\pi\) | ||||
−0.134729 | + | 0.990883i | \(0.543016\pi\) | |||||||
\(180\) | −4.83758 | −0.360572 | ||||||||
\(181\) | 11.5782 | 0.860603 | 0.430301 | − | 0.902685i | \(-0.358407\pi\) | ||||
0.430301 | + | 0.902685i | \(0.358407\pi\) | |||||||
\(182\) | 4.44255 | 0.329304 | ||||||||
\(183\) | −14.7513 | −1.09045 | ||||||||
\(184\) | −2.81157 | −0.207272 | ||||||||
\(185\) | −32.2026 | −2.36758 | ||||||||
\(186\) | −18.6665 | −1.36870 | ||||||||
\(187\) | 0.164374 | 0.0120202 | ||||||||
\(188\) | 5.77836 | 0.421430 | ||||||||
\(189\) | −12.0593 | −0.877187 | ||||||||
\(190\) | −15.9404 | −1.15644 | ||||||||
\(191\) | −5.72854 | −0.414503 | −0.207251 | − | 0.978288i | \(-0.566452\pi\) | ||||
−0.207251 | + | 0.978288i | \(0.566452\pi\) | |||||||
\(192\) | −2.07802 | −0.149968 | ||||||||
\(193\) | −13.8501 | −0.996955 | −0.498478 | − | 0.866903i | \(-0.666107\pi\) | ||||
−0.498478 | + | 0.866903i | \(0.666107\pi\) | |||||||
\(194\) | 12.0758 | 0.866994 | ||||||||
\(195\) | −9.81861 | −0.703125 | ||||||||
\(196\) | 4.90639 | 0.350457 | ||||||||
\(197\) | 7.70435 | 0.548913 | 0.274456 | − | 0.961600i | \(-0.411502\pi\) | ||||
0.274456 | + | 0.961600i | \(0.411502\pi\) | |||||||
\(198\) | −0.0542636 | −0.00385635 | ||||||||
\(199\) | −0.384256 | −0.0272392 | −0.0136196 | − | 0.999907i | \(-0.504335\pi\) | ||||
−0.0136196 | + | 0.999907i | \(0.504335\pi\) | |||||||
\(200\) | 8.46842 | 0.598807 | ||||||||
\(201\) | 21.7172 | 1.53181 | ||||||||
\(202\) | 5.35286 | 0.376626 | ||||||||
\(203\) | 9.41193 | 0.660588 | ||||||||
\(204\) | 8.29742 | 0.580935 | ||||||||
\(205\) | −1.63643 | −0.114293 | ||||||||
\(206\) | −17.2376 | −1.20100 | ||||||||
\(207\) | −3.70612 | −0.257593 | ||||||||
\(208\) | −1.28748 | −0.0892710 | ||||||||
\(209\) | −0.178805 | −0.0123682 | ||||||||
\(210\) | −26.3147 | −1.81589 | ||||||||
\(211\) | 21.3716 | 1.47129 | 0.735643 | − | 0.677370i | \(-0.236880\pi\) | ||||
0.735643 | + | 0.677370i | \(0.236880\pi\) | |||||||
\(212\) | 7.93141 | 0.544731 | ||||||||
\(213\) | −15.7525 | −1.07935 | ||||||||
\(214\) | 6.06603 | 0.414665 | ||||||||
\(215\) | 36.0006 | 2.45522 | ||||||||
\(216\) | 3.49488 | 0.237797 | ||||||||
\(217\) | −30.9959 | −2.10414 | ||||||||
\(218\) | −17.9980 | −1.21898 | ||||||||
\(219\) | 7.96135 | 0.537978 | ||||||||
\(220\) | 0.151077 | 0.0101856 | ||||||||
\(221\) | 5.14085 | 0.345811 | ||||||||
\(222\) | −18.2340 | −1.22379 | ||||||||
\(223\) | −7.32606 | −0.490589 | −0.245295 | − | 0.969449i | \(-0.578885\pi\) | ||||
−0.245295 | + | 0.969449i | \(0.578885\pi\) | |||||||
\(224\) | −3.45056 | −0.230551 | ||||||||
\(225\) | 11.1628 | 0.744185 | ||||||||
\(226\) | 7.54476 | 0.501870 | ||||||||
\(227\) | 3.35917 | 0.222956 | 0.111478 | − | 0.993767i | \(-0.464442\pi\) | ||||
0.111478 | + | 0.993767i | \(0.464442\pi\) | |||||||
\(228\) | −9.02591 | −0.597756 | ||||||||
\(229\) | 4.02544 | 0.266008 | 0.133004 | − | 0.991115i | \(-0.457538\pi\) | ||||
0.133004 | + | 0.991115i | \(0.457538\pi\) | |||||||
\(230\) | 10.3183 | 0.680367 | ||||||||
\(231\) | −0.295174 | −0.0194210 | ||||||||
\(232\) | −2.72765 | −0.179079 | ||||||||
\(233\) | 2.12563 | 0.139255 | 0.0696273 | − | 0.997573i | \(-0.477819\pi\) | ||||
0.0696273 | + | 0.997573i | \(0.477819\pi\) | |||||||
\(234\) | −1.69712 | −0.110944 | ||||||||
\(235\) | −21.2062 | −1.38334 | ||||||||
\(236\) | −4.48136 | −0.291712 | ||||||||
\(237\) | 2.49935 | 0.162350 | ||||||||
\(238\) | 13.7779 | 0.893089 | ||||||||
\(239\) | 0.817349 | 0.0528699 | 0.0264350 | − | 0.999651i | \(-0.491585\pi\) | ||||
0.0264350 | + | 0.999651i | \(0.491585\pi\) | |||||||
\(240\) | 7.62619 | 0.492269 | ||||||||
\(241\) | 25.8208 | 1.66326 | 0.831631 | − | 0.555329i | \(-0.187407\pi\) | ||||
0.831631 | + | 0.555329i | \(0.187407\pi\) | |||||||
\(242\) | −10.9983 | −0.706998 | ||||||||
\(243\) | 12.8244 | 0.822683 | ||||||||
\(244\) | 7.09875 | 0.454451 | ||||||||
\(245\) | −18.0061 | −1.15037 | ||||||||
\(246\) | −0.926591 | −0.0590773 | ||||||||
\(247\) | −5.59221 | −0.355824 | ||||||||
\(248\) | 8.98284 | 0.570411 | ||||||||
\(249\) | −8.81375 | −0.558549 | ||||||||
\(250\) | −12.7289 | −0.805043 | ||||||||
\(251\) | 19.2137 | 1.21276 | 0.606380 | − | 0.795175i | \(-0.292621\pi\) | ||||
0.606380 | + | 0.795175i | \(0.292621\pi\) | |||||||
\(252\) | −4.54842 | −0.286523 | ||||||||
\(253\) | 0.115741 | 0.00727658 | ||||||||
\(254\) | −14.4684 | −0.907828 | ||||||||
\(255\) | −30.4510 | −1.90691 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.3353 | 1.26848 | 0.634242 | − | 0.773135i | \(-0.281312\pi\) | ||||
0.634242 | + | 0.773135i | \(0.281312\pi\) | |||||||
\(258\) | 20.3846 | 1.26909 | ||||||||
\(259\) | −30.2777 | −1.88137 | ||||||||
\(260\) | 4.72498 | 0.293031 | ||||||||
\(261\) | −3.59550 | −0.222556 | ||||||||
\(262\) | 13.9591 | 0.862396 | ||||||||
\(263\) | 16.2149 | 0.999851 | 0.499925 | − | 0.866069i | \(-0.333361\pi\) | ||||
0.499925 | + | 0.866069i | \(0.333361\pi\) | |||||||
\(264\) | 0.0855438 | 0.00526486 | ||||||||
\(265\) | −29.1077 | −1.78807 | ||||||||
\(266\) | −14.9876 | −0.918948 | ||||||||
\(267\) | −16.0668 | −0.983275 | ||||||||
\(268\) | −10.4509 | −0.638391 | ||||||||
\(269\) | 0.420135 | 0.0256161 | 0.0128080 | − | 0.999918i | \(-0.495923\pi\) | ||||
0.0128080 | + | 0.999918i | \(0.495923\pi\) | |||||||
\(270\) | −12.8260 | −0.780565 | ||||||||
\(271\) | −23.0699 | −1.40140 | −0.700698 | − | 0.713458i | \(-0.747128\pi\) | ||||
−0.700698 | + | 0.713458i | \(0.747128\pi\) | |||||||
\(272\) | −3.99294 | −0.242108 | ||||||||
\(273\) | −9.23170 | −0.558728 | ||||||||
\(274\) | 17.7070 | 1.06972 | ||||||||
\(275\) | −0.348611 | −0.0210220 | ||||||||
\(276\) | 5.84250 | 0.351677 | ||||||||
\(277\) | −26.8417 | −1.61276 | −0.806381 | − | 0.591396i | \(-0.798577\pi\) | ||||
−0.806381 | + | 0.591396i | \(0.798577\pi\) | |||||||
\(278\) | −10.8347 | −0.649824 | ||||||||
\(279\) | 11.8409 | 0.708895 | ||||||||
\(280\) | 12.6633 | 0.756780 | ||||||||
\(281\) | −17.3013 | −1.03211 | −0.516055 | − | 0.856556i | \(-0.672600\pi\) | ||||
−0.516055 | + | 0.856556i | \(0.672600\pi\) | |||||||
\(282\) | −12.0075 | −0.715039 | ||||||||
\(283\) | −33.2822 | −1.97842 | −0.989212 | − | 0.146492i | \(-0.953202\pi\) | ||||
−0.989212 | + | 0.146492i | \(0.953202\pi\) | |||||||
\(284\) | 7.58055 | 0.449823 | ||||||||
\(285\) | 33.1245 | 1.96213 | ||||||||
\(286\) | 0.0530006 | 0.00313399 | ||||||||
\(287\) | −1.53861 | −0.0908213 | ||||||||
\(288\) | 1.31817 | 0.0776737 | ||||||||
\(289\) | −1.05639 | −0.0621407 | ||||||||
\(290\) | 10.0103 | 0.587825 | ||||||||
\(291\) | −25.0938 | −1.47103 | ||||||||
\(292\) | −3.83122 | −0.224205 | ||||||||
\(293\) | 6.49404 | 0.379386 | 0.189693 | − | 0.981843i | \(-0.439251\pi\) | ||||
0.189693 | + | 0.981843i | \(0.439251\pi\) | |||||||
\(294\) | −10.1956 | −0.594619 | ||||||||
\(295\) | 16.4463 | 0.957541 | ||||||||
\(296\) | 8.77471 | 0.510020 | ||||||||
\(297\) | −0.143870 | −0.00834821 | ||||||||
\(298\) | −13.2508 | −0.767599 | ||||||||
\(299\) | 3.61985 | 0.209342 | ||||||||
\(300\) | −17.5975 | −1.01599 | ||||||||
\(301\) | 33.8487 | 1.95101 | ||||||||
\(302\) | 10.1082 | 0.581661 | ||||||||
\(303\) | −11.1234 | −0.639020 | ||||||||
\(304\) | 4.34352 | 0.249118 | ||||||||
\(305\) | −26.0519 | −1.49173 | ||||||||
\(306\) | −5.26336 | −0.300886 | ||||||||
\(307\) | −6.26311 | −0.357455 | −0.178727 | − | 0.983899i | \(-0.557198\pi\) | ||||
−0.178727 | + | 0.983899i | \(0.557198\pi\) | |||||||
\(308\) | 0.142046 | 0.00809382 | ||||||||
\(309\) | 35.8201 | 2.03773 | ||||||||
\(310\) | −32.9664 | −1.87237 | ||||||||
\(311\) | −27.9835 | −1.58680 | −0.793400 | − | 0.608701i | \(-0.791691\pi\) | ||||
−0.793400 | + | 0.608701i | \(0.791691\pi\) | |||||||
\(312\) | 2.67542 | 0.151466 | ||||||||
\(313\) | 2.37282 | 0.134119 | 0.0670597 | − | 0.997749i | \(-0.478638\pi\) | ||||
0.0670597 | + | 0.997749i | \(0.478638\pi\) | |||||||
\(314\) | 3.55120 | 0.200406 | ||||||||
\(315\) | 16.6924 | 0.940509 | ||||||||
\(316\) | −1.20276 | −0.0676604 | ||||||||
\(317\) | 0.321234 | 0.0180423 | 0.00902116 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902116 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(318\) | −16.4816 | −0.924243 | ||||||||
\(319\) | 0.112286 | 0.00628684 | ||||||||
\(320\) | −3.66993 | −0.205156 | ||||||||
\(321\) | −12.6053 | −0.703560 | ||||||||
\(322\) | 9.70151 | 0.540644 | ||||||||
\(323\) | −17.3434 | −0.965014 | ||||||||
\(324\) | −11.2169 | −0.623163 | ||||||||
\(325\) | −10.9030 | −0.604787 | ||||||||
\(326\) | 2.35726 | 0.130557 | ||||||||
\(327\) | 37.4002 | 2.06824 | ||||||||
\(328\) | 0.445901 | 0.0246208 | ||||||||
\(329\) | −19.9386 | −1.09925 | ||||||||
\(330\) | −0.313940 | −0.0172818 | ||||||||
\(331\) | 21.4885 | 1.18111 | 0.590557 | − | 0.806996i | \(-0.298908\pi\) | ||||
0.590557 | + | 0.806996i | \(0.298908\pi\) | |||||||
\(332\) | 4.24142 | 0.232778 | ||||||||
\(333\) | 11.5665 | 0.633842 | ||||||||
\(334\) | −1.22613 | −0.0670910 | ||||||||
\(335\) | 38.3541 | 2.09551 | ||||||||
\(336\) | 7.17034 | 0.391174 | ||||||||
\(337\) | −25.7783 | −1.40423 | −0.702117 | − | 0.712061i | \(-0.747762\pi\) | ||||
−0.702117 | + | 0.712061i | \(0.747762\pi\) | |||||||
\(338\) | −11.3424 | −0.616944 | ||||||||
\(339\) | −15.6782 | −0.851521 | ||||||||
\(340\) | 14.6538 | 0.794716 | ||||||||
\(341\) | −0.369788 | −0.0200251 | ||||||||
\(342\) | 5.72547 | 0.309598 | ||||||||
\(343\) | 7.22412 | 0.390066 | ||||||||
\(344\) | −9.80961 | −0.528899 | ||||||||
\(345\) | −21.4416 | −1.15438 | ||||||||
\(346\) | −13.1214 | −0.705409 | ||||||||
\(347\) | −7.15996 | −0.384367 | −0.192183 | − | 0.981359i | \(-0.561557\pi\) | ||||
−0.192183 | + | 0.981359i | \(0.561557\pi\) | |||||||
\(348\) | 5.66811 | 0.303843 | ||||||||
\(349\) | −13.5643 | −0.726082 | −0.363041 | − | 0.931773i | \(-0.618261\pi\) | ||||
−0.363041 | + | 0.931773i | \(0.618261\pi\) | |||||||
\(350\) | −29.2208 | −1.56192 | ||||||||
\(351\) | −4.49961 | −0.240171 | ||||||||
\(352\) | −0.0411660 | −0.00219416 | ||||||||
\(353\) | −8.32890 | −0.443303 | −0.221651 | − | 0.975126i | \(-0.571145\pi\) | ||||
−0.221651 | + | 0.975126i | \(0.571145\pi\) | |||||||
\(354\) | 9.31236 | 0.494947 | ||||||||
\(355\) | −27.8201 | −1.47654 | ||||||||
\(356\) | 7.73181 | 0.409785 | ||||||||
\(357\) | −28.6308 | −1.51530 | ||||||||
\(358\) | −3.60509 | −0.190535 | ||||||||
\(359\) | 29.6768 | 1.56628 | 0.783140 | − | 0.621845i | \(-0.213617\pi\) | ||||
0.783140 | + | 0.621845i | \(0.213617\pi\) | |||||||
\(360\) | −4.83758 | −0.254963 | ||||||||
\(361\) | −0.133871 | −0.00704582 | ||||||||
\(362\) | 11.5782 | 0.608538 | ||||||||
\(363\) | 22.8547 | 1.19956 | ||||||||
\(364\) | 4.44255 | 0.232853 | ||||||||
\(365\) | 14.0603 | 0.735951 | ||||||||
\(366\) | −14.7513 | −0.771065 | ||||||||
\(367\) | −0.0919967 | −0.00480219 | −0.00240110 | − | 0.999997i | \(-0.500764\pi\) | ||||
−0.00240110 | + | 0.999997i | \(0.500764\pi\) | |||||||
\(368\) | −2.81157 | −0.146563 | ||||||||
\(369\) | 0.587771 | 0.0305982 | ||||||||
\(370\) | −32.2026 | −1.67413 | ||||||||
\(371\) | −27.3678 | −1.42087 | ||||||||
\(372\) | −18.6665 | −0.967814 | ||||||||
\(373\) | −21.5505 | −1.11584 | −0.557921 | − | 0.829894i | \(-0.688401\pi\) | ||||
−0.557921 | + | 0.829894i | \(0.688401\pi\) | |||||||
\(374\) | 0.164374 | 0.00849956 | ||||||||
\(375\) | 26.4508 | 1.36591 | ||||||||
\(376\) | 5.77836 | 0.297996 | ||||||||
\(377\) | 3.51181 | 0.180867 | ||||||||
\(378\) | −12.0593 | −0.620265 | ||||||||
\(379\) | 26.9935 | 1.38656 | 0.693281 | − | 0.720667i | \(-0.256164\pi\) | ||||
0.693281 | + | 0.720667i | \(0.256164\pi\) | |||||||
\(380\) | −15.9404 | −0.817726 | ||||||||
\(381\) | 30.0656 | 1.54031 | ||||||||
\(382\) | −5.72854 | −0.293098 | ||||||||
\(383\) | −7.01748 | −0.358576 | −0.179288 | − | 0.983797i | \(-0.557379\pi\) | ||||
−0.179288 | + | 0.983797i | \(0.557379\pi\) | |||||||
\(384\) | −2.07802 | −0.106043 | ||||||||
\(385\) | −0.521299 | −0.0265679 | ||||||||
\(386\) | −13.8501 | −0.704954 | ||||||||
\(387\) | −12.9307 | −0.657304 | ||||||||
\(388\) | 12.0758 | 0.613057 | ||||||||
\(389\) | 14.4447 | 0.732373 | 0.366187 | − | 0.930541i | \(-0.380663\pi\) | ||||
0.366187 | + | 0.930541i | \(0.380663\pi\) | |||||||
\(390\) | −9.81861 | −0.497184 | ||||||||
\(391\) | 11.2264 | 0.567746 | ||||||||
\(392\) | 4.90639 | 0.247810 | ||||||||
\(393\) | −29.0073 | −1.46322 | ||||||||
\(394\) | 7.70435 | 0.388140 | ||||||||
\(395\) | 4.41404 | 0.222094 | ||||||||
\(396\) | −0.0542636 | −0.00272685 | ||||||||
\(397\) | −20.9947 | −1.05369 | −0.526847 | − | 0.849960i | \(-0.676626\pi\) | ||||
−0.526847 | + | 0.849960i | \(0.676626\pi\) | |||||||
\(398\) | −0.384256 | −0.0192610 | ||||||||
\(399\) | 31.1445 | 1.55917 | ||||||||
\(400\) | 8.46842 | 0.423421 | ||||||||
\(401\) | −30.2401 | −1.51012 | −0.755060 | − | 0.655655i | \(-0.772393\pi\) | ||||
−0.755060 | + | 0.655655i | \(0.772393\pi\) | |||||||
\(402\) | 21.7172 | 1.08315 | ||||||||
\(403\) | −11.5653 | −0.576107 | ||||||||
\(404\) | 5.35286 | 0.266315 | ||||||||
\(405\) | 41.1654 | 2.04553 | ||||||||
\(406\) | 9.41193 | 0.467106 | ||||||||
\(407\) | −0.361220 | −0.0179050 | ||||||||
\(408\) | 8.29742 | 0.410783 | ||||||||
\(409\) | 4.69838 | 0.232320 | 0.116160 | − | 0.993231i | \(-0.462941\pi\) | ||||
0.116160 | + | 0.993231i | \(0.462941\pi\) | |||||||
\(410\) | −1.63643 | −0.0808174 | ||||||||
\(411\) | −36.7956 | −1.81499 | ||||||||
\(412\) | −17.2376 | −0.849236 | ||||||||
\(413\) | 15.4632 | 0.760896 | ||||||||
\(414\) | −3.70612 | −0.182146 | ||||||||
\(415\) | −15.5657 | −0.764091 | ||||||||
\(416\) | −1.28748 | −0.0631241 | ||||||||
\(417\) | 22.5148 | 1.10255 | ||||||||
\(418\) | −0.178805 | −0.00874565 | ||||||||
\(419\) | 27.6248 | 1.34956 | 0.674779 | − | 0.738020i | \(-0.264239\pi\) | ||||
0.674779 | + | 0.738020i | \(0.264239\pi\) | |||||||
\(420\) | −26.3147 | −1.28402 | ||||||||
\(421\) | −4.20494 | −0.204936 | −0.102468 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102468 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(422\) | 21.3716 | 1.04036 | ||||||||
\(423\) | 7.61683 | 0.370343 | ||||||||
\(424\) | 7.93141 | 0.385183 | ||||||||
\(425\) | −33.8139 | −1.64022 | ||||||||
\(426\) | −15.7525 | −0.763213 | ||||||||
\(427\) | −24.4947 | −1.18538 | ||||||||
\(428\) | 6.06603 | 0.293212 | ||||||||
\(429\) | −0.110136 | −0.00531743 | ||||||||
\(430\) | 36.0006 | 1.73610 | ||||||||
\(431\) | 27.4258 | 1.32105 | 0.660527 | − | 0.750803i | \(-0.270333\pi\) | ||||
0.660527 | + | 0.750803i | \(0.270333\pi\) | |||||||
\(432\) | 3.49488 | 0.168148 | ||||||||
\(433\) | −17.7193 | −0.851534 | −0.425767 | − | 0.904833i | \(-0.639996\pi\) | ||||
−0.425767 | + | 0.904833i | \(0.639996\pi\) | |||||||
\(434\) | −30.9959 | −1.48785 | ||||||||
\(435\) | −20.8016 | −0.997360 | ||||||||
\(436\) | −17.9980 | −0.861949 | ||||||||
\(437\) | −12.2121 | −0.584184 | ||||||||
\(438\) | 7.96135 | 0.380408 | ||||||||
\(439\) | −11.2775 | −0.538247 | −0.269124 | − | 0.963106i | \(-0.586734\pi\) | ||||
−0.269124 | + | 0.963106i | \(0.586734\pi\) | |||||||
\(440\) | 0.151077 | 0.00720229 | ||||||||
\(441\) | 6.46744 | 0.307973 | ||||||||
\(442\) | 5.14085 | 0.244526 | ||||||||
\(443\) | 6.29496 | 0.299083 | 0.149541 | − | 0.988755i | \(-0.452220\pi\) | ||||
0.149541 | + | 0.988755i | \(0.452220\pi\) | |||||||
\(444\) | −18.2340 | −0.865349 | ||||||||
\(445\) | −28.3752 | −1.34511 | ||||||||
\(446\) | −7.32606 | −0.346899 | ||||||||
\(447\) | 27.5354 | 1.30238 | ||||||||
\(448\) | −3.45056 | −0.163024 | ||||||||
\(449\) | 30.4039 | 1.43485 | 0.717425 | − | 0.696636i | \(-0.245321\pi\) | ||||
0.717425 | + | 0.696636i | \(0.245321\pi\) | |||||||
\(450\) | 11.1628 | 0.526218 | ||||||||
\(451\) | −0.0183560 | −0.000864348 0 | ||||||||
\(452\) | 7.54476 | 0.354876 | ||||||||
\(453\) | −21.0050 | −0.986901 | ||||||||
\(454\) | 3.35917 | 0.157653 | ||||||||
\(455\) | −16.3039 | −0.764337 | ||||||||
\(456\) | −9.02591 | −0.422677 | ||||||||
\(457\) | −35.3996 | −1.65592 | −0.827962 | − | 0.560785i | \(-0.810500\pi\) | ||||
−0.827962 | + | 0.560785i | \(0.810500\pi\) | |||||||
\(458\) | 4.02544 | 0.188096 | ||||||||
\(459\) | −13.9549 | −0.651358 | ||||||||
\(460\) | 10.3183 | 0.481092 | ||||||||
\(461\) | 0.985230 | 0.0458867 | 0.0229434 | − | 0.999737i | \(-0.492696\pi\) | ||||
0.0229434 | + | 0.999737i | \(0.492696\pi\) | |||||||
\(462\) | −0.295174 | −0.0137328 | ||||||||
\(463\) | −31.2127 | −1.45058 | −0.725288 | − | 0.688446i | \(-0.758293\pi\) | ||||
−0.725288 | + | 0.688446i | \(0.758293\pi\) | |||||||
\(464\) | −2.72765 | −0.126628 | ||||||||
\(465\) | 68.5049 | 3.17684 | ||||||||
\(466\) | 2.12563 | 0.0984679 | ||||||||
\(467\) | −41.4673 | −1.91888 | −0.959440 | − | 0.281913i | \(-0.909031\pi\) | ||||
−0.959440 | + | 0.281913i | \(0.909031\pi\) | |||||||
\(468\) | −1.69712 | −0.0784493 | ||||||||
\(469\) | 36.0615 | 1.66517 | ||||||||
\(470\) | −21.2062 | −0.978169 | ||||||||
\(471\) | −7.37946 | −0.340027 | ||||||||
\(472\) | −4.48136 | −0.206272 | ||||||||
\(473\) | 0.403823 | 0.0185678 | ||||||||
\(474\) | 2.49935 | 0.114799 | ||||||||
\(475\) | 36.7827 | 1.68771 | ||||||||
\(476\) | 13.7779 | 0.631510 | ||||||||
\(477\) | 10.4549 | 0.478697 | ||||||||
\(478\) | 0.817349 | 0.0373847 | ||||||||
\(479\) | 25.1228 | 1.14789 | 0.573946 | − | 0.818893i | \(-0.305412\pi\) | ||||
0.573946 | + | 0.818893i | \(0.305412\pi\) | |||||||
\(480\) | 7.62619 | 0.348087 | ||||||||
\(481\) | −11.2973 | −0.515113 | ||||||||
\(482\) | 25.8208 | 1.17610 | ||||||||
\(483\) | −20.1599 | −0.917308 | ||||||||
\(484\) | −10.9983 | −0.499923 | ||||||||
\(485\) | −44.3175 | −2.01235 | ||||||||
\(486\) | 12.8244 | 0.581725 | ||||||||
\(487\) | −1.05337 | −0.0477326 | −0.0238663 | − | 0.999715i | \(-0.507598\pi\) | ||||
−0.0238663 | + | 0.999715i | \(0.507598\pi\) | |||||||
\(488\) | 7.09875 | 0.321345 | ||||||||
\(489\) | −4.89844 | −0.221515 | ||||||||
\(490\) | −18.0061 | −0.813435 | ||||||||
\(491\) | −11.2134 | −0.506054 | −0.253027 | − | 0.967459i | \(-0.581426\pi\) | ||||
−0.253027 | + | 0.967459i | \(0.581426\pi\) | |||||||
\(492\) | −0.926591 | −0.0417739 | ||||||||
\(493\) | 10.8914 | 0.490522 | ||||||||
\(494\) | −5.59221 | −0.251605 | ||||||||
\(495\) | 0.199144 | 0.00895085 | ||||||||
\(496\) | 8.98284 | 0.403342 | ||||||||
\(497\) | −26.1572 | −1.17331 | ||||||||
\(498\) | −8.81375 | −0.394954 | ||||||||
\(499\) | 14.7997 | 0.662524 | 0.331262 | − | 0.943539i | \(-0.392526\pi\) | ||||
0.331262 | + | 0.943539i | \(0.392526\pi\) | |||||||
\(500\) | −12.7289 | −0.569252 | ||||||||
\(501\) | 2.54793 | 0.113833 | ||||||||
\(502\) | 19.2137 | 0.857551 | ||||||||
\(503\) | 31.2459 | 1.39319 | 0.696594 | − | 0.717466i | \(-0.254698\pi\) | ||||
0.696594 | + | 0.717466i | \(0.254698\pi\) | |||||||
\(504\) | −4.54842 | −0.202603 | ||||||||
\(505\) | −19.6447 | −0.874176 | ||||||||
\(506\) | 0.115741 | 0.00514532 | ||||||||
\(507\) | 23.5697 | 1.04677 | ||||||||
\(508\) | −14.4684 | −0.641932 | ||||||||
\(509\) | −17.5494 | −0.777861 | −0.388931 | − | 0.921267i | \(-0.627155\pi\) | ||||
−0.388931 | + | 0.921267i | \(0.627155\pi\) | |||||||
\(510\) | −30.4510 | −1.34839 | ||||||||
\(511\) | 13.2199 | 0.584812 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.1801 | 0.670217 | ||||||||
\(514\) | 20.3353 | 0.896953 | ||||||||
\(515\) | 63.2609 | 2.78761 | ||||||||
\(516\) | 20.3846 | 0.897381 | ||||||||
\(517\) | −0.237872 | −0.0104616 | ||||||||
\(518\) | −30.2777 | −1.33033 | ||||||||
\(519\) | 27.2665 | 1.19687 | ||||||||
\(520\) | 4.72498 | 0.207204 | ||||||||
\(521\) | −22.8519 | −1.00116 | −0.500580 | − | 0.865690i | \(-0.666880\pi\) | ||||
−0.500580 | + | 0.865690i | \(0.666880\pi\) | |||||||
\(522\) | −3.59550 | −0.157371 | ||||||||
\(523\) | 30.8207 | 1.34769 | 0.673847 | − | 0.738871i | \(-0.264641\pi\) | ||||
0.673847 | + | 0.738871i | \(0.264641\pi\) | |||||||
\(524\) | 13.9591 | 0.609806 | ||||||||
\(525\) | 60.7214 | 2.65010 | ||||||||
\(526\) | 16.2149 | 0.707001 | ||||||||
\(527\) | −35.8680 | −1.56243 | ||||||||
\(528\) | 0.0855438 | 0.00372281 | ||||||||
\(529\) | −15.0951 | −0.656307 | ||||||||
\(530\) | −29.1077 | −1.26436 | ||||||||
\(531\) | −5.90718 | −0.256350 | ||||||||
\(532\) | −14.9876 | −0.649794 | ||||||||
\(533\) | −0.574090 | −0.0248666 | ||||||||
\(534\) | −16.0668 | −0.695280 | ||||||||
\(535\) | −22.2619 | −0.962466 | ||||||||
\(536\) | −10.4509 | −0.451410 | ||||||||
\(537\) | 7.49145 | 0.323280 | ||||||||
\(538\) | 0.420135 | 0.0181133 | ||||||||
\(539\) | −0.201977 | −0.00869975 | ||||||||
\(540\) | −12.8260 | −0.551943 | ||||||||
\(541\) | 20.3551 | 0.875134 | 0.437567 | − | 0.899186i | \(-0.355840\pi\) | ||||
0.437567 | + | 0.899186i | \(0.355840\pi\) | |||||||
\(542\) | −23.0699 | −0.990936 | ||||||||
\(543\) | −24.0598 | −1.03250 | ||||||||
\(544\) | −3.99294 | −0.171196 | ||||||||
\(545\) | 66.0516 | 2.82934 | ||||||||
\(546\) | −9.23170 | −0.395080 | ||||||||
\(547\) | 20.3339 | 0.869416 | 0.434708 | − | 0.900571i | \(-0.356852\pi\) | ||||
0.434708 | + | 0.900571i | \(0.356852\pi\) | |||||||
\(548\) | 17.7070 | 0.756408 | ||||||||
\(549\) | 9.35733 | 0.399361 | ||||||||
\(550\) | −0.348611 | −0.0148648 | ||||||||
\(551\) | −11.8476 | −0.504724 | ||||||||
\(552\) | 5.84250 | 0.248673 | ||||||||
\(553\) | 4.15019 | 0.176484 | ||||||||
\(554\) | −26.8417 | −1.14039 | ||||||||
\(555\) | 66.9177 | 2.84050 | ||||||||
\(556\) | −10.8347 | −0.459495 | ||||||||
\(557\) | −45.6190 | −1.93294 | −0.966469 | − | 0.256782i | \(-0.917338\pi\) | ||||
−0.966469 | + | 0.256782i | \(0.917338\pi\) | |||||||
\(558\) | 11.8409 | 0.501264 | ||||||||
\(559\) | 12.6297 | 0.534180 | ||||||||
\(560\) | 12.6633 | 0.535124 | ||||||||
\(561\) | −0.341572 | −0.0144212 | ||||||||
\(562\) | −17.3013 | −0.729812 | ||||||||
\(563\) | 29.8794 | 1.25926 | 0.629632 | − | 0.776893i | \(-0.283206\pi\) | ||||
0.629632 | + | 0.776893i | \(0.283206\pi\) | |||||||
\(564\) | −12.0075 | −0.505609 | ||||||||
\(565\) | −27.6888 | −1.16488 | ||||||||
\(566\) | −33.2822 | −1.39896 | ||||||||
\(567\) | 38.7048 | 1.62545 | ||||||||
\(568\) | 7.58055 | 0.318073 | ||||||||
\(569\) | −29.2356 | −1.22562 | −0.612811 | − | 0.790229i | \(-0.709961\pi\) | ||||
−0.612811 | + | 0.790229i | \(0.709961\pi\) | |||||||
\(570\) | 33.1245 | 1.38743 | ||||||||
\(571\) | −20.3269 | −0.850655 | −0.425327 | − | 0.905040i | \(-0.639841\pi\) | ||||
−0.425327 | + | 0.905040i | \(0.639841\pi\) | |||||||
\(572\) | 0.0530006 | 0.00221607 | ||||||||
\(573\) | 11.9040 | 0.497298 | ||||||||
\(574\) | −1.53861 | −0.0642203 | ||||||||
\(575\) | −23.8096 | −0.992927 | ||||||||
\(576\) | 1.31817 | 0.0549236 | ||||||||
\(577\) | 10.7226 | 0.446386 | 0.223193 | − | 0.974774i | \(-0.428352\pi\) | ||||
0.223193 | + | 0.974774i | \(0.428352\pi\) | |||||||
\(578\) | −1.05639 | −0.0439401 | ||||||||
\(579\) | 28.7809 | 1.19609 | ||||||||
\(580\) | 10.0103 | 0.415655 | ||||||||
\(581\) | −14.6353 | −0.607174 | ||||||||
\(582\) | −25.0938 | −1.04017 | ||||||||
\(583\) | −0.326504 | −0.0135224 | ||||||||
\(584\) | −3.83122 | −0.158537 | ||||||||
\(585\) | 6.22831 | 0.257509 | ||||||||
\(586\) | 6.49404 | 0.268266 | ||||||||
\(587\) | 5.29535 | 0.218563 | 0.109281 | − | 0.994011i | \(-0.465145\pi\) | ||||
0.109281 | + | 0.994011i | \(0.465145\pi\) | |||||||
\(588\) | −10.1956 | −0.420459 | ||||||||
\(589\) | 39.0171 | 1.60767 | ||||||||
\(590\) | 16.4463 | 0.677084 | ||||||||
\(591\) | −16.0098 | −0.658555 | ||||||||
\(592\) | 8.77471 | 0.360639 | ||||||||
\(593\) | 19.4576 | 0.799027 | 0.399513 | − | 0.916727i | \(-0.369179\pi\) | ||||
0.399513 | + | 0.916727i | \(0.369179\pi\) | |||||||
\(594\) | −0.143870 | −0.00590308 | ||||||||
\(595\) | −50.5640 | −2.07292 | ||||||||
\(596\) | −13.2508 | −0.542774 | ||||||||
\(597\) | 0.798492 | 0.0326801 | ||||||||
\(598\) | 3.61985 | 0.148027 | ||||||||
\(599\) | 18.2888 | 0.747259 | 0.373629 | − | 0.927578i | \(-0.378113\pi\) | ||||
0.373629 | + | 0.927578i | \(0.378113\pi\) | |||||||
\(600\) | −17.5975 | −0.718416 | ||||||||
\(601\) | −0.625965 | −0.0255337 | −0.0127668 | − | 0.999919i | \(-0.504064\pi\) | ||||
−0.0127668 | + | 0.999919i | \(0.504064\pi\) | |||||||
\(602\) | 33.8487 | 1.37957 | ||||||||
\(603\) | −13.7760 | −0.561003 | ||||||||
\(604\) | 10.1082 | 0.411296 | ||||||||
\(605\) | 40.3631 | 1.64099 | ||||||||
\(606\) | −11.1234 | −0.451855 | ||||||||
\(607\) | 8.69823 | 0.353050 | 0.176525 | − | 0.984296i | \(-0.443514\pi\) | ||||
0.176525 | + | 0.984296i | \(0.443514\pi\) | |||||||
\(608\) | 4.34352 | 0.176153 | ||||||||
\(609\) | −19.5582 | −0.792538 | ||||||||
\(610\) | −26.0519 | −1.05481 | ||||||||
\(611\) | −7.43955 | −0.300972 | ||||||||
\(612\) | −5.26336 | −0.212759 | ||||||||
\(613\) | 28.3724 | 1.14595 | 0.572975 | − | 0.819573i | \(-0.305789\pi\) | ||||
0.572975 | + | 0.819573i | \(0.305789\pi\) | |||||||
\(614\) | −6.26311 | −0.252759 | ||||||||
\(615\) | 3.40053 | 0.137122 | ||||||||
\(616\) | 0.142046 | 0.00572319 | ||||||||
\(617\) | 16.5979 | 0.668208 | 0.334104 | − | 0.942536i | \(-0.391566\pi\) | ||||
0.334104 | + | 0.942536i | \(0.391566\pi\) | |||||||
\(618\) | 35.8201 | 1.44089 | ||||||||
\(619\) | 41.6792 | 1.67523 | 0.837614 | − | 0.546263i | \(-0.183950\pi\) | ||||
0.837614 | + | 0.546263i | \(0.183950\pi\) | |||||||
\(620\) | −32.9664 | −1.32396 | ||||||||
\(621\) | −9.82612 | −0.394308 | ||||||||
\(622\) | −27.9835 | −1.12204 | ||||||||
\(623\) | −26.6791 | −1.06888 | ||||||||
\(624\) | 2.67542 | 0.107102 | ||||||||
\(625\) | 4.37198 | 0.174879 | ||||||||
\(626\) | 2.37282 | 0.0948368 | ||||||||
\(627\) | 0.371561 | 0.0148387 | ||||||||
\(628\) | 3.55120 | 0.141708 | ||||||||
\(629\) | −35.0370 | −1.39701 | ||||||||
\(630\) | 16.6924 | 0.665041 | ||||||||
\(631\) | −23.1327 | −0.920897 | −0.460449 | − | 0.887686i | \(-0.652311\pi\) | ||||
−0.460449 | + | 0.887686i | \(0.652311\pi\) | |||||||
\(632\) | −1.20276 | −0.0478431 | ||||||||
\(633\) | −44.4107 | −1.76517 | ||||||||
\(634\) | 0.321234 | 0.0127578 | ||||||||
\(635\) | 53.0981 | 2.10713 | ||||||||
\(636\) | −16.4816 | −0.653539 | ||||||||
\(637\) | −6.31691 | −0.250285 | ||||||||
\(638\) | 0.112286 | 0.00444546 | ||||||||
\(639\) | 9.99242 | 0.395294 | ||||||||
\(640\) | −3.66993 | −0.145067 | ||||||||
\(641\) | −39.9116 | −1.57641 | −0.788207 | − | 0.615410i | \(-0.788990\pi\) | ||||
−0.788207 | + | 0.615410i | \(0.788990\pi\) | |||||||
\(642\) | −12.6053 | −0.497492 | ||||||||
\(643\) | 12.5138 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(644\) | 9.70151 | 0.382293 | ||||||||
\(645\) | −74.8100 | −2.94564 | ||||||||
\(646\) | −17.3434 | −0.682368 | ||||||||
\(647\) | 40.4521 | 1.59034 | 0.795169 | − | 0.606388i | \(-0.207382\pi\) | ||||
0.795169 | + | 0.606388i | \(0.207382\pi\) | |||||||
\(648\) | −11.2169 | −0.440643 | ||||||||
\(649\) | 0.184480 | 0.00724147 | ||||||||
\(650\) | −10.9030 | −0.427649 | ||||||||
\(651\) | 64.4100 | 2.52443 | ||||||||
\(652\) | 2.35726 | 0.0923175 | ||||||||
\(653\) | −42.5996 | −1.66705 | −0.833526 | − | 0.552480i | \(-0.813681\pi\) | ||||
−0.833526 | + | 0.552480i | \(0.813681\pi\) | |||||||
\(654\) | 37.4002 | 1.46247 | ||||||||
\(655\) | −51.2290 | −2.00168 | ||||||||
\(656\) | 0.445901 | 0.0174095 | ||||||||
\(657\) | −5.05018 | −0.197026 | ||||||||
\(658\) | −19.9386 | −0.777287 | ||||||||
\(659\) | 7.20073 | 0.280501 | 0.140250 | − | 0.990116i | \(-0.455209\pi\) | ||||
0.140250 | + | 0.990116i | \(0.455209\pi\) | |||||||
\(660\) | −0.313940 | −0.0122201 | ||||||||
\(661\) | 5.49090 | 0.213571 | 0.106786 | − | 0.994282i | \(-0.465944\pi\) | ||||
0.106786 | + | 0.994282i | \(0.465944\pi\) | |||||||
\(662\) | 21.4885 | 0.835173 | ||||||||
\(663\) | −10.6828 | −0.414885 | ||||||||
\(664\) | 4.24142 | 0.164599 | ||||||||
\(665\) | 55.0034 | 2.13294 | ||||||||
\(666\) | 11.5665 | 0.448194 | ||||||||
\(667\) | 7.66898 | 0.296944 | ||||||||
\(668\) | −1.22613 | −0.0474405 | ||||||||
\(669\) | 15.2237 | 0.588582 | ||||||||
\(670\) | 38.3541 | 1.48175 | ||||||||
\(671\) | −0.292227 | −0.0112813 | ||||||||
\(672\) | 7.17034 | 0.276602 | ||||||||
\(673\) | 6.34218 | 0.244473 | 0.122237 | − | 0.992501i | \(-0.460993\pi\) | ||||
0.122237 | + | 0.992501i | \(0.460993\pi\) | |||||||
\(674\) | −25.7783 | −0.992944 | ||||||||
\(675\) | 29.5961 | 1.13916 | ||||||||
\(676\) | −11.3424 | −0.436246 | ||||||||
\(677\) | −29.6556 | −1.13976 | −0.569879 | − | 0.821729i | \(-0.693010\pi\) | ||||
−0.569879 | + | 0.821729i | \(0.693010\pi\) | |||||||
\(678\) | −15.6782 | −0.602116 | ||||||||
\(679\) | −41.6684 | −1.59909 | ||||||||
\(680\) | 14.6538 | 0.561949 | ||||||||
\(681\) | −6.98041 | −0.267490 | ||||||||
\(682\) | −0.369788 | −0.0141599 | ||||||||
\(683\) | −12.0924 | −0.462702 | −0.231351 | − | 0.972870i | \(-0.574315\pi\) | ||||
−0.231351 | + | 0.972870i | \(0.574315\pi\) | |||||||
\(684\) | 5.72547 | 0.218919 | ||||||||
\(685\) | −64.9837 | −2.48290 | ||||||||
\(686\) | 7.22412 | 0.275818 | ||||||||
\(687\) | −8.36494 | −0.319142 | ||||||||
\(688\) | −9.80961 | −0.373988 | ||||||||
\(689\) | −10.2116 | −0.389029 | ||||||||
\(690\) | −21.4416 | −0.816267 | ||||||||
\(691\) | 43.8358 | 1.66759 | 0.833795 | − | 0.552074i | \(-0.186163\pi\) | ||||
0.833795 | + | 0.552074i | \(0.186163\pi\) | |||||||
\(692\) | −13.1214 | −0.498800 | ||||||||
\(693\) | 0.187240 | 0.00711266 | ||||||||
\(694\) | −7.15996 | −0.271788 | ||||||||
\(695\) | 39.7627 | 1.50829 | ||||||||
\(696\) | 5.66811 | 0.214849 | ||||||||
\(697\) | −1.78046 | −0.0674396 | ||||||||
\(698\) | −13.5643 | −0.513417 | ||||||||
\(699\) | −4.41710 | −0.167070 | ||||||||
\(700\) | −29.2208 | −1.10444 | ||||||||
\(701\) | −25.8701 | −0.977101 | −0.488551 | − | 0.872536i | \(-0.662474\pi\) | ||||
−0.488551 | + | 0.872536i | \(0.662474\pi\) | |||||||
\(702\) | −4.49961 | −0.169827 | ||||||||
\(703\) | 38.1131 | 1.43746 | ||||||||
\(704\) | −0.0411660 | −0.00155150 | ||||||||
\(705\) | 44.0669 | 1.65965 | ||||||||
\(706\) | −8.32890 | −0.313462 | ||||||||
\(707\) | −18.4704 | −0.694651 | ||||||||
\(708\) | 9.31236 | 0.349980 | ||||||||
\(709\) | 16.0301 | 0.602024 | 0.301012 | − | 0.953620i | \(-0.402676\pi\) | ||||
0.301012 | + | 0.953620i | \(0.402676\pi\) | |||||||
\(710\) | −27.8201 | −1.04407 | ||||||||
\(711\) | −1.58543 | −0.0594584 | ||||||||
\(712\) | 7.73181 | 0.289762 | ||||||||
\(713\) | −25.2559 | −0.945841 | ||||||||
\(714\) | −28.6308 | −1.07148 | ||||||||
\(715\) | −0.194509 | −0.00727421 | ||||||||
\(716\) | −3.60509 | −0.134729 | ||||||||
\(717\) | −1.69847 | −0.0634304 | ||||||||
\(718\) | 29.6768 | 1.10753 | ||||||||
\(719\) | 0.101795 | 0.00379630 | 0.00189815 | − | 0.999998i | \(-0.499396\pi\) | ||||
0.00189815 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(720\) | −4.83758 | −0.180286 | ||||||||
\(721\) | 59.4795 | 2.21513 | ||||||||
\(722\) | −0.133871 | −0.00498215 | ||||||||
\(723\) | −53.6561 | −1.99549 | ||||||||
\(724\) | 11.5782 | 0.430301 | ||||||||
\(725\) | −23.0989 | −0.857871 | ||||||||
\(726\) | 22.8547 | 0.848217 | ||||||||
\(727\) | −12.1973 | −0.452374 | −0.226187 | − | 0.974084i | \(-0.572626\pi\) | ||||
−0.226187 | + | 0.974084i | \(0.572626\pi\) | |||||||
\(728\) | 4.44255 | 0.164652 | ||||||||
\(729\) | 7.00154 | 0.259316 | ||||||||
\(730\) | 14.0603 | 0.520396 | ||||||||
\(731\) | 39.1692 | 1.44873 | ||||||||
\(732\) | −14.7513 | −0.545225 | ||||||||
\(733\) | 34.5973 | 1.27788 | 0.638940 | − | 0.769256i | \(-0.279373\pi\) | ||||
0.638940 | + | 0.769256i | \(0.279373\pi\) | |||||||
\(734\) | −0.0919967 | −0.00339566 | ||||||||
\(735\) | 37.4171 | 1.38015 | ||||||||
\(736\) | −2.81157 | −0.103636 | ||||||||
\(737\) | 0.430222 | 0.0158474 | ||||||||
\(738\) | 0.587771 | 0.0216362 | ||||||||
\(739\) | −20.8959 | −0.768668 | −0.384334 | − | 0.923194i | \(-0.625569\pi\) | ||||
−0.384334 | + | 0.923194i | \(0.625569\pi\) | |||||||
\(740\) | −32.2026 | −1.18379 | ||||||||
\(741\) | 11.6207 | 0.426898 | ||||||||
\(742\) | −27.3678 | −1.00470 | ||||||||
\(743\) | −39.9977 | −1.46737 | −0.733686 | − | 0.679488i | \(-0.762202\pi\) | ||||
−0.733686 | + | 0.679488i | \(0.762202\pi\) | |||||||
\(744\) | −18.6665 | −0.684348 | ||||||||
\(745\) | 48.6296 | 1.78165 | ||||||||
\(746\) | −21.5505 | −0.789020 | ||||||||
\(747\) | 5.59089 | 0.204560 | ||||||||
\(748\) | 0.164374 | 0.00601009 | ||||||||
\(749\) | −20.9312 | −0.764810 | ||||||||
\(750\) | 26.4508 | 0.965847 | ||||||||
\(751\) | 19.7539 | 0.720829 | 0.360414 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360414 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(752\) | 5.77836 | 0.210715 | ||||||||
\(753\) | −39.9265 | −1.45500 | ||||||||
\(754\) | 3.51181 | 0.127892 | ||||||||
\(755\) | −37.0964 | −1.35007 | ||||||||
\(756\) | −12.0593 | −0.438593 | ||||||||
\(757\) | −37.1317 | −1.34958 | −0.674788 | − | 0.738012i | \(-0.735765\pi\) | ||||
−0.674788 | + | 0.738012i | \(0.735765\pi\) | |||||||
\(758\) | 26.9935 | 0.980447 | ||||||||
\(759\) | −0.240512 | −0.00873005 | ||||||||
\(760\) | −15.9404 | −0.578220 | ||||||||
\(761\) | 39.1816 | 1.42033 | 0.710165 | − | 0.704035i | \(-0.248620\pi\) | ||||
0.710165 | + | 0.704035i | \(0.248620\pi\) | |||||||
\(762\) | 30.0656 | 1.08916 | ||||||||
\(763\) | 62.1033 | 2.24829 | ||||||||
\(764\) | −5.72854 | −0.207251 | ||||||||
\(765\) | 19.3162 | 0.698379 | ||||||||
\(766\) | −7.01748 | −0.253552 | ||||||||
\(767\) | 5.76969 | 0.208331 | ||||||||
\(768\) | −2.07802 | −0.0749841 | ||||||||
\(769\) | 27.1506 | 0.979076 | 0.489538 | − | 0.871982i | \(-0.337166\pi\) | ||||
0.489538 | + | 0.871982i | \(0.337166\pi\) | |||||||
\(770\) | −0.521299 | −0.0187863 | ||||||||
\(771\) | −42.2572 | −1.52186 | ||||||||
\(772\) | −13.8501 | −0.498478 | ||||||||
\(773\) | −4.52177 | −0.162637 | −0.0813185 | − | 0.996688i | \(-0.525913\pi\) | ||||
−0.0813185 | + | 0.996688i | \(0.525913\pi\) | |||||||
\(774\) | −12.9307 | −0.464784 | ||||||||
\(775\) | 76.0704 | 2.73253 | ||||||||
\(776\) | 12.0758 | 0.433497 | ||||||||
\(777\) | 62.9177 | 2.25716 | ||||||||
\(778\) | 14.4447 | 0.517866 | ||||||||
\(779\) | 1.93678 | 0.0693923 | ||||||||
\(780\) | −9.81861 | −0.351563 | ||||||||
\(781\) | −0.312061 | −0.0111664 | ||||||||
\(782\) | 11.2264 | 0.401457 | ||||||||
\(783\) | −9.53282 | −0.340675 | ||||||||
\(784\) | 4.90639 | 0.175228 | ||||||||
\(785\) | −13.0327 | −0.465155 | ||||||||
\(786\) | −29.0073 | −1.03466 | ||||||||
\(787\) | 17.5622 | 0.626023 | 0.313012 | − | 0.949749i | \(-0.398662\pi\) | ||||
0.313012 | + | 0.949749i | \(0.398662\pi\) | |||||||
\(788\) | 7.70435 | 0.274456 | ||||||||
\(789\) | −33.6948 | −1.19957 | ||||||||
\(790\) | 4.41404 | 0.157044 | ||||||||
\(791\) | −26.0337 | −0.925651 | ||||||||
\(792\) | −0.0542636 | −0.00192817 | ||||||||
\(793\) | −9.13953 | −0.324554 | ||||||||
\(794\) | −20.9947 | −0.745074 | ||||||||
\(795\) | 60.4864 | 2.14523 | ||||||||
\(796\) | −0.384256 | −0.0136196 | ||||||||
\(797\) | −38.5622 | −1.36594 | −0.682972 | − | 0.730445i | \(-0.739313\pi\) | ||||
−0.682972 | + | 0.730445i | \(0.739313\pi\) | |||||||
\(798\) | 31.1445 | 1.10250 | ||||||||
\(799\) | −23.0727 | −0.816252 | ||||||||
\(800\) | 8.46842 | 0.299404 | ||||||||
\(801\) | 10.1918 | 0.360110 | ||||||||
\(802\) | −30.2401 | −1.06782 | ||||||||
\(803\) | 0.157716 | 0.00556567 | ||||||||
\(804\) | 21.7172 | 0.765906 | ||||||||
\(805\) | −35.6039 | −1.25487 | ||||||||
\(806\) | −11.5653 | −0.407369 | ||||||||
\(807\) | −0.873049 | −0.0307328 | ||||||||
\(808\) | 5.35286 | 0.188313 | ||||||||
\(809\) | 22.2328 | 0.781664 | 0.390832 | − | 0.920462i | \(-0.372187\pi\) | ||||
0.390832 | + | 0.920462i | \(0.372187\pi\) | |||||||
\(810\) | 41.1654 | 1.44641 | ||||||||
\(811\) | −22.5824 | −0.792975 | −0.396488 | − | 0.918040i | \(-0.629771\pi\) | ||||
−0.396488 | + | 0.918040i | \(0.629771\pi\) | |||||||
\(812\) | 9.41193 | 0.330294 | ||||||||
\(813\) | 47.9397 | 1.68132 | ||||||||
\(814\) | −0.361220 | −0.0126608 | ||||||||
\(815\) | −8.65100 | −0.303031 | ||||||||
\(816\) | 8.29742 | 0.290468 | ||||||||
\(817\) | −42.6082 | −1.49067 | ||||||||
\(818\) | 4.69838 | 0.164275 | ||||||||
\(819\) | 5.85601 | 0.204626 | ||||||||
\(820\) | −1.63643 | −0.0571465 | ||||||||
\(821\) | 36.4722 | 1.27289 | 0.636444 | − | 0.771323i | \(-0.280405\pi\) | ||||
0.636444 | + | 0.771323i | \(0.280405\pi\) | |||||||
\(822\) | −36.7956 | −1.28339 | ||||||||
\(823\) | −41.4219 | −1.44388 | −0.721938 | − | 0.691958i | \(-0.756748\pi\) | ||||
−0.721938 | + | 0.691958i | \(0.756748\pi\) | |||||||
\(824\) | −17.2376 | −0.600500 | ||||||||
\(825\) | 0.724420 | 0.0252211 | ||||||||
\(826\) | 15.4632 | 0.538035 | ||||||||
\(827\) | 10.3127 | 0.358608 | 0.179304 | − | 0.983794i | \(-0.442615\pi\) | ||||
0.179304 | + | 0.983794i | \(0.442615\pi\) | |||||||
\(828\) | −3.70612 | −0.128796 | ||||||||
\(829\) | −1.45972 | −0.0506982 | −0.0253491 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253491 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(830\) | −15.5657 | −0.540294 | ||||||||
\(831\) | 55.7776 | 1.93490 | ||||||||
\(832\) | −1.28748 | −0.0446355 | ||||||||
\(833\) | −19.5910 | −0.678787 | ||||||||
\(834\) | 22.5148 | 0.779623 | ||||||||
\(835\) | 4.49983 | 0.155723 | ||||||||
\(836\) | −0.178805 | −0.00618411 | ||||||||
\(837\) | 31.3940 | 1.08514 | ||||||||
\(838\) | 27.6248 | 0.954282 | ||||||||
\(839\) | −41.5883 | −1.43579 | −0.717894 | − | 0.696153i | \(-0.754894\pi\) | ||||
−0.717894 | + | 0.696153i | \(0.754894\pi\) | |||||||
\(840\) | −26.3147 | −0.907943 | ||||||||
\(841\) | −21.5599 | −0.743446 | ||||||||
\(842\) | −4.20494 | −0.144912 | ||||||||
\(843\) | 35.9525 | 1.23827 | ||||||||
\(844\) | 21.3716 | 0.735643 | ||||||||
\(845\) | 41.6258 | 1.43197 | ||||||||
\(846\) | 7.61683 | 0.261872 | ||||||||
\(847\) | 37.9504 | 1.30399 | ||||||||
\(848\) | 7.93141 | 0.272366 | ||||||||
\(849\) | 69.1611 | 2.37360 | ||||||||
\(850\) | −33.8139 | −1.15981 | ||||||||
\(851\) | −24.6707 | −0.845702 | ||||||||
\(852\) | −15.7525 | −0.539673 | ||||||||
\(853\) | 36.7505 | 1.25831 | 0.629157 | − | 0.777279i | \(-0.283400\pi\) | ||||
0.629157 | + | 0.777279i | \(0.283400\pi\) | |||||||
\(854\) | −24.4947 | −0.838191 | ||||||||
\(855\) | −21.0121 | −0.718599 | ||||||||
\(856\) | 6.06603 | 0.207332 | ||||||||
\(857\) | −40.0036 | −1.36650 | −0.683249 | − | 0.730186i | \(-0.739433\pi\) | ||||
−0.683249 | + | 0.730186i | \(0.739433\pi\) | |||||||
\(858\) | −0.110136 | −0.00375999 | ||||||||
\(859\) | −11.6933 | −0.398971 | −0.199485 | − | 0.979901i | \(-0.563927\pi\) | ||||
−0.199485 | + | 0.979901i | \(0.563927\pi\) | |||||||
\(860\) | 36.0006 | 1.22761 | ||||||||
\(861\) | 3.19726 | 0.108962 | ||||||||
\(862\) | 27.4258 | 0.934126 | ||||||||
\(863\) | −13.9631 | −0.475311 | −0.237655 | − | 0.971350i | \(-0.576379\pi\) | ||||
−0.237655 | + | 0.971350i | \(0.576379\pi\) | |||||||
\(864\) | 3.49488 | 0.118898 | ||||||||
\(865\) | 48.1546 | 1.63730 | ||||||||
\(866\) | −17.7193 | −0.602125 | ||||||||
\(867\) | 2.19520 | 0.0745530 | ||||||||
\(868\) | −30.9959 | −1.05207 | ||||||||
\(869\) | 0.0495127 | 0.00167960 | ||||||||
\(870\) | −20.8016 | −0.705240 | ||||||||
\(871\) | 13.4554 | 0.455918 | ||||||||
\(872\) | −17.9980 | −0.609490 | ||||||||
\(873\) | 15.9179 | 0.538741 | ||||||||
\(874\) | −12.2121 | −0.413081 | ||||||||
\(875\) | 43.9217 | 1.48483 | ||||||||
\(876\) | 7.96135 | 0.268989 | ||||||||
\(877\) | 46.4762 | 1.56939 | 0.784695 | − | 0.619882i | \(-0.212820\pi\) | ||||
0.784695 | + | 0.619882i | \(0.212820\pi\) | |||||||
\(878\) | −11.2775 | −0.380598 | ||||||||
\(879\) | −13.4947 | −0.455166 | ||||||||
\(880\) | 0.151077 | 0.00509279 | ||||||||
\(881\) | −25.6684 | −0.864792 | −0.432396 | − | 0.901684i | \(-0.642332\pi\) | ||||
−0.432396 | + | 0.901684i | \(0.642332\pi\) | |||||||
\(882\) | 6.46744 | 0.217770 | ||||||||
\(883\) | −2.14740 | −0.0722658 | −0.0361329 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361329 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(884\) | 5.14085 | 0.172906 | ||||||||
\(885\) | −34.1758 | −1.14881 | ||||||||
\(886\) | 6.29496 | 0.211483 | ||||||||
\(887\) | −40.5477 | −1.36146 | −0.680729 | − | 0.732535i | \(-0.738337\pi\) | ||||
−0.680729 | + | 0.732535i | \(0.738337\pi\) | |||||||
\(888\) | −18.2340 | −0.611894 | ||||||||
\(889\) | 49.9242 | 1.67440 | ||||||||
\(890\) | −28.3752 | −0.951139 | ||||||||
\(891\) | 0.461756 | 0.0154694 | ||||||||
\(892\) | −7.32606 | −0.245295 | ||||||||
\(893\) | 25.0984 | 0.839886 | ||||||||
\(894\) | 27.5354 | 0.920923 | ||||||||
\(895\) | 13.2304 | 0.442245 | ||||||||
\(896\) | −3.45056 | −0.115275 | ||||||||
\(897\) | −7.52213 | −0.251157 | ||||||||
\(898\) | 30.4039 | 1.01459 | ||||||||
\(899\) | −24.5021 | −0.817189 | ||||||||
\(900\) | 11.1628 | 0.372092 | ||||||||
\(901\) | −31.6697 | −1.05507 | ||||||||
\(902\) | −0.0183560 | −0.000611187 0 | ||||||||
\(903\) | −70.3383 | −2.34071 | ||||||||
\(904\) | 7.54476 | 0.250935 | ||||||||
\(905\) | −42.4913 | −1.41246 | ||||||||
\(906\) | −21.0050 | −0.697844 | ||||||||
\(907\) | 27.3524 | 0.908223 | 0.454112 | − | 0.890945i | \(-0.349957\pi\) | ||||
0.454112 | + | 0.890945i | \(0.349957\pi\) | |||||||
\(908\) | 3.35917 | 0.111478 | ||||||||
\(909\) | 7.05596 | 0.234031 | ||||||||
\(910\) | −16.3039 | −0.540468 | ||||||||
\(911\) | 36.5608 | 1.21131 | 0.605656 | − | 0.795726i | \(-0.292911\pi\) | ||||
0.605656 | + | 0.795726i | \(0.292911\pi\) | |||||||
\(912\) | −9.02591 | −0.298878 | ||||||||
\(913\) | −0.174602 | −0.00577849 | ||||||||
\(914\) | −35.3996 | −1.17091 | ||||||||
\(915\) | 54.1364 | 1.78970 | ||||||||
\(916\) | 4.02544 | 0.133004 | ||||||||
\(917\) | −48.1668 | −1.59061 | ||||||||
\(918\) | −13.9549 | −0.460580 | ||||||||
\(919\) | −42.6438 | −1.40669 | −0.703345 | − | 0.710849i | \(-0.748311\pi\) | ||||
−0.703345 | + | 0.710849i | \(0.748311\pi\) | |||||||
\(920\) | 10.3183 | 0.340184 | ||||||||
\(921\) | 13.0149 | 0.428855 | ||||||||
\(922\) | 0.985230 | 0.0324468 | ||||||||
\(923\) | −9.75984 | −0.321249 | ||||||||
\(924\) | −0.295174 | −0.00971052 | ||||||||
\(925\) | 74.3079 | 2.44323 | ||||||||
\(926\) | −31.2127 | −1.02571 | ||||||||
\(927\) | −22.7220 | −0.746289 | ||||||||
\(928\) | −2.72765 | −0.0895395 | ||||||||
\(929\) | 27.3470 | 0.897224 | 0.448612 | − | 0.893727i | \(-0.351918\pi\) | ||||
0.448612 | + | 0.893727i | \(0.351918\pi\) | |||||||
\(930\) | 68.5049 | 2.24636 | ||||||||
\(931\) | 21.3110 | 0.698440 | ||||||||
\(932\) | 2.12563 | 0.0696273 | ||||||||
\(933\) | 58.1503 | 1.90376 | ||||||||
\(934\) | −41.4673 | −1.35685 | ||||||||
\(935\) | −0.603240 | −0.0197281 | ||||||||
\(936\) | −1.69712 | −0.0554720 | ||||||||
\(937\) | 15.0547 | 0.491816 | 0.245908 | − | 0.969293i | \(-0.420914\pi\) | ||||
0.245908 | + | 0.969293i | \(0.420914\pi\) | |||||||
\(938\) | 36.0615 | 1.17745 | ||||||||
\(939\) | −4.93076 | −0.160909 | ||||||||
\(940\) | −21.2062 | −0.691670 | ||||||||
\(941\) | 49.2447 | 1.60533 | 0.802666 | − | 0.596429i | \(-0.203414\pi\) | ||||
0.802666 | + | 0.596429i | \(0.203414\pi\) | |||||||
\(942\) | −7.37946 | −0.240436 | ||||||||
\(943\) | −1.25368 | −0.0408255 | ||||||||
\(944\) | −4.48136 | −0.145856 | ||||||||
\(945\) | 44.2569 | 1.43968 | ||||||||
\(946\) | 0.403823 | 0.0131294 | ||||||||
\(947\) | 38.9341 | 1.26519 | 0.632594 | − | 0.774484i | \(-0.281990\pi\) | ||||
0.632594 | + | 0.774484i | \(0.281990\pi\) | |||||||
\(948\) | 2.49935 | 0.0811752 | ||||||||
\(949\) | 4.93263 | 0.160120 | ||||||||
\(950\) | 36.7827 | 1.19339 | ||||||||
\(951\) | −0.667531 | −0.0216462 | ||||||||
\(952\) | 13.7779 | 0.446545 | ||||||||
\(953\) | −48.4828 | −1.57051 | −0.785256 | − | 0.619171i | \(-0.787469\pi\) | ||||
−0.785256 | + | 0.619171i | \(0.787469\pi\) | |||||||
\(954\) | 10.4549 | 0.338490 | ||||||||
\(955\) | 21.0234 | 0.680301 | ||||||||
\(956\) | 0.817349 | 0.0264350 | ||||||||
\(957\) | −0.233334 | −0.00754260 | ||||||||
\(958\) | 25.1228 | 0.811682 | ||||||||
\(959\) | −61.0993 | −1.97300 | ||||||||
\(960\) | 7.62619 | 0.246134 | ||||||||
\(961\) | 49.6915 | 1.60295 | ||||||||
\(962\) | −11.2973 | −0.364240 | ||||||||
\(963\) | 7.99603 | 0.257668 | ||||||||
\(964\) | 25.8208 | 0.831631 | ||||||||
\(965\) | 50.8291 | 1.63625 | ||||||||
\(966\) | −20.1599 | −0.648635 | ||||||||
\(967\) | −17.5222 | −0.563476 | −0.281738 | − | 0.959491i | \(-0.590911\pi\) | ||||
−0.281738 | + | 0.959491i | \(0.590911\pi\) | |||||||
\(968\) | −10.9983 | −0.353499 | ||||||||
\(969\) | 36.0400 | 1.15777 | ||||||||
\(970\) | −44.3175 | −1.42295 | ||||||||
\(971\) | 41.9650 | 1.34672 | 0.673360 | − | 0.739315i | \(-0.264850\pi\) | ||||
0.673360 | + | 0.739315i | \(0.264850\pi\) | |||||||
\(972\) | 12.8244 | 0.411342 | ||||||||
\(973\) | 37.3859 | 1.19854 | ||||||||
\(974\) | −1.05337 | −0.0337520 | ||||||||
\(975\) | 22.6565 | 0.725590 | ||||||||
\(976\) | 7.09875 | 0.227225 | ||||||||
\(977\) | 13.2720 | 0.424607 | 0.212304 | − | 0.977204i | \(-0.431903\pi\) | ||||
0.212304 | + | 0.977204i | \(0.431903\pi\) | |||||||
\(978\) | −4.89844 | −0.156635 | ||||||||
\(979\) | −0.318288 | −0.0101725 | ||||||||
\(980\) | −18.0061 | −0.575185 | ||||||||
\(981\) | −23.7244 | −0.757461 | ||||||||
\(982\) | −11.2134 | −0.357834 | ||||||||
\(983\) | −13.9796 | −0.445879 | −0.222939 | − | 0.974832i | \(-0.571565\pi\) | ||||
−0.222939 | + | 0.974832i | \(0.571565\pi\) | |||||||
\(984\) | −0.926591 | −0.0295386 | ||||||||
\(985\) | −28.2745 | −0.900900 | ||||||||
\(986\) | 10.8914 | 0.346852 | ||||||||
\(987\) | 41.4328 | 1.31882 | ||||||||
\(988\) | −5.59221 | −0.177912 | ||||||||
\(989\) | 27.5804 | 0.877007 | ||||||||
\(990\) | 0.199144 | 0.00632921 | ||||||||
\(991\) | 36.1350 | 1.14787 | 0.573933 | − | 0.818902i | \(-0.305417\pi\) | ||||
0.573933 | + | 0.818902i | \(0.305417\pi\) | |||||||
\(992\) | 8.98284 | 0.285206 | ||||||||
\(993\) | −44.6535 | −1.41704 | ||||||||
\(994\) | −26.1572 | −0.829655 | ||||||||
\(995\) | 1.41020 | 0.0447062 | ||||||||
\(996\) | −8.81375 | −0.279274 | ||||||||
\(997\) | 55.1563 | 1.74682 | 0.873409 | − | 0.486988i | \(-0.161904\pi\) | ||||
0.873409 | + | 0.486988i | \(0.161904\pi\) | |||||||
\(998\) | 14.7997 | 0.468475 | ||||||||
\(999\) | 30.6666 | 0.970249 |
(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 | 8042.2.a.a.1.14 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.14 | ✓ | 67 | 1.1 | even | 1 | trivial |