Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8014,2,Mod(1,8014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8014, 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("8014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8014 = 2 \cdot 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8014.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: | \(63.9921121799\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8014.1 |
$q$-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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.61803 | 0.723607 | 0.361803 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361803 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(6\) | −3.23607 | −1.32112 | ||||||||
\(7\) | 2.85410 | 1.07875 | 0.539375 | − | 0.842066i | \(-0.318661\pi\) | ||||
0.539375 | + | 0.842066i | \(0.318661\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 1.61803 | 0.511667 | ||||||||
\(11\) | 2.85410 | 0.860544 | 0.430272 | − | 0.902699i | \(-0.358418\pi\) | ||||
0.430272 | + | 0.902699i | \(0.358418\pi\) | |||||||
\(12\) | −3.23607 | −0.934172 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 2.85410 | 0.762791 | ||||||||
\(15\) | −5.23607 | −1.35195 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.70820 | −1.86951 | −0.934757 | − | 0.355288i | \(-0.884383\pi\) | ||||
−0.934757 | + | 0.355288i | \(0.884383\pi\) | |||||||
\(18\) | 7.47214 | 1.76120 | ||||||||
\(19\) | −1.85410 | −0.425360 | −0.212680 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212680 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(20\) | 1.61803 | 0.361803 | ||||||||
\(21\) | −9.23607 | −2.01548 | ||||||||
\(22\) | 2.85410 | 0.608497 | ||||||||
\(23\) | 6.09017 | 1.26989 | 0.634944 | − | 0.772558i | \(-0.281023\pi\) | ||||
0.634944 | + | 0.772558i | \(0.281023\pi\) | |||||||
\(24\) | −3.23607 | −0.660560 | ||||||||
\(25\) | −2.38197 | −0.476393 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 2.85410 | 0.539375 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −5.23607 | −0.955971 | ||||||||
\(31\) | 3.23607 | 0.581215 | 0.290607 | − | 0.956842i | \(-0.406143\pi\) | ||||
0.290607 | + | 0.956842i | \(0.406143\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −9.23607 | −1.60779 | ||||||||
\(34\) | −7.70820 | −1.32195 | ||||||||
\(35\) | 4.61803 | 0.780590 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | 4.76393 | 0.783186 | 0.391593 | − | 0.920139i | \(-0.371924\pi\) | ||||
0.391593 | + | 0.920139i | \(0.371924\pi\) | |||||||
\(38\) | −1.85410 | −0.300775 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 1.61803 | 0.255834 | ||||||||
\(41\) | 11.2361 | 1.75478 | 0.877390 | − | 0.479779i | \(-0.159283\pi\) | ||||
0.877390 | + | 0.479779i | \(0.159283\pi\) | |||||||
\(42\) | −9.23607 | −1.42516 | ||||||||
\(43\) | −4.47214 | −0.681994 | −0.340997 | − | 0.940064i | \(-0.610765\pi\) | ||||
−0.340997 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(44\) | 2.85410 | 0.430272 | ||||||||
\(45\) | 12.0902 | 1.80230 | ||||||||
\(46\) | 6.09017 | 0.897947 | ||||||||
\(47\) | 5.23607 | 0.763759 | 0.381880 | − | 0.924212i | \(-0.375277\pi\) | ||||
0.381880 | + | 0.924212i | \(0.375277\pi\) | |||||||
\(48\) | −3.23607 | −0.467086 | ||||||||
\(49\) | 1.14590 | 0.163700 | ||||||||
\(50\) | −2.38197 | −0.336861 | ||||||||
\(51\) | 24.9443 | 3.49290 | ||||||||
\(52\) | 1.23607 | 0.171412 | ||||||||
\(53\) | 12.0902 | 1.66071 | 0.830356 | − | 0.557233i | \(-0.188137\pi\) | ||||
0.830356 | + | 0.557233i | \(0.188137\pi\) | |||||||
\(54\) | −14.4721 | −1.96941 | ||||||||
\(55\) | 4.61803 | 0.622696 | ||||||||
\(56\) | 2.85410 | 0.381395 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 0.291796 | 0.0379886 | 0.0189943 | − | 0.999820i | \(-0.493954\pi\) | ||||
0.0189943 | + | 0.999820i | \(0.493954\pi\) | |||||||
\(60\) | −5.23607 | −0.675973 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 3.23607 | 0.410981 | ||||||||
\(63\) | 21.3262 | 2.68685 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −9.23607 | −1.13688 | ||||||||
\(67\) | −0.618034 | −0.0755049 | −0.0377524 | − | 0.999287i | \(-0.512020\pi\) | ||||
−0.0377524 | + | 0.999287i | \(0.512020\pi\) | |||||||
\(68\) | −7.70820 | −0.934757 | ||||||||
\(69\) | −19.7082 | −2.37259 | ||||||||
\(70\) | 4.61803 | 0.551961 | ||||||||
\(71\) | −11.7984 | −1.40021 | −0.700105 | − | 0.714040i | \(-0.746863\pi\) | ||||
−0.700105 | + | 0.714040i | \(0.746863\pi\) | |||||||
\(72\) | 7.47214 | 0.880600 | ||||||||
\(73\) | −1.85410 | −0.217006 | −0.108503 | − | 0.994096i | \(-0.534606\pi\) | ||||
−0.108503 | + | 0.994096i | \(0.534606\pi\) | |||||||
\(74\) | 4.76393 | 0.553796 | ||||||||
\(75\) | 7.70820 | 0.890067 | ||||||||
\(76\) | −1.85410 | −0.212680 | ||||||||
\(77\) | 8.14590 | 0.928311 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 1.61803 | 0.180902 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 11.2361 | 1.24082 | ||||||||
\(83\) | −6.85410 | −0.752335 | −0.376168 | − | 0.926552i | \(-0.622758\pi\) | ||||
−0.376168 | + | 0.926552i | \(0.622758\pi\) | |||||||
\(84\) | −9.23607 | −1.00774 | ||||||||
\(85\) | −12.4721 | −1.35279 | ||||||||
\(86\) | −4.47214 | −0.482243 | ||||||||
\(87\) | −6.47214 | −0.693886 | ||||||||
\(88\) | 2.85410 | 0.304248 | ||||||||
\(89\) | −5.61803 | −0.595510 | −0.297755 | − | 0.954642i | \(-0.596238\pi\) | ||||
−0.297755 | + | 0.954642i | \(0.596238\pi\) | |||||||
\(90\) | 12.0902 | 1.27442 | ||||||||
\(91\) | 3.52786 | 0.369821 | ||||||||
\(92\) | 6.09017 | 0.634944 | ||||||||
\(93\) | −10.4721 | −1.08591 | ||||||||
\(94\) | 5.23607 | 0.540059 | ||||||||
\(95\) | −3.00000 | −0.307794 | ||||||||
\(96\) | −3.23607 | −0.330280 | ||||||||
\(97\) | −12.7639 | −1.29598 | −0.647990 | − | 0.761648i | \(-0.724390\pi\) | ||||
−0.647990 | + | 0.761648i | \(0.724390\pi\) | |||||||
\(98\) | 1.14590 | 0.115753 | ||||||||
\(99\) | 21.3262 | 2.14337 | ||||||||
\(100\) | −2.38197 | −0.238197 | ||||||||
\(101\) | 0.763932 | 0.0760141 | 0.0380070 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380070 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(102\) | 24.9443 | 2.46985 | ||||||||
\(103\) | 14.7639 | 1.45473 | 0.727367 | − | 0.686249i | \(-0.240744\pi\) | ||||
0.727367 | + | 0.686249i | \(0.240744\pi\) | |||||||
\(104\) | 1.23607 | 0.121206 | ||||||||
\(105\) | −14.9443 | −1.45841 | ||||||||
\(106\) | 12.0902 | 1.17430 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −14.4721 | −1.39258 | ||||||||
\(109\) | 10.4721 | 1.00305 | 0.501524 | − | 0.865144i | \(-0.332773\pi\) | ||||
0.501524 | + | 0.865144i | \(0.332773\pi\) | |||||||
\(110\) | 4.61803 | 0.440312 | ||||||||
\(111\) | −15.4164 | −1.46326 | ||||||||
\(112\) | 2.85410 | 0.269687 | ||||||||
\(113\) | −2.38197 | −0.224077 | −0.112038 | − | 0.993704i | \(-0.535738\pi\) | ||||
−0.112038 | + | 0.993704i | \(0.535738\pi\) | |||||||
\(114\) | 6.00000 | 0.561951 | ||||||||
\(115\) | 9.85410 | 0.918900 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 9.23607 | 0.853875 | ||||||||
\(118\) | 0.291796 | 0.0268620 | ||||||||
\(119\) | −22.0000 | −2.01674 | ||||||||
\(120\) | −5.23607 | −0.477985 | ||||||||
\(121\) | −2.85410 | −0.259464 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | −36.3607 | −3.27853 | ||||||||
\(124\) | 3.23607 | 0.290607 | ||||||||
\(125\) | −11.9443 | −1.06833 | ||||||||
\(126\) | 21.3262 | 1.89989 | ||||||||
\(127\) | 11.2361 | 0.997040 | 0.498520 | − | 0.866878i | \(-0.333877\pi\) | ||||
0.498520 | + | 0.866878i | \(0.333877\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 14.4721 | 1.27420 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | 1.56231 | 0.136499 | 0.0682497 | − | 0.997668i | \(-0.478259\pi\) | ||||
0.0682497 | + | 0.997668i | \(0.478259\pi\) | |||||||
\(132\) | −9.23607 | −0.803897 | ||||||||
\(133\) | −5.29180 | −0.458857 | ||||||||
\(134\) | −0.618034 | −0.0533900 | ||||||||
\(135\) | −23.4164 | −2.01536 | ||||||||
\(136\) | −7.70820 | −0.660973 | ||||||||
\(137\) | −11.5279 | −0.984892 | −0.492446 | − | 0.870343i | \(-0.663897\pi\) | ||||
−0.492446 | + | 0.870343i | \(0.663897\pi\) | |||||||
\(138\) | −19.7082 | −1.67767 | ||||||||
\(139\) | −2.47214 | −0.209684 | −0.104842 | − | 0.994489i | \(-0.533434\pi\) | ||||
−0.104842 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(140\) | 4.61803 | 0.390295 | ||||||||
\(141\) | −16.9443 | −1.42697 | ||||||||
\(142\) | −11.7984 | −0.990098 | ||||||||
\(143\) | 3.52786 | 0.295015 | ||||||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | 3.23607 | 0.268741 | ||||||||
\(146\) | −1.85410 | −0.153447 | ||||||||
\(147\) | −3.70820 | −0.305848 | ||||||||
\(148\) | 4.76393 | 0.391593 | ||||||||
\(149\) | −7.23607 | −0.592802 | −0.296401 | − | 0.955064i | \(-0.595786\pi\) | ||||
−0.296401 | + | 0.955064i | \(0.595786\pi\) | |||||||
\(150\) | 7.70820 | 0.629372 | ||||||||
\(151\) | 7.70820 | 0.627285 | 0.313642 | − | 0.949541i | \(-0.398451\pi\) | ||||
0.313642 | + | 0.949541i | \(0.398451\pi\) | |||||||
\(152\) | −1.85410 | −0.150388 | ||||||||
\(153\) | −57.5967 | −4.65642 | ||||||||
\(154\) | 8.14590 | 0.656415 | ||||||||
\(155\) | 5.23607 | 0.420571 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | 20.6525 | 1.64825 | 0.824124 | − | 0.566410i | \(-0.191668\pi\) | ||||
0.824124 | + | 0.566410i | \(0.191668\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | −39.1246 | −3.10278 | ||||||||
\(160\) | 1.61803 | 0.127917 | ||||||||
\(161\) | 17.3820 | 1.36989 | ||||||||
\(162\) | 24.4164 | 1.91833 | ||||||||
\(163\) | 9.32624 | 0.730487 | 0.365244 | − | 0.930912i | \(-0.380986\pi\) | ||||
0.365244 | + | 0.930912i | \(0.380986\pi\) | |||||||
\(164\) | 11.2361 | 0.877390 | ||||||||
\(165\) | −14.9443 | −1.16341 | ||||||||
\(166\) | −6.85410 | −0.531981 | ||||||||
\(167\) | −8.32624 | −0.644304 | −0.322152 | − | 0.946688i | \(-0.604406\pi\) | ||||
−0.322152 | + | 0.946688i | \(0.604406\pi\) | |||||||
\(168\) | −9.23607 | −0.712578 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | −12.4721 | −0.956569 | ||||||||
\(171\) | −13.8541 | −1.05945 | ||||||||
\(172\) | −4.47214 | −0.340997 | ||||||||
\(173\) | −22.9443 | −1.74442 | −0.872210 | − | 0.489131i | \(-0.837314\pi\) | ||||
−0.872210 | + | 0.489131i | \(0.837314\pi\) | |||||||
\(174\) | −6.47214 | −0.490651 | ||||||||
\(175\) | −6.79837 | −0.513909 | ||||||||
\(176\) | 2.85410 | 0.215136 | ||||||||
\(177\) | −0.944272 | −0.0709758 | ||||||||
\(178\) | −5.61803 | −0.421089 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 12.0902 | 0.901148 | ||||||||
\(181\) | 2.76393 | 0.205441 | 0.102721 | − | 0.994710i | \(-0.467245\pi\) | ||||
0.102721 | + | 0.994710i | \(0.467245\pi\) | |||||||
\(182\) | 3.52786 | 0.261503 | ||||||||
\(183\) | −19.4164 | −1.43530 | ||||||||
\(184\) | 6.09017 | 0.448973 | ||||||||
\(185\) | 7.70820 | 0.566718 | ||||||||
\(186\) | −10.4721 | −0.767854 | ||||||||
\(187\) | −22.0000 | −1.60880 | ||||||||
\(188\) | 5.23607 | 0.381880 | ||||||||
\(189\) | −41.3050 | −3.00449 | ||||||||
\(190\) | −3.00000 | −0.217643 | ||||||||
\(191\) | 25.5623 | 1.84962 | 0.924812 | − | 0.380425i | \(-0.124222\pi\) | ||||
0.924812 | + | 0.380425i | \(0.124222\pi\) | |||||||
\(192\) | −3.23607 | −0.233543 | ||||||||
\(193\) | −4.61803 | −0.332413 | −0.166207 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166207 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(194\) | −12.7639 | −0.916397 | ||||||||
\(195\) | −6.47214 | −0.463479 | ||||||||
\(196\) | 1.14590 | 0.0818499 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 21.3262 | 1.51559 | ||||||||
\(199\) | 12.6180 | 0.894469 | 0.447234 | − | 0.894417i | \(-0.352409\pi\) | ||||
0.447234 | + | 0.894417i | \(0.352409\pi\) | |||||||
\(200\) | −2.38197 | −0.168430 | ||||||||
\(201\) | 2.00000 | 0.141069 | ||||||||
\(202\) | 0.763932 | 0.0537501 | ||||||||
\(203\) | 5.70820 | 0.400637 | ||||||||
\(204\) | 24.9443 | 1.74645 | ||||||||
\(205\) | 18.1803 | 1.26977 | ||||||||
\(206\) | 14.7639 | 1.02865 | ||||||||
\(207\) | 45.5066 | 3.16293 | ||||||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | −5.29180 | −0.366041 | ||||||||
\(210\) | −14.9443 | −1.03125 | ||||||||
\(211\) | 4.32624 | 0.297831 | 0.148915 | − | 0.988850i | \(-0.452422\pi\) | ||||
0.148915 | + | 0.988850i | \(0.452422\pi\) | |||||||
\(212\) | 12.0902 | 0.830356 | ||||||||
\(213\) | 38.1803 | 2.61607 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.23607 | −0.493496 | ||||||||
\(216\) | −14.4721 | −0.984704 | ||||||||
\(217\) | 9.23607 | 0.626985 | ||||||||
\(218\) | 10.4721 | 0.709263 | ||||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | 4.61803 | 0.311348 | ||||||||
\(221\) | −9.52786 | −0.640913 | ||||||||
\(222\) | −15.4164 | −1.03468 | ||||||||
\(223\) | −3.38197 | −0.226473 | −0.113237 | − | 0.993568i | \(-0.536122\pi\) | ||||
−0.113237 | + | 0.993568i | \(0.536122\pi\) | |||||||
\(224\) | 2.85410 | 0.190698 | ||||||||
\(225\) | −17.7984 | −1.18656 | ||||||||
\(226\) | −2.38197 | −0.158446 | ||||||||
\(227\) | −5.23607 | −0.347530 | −0.173765 | − | 0.984787i | \(-0.555593\pi\) | ||||
−0.173765 | + | 0.984787i | \(0.555593\pi\) | |||||||
\(228\) | 6.00000 | 0.397360 | ||||||||
\(229\) | −4.61803 | −0.305168 | −0.152584 | − | 0.988290i | \(-0.548760\pi\) | ||||
−0.152584 | + | 0.988290i | \(0.548760\pi\) | |||||||
\(230\) | 9.85410 | 0.649760 | ||||||||
\(231\) | −26.3607 | −1.73441 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | −8.09017 | −0.530005 | −0.265002 | − | 0.964248i | \(-0.585373\pi\) | ||||
−0.265002 | + | 0.964248i | \(0.585373\pi\) | |||||||
\(234\) | 9.23607 | 0.603781 | ||||||||
\(235\) | 8.47214 | 0.552661 | ||||||||
\(236\) | 0.291796 | 0.0189943 | ||||||||
\(237\) | −12.9443 | −0.840821 | ||||||||
\(238\) | −22.0000 | −1.42605 | ||||||||
\(239\) | 16.2918 | 1.05383 | 0.526914 | − | 0.849918i | \(-0.323349\pi\) | ||||
0.526914 | + | 0.849918i | \(0.323349\pi\) | |||||||
\(240\) | −5.23607 | −0.337987 | ||||||||
\(241\) | 5.05573 | 0.325668 | 0.162834 | − | 0.986653i | \(-0.447936\pi\) | ||||
0.162834 | + | 0.986653i | \(0.447936\pi\) | |||||||
\(242\) | −2.85410 | −0.183469 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 1.85410 | 0.118454 | ||||||||
\(246\) | −36.3607 | −2.31827 | ||||||||
\(247\) | −2.29180 | −0.145823 | ||||||||
\(248\) | 3.23607 | 0.205491 | ||||||||
\(249\) | 22.1803 | 1.40562 | ||||||||
\(250\) | −11.9443 | −0.755422 | ||||||||
\(251\) | 7.70820 | 0.486538 | 0.243269 | − | 0.969959i | \(-0.421780\pi\) | ||||
0.243269 | + | 0.969959i | \(0.421780\pi\) | |||||||
\(252\) | 21.3262 | 1.34343 | ||||||||
\(253\) | 17.3820 | 1.09279 | ||||||||
\(254\) | 11.2361 | 0.705014 | ||||||||
\(255\) | 40.3607 | 2.52748 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.4721 | 1.15226 | 0.576130 | − | 0.817358i | \(-0.304562\pi\) | ||||
0.576130 | + | 0.817358i | \(0.304562\pi\) | |||||||
\(258\) | 14.4721 | 0.900996 | ||||||||
\(259\) | 13.5967 | 0.844861 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 14.9443 | 0.925027 | ||||||||
\(262\) | 1.56231 | 0.0965196 | ||||||||
\(263\) | 21.4164 | 1.32059 | 0.660296 | − | 0.751005i | \(-0.270431\pi\) | ||||
0.660296 | + | 0.751005i | \(0.270431\pi\) | |||||||
\(264\) | −9.23607 | −0.568441 | ||||||||
\(265\) | 19.5623 | 1.20170 | ||||||||
\(266\) | −5.29180 | −0.324461 | ||||||||
\(267\) | 18.1803 | 1.11262 | ||||||||
\(268\) | −0.618034 | −0.0377524 | ||||||||
\(269\) | 7.09017 | 0.432295 | 0.216148 | − | 0.976361i | \(-0.430651\pi\) | ||||
0.216148 | + | 0.976361i | \(0.430651\pi\) | |||||||
\(270\) | −23.4164 | −1.42508 | ||||||||
\(271\) | 4.76393 | 0.289388 | 0.144694 | − | 0.989476i | \(-0.453780\pi\) | ||||
0.144694 | + | 0.989476i | \(0.453780\pi\) | |||||||
\(272\) | −7.70820 | −0.467379 | ||||||||
\(273\) | −11.4164 | −0.690952 | ||||||||
\(274\) | −11.5279 | −0.696424 | ||||||||
\(275\) | −6.79837 | −0.409957 | ||||||||
\(276\) | −19.7082 | −1.18629 | ||||||||
\(277\) | −29.4164 | −1.76746 | −0.883730 | − | 0.467996i | \(-0.844976\pi\) | ||||
−0.883730 | + | 0.467996i | \(0.844976\pi\) | |||||||
\(278\) | −2.47214 | −0.148269 | ||||||||
\(279\) | 24.1803 | 1.44764 | ||||||||
\(280\) | 4.61803 | 0.275980 | ||||||||
\(281\) | −21.7082 | −1.29500 | −0.647501 | − | 0.762064i | \(-0.724186\pi\) | ||||
−0.647501 | + | 0.762064i | \(0.724186\pi\) | |||||||
\(282\) | −16.9443 | −1.00902 | ||||||||
\(283\) | 7.05573 | 0.419419 | 0.209710 | − | 0.977764i | \(-0.432748\pi\) | ||||
0.209710 | + | 0.977764i | \(0.432748\pi\) | |||||||
\(284\) | −11.7984 | −0.700105 | ||||||||
\(285\) | 9.70820 | 0.575064 | ||||||||
\(286\) | 3.52786 | 0.208607 | ||||||||
\(287\) | 32.0689 | 1.89297 | ||||||||
\(288\) | 7.47214 | 0.440300 | ||||||||
\(289\) | 42.4164 | 2.49508 | ||||||||
\(290\) | 3.23607 | 0.190028 | ||||||||
\(291\) | 41.3050 | 2.42134 | ||||||||
\(292\) | −1.85410 | −0.108503 | ||||||||
\(293\) | −15.7082 | −0.917683 | −0.458842 | − | 0.888518i | \(-0.651735\pi\) | ||||
−0.458842 | + | 0.888518i | \(0.651735\pi\) | |||||||
\(294\) | −3.70820 | −0.216267 | ||||||||
\(295\) | 0.472136 | 0.0274888 | ||||||||
\(296\) | 4.76393 | 0.276898 | ||||||||
\(297\) | −41.3050 | −2.39676 | ||||||||
\(298\) | −7.23607 | −0.419174 | ||||||||
\(299\) | 7.52786 | 0.435348 | ||||||||
\(300\) | 7.70820 | 0.445033 | ||||||||
\(301\) | −12.7639 | −0.735701 | ||||||||
\(302\) | 7.70820 | 0.443557 | ||||||||
\(303\) | −2.47214 | −0.142020 | ||||||||
\(304\) | −1.85410 | −0.106340 | ||||||||
\(305\) | 9.70820 | 0.555890 | ||||||||
\(306\) | −57.5967 | −3.29259 | ||||||||
\(307\) | −20.6180 | −1.17673 | −0.588367 | − | 0.808594i | \(-0.700229\pi\) | ||||
−0.588367 | + | 0.808594i | \(0.700229\pi\) | |||||||
\(308\) | 8.14590 | 0.464156 | ||||||||
\(309\) | −47.7771 | −2.71794 | ||||||||
\(310\) | 5.23607 | 0.297389 | ||||||||
\(311\) | −10.5066 | −0.595773 | −0.297887 | − | 0.954601i | \(-0.596282\pi\) | ||||
−0.297887 | + | 0.954601i | \(0.596282\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | 20.4721 | 1.15715 | 0.578577 | − | 0.815628i | \(-0.303608\pi\) | ||||
0.578577 | + | 0.815628i | \(0.303608\pi\) | |||||||
\(314\) | 20.6525 | 1.16549 | ||||||||
\(315\) | 34.5066 | 1.94423 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 30.5066 | 1.71342 | 0.856710 | − | 0.515798i | \(-0.172505\pi\) | ||||
0.856710 | + | 0.515798i | \(0.172505\pi\) | |||||||
\(318\) | −39.1246 | −2.19400 | ||||||||
\(319\) | 5.70820 | 0.319598 | ||||||||
\(320\) | 1.61803 | 0.0904508 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.3820 | 0.968659 | ||||||||
\(323\) | 14.2918 | 0.795217 | ||||||||
\(324\) | 24.4164 | 1.35647 | ||||||||
\(325\) | −2.94427 | −0.163319 | ||||||||
\(326\) | 9.32624 | 0.516533 | ||||||||
\(327\) | −33.8885 | −1.87404 | ||||||||
\(328\) | 11.2361 | 0.620408 | ||||||||
\(329\) | 14.9443 | 0.823904 | ||||||||
\(330\) | −14.9443 | −0.822655 | ||||||||
\(331\) | 26.8328 | 1.47486 | 0.737432 | − | 0.675421i | \(-0.236038\pi\) | ||||
0.737432 | + | 0.675421i | \(0.236038\pi\) | |||||||
\(332\) | −6.85410 | −0.376168 | ||||||||
\(333\) | 35.5967 | 1.95069 | ||||||||
\(334\) | −8.32624 | −0.455591 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | −9.23607 | −0.503869 | ||||||||
\(337\) | 34.5066 | 1.87969 | 0.939847 | − | 0.341597i | \(-0.110968\pi\) | ||||
0.939847 | + | 0.341597i | \(0.110968\pi\) | |||||||
\(338\) | −11.4721 | −0.624002 | ||||||||
\(339\) | 7.70820 | 0.418652 | ||||||||
\(340\) | −12.4721 | −0.676397 | ||||||||
\(341\) | 9.23607 | 0.500161 | ||||||||
\(342\) | −13.8541 | −0.749144 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | −4.47214 | −0.241121 | ||||||||
\(345\) | −31.8885 | −1.71682 | ||||||||
\(346\) | −22.9443 | −1.23349 | ||||||||
\(347\) | −14.9443 | −0.802251 | −0.401125 | − | 0.916023i | \(-0.631381\pi\) | ||||
−0.401125 | + | 0.916023i | \(0.631381\pi\) | |||||||
\(348\) | −6.47214 | −0.346943 | ||||||||
\(349\) | −26.3607 | −1.41105 | −0.705527 | − | 0.708683i | \(-0.749290\pi\) | ||||
−0.705527 | + | 0.708683i | \(0.749290\pi\) | |||||||
\(350\) | −6.79837 | −0.363388 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 2.85410 | 0.152124 | ||||||||
\(353\) | −8.00000 | −0.425797 | −0.212899 | − | 0.977074i | \(-0.568290\pi\) | ||||
−0.212899 | + | 0.977074i | \(0.568290\pi\) | |||||||
\(354\) | −0.944272 | −0.0501875 | ||||||||
\(355\) | −19.0902 | −1.01320 | ||||||||
\(356\) | −5.61803 | −0.297755 | ||||||||
\(357\) | 71.1935 | 3.76796 | ||||||||
\(358\) | 10.0000 | 0.528516 | ||||||||
\(359\) | 29.8541 | 1.57564 | 0.787820 | − | 0.615906i | \(-0.211210\pi\) | ||||
0.787820 | + | 0.615906i | \(0.211210\pi\) | |||||||
\(360\) | 12.0902 | 0.637208 | ||||||||
\(361\) | −15.5623 | −0.819069 | ||||||||
\(362\) | 2.76393 | 0.145269 | ||||||||
\(363\) | 9.23607 | 0.484768 | ||||||||
\(364\) | 3.52786 | 0.184910 | ||||||||
\(365\) | −3.00000 | −0.157027 | ||||||||
\(366\) | −19.4164 | −1.01491 | ||||||||
\(367\) | −28.7426 | −1.50035 | −0.750177 | − | 0.661237i | \(-0.770032\pi\) | ||||
−0.750177 | + | 0.661237i | \(0.770032\pi\) | |||||||
\(368\) | 6.09017 | 0.317472 | ||||||||
\(369\) | 83.9574 | 4.37065 | ||||||||
\(370\) | 7.70820 | 0.400730 | ||||||||
\(371\) | 34.5066 | 1.79149 | ||||||||
\(372\) | −10.4721 | −0.542955 | ||||||||
\(373\) | −8.03444 | −0.416008 | −0.208004 | − | 0.978128i | \(-0.566697\pi\) | ||||
−0.208004 | + | 0.978128i | \(0.566697\pi\) | |||||||
\(374\) | −22.0000 | −1.13759 | ||||||||
\(375\) | 38.6525 | 1.99601 | ||||||||
\(376\) | 5.23607 | 0.270030 | ||||||||
\(377\) | 2.47214 | 0.127321 | ||||||||
\(378\) | −41.3050 | −2.12450 | ||||||||
\(379\) | 7.61803 | 0.391312 | 0.195656 | − | 0.980673i | \(-0.437316\pi\) | ||||
0.195656 | + | 0.980673i | \(0.437316\pi\) | |||||||
\(380\) | −3.00000 | −0.153897 | ||||||||
\(381\) | −36.3607 | −1.86281 | ||||||||
\(382\) | 25.5623 | 1.30788 | ||||||||
\(383\) | 17.9098 | 0.915150 | 0.457575 | − | 0.889171i | \(-0.348718\pi\) | ||||
0.457575 | + | 0.889171i | \(0.348718\pi\) | |||||||
\(384\) | −3.23607 | −0.165140 | ||||||||
\(385\) | 13.1803 | 0.671732 | ||||||||
\(386\) | −4.61803 | −0.235052 | ||||||||
\(387\) | −33.4164 | −1.69865 | ||||||||
\(388\) | −12.7639 | −0.647990 | ||||||||
\(389\) | 32.3607 | 1.64075 | 0.820376 | − | 0.571825i | \(-0.193764\pi\) | ||||
0.820376 | + | 0.571825i | \(0.193764\pi\) | |||||||
\(390\) | −6.47214 | −0.327729 | ||||||||
\(391\) | −46.9443 | −2.37407 | ||||||||
\(392\) | 1.14590 | 0.0578766 | ||||||||
\(393\) | −5.05573 | −0.255028 | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | 6.47214 | 0.325649 | ||||||||
\(396\) | 21.3262 | 1.07168 | ||||||||
\(397\) | 11.5279 | 0.578567 | 0.289283 | − | 0.957243i | \(-0.406583\pi\) | ||||
0.289283 | + | 0.957243i | \(0.406583\pi\) | |||||||
\(398\) | 12.6180 | 0.632485 | ||||||||
\(399\) | 17.1246 | 0.857303 | ||||||||
\(400\) | −2.38197 | −0.119098 | ||||||||
\(401\) | −12.2918 | −0.613823 | −0.306912 | − | 0.951738i | \(-0.599296\pi\) | ||||
−0.306912 | + | 0.951738i | \(0.599296\pi\) | |||||||
\(402\) | 2.00000 | 0.0997509 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | 0.763932 | 0.0380070 | ||||||||
\(405\) | 39.5066 | 1.96310 | ||||||||
\(406\) | 5.70820 | 0.283293 | ||||||||
\(407\) | 13.5967 | 0.673966 | ||||||||
\(408\) | 24.9443 | 1.23493 | ||||||||
\(409\) | −27.3262 | −1.35120 | −0.675598 | − | 0.737270i | \(-0.736114\pi\) | ||||
−0.675598 | + | 0.737270i | \(0.736114\pi\) | |||||||
\(410\) | 18.1803 | 0.897863 | ||||||||
\(411\) | 37.3050 | 1.84012 | ||||||||
\(412\) | 14.7639 | 0.727367 | ||||||||
\(413\) | 0.832816 | 0.0409802 | ||||||||
\(414\) | 45.5066 | 2.23653 | ||||||||
\(415\) | −11.0902 | −0.544395 | ||||||||
\(416\) | 1.23607 | 0.0606032 | ||||||||
\(417\) | 8.00000 | 0.391762 | ||||||||
\(418\) | −5.29180 | −0.258830 | ||||||||
\(419\) | 26.8328 | 1.31087 | 0.655434 | − | 0.755252i | \(-0.272486\pi\) | ||||
0.655434 | + | 0.755252i | \(0.272486\pi\) | |||||||
\(420\) | −14.9443 | −0.729206 | ||||||||
\(421\) | −11.0902 | −0.540502 | −0.270251 | − | 0.962790i | \(-0.587107\pi\) | ||||
−0.270251 | + | 0.962790i | \(0.587107\pi\) | |||||||
\(422\) | 4.32624 | 0.210598 | ||||||||
\(423\) | 39.1246 | 1.90230 | ||||||||
\(424\) | 12.0902 | 0.587151 | ||||||||
\(425\) | 18.3607 | 0.890624 | ||||||||
\(426\) | 38.1803 | 1.84984 | ||||||||
\(427\) | 17.1246 | 0.828718 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.4164 | −0.551189 | ||||||||
\(430\) | −7.23607 | −0.348954 | ||||||||
\(431\) | −24.3607 | −1.17341 | −0.586706 | − | 0.809800i | \(-0.699576\pi\) | ||||
−0.586706 | + | 0.809800i | \(0.699576\pi\) | |||||||
\(432\) | −14.4721 | −0.696291 | ||||||||
\(433\) | −11.1246 | −0.534615 | −0.267307 | − | 0.963611i | \(-0.586134\pi\) | ||||
−0.267307 | + | 0.963611i | \(0.586134\pi\) | |||||||
\(434\) | 9.23607 | 0.443345 | ||||||||
\(435\) | −10.4721 | −0.502100 | ||||||||
\(436\) | 10.4721 | 0.501524 | ||||||||
\(437\) | −11.2918 | −0.540160 | ||||||||
\(438\) | 6.00000 | 0.286691 | ||||||||
\(439\) | −14.1803 | −0.676791 | −0.338395 | − | 0.941004i | \(-0.609884\pi\) | ||||
−0.338395 | + | 0.941004i | \(0.609884\pi\) | |||||||
\(440\) | 4.61803 | 0.220156 | ||||||||
\(441\) | 8.56231 | 0.407729 | ||||||||
\(442\) | −9.52786 | −0.453194 | ||||||||
\(443\) | −0.111456 | −0.00529544 | −0.00264772 | − | 0.999996i | \(-0.500843\pi\) | ||||
−0.00264772 | + | 0.999996i | \(0.500843\pi\) | |||||||
\(444\) | −15.4164 | −0.731630 | ||||||||
\(445\) | −9.09017 | −0.430915 | ||||||||
\(446\) | −3.38197 | −0.160141 | ||||||||
\(447\) | 23.4164 | 1.10756 | ||||||||
\(448\) | 2.85410 | 0.134844 | ||||||||
\(449\) | 4.94427 | 0.233335 | 0.116667 | − | 0.993171i | \(-0.462779\pi\) | ||||
0.116667 | + | 0.993171i | \(0.462779\pi\) | |||||||
\(450\) | −17.7984 | −0.839023 | ||||||||
\(451\) | 32.0689 | 1.51006 | ||||||||
\(452\) | −2.38197 | −0.112038 | ||||||||
\(453\) | −24.9443 | −1.17198 | ||||||||
\(454\) | −5.23607 | −0.245741 | ||||||||
\(455\) | 5.70820 | 0.267605 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −11.8197 | −0.552900 | −0.276450 | − | 0.961028i | \(-0.589158\pi\) | ||||
−0.276450 | + | 0.961028i | \(0.589158\pi\) | |||||||
\(458\) | −4.61803 | −0.215787 | ||||||||
\(459\) | 111.554 | 5.20690 | ||||||||
\(460\) | 9.85410 | 0.459450 | ||||||||
\(461\) | 8.58359 | 0.399778 | 0.199889 | − | 0.979819i | \(-0.435942\pi\) | ||||
0.199889 | + | 0.979819i | \(0.435942\pi\) | |||||||
\(462\) | −26.3607 | −1.22641 | ||||||||
\(463\) | −0.583592 | −0.0271218 | −0.0135609 | − | 0.999908i | \(-0.504317\pi\) | ||||
−0.0135609 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | −16.9443 | −0.785772 | ||||||||
\(466\) | −8.09017 | −0.374770 | ||||||||
\(467\) | 6.47214 | 0.299495 | 0.149747 | − | 0.988724i | \(-0.452154\pi\) | ||||
0.149747 | + | 0.988724i | \(0.452154\pi\) | |||||||
\(468\) | 9.23607 | 0.426937 | ||||||||
\(469\) | −1.76393 | −0.0814508 | ||||||||
\(470\) | 8.47214 | 0.390790 | ||||||||
\(471\) | −66.8328 | −3.07949 | ||||||||
\(472\) | 0.291796 | 0.0134310 | ||||||||
\(473\) | −12.7639 | −0.586886 | ||||||||
\(474\) | −12.9443 | −0.594550 | ||||||||
\(475\) | 4.41641 | 0.202639 | ||||||||
\(476\) | −22.0000 | −1.00837 | ||||||||
\(477\) | 90.3394 | 4.13636 | ||||||||
\(478\) | 16.2918 | 0.745169 | ||||||||
\(479\) | −27.1246 | −1.23936 | −0.619678 | − | 0.784856i | \(-0.712737\pi\) | ||||
−0.619678 | + | 0.784856i | \(0.712737\pi\) | |||||||
\(480\) | −5.23607 | −0.238993 | ||||||||
\(481\) | 5.88854 | 0.268494 | ||||||||
\(482\) | 5.05573 | 0.230282 | ||||||||
\(483\) | −56.2492 | −2.55943 | ||||||||
\(484\) | −2.85410 | −0.129732 | ||||||||
\(485\) | −20.6525 | −0.937781 | ||||||||
\(486\) | −35.5967 | −1.61470 | ||||||||
\(487\) | 3.41641 | 0.154812 | 0.0774061 | − | 0.997000i | \(-0.475336\pi\) | ||||
0.0774061 | + | 0.997000i | \(0.475336\pi\) | |||||||
\(488\) | 6.00000 | 0.271607 | ||||||||
\(489\) | −30.1803 | −1.36480 | ||||||||
\(490\) | 1.85410 | 0.0837598 | ||||||||
\(491\) | 18.4377 | 0.832081 | 0.416041 | − | 0.909346i | \(-0.363417\pi\) | ||||
0.416041 | + | 0.909346i | \(0.363417\pi\) | |||||||
\(492\) | −36.3607 | −1.63927 | ||||||||
\(493\) | −15.4164 | −0.694320 | ||||||||
\(494\) | −2.29180 | −0.103113 | ||||||||
\(495\) | 34.5066 | 1.55096 | ||||||||
\(496\) | 3.23607 | 0.145304 | ||||||||
\(497\) | −33.6738 | −1.51047 | ||||||||
\(498\) | 22.1803 | 0.993925 | ||||||||
\(499\) | −14.4721 | −0.647862 | −0.323931 | − | 0.946081i | \(-0.605005\pi\) | ||||
−0.323931 | + | 0.946081i | \(0.605005\pi\) | |||||||
\(500\) | −11.9443 | −0.534164 | ||||||||
\(501\) | 26.9443 | 1.20378 | ||||||||
\(502\) | 7.70820 | 0.344034 | ||||||||
\(503\) | 32.9443 | 1.46891 | 0.734456 | − | 0.678656i | \(-0.237437\pi\) | ||||
0.734456 | + | 0.678656i | \(0.237437\pi\) | |||||||
\(504\) | 21.3262 | 0.949946 | ||||||||
\(505\) | 1.23607 | 0.0550043 | ||||||||
\(506\) | 17.3820 | 0.772723 | ||||||||
\(507\) | 37.1246 | 1.64876 | ||||||||
\(508\) | 11.2361 | 0.498520 | ||||||||
\(509\) | 8.47214 | 0.375521 | 0.187760 | − | 0.982215i | \(-0.439877\pi\) | ||||
0.187760 | + | 0.982215i | \(0.439877\pi\) | |||||||
\(510\) | 40.3607 | 1.78720 | ||||||||
\(511\) | −5.29180 | −0.234095 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 26.8328 | 1.18470 | ||||||||
\(514\) | 18.4721 | 0.814771 | ||||||||
\(515\) | 23.8885 | 1.05266 | ||||||||
\(516\) | 14.4721 | 0.637100 | ||||||||
\(517\) | 14.9443 | 0.657248 | ||||||||
\(518\) | 13.5967 | 0.597407 | ||||||||
\(519\) | 74.2492 | 3.25918 | ||||||||
\(520\) | 2.00000 | 0.0877058 | ||||||||
\(521\) | −33.7984 | −1.48073 | −0.740367 | − | 0.672203i | \(-0.765348\pi\) | ||||
−0.740367 | + | 0.672203i | \(0.765348\pi\) | |||||||
\(522\) | 14.9443 | 0.654093 | ||||||||
\(523\) | −10.1803 | −0.445155 | −0.222578 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222578 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(524\) | 1.56231 | 0.0682497 | ||||||||
\(525\) | 22.0000 | 0.960159 | ||||||||
\(526\) | 21.4164 | 0.933800 | ||||||||
\(527\) | −24.9443 | −1.08659 | ||||||||
\(528\) | −9.23607 | −0.401948 | ||||||||
\(529\) | 14.0902 | 0.612616 | ||||||||
\(530\) | 19.5623 | 0.849732 | ||||||||
\(531\) | 2.18034 | 0.0946187 | ||||||||
\(532\) | −5.29180 | −0.229428 | ||||||||
\(533\) | 13.8885 | 0.601580 | ||||||||
\(534\) | 18.1803 | 0.786740 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.618034 | −0.0266950 | ||||||||
\(537\) | −32.3607 | −1.39647 | ||||||||
\(538\) | 7.09017 | 0.305679 | ||||||||
\(539\) | 3.27051 | 0.140871 | ||||||||
\(540\) | −23.4164 | −1.00768 | ||||||||
\(541\) | 20.9098 | 0.898984 | 0.449492 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449492 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(542\) | 4.76393 | 0.204628 | ||||||||
\(543\) | −8.94427 | −0.383835 | ||||||||
\(544\) | −7.70820 | −0.330487 | ||||||||
\(545\) | 16.9443 | 0.725813 | ||||||||
\(546\) | −11.4164 | −0.488577 | ||||||||
\(547\) | 15.6738 | 0.670162 | 0.335081 | − | 0.942189i | \(-0.391236\pi\) | ||||
0.335081 | + | 0.942189i | \(0.391236\pi\) | |||||||
\(548\) | −11.5279 | −0.492446 | ||||||||
\(549\) | 44.8328 | 1.91342 | ||||||||
\(550\) | −6.79837 | −0.289884 | ||||||||
\(551\) | −3.70820 | −0.157975 | ||||||||
\(552\) | −19.7082 | −0.838837 | ||||||||
\(553\) | 11.4164 | 0.485475 | ||||||||
\(554\) | −29.4164 | −1.24978 | ||||||||
\(555\) | −24.9443 | −1.05883 | ||||||||
\(556\) | −2.47214 | −0.104842 | ||||||||
\(557\) | −28.3262 | −1.20022 | −0.600111 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600111 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(558\) | 24.1803 | 1.02364 | ||||||||
\(559\) | −5.52786 | −0.233804 | ||||||||
\(560\) | 4.61803 | 0.195148 | ||||||||
\(561\) | 71.1935 | 3.00579 | ||||||||
\(562\) | −21.7082 | −0.915705 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | −16.9443 | −0.713483 | ||||||||
\(565\) | −3.85410 | −0.162143 | ||||||||
\(566\) | 7.05573 | 0.296574 | ||||||||
\(567\) | 69.6869 | 2.92658 | ||||||||
\(568\) | −11.7984 | −0.495049 | ||||||||
\(569\) | 16.2918 | 0.682988 | 0.341494 | − | 0.939884i | \(-0.389067\pi\) | ||||
0.341494 | + | 0.939884i | \(0.389067\pi\) | |||||||
\(570\) | 9.70820 | 0.406632 | ||||||||
\(571\) | 40.4721 | 1.69371 | 0.846853 | − | 0.531827i | \(-0.178494\pi\) | ||||
0.846853 | + | 0.531827i | \(0.178494\pi\) | |||||||
\(572\) | 3.52786 | 0.147507 | ||||||||
\(573\) | −82.7214 | −3.45573 | ||||||||
\(574\) | 32.0689 | 1.33853 | ||||||||
\(575\) | −14.5066 | −0.604966 | ||||||||
\(576\) | 7.47214 | 0.311339 | ||||||||
\(577\) | −13.0344 | −0.542631 | −0.271315 | − | 0.962490i | \(-0.587459\pi\) | ||||
−0.271315 | + | 0.962490i | \(0.587459\pi\) | |||||||
\(578\) | 42.4164 | 1.76429 | ||||||||
\(579\) | 14.9443 | 0.621063 | ||||||||
\(580\) | 3.23607 | 0.134370 | ||||||||
\(581\) | −19.5623 | −0.811581 | ||||||||
\(582\) | 41.3050 | 1.71215 | ||||||||
\(583\) | 34.5066 | 1.42912 | ||||||||
\(584\) | −1.85410 | −0.0767233 | ||||||||
\(585\) | 14.9443 | 0.617870 | ||||||||
\(586\) | −15.7082 | −0.648900 | ||||||||
\(587\) | −8.74265 | −0.360848 | −0.180424 | − | 0.983589i | \(-0.557747\pi\) | ||||
−0.180424 | + | 0.983589i | \(0.557747\pi\) | |||||||
\(588\) | −3.70820 | −0.152924 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0.472136 | 0.0194375 | ||||||||
\(591\) | 32.3607 | 1.33114 | ||||||||
\(592\) | 4.76393 | 0.195796 | ||||||||
\(593\) | −3.90983 | −0.160557 | −0.0802787 | − | 0.996772i | \(-0.525581\pi\) | ||||
−0.0802787 | + | 0.996772i | \(0.525581\pi\) | |||||||
\(594\) | −41.3050 | −1.69476 | ||||||||
\(595\) | −35.5967 | −1.45932 | ||||||||
\(596\) | −7.23607 | −0.296401 | ||||||||
\(597\) | −40.8328 | −1.67118 | ||||||||
\(598\) | 7.52786 | 0.307837 | ||||||||
\(599\) | −6.00000 | −0.245153 | −0.122577 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122577 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(600\) | 7.70820 | 0.314686 | ||||||||
\(601\) | −34.5623 | −1.40983 | −0.704913 | − | 0.709294i | \(-0.749014\pi\) | ||||
−0.704913 | + | 0.709294i | \(0.749014\pi\) | |||||||
\(602\) | −12.7639 | −0.520219 | ||||||||
\(603\) | −4.61803 | −0.188061 | ||||||||
\(604\) | 7.70820 | 0.313642 | ||||||||
\(605\) | −4.61803 | −0.187750 | ||||||||
\(606\) | −2.47214 | −0.100424 | ||||||||
\(607\) | −27.7984 | −1.12830 | −0.564151 | − | 0.825672i | \(-0.690796\pi\) | ||||
−0.564151 | + | 0.825672i | \(0.690796\pi\) | |||||||
\(608\) | −1.85410 | −0.0751938 | ||||||||
\(609\) | −18.4721 | −0.748529 | ||||||||
\(610\) | 9.70820 | 0.393074 | ||||||||
\(611\) | 6.47214 | 0.261835 | ||||||||
\(612\) | −57.5967 | −2.32821 | ||||||||
\(613\) | 11.7082 | 0.472890 | 0.236445 | − | 0.971645i | \(-0.424018\pi\) | ||||
0.236445 | + | 0.971645i | \(0.424018\pi\) | |||||||
\(614\) | −20.6180 | −0.832076 | ||||||||
\(615\) | −58.8328 | −2.37237 | ||||||||
\(616\) | 8.14590 | 0.328208 | ||||||||
\(617\) | 0.909830 | 0.0366284 | 0.0183142 | − | 0.999832i | \(-0.494170\pi\) | ||||
0.0183142 | + | 0.999832i | \(0.494170\pi\) | |||||||
\(618\) | −47.7771 | −1.92188 | ||||||||
\(619\) | 29.3262 | 1.17872 | 0.589361 | − | 0.807870i | \(-0.299380\pi\) | ||||
0.589361 | + | 0.807870i | \(0.299380\pi\) | |||||||
\(620\) | 5.23607 | 0.210286 | ||||||||
\(621\) | −88.1378 | −3.53685 | ||||||||
\(622\) | −10.5066 | −0.421275 | ||||||||
\(623\) | −16.0344 | −0.642406 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −7.41641 | −0.296656 | ||||||||
\(626\) | 20.4721 | 0.818231 | ||||||||
\(627\) | 17.1246 | 0.683891 | ||||||||
\(628\) | 20.6525 | 0.824124 | ||||||||
\(629\) | −36.7214 | −1.46418 | ||||||||
\(630\) | 34.5066 | 1.37477 | ||||||||
\(631\) | 3.09017 | 0.123018 | 0.0615089 | − | 0.998107i | \(-0.480409\pi\) | ||||
0.0615089 | + | 0.998107i | \(0.480409\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | −14.0000 | −0.556450 | ||||||||
\(634\) | 30.5066 | 1.21157 | ||||||||
\(635\) | 18.1803 | 0.721465 | ||||||||
\(636\) | −39.1246 | −1.55139 | ||||||||
\(637\) | 1.41641 | 0.0561201 | ||||||||
\(638\) | 5.70820 | 0.225990 | ||||||||
\(639\) | −88.1591 | −3.48752 | ||||||||
\(640\) | 1.61803 | 0.0639584 | ||||||||
\(641\) | 18.5836 | 0.734008 | 0.367004 | − | 0.930219i | \(-0.380384\pi\) | ||||
0.367004 | + | 0.930219i | \(0.380384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.3262 | 1.90580 | 0.952900 | − | 0.303283i | \(-0.0980829\pi\) | ||||
0.952900 | + | 0.303283i | \(0.0980829\pi\) | |||||||
\(644\) | 17.3820 | 0.684945 | ||||||||
\(645\) | 23.4164 | 0.922020 | ||||||||
\(646\) | 14.2918 | 0.562303 | ||||||||
\(647\) | −1.85410 | −0.0728923 | −0.0364461 | − | 0.999336i | \(-0.511604\pi\) | ||||
−0.0364461 | + | 0.999336i | \(0.511604\pi\) | |||||||
\(648\) | 24.4164 | 0.959167 | ||||||||
\(649\) | 0.832816 | 0.0326909 | ||||||||
\(650\) | −2.94427 | −0.115484 | ||||||||
\(651\) | −29.8885 | −1.17142 | ||||||||
\(652\) | 9.32624 | 0.365244 | ||||||||
\(653\) | 26.5066 | 1.03728 | 0.518641 | − | 0.854992i | \(-0.326438\pi\) | ||||
0.518641 | + | 0.854992i | \(0.326438\pi\) | |||||||
\(654\) | −33.8885 | −1.32515 | ||||||||
\(655\) | 2.52786 | 0.0987718 | ||||||||
\(656\) | 11.2361 | 0.438695 | ||||||||
\(657\) | −13.8541 | −0.540500 | ||||||||
\(658\) | 14.9443 | 0.582588 | ||||||||
\(659\) | 25.3050 | 0.985741 | 0.492870 | − | 0.870103i | \(-0.335948\pi\) | ||||
0.492870 | + | 0.870103i | \(0.335948\pi\) | |||||||
\(660\) | −14.9443 | −0.581705 | ||||||||
\(661\) | 8.76393 | 0.340877 | 0.170439 | − | 0.985368i | \(-0.445482\pi\) | ||||
0.170439 | + | 0.985368i | \(0.445482\pi\) | |||||||
\(662\) | 26.8328 | 1.04289 | ||||||||
\(663\) | 30.8328 | 1.19745 | ||||||||
\(664\) | −6.85410 | −0.265991 | ||||||||
\(665\) | −8.56231 | −0.332032 | ||||||||
\(666\) | 35.5967 | 1.37935 | ||||||||
\(667\) | 12.1803 | 0.471625 | ||||||||
\(668\) | −8.32624 | −0.322152 | ||||||||
\(669\) | 10.9443 | 0.423130 | ||||||||
\(670\) | −1.00000 | −0.0386334 | ||||||||
\(671\) | 17.1246 | 0.661088 | ||||||||
\(672\) | −9.23607 | −0.356289 | ||||||||
\(673\) | −50.2492 | −1.93697 | −0.968483 | − | 0.249081i | \(-0.919871\pi\) | ||||
−0.968483 | + | 0.249081i | \(0.919871\pi\) | |||||||
\(674\) | 34.5066 | 1.32914 | ||||||||
\(675\) | 34.4721 | 1.32683 | ||||||||
\(676\) | −11.4721 | −0.441236 | ||||||||
\(677\) | 7.88854 | 0.303181 | 0.151591 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151591 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(678\) | 7.70820 | 0.296032 | ||||||||
\(679\) | −36.4296 | −1.39804 | ||||||||
\(680\) | −12.4721 | −0.478285 | ||||||||
\(681\) | 16.9443 | 0.649306 | ||||||||
\(682\) | 9.23607 | 0.353667 | ||||||||
\(683\) | −12.5836 | −0.481498 | −0.240749 | − | 0.970587i | \(-0.577393\pi\) | ||||
−0.240749 | + | 0.970587i | \(0.577393\pi\) | |||||||
\(684\) | −13.8541 | −0.529725 | ||||||||
\(685\) | −18.6525 | −0.712674 | ||||||||
\(686\) | −16.7082 | −0.637922 | ||||||||
\(687\) | 14.9443 | 0.570160 | ||||||||
\(688\) | −4.47214 | −0.170499 | ||||||||
\(689\) | 14.9443 | 0.569331 | ||||||||
\(690\) | −31.8885 | −1.21398 | ||||||||
\(691\) | 30.0689 | 1.14387 | 0.571937 | − | 0.820297i | \(-0.306192\pi\) | ||||
0.571937 | + | 0.820297i | \(0.306192\pi\) | |||||||
\(692\) | −22.9443 | −0.872210 | ||||||||
\(693\) | 60.8673 | 2.31216 | ||||||||
\(694\) | −14.9443 | −0.567277 | ||||||||
\(695\) | −4.00000 | −0.151729 | ||||||||
\(696\) | −6.47214 | −0.245326 | ||||||||
\(697\) | −86.6099 | −3.28058 | ||||||||
\(698\) | −26.3607 | −0.997766 | ||||||||
\(699\) | 26.1803 | 0.990231 | ||||||||
\(700\) | −6.79837 | −0.256954 | ||||||||
\(701\) | 40.1803 | 1.51759 | 0.758795 | − | 0.651329i | \(-0.225788\pi\) | ||||
0.758795 | + | 0.651329i | \(0.225788\pi\) | |||||||
\(702\) | −17.8885 | −0.675160 | ||||||||
\(703\) | −8.83282 | −0.333136 | ||||||||
\(704\) | 2.85410 | 0.107568 | ||||||||
\(705\) | −27.4164 | −1.03256 | ||||||||
\(706\) | −8.00000 | −0.301084 | ||||||||
\(707\) | 2.18034 | 0.0820001 | ||||||||
\(708\) | −0.944272 | −0.0354879 | ||||||||
\(709\) | 37.7771 | 1.41875 | 0.709374 | − | 0.704832i | \(-0.248978\pi\) | ||||
0.709374 | + | 0.704832i | \(0.248978\pi\) | |||||||
\(710\) | −19.0902 | −0.716441 | ||||||||
\(711\) | 29.8885 | 1.12091 | ||||||||
\(712\) | −5.61803 | −0.210545 | ||||||||
\(713\) | 19.7082 | 0.738078 | ||||||||
\(714\) | 71.1935 | 2.66435 | ||||||||
\(715\) | 5.70820 | 0.213475 | ||||||||
\(716\) | 10.0000 | 0.373718 | ||||||||
\(717\) | −52.7214 | −1.96892 | ||||||||
\(718\) | 29.8541 | 1.11415 | ||||||||
\(719\) | 38.2918 | 1.42804 | 0.714022 | − | 0.700124i | \(-0.246872\pi\) | ||||
0.714022 | + | 0.700124i | \(0.246872\pi\) | |||||||
\(720\) | 12.0902 | 0.450574 | ||||||||
\(721\) | 42.1378 | 1.56929 | ||||||||
\(722\) | −15.5623 | −0.579169 | ||||||||
\(723\) | −16.3607 | −0.608460 | ||||||||
\(724\) | 2.76393 | 0.102721 | ||||||||
\(725\) | −4.76393 | −0.176928 | ||||||||
\(726\) | 9.23607 | 0.342783 | ||||||||
\(727\) | −16.3607 | −0.606784 | −0.303392 | − | 0.952866i | \(-0.598119\pi\) | ||||
−0.303392 | + | 0.952866i | \(0.598119\pi\) | |||||||
\(728\) | 3.52786 | 0.130751 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | −3.00000 | −0.111035 | ||||||||
\(731\) | 34.4721 | 1.27500 | ||||||||
\(732\) | −19.4164 | −0.717651 | ||||||||
\(733\) | −17.6180 | −0.650737 | −0.325368 | − | 0.945587i | \(-0.605488\pi\) | ||||
−0.325368 | + | 0.945587i | \(0.605488\pi\) | |||||||
\(734\) | −28.7426 | −1.06091 | ||||||||
\(735\) | −6.00000 | −0.221313 | ||||||||
\(736\) | 6.09017 | 0.224487 | ||||||||
\(737\) | −1.76393 | −0.0649753 | ||||||||
\(738\) | 83.9574 | 3.09052 | ||||||||
\(739\) | 20.4721 | 0.753080 | 0.376540 | − | 0.926400i | \(-0.377114\pi\) | ||||
0.376540 | + | 0.926400i | \(0.377114\pi\) | |||||||
\(740\) | 7.70820 | 0.283359 | ||||||||
\(741\) | 7.41641 | 0.272449 | ||||||||
\(742\) | 34.5066 | 1.26678 | ||||||||
\(743\) | 17.2016 | 0.631066 | 0.315533 | − | 0.948915i | \(-0.397817\pi\) | ||||
0.315533 | + | 0.948915i | \(0.397817\pi\) | |||||||
\(744\) | −10.4721 | −0.383927 | ||||||||
\(745\) | −11.7082 | −0.428955 | ||||||||
\(746\) | −8.03444 | −0.294162 | ||||||||
\(747\) | −51.2148 | −1.87385 | ||||||||
\(748\) | −22.0000 | −0.804400 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 38.6525 | 1.41139 | ||||||||
\(751\) | −42.6312 | −1.55563 | −0.777817 | − | 0.628491i | \(-0.783673\pi\) | ||||
−0.777817 | + | 0.628491i | \(0.783673\pi\) | |||||||
\(752\) | 5.23607 | 0.190940 | ||||||||
\(753\) | −24.9443 | −0.909020 | ||||||||
\(754\) | 2.47214 | 0.0900299 | ||||||||
\(755\) | 12.4721 | 0.453908 | ||||||||
\(756\) | −41.3050 | −1.50225 | ||||||||
\(757\) | 1.81966 | 0.0661367 | 0.0330683 | − | 0.999453i | \(-0.489472\pi\) | ||||
0.0330683 | + | 0.999453i | \(0.489472\pi\) | |||||||
\(758\) | 7.61803 | 0.276699 | ||||||||
\(759\) | −56.2492 | −2.04172 | ||||||||
\(760\) | −3.00000 | −0.108821 | ||||||||
\(761\) | −45.2705 | −1.64105 | −0.820527 | − | 0.571607i | \(-0.806320\pi\) | ||||
−0.820527 | + | 0.571607i | \(0.806320\pi\) | |||||||
\(762\) | −36.3607 | −1.31721 | ||||||||
\(763\) | 29.8885 | 1.08204 | ||||||||
\(764\) | 25.5623 | 0.924812 | ||||||||
\(765\) | −93.1935 | −3.36942 | ||||||||
\(766\) | 17.9098 | 0.647108 | ||||||||
\(767\) | 0.360680 | 0.0130234 | ||||||||
\(768\) | −3.23607 | −0.116772 | ||||||||
\(769\) | 25.5623 | 0.921800 | 0.460900 | − | 0.887452i | \(-0.347527\pi\) | ||||
0.460900 | + | 0.887452i | \(0.347527\pi\) | |||||||
\(770\) | 13.1803 | 0.474986 | ||||||||
\(771\) | −59.7771 | −2.15282 | ||||||||
\(772\) | −4.61803 | −0.166207 | ||||||||
\(773\) | −40.8328 | −1.46865 | −0.734327 | − | 0.678796i | \(-0.762502\pi\) | ||||
−0.734327 | + | 0.678796i | \(0.762502\pi\) | |||||||
\(774\) | −33.4164 | −1.20113 | ||||||||
\(775\) | −7.70820 | −0.276887 | ||||||||
\(776\) | −12.7639 | −0.458198 | ||||||||
\(777\) | −44.0000 | −1.57849 | ||||||||
\(778\) | 32.3607 | 1.16019 | ||||||||
\(779\) | −20.8328 | −0.746413 | ||||||||
\(780\) | −6.47214 | −0.231740 | ||||||||
\(781\) | −33.6738 | −1.20494 | ||||||||
\(782\) | −46.9443 | −1.67872 | ||||||||
\(783\) | −28.9443 | −1.03438 | ||||||||
\(784\) | 1.14590 | 0.0409249 | ||||||||
\(785\) | 33.4164 | 1.19268 | ||||||||
\(786\) | −5.05573 | −0.180332 | ||||||||
\(787\) | −8.18034 | −0.291598 | −0.145799 | − | 0.989314i | \(-0.546575\pi\) | ||||
−0.145799 | + | 0.989314i | \(0.546575\pi\) | |||||||
\(788\) | −10.0000 | −0.356235 | ||||||||
\(789\) | −69.3050 | −2.46732 | ||||||||
\(790\) | 6.47214 | 0.230268 | ||||||||
\(791\) | −6.79837 | −0.241722 | ||||||||
\(792\) | 21.3262 | 0.757795 | ||||||||
\(793\) | 7.41641 | 0.263364 | ||||||||
\(794\) | 11.5279 | 0.409109 | ||||||||
\(795\) | −63.3050 | −2.24520 | ||||||||
\(796\) | 12.6180 | 0.447234 | ||||||||
\(797\) | −13.2016 | −0.467626 | −0.233813 | − | 0.972282i | \(-0.575120\pi\) | ||||
−0.233813 | + | 0.972282i | \(0.575120\pi\) | |||||||
\(798\) | 17.1246 | 0.606205 | ||||||||
\(799\) | −40.3607 | −1.42786 | ||||||||
\(800\) | −2.38197 | −0.0842152 | ||||||||
\(801\) | −41.9787 | −1.48324 | ||||||||
\(802\) | −12.2918 | −0.434038 | ||||||||
\(803\) | −5.29180 | −0.186743 | ||||||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 28.1246 | 0.991262 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | −22.9443 | −0.807677 | ||||||||
\(808\) | 0.763932 | 0.0268750 | ||||||||
\(809\) | −34.3607 | −1.20806 | −0.604029 | − | 0.796963i | \(-0.706439\pi\) | ||||
−0.604029 | + | 0.796963i | \(0.706439\pi\) | |||||||
\(810\) | 39.5066 | 1.38812 | ||||||||
\(811\) | 38.8541 | 1.36435 | 0.682176 | − | 0.731188i | \(-0.261034\pi\) | ||||
0.682176 | + | 0.731188i | \(0.261034\pi\) | |||||||
\(812\) | 5.70820 | 0.200319 | ||||||||
\(813\) | −15.4164 | −0.540677 | ||||||||
\(814\) | 13.5967 | 0.476566 | ||||||||
\(815\) | 15.0902 | 0.528586 | ||||||||
\(816\) | 24.9443 | 0.873224 | ||||||||
\(817\) | 8.29180 | 0.290093 | ||||||||
\(818\) | −27.3262 | −0.955440 | ||||||||
\(819\) | 26.3607 | 0.921117 | ||||||||
\(820\) | 18.1803 | 0.634885 | ||||||||
\(821\) | 31.9098 | 1.11366 | 0.556830 | − | 0.830626i | \(-0.312017\pi\) | ||||
0.556830 | + | 0.830626i | \(0.312017\pi\) | |||||||
\(822\) | 37.3050 | 1.30116 | ||||||||
\(823\) | −7.81966 | −0.272576 | −0.136288 | − | 0.990669i | \(-0.543517\pi\) | ||||
−0.136288 | + | 0.990669i | \(0.543517\pi\) | |||||||
\(824\) | 14.7639 | 0.514326 | ||||||||
\(825\) | 22.0000 | 0.765942 | ||||||||
\(826\) | 0.832816 | 0.0289774 | ||||||||
\(827\) | 40.7426 | 1.41676 | 0.708380 | − | 0.705831i | \(-0.249426\pi\) | ||||
0.708380 | + | 0.705831i | \(0.249426\pi\) | |||||||
\(828\) | 45.5066 | 1.58146 | ||||||||
\(829\) | 40.6312 | 1.41118 | 0.705590 | − | 0.708621i | \(-0.250682\pi\) | ||||
0.705590 | + | 0.708621i | \(0.250682\pi\) | |||||||
\(830\) | −11.0902 | −0.384945 | ||||||||
\(831\) | 95.1935 | 3.30223 | ||||||||
\(832\) | 1.23607 | 0.0428529 | ||||||||
\(833\) | −8.83282 | −0.306039 | ||||||||
\(834\) | 8.00000 | 0.277017 | ||||||||
\(835\) | −13.4721 | −0.466222 | ||||||||
\(836\) | −5.29180 | −0.183021 | ||||||||
\(837\) | −46.8328 | −1.61878 | ||||||||
\(838\) | 26.8328 | 0.926924 | ||||||||
\(839\) | 14.4721 | 0.499634 | 0.249817 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249817 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(840\) | −14.9443 | −0.515626 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −11.0902 | −0.382192 | ||||||||
\(843\) | 70.2492 | 2.41951 | ||||||||
\(844\) | 4.32624 | 0.148915 | ||||||||
\(845\) | −18.5623 | −0.638563 | ||||||||
\(846\) | 39.1246 | 1.34513 | ||||||||
\(847\) | −8.14590 | −0.279896 | ||||||||
\(848\) | 12.0902 | 0.415178 | ||||||||
\(849\) | −22.8328 | −0.783620 | ||||||||
\(850\) | 18.3607 | 0.629766 | ||||||||
\(851\) | 29.0132 | 0.994558 | ||||||||
\(852\) | 38.1803 | 1.30804 | ||||||||
\(853\) | −38.9230 | −1.33270 | −0.666349 | − | 0.745640i | \(-0.732144\pi\) | ||||
−0.666349 | + | 0.745640i | \(0.732144\pi\) | |||||||
\(854\) | 17.1246 | 0.585992 | ||||||||
\(855\) | −22.4164 | −0.766625 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.12461 | −0.311691 | −0.155845 | − | 0.987781i | \(-0.549810\pi\) | ||||
−0.155845 | + | 0.987781i | \(0.549810\pi\) | |||||||
\(858\) | −11.4164 | −0.389750 | ||||||||
\(859\) | 2.67376 | 0.0912276 | 0.0456138 | − | 0.998959i | \(-0.485476\pi\) | ||||
0.0456138 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(860\) | −7.23607 | −0.246748 | ||||||||
\(861\) | −103.777 | −3.53671 | ||||||||
\(862\) | −24.3607 | −0.829728 | ||||||||
\(863\) | 8.74265 | 0.297603 | 0.148802 | − | 0.988867i | \(-0.452458\pi\) | ||||
0.148802 | + | 0.988867i | \(0.452458\pi\) | |||||||
\(864\) | −14.4721 | −0.492352 | ||||||||
\(865\) | −37.1246 | −1.26227 | ||||||||
\(866\) | −11.1246 | −0.378030 | ||||||||
\(867\) | −137.262 | −4.66167 | ||||||||
\(868\) | 9.23607 | 0.313493 | ||||||||
\(869\) | 11.4164 | 0.387275 | ||||||||
\(870\) | −10.4721 | −0.355039 | ||||||||
\(871\) | −0.763932 | −0.0258848 | ||||||||
\(872\) | 10.4721 | 0.354631 | ||||||||
\(873\) | −95.3738 | −3.22792 | ||||||||
\(874\) | −11.2918 | −0.381951 | ||||||||
\(875\) | −34.0902 | −1.15246 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −46.8673 | −1.58259 | −0.791297 | − | 0.611431i | \(-0.790594\pi\) | ||||
−0.791297 | + | 0.611431i | \(0.790594\pi\) | |||||||
\(878\) | −14.1803 | −0.478563 | ||||||||
\(879\) | 50.8328 | 1.71455 | ||||||||
\(880\) | 4.61803 | 0.155674 | ||||||||
\(881\) | 10.6525 | 0.358891 | 0.179446 | − | 0.983768i | \(-0.442570\pi\) | ||||
0.179446 | + | 0.983768i | \(0.442570\pi\) | |||||||
\(882\) | 8.56231 | 0.288308 | ||||||||
\(883\) | 31.4853 | 1.05956 | 0.529782 | − | 0.848134i | \(-0.322274\pi\) | ||||
0.529782 | + | 0.848134i | \(0.322274\pi\) | |||||||
\(884\) | −9.52786 | −0.320457 | ||||||||
\(885\) | −1.52786 | −0.0513586 | ||||||||
\(886\) | −0.111456 | −0.00374444 | ||||||||
\(887\) | −40.3262 | −1.35402 | −0.677011 | − | 0.735973i | \(-0.736725\pi\) | ||||
−0.677011 | + | 0.735973i | \(0.736725\pi\) | |||||||
\(888\) | −15.4164 | −0.517341 | ||||||||
\(889\) | 32.0689 | 1.07556 | ||||||||
\(890\) | −9.09017 | −0.304703 | ||||||||
\(891\) | 69.6869 | 2.33460 | ||||||||
\(892\) | −3.38197 | −0.113237 | ||||||||
\(893\) | −9.70820 | −0.324873 | ||||||||
\(894\) | 23.4164 | 0.783162 | ||||||||
\(895\) | 16.1803 | 0.540849 | ||||||||
\(896\) | 2.85410 | 0.0953489 | ||||||||
\(897\) | −24.3607 | −0.813379 | ||||||||
\(898\) | 4.94427 | 0.164992 | ||||||||
\(899\) | 6.47214 | 0.215858 | ||||||||
\(900\) | −17.7984 | −0.593279 | ||||||||
\(901\) | −93.1935 | −3.10473 | ||||||||
\(902\) | 32.0689 | 1.06778 | ||||||||
\(903\) | 41.3050 | 1.37454 | ||||||||
\(904\) | −2.38197 | −0.0792230 | ||||||||
\(905\) | 4.47214 | 0.148659 | ||||||||
\(906\) | −24.9443 | −0.828718 | ||||||||
\(907\) | −54.1803 | −1.79903 | −0.899514 | − | 0.436891i | \(-0.856079\pi\) | ||||
−0.899514 | + | 0.436891i | \(0.856079\pi\) | |||||||
\(908\) | −5.23607 | −0.173765 | ||||||||
\(909\) | 5.70820 | 0.189329 | ||||||||
\(910\) | 5.70820 | 0.189225 | ||||||||
\(911\) | −54.3607 | −1.80105 | −0.900525 | − | 0.434805i | \(-0.856817\pi\) | ||||
−0.900525 | + | 0.434805i | \(0.856817\pi\) | |||||||
\(912\) | 6.00000 | 0.198680 | ||||||||
\(913\) | −19.5623 | −0.647418 | ||||||||
\(914\) | −11.8197 | −0.390960 | ||||||||
\(915\) | −31.4164 | −1.03859 | ||||||||
\(916\) | −4.61803 | −0.152584 | ||||||||
\(917\) | 4.45898 | 0.147249 | ||||||||
\(918\) | 111.554 | 3.68184 | ||||||||
\(919\) | 19.7082 | 0.650114 | 0.325057 | − | 0.945694i | \(-0.394617\pi\) | ||||
0.325057 | + | 0.945694i | \(0.394617\pi\) | |||||||
\(920\) | 9.85410 | 0.324880 | ||||||||
\(921\) | 66.7214 | 2.19854 | ||||||||
\(922\) | 8.58359 | 0.282686 | ||||||||
\(923\) | −14.5836 | −0.480025 | ||||||||
\(924\) | −26.3607 | −0.867203 | ||||||||
\(925\) | −11.3475 | −0.373104 | ||||||||
\(926\) | −0.583592 | −0.0191780 | ||||||||
\(927\) | 110.318 | 3.62332 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | −24.4508 | −0.802206 | −0.401103 | − | 0.916033i | \(-0.631373\pi\) | ||||
−0.401103 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(930\) | −16.9443 | −0.555625 | ||||||||
\(931\) | −2.12461 | −0.0696313 | ||||||||
\(932\) | −8.09017 | −0.265002 | ||||||||
\(933\) | 34.0000 | 1.11311 | ||||||||
\(934\) | 6.47214 | 0.211775 | ||||||||
\(935\) | −35.5967 | −1.16414 | ||||||||
\(936\) | 9.23607 | 0.301890 | ||||||||
\(937\) | −48.0689 | −1.57034 | −0.785171 | − | 0.619279i | \(-0.787425\pi\) | ||||
−0.785171 | + | 0.619279i | \(0.787425\pi\) | |||||||
\(938\) | −1.76393 | −0.0575944 | ||||||||
\(939\) | −66.2492 | −2.16196 | ||||||||
\(940\) | 8.47214 | 0.276331 | ||||||||
\(941\) | 3.88854 | 0.126763 | 0.0633815 | − | 0.997989i | \(-0.479812\pi\) | ||||
0.0633815 | + | 0.997989i | \(0.479812\pi\) | |||||||
\(942\) | −66.8328 | −2.17753 | ||||||||
\(943\) | 68.4296 | 2.22837 | ||||||||
\(944\) | 0.291796 | 0.00949715 | ||||||||
\(945\) | −66.8328 | −2.17407 | ||||||||
\(946\) | −12.7639 | −0.414991 | ||||||||
\(947\) | −24.6869 | −0.802217 | −0.401109 | − | 0.916031i | \(-0.631375\pi\) | ||||
−0.401109 | + | 0.916031i | \(0.631375\pi\) | |||||||
\(948\) | −12.9443 | −0.420410 | ||||||||
\(949\) | −2.29180 | −0.0743948 | ||||||||
\(950\) | 4.41641 | 0.143287 | ||||||||
\(951\) | −98.7214 | −3.20126 | ||||||||
\(952\) | −22.0000 | −0.713024 | ||||||||
\(953\) | 28.3951 | 0.919808 | 0.459904 | − | 0.887969i | \(-0.347884\pi\) | ||||
0.459904 | + | 0.887969i | \(0.347884\pi\) | |||||||
\(954\) | 90.3394 | 2.92485 | ||||||||
\(955\) | 41.3607 | 1.33840 | ||||||||
\(956\) | 16.2918 | 0.526914 | ||||||||
\(957\) | −18.4721 | −0.597119 | ||||||||
\(958\) | −27.1246 | −0.876356 | ||||||||
\(959\) | −32.9017 | −1.06245 | ||||||||
\(960\) | −5.23607 | −0.168993 | ||||||||
\(961\) | −20.5279 | −0.662189 | ||||||||
\(962\) | 5.88854 | 0.189854 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.05573 | 0.162834 | ||||||||
\(965\) | −7.47214 | −0.240537 | ||||||||
\(966\) | −56.2492 | −1.80979 | ||||||||
\(967\) | 34.5410 | 1.11076 | 0.555382 | − | 0.831595i | \(-0.312572\pi\) | ||||
0.555382 | + | 0.831595i | \(0.312572\pi\) | |||||||
\(968\) | −2.85410 | −0.0917343 | ||||||||
\(969\) | −46.2492 | −1.48574 | ||||||||
\(970\) | −20.6525 | −0.663111 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | −35.5967 | −1.14177 | ||||||||
\(973\) | −7.05573 | −0.226196 | ||||||||
\(974\) | 3.41641 | 0.109469 | ||||||||
\(975\) | 9.52786 | 0.305136 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 32.4721 | 1.03888 | 0.519438 | − | 0.854508i | \(-0.326141\pi\) | ||||
0.519438 | + | 0.854508i | \(0.326141\pi\) | |||||||
\(978\) | −30.1803 | −0.965061 | ||||||||
\(979\) | −16.0344 | −0.512463 | ||||||||
\(980\) | 1.85410 | 0.0592271 | ||||||||
\(981\) | 78.2492 | 2.49831 | ||||||||
\(982\) | 18.4377 | 0.588370 | ||||||||
\(983\) | −11.7082 | −0.373434 | −0.186717 | − | 0.982414i | \(-0.559785\pi\) | ||||
−0.186717 | + | 0.982414i | \(0.559785\pi\) | |||||||
\(984\) | −36.3607 | −1.15914 | ||||||||
\(985\) | −16.1803 | −0.515548 | ||||||||
\(986\) | −15.4164 | −0.490958 | ||||||||
\(987\) | −48.3607 | −1.53934 | ||||||||
\(988\) | −2.29180 | −0.0729117 | ||||||||
\(989\) | −27.2361 | −0.866057 | ||||||||
\(990\) | 34.5066 | 1.09669 | ||||||||
\(991\) | 13.5279 | 0.429727 | 0.214863 | − | 0.976644i | \(-0.431069\pi\) | ||||
0.214863 | + | 0.976644i | \(0.431069\pi\) | |||||||
\(992\) | 3.23607 | 0.102745 | ||||||||
\(993\) | −86.8328 | −2.75556 | ||||||||
\(994\) | −33.6738 | −1.06807 | ||||||||
\(995\) | 20.4164 | 0.647244 | ||||||||
\(996\) | 22.1803 | 0.702811 | ||||||||
\(997\) | 16.9443 | 0.536630 | 0.268315 | − | 0.963331i | \(-0.413533\pi\) | ||||
0.268315 | + | 0.963331i | \(0.413533\pi\) | |||||||
\(998\) | −14.4721 | −0.458107 | ||||||||
\(999\) | −68.9443 | −2.18130 |
(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 | 8014.2.a.a.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8014.2.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |