Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 0.677734 | 0.391290 | 0.195645 | − | 0.980675i | \(-0.437320\pi\) | ||||
0.195645 | + | 0.980675i | \(0.437320\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.37664 | −1.95729 | −0.978647 | − | 0.205546i | \(-0.934103\pi\) | ||||
−0.978647 | + | 0.205546i | \(0.934103\pi\) | |||||||
\(6\) | 0.677734 | 0.276684 | ||||||||
\(7\) | −1.03965 | −0.392952 | −0.196476 | − | 0.980509i | \(-0.562950\pi\) | ||||
−0.196476 | + | 0.980509i | \(0.562950\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.54068 | −0.846892 | ||||||||
\(10\) | −4.37664 | −1.38402 | ||||||||
\(11\) | 1.08793 | 0.328024 | 0.164012 | − | 0.986458i | \(-0.447556\pi\) | ||||
0.164012 | + | 0.986458i | \(0.447556\pi\) | |||||||
\(12\) | 0.677734 | 0.195645 | ||||||||
\(13\) | 1.73790 | 0.482007 | 0.241003 | − | 0.970524i | \(-0.422524\pi\) | ||||
0.241003 | + | 0.970524i | \(0.422524\pi\) | |||||||
\(14\) | −1.03965 | −0.277859 | ||||||||
\(15\) | −2.96620 | −0.765869 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.23599 | 0.784844 | 0.392422 | − | 0.919785i | \(-0.371637\pi\) | ||||
0.392422 | + | 0.919785i | \(0.371637\pi\) | |||||||
\(18\) | −2.54068 | −0.598843 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −4.37664 | −0.978647 | ||||||||
\(21\) | −0.704609 | −0.153758 | ||||||||
\(22\) | 1.08793 | 0.231948 | ||||||||
\(23\) | 0.112769 | 0.0235140 | 0.0117570 | − | 0.999931i | \(-0.496258\pi\) | ||||
0.0117570 | + | 0.999931i | \(0.496258\pi\) | |||||||
\(24\) | 0.677734 | 0.138342 | ||||||||
\(25\) | 14.1550 | 2.83100 | ||||||||
\(26\) | 1.73790 | 0.340830 | ||||||||
\(27\) | −3.75510 | −0.722670 | ||||||||
\(28\) | −1.03965 | −0.196476 | ||||||||
\(29\) | 3.19669 | 0.593610 | 0.296805 | − | 0.954938i | \(-0.404079\pi\) | ||||
0.296805 | + | 0.954938i | \(0.404079\pi\) | |||||||
\(30\) | −2.96620 | −0.541551 | ||||||||
\(31\) | −0.880743 | −0.158186 | −0.0790930 | − | 0.996867i | \(-0.525202\pi\) | ||||
−0.0790930 | + | 0.996867i | \(0.525202\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.737328 | 0.128352 | ||||||||
\(34\) | 3.23599 | 0.554969 | ||||||||
\(35\) | 4.55020 | 0.769123 | ||||||||
\(36\) | −2.54068 | −0.423446 | ||||||||
\(37\) | −5.39162 | −0.886376 | −0.443188 | − | 0.896429i | \(-0.646153\pi\) | ||||
−0.443188 | + | 0.896429i | \(0.646153\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 1.17783 | 0.188604 | ||||||||
\(40\) | −4.37664 | −0.692008 | ||||||||
\(41\) | −3.58857 | −0.560440 | −0.280220 | − | 0.959936i | \(-0.590407\pi\) | ||||
−0.280220 | + | 0.959936i | \(0.590407\pi\) | |||||||
\(42\) | −0.704609 | −0.108723 | ||||||||
\(43\) | 4.67245 | 0.712542 | 0.356271 | − | 0.934383i | \(-0.384048\pi\) | ||||
0.356271 | + | 0.934383i | \(0.384048\pi\) | |||||||
\(44\) | 1.08793 | 0.164012 | ||||||||
\(45\) | 11.1196 | 1.65762 | ||||||||
\(46\) | 0.112769 | 0.0166269 | ||||||||
\(47\) | 11.3703 | 1.65853 | 0.829264 | − | 0.558856i | \(-0.188760\pi\) | ||||
0.829264 | + | 0.558856i | \(0.188760\pi\) | |||||||
\(48\) | 0.677734 | 0.0978225 | ||||||||
\(49\) | −5.91912 | −0.845589 | ||||||||
\(50\) | 14.1550 | 2.00182 | ||||||||
\(51\) | 2.19314 | 0.307101 | ||||||||
\(52\) | 1.73790 | 0.241003 | ||||||||
\(53\) | 6.66703 | 0.915786 | 0.457893 | − | 0.889007i | \(-0.348604\pi\) | ||||
0.457893 | + | 0.889007i | \(0.348604\pi\) | |||||||
\(54\) | −3.75510 | −0.511005 | ||||||||
\(55\) | −4.76149 | −0.642039 | ||||||||
\(56\) | −1.03965 | −0.138930 | ||||||||
\(57\) | 0.677734 | 0.0897680 | ||||||||
\(58\) | 3.19669 | 0.419745 | ||||||||
\(59\) | −6.07647 | −0.791090 | −0.395545 | − | 0.918447i | \(-0.629444\pi\) | ||||
−0.395545 | + | 0.918447i | \(0.629444\pi\) | |||||||
\(60\) | −2.96620 | −0.382935 | ||||||||
\(61\) | −3.81434 | −0.488376 | −0.244188 | − | 0.969728i | \(-0.578521\pi\) | ||||
−0.244188 | + | 0.969728i | \(0.578521\pi\) | |||||||
\(62\) | −0.880743 | −0.111854 | ||||||||
\(63\) | 2.64142 | 0.332788 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.60617 | −0.943429 | ||||||||
\(66\) | 0.737328 | 0.0907588 | ||||||||
\(67\) | −11.5399 | −1.40982 | −0.704909 | − | 0.709298i | \(-0.749012\pi\) | ||||
−0.704909 | + | 0.709298i | \(0.749012\pi\) | |||||||
\(68\) | 3.23599 | 0.392422 | ||||||||
\(69\) | 0.0764274 | 0.00920077 | ||||||||
\(70\) | 4.55020 | 0.543852 | ||||||||
\(71\) | −8.52973 | −1.01229 | −0.506146 | − | 0.862448i | \(-0.668930\pi\) | ||||
−0.506146 | + | 0.862448i | \(0.668930\pi\) | |||||||
\(72\) | −2.54068 | −0.299422 | ||||||||
\(73\) | −3.18541 | −0.372824 | −0.186412 | − | 0.982472i | \(-0.559686\pi\) | ||||
−0.186412 | + | 0.982472i | \(0.559686\pi\) | |||||||
\(74\) | −5.39162 | −0.626763 | ||||||||
\(75\) | 9.59333 | 1.10774 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −1.13107 | −0.128898 | ||||||||
\(78\) | 1.17783 | 0.133363 | ||||||||
\(79\) | −9.57466 | −1.07723 | −0.538616 | − | 0.842551i | \(-0.681053\pi\) | ||||
−0.538616 | + | 0.842551i | \(0.681053\pi\) | |||||||
\(80\) | −4.37664 | −0.489324 | ||||||||
\(81\) | 5.07707 | 0.564119 | ||||||||
\(82\) | −3.58857 | −0.396291 | ||||||||
\(83\) | 12.4902 | 1.37098 | 0.685489 | − | 0.728083i | \(-0.259589\pi\) | ||||
0.685489 | + | 0.728083i | \(0.259589\pi\) | |||||||
\(84\) | −0.704609 | −0.0768791 | ||||||||
\(85\) | −14.1628 | −1.53617 | ||||||||
\(86\) | 4.67245 | 0.503843 | ||||||||
\(87\) | 2.16650 | 0.232273 | ||||||||
\(88\) | 1.08793 | 0.115974 | ||||||||
\(89\) | −12.6888 | −1.34501 | −0.672503 | − | 0.740094i | \(-0.734781\pi\) | ||||
−0.672503 | + | 0.740094i | \(0.734781\pi\) | |||||||
\(90\) | 11.1196 | 1.17211 | ||||||||
\(91\) | −1.80681 | −0.189406 | ||||||||
\(92\) | 0.112769 | 0.0117570 | ||||||||
\(93\) | −0.596909 | −0.0618966 | ||||||||
\(94\) | 11.3703 | 1.17276 | ||||||||
\(95\) | −4.37664 | −0.449034 | ||||||||
\(96\) | 0.677734 | 0.0691709 | ||||||||
\(97\) | 9.17511 | 0.931591 | 0.465796 | − | 0.884892i | \(-0.345768\pi\) | ||||
0.465796 | + | 0.884892i | \(0.345768\pi\) | |||||||
\(98\) | −5.91912 | −0.597921 | ||||||||
\(99\) | −2.76408 | −0.277801 | ||||||||
\(100\) | 14.1550 | 1.41550 | ||||||||
\(101\) | −14.1641 | −1.40938 | −0.704691 | − | 0.709514i | \(-0.748914\pi\) | ||||
−0.704691 | + | 0.709514i | \(0.748914\pi\) | |||||||
\(102\) | 2.19314 | 0.217154 | ||||||||
\(103\) | −3.16377 | −0.311736 | −0.155868 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155868 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(104\) | 1.73790 | 0.170415 | ||||||||
\(105\) | 3.08382 | 0.300950 | ||||||||
\(106\) | 6.66703 | 0.647559 | ||||||||
\(107\) | 2.48968 | 0.240686 | 0.120343 | − | 0.992732i | \(-0.461601\pi\) | ||||
0.120343 | + | 0.992732i | \(0.461601\pi\) | |||||||
\(108\) | −3.75510 | −0.361335 | ||||||||
\(109\) | 7.05283 | 0.675539 | 0.337769 | − | 0.941229i | \(-0.390328\pi\) | ||||
0.337769 | + | 0.941229i | \(0.390328\pi\) | |||||||
\(110\) | −4.76149 | −0.453990 | ||||||||
\(111\) | −3.65408 | −0.346830 | ||||||||
\(112\) | −1.03965 | −0.0982381 | ||||||||
\(113\) | −16.5892 | −1.56058 | −0.780291 | − | 0.625416i | \(-0.784929\pi\) | ||||
−0.780291 | + | 0.625416i | \(0.784929\pi\) | |||||||
\(114\) | 0.677734 | 0.0634756 | ||||||||
\(115\) | −0.493550 | −0.0460237 | ||||||||
\(116\) | 3.19669 | 0.296805 | ||||||||
\(117\) | −4.41544 | −0.408208 | ||||||||
\(118\) | −6.07647 | −0.559385 | ||||||||
\(119\) | −3.36431 | −0.308406 | ||||||||
\(120\) | −2.96620 | −0.270776 | ||||||||
\(121\) | −9.81641 | −0.892401 | ||||||||
\(122\) | −3.81434 | −0.345334 | ||||||||
\(123\) | −2.43209 | −0.219295 | ||||||||
\(124\) | −0.880743 | −0.0790930 | ||||||||
\(125\) | −40.0682 | −3.58381 | ||||||||
\(126\) | 2.64142 | 0.235317 | ||||||||
\(127\) | −3.51464 | −0.311874 | −0.155937 | − | 0.987767i | \(-0.549840\pi\) | ||||
−0.155937 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.16668 | 0.278810 | ||||||||
\(130\) | −7.60617 | −0.667105 | ||||||||
\(131\) | −12.9808 | −1.13414 | −0.567070 | − | 0.823669i | \(-0.691923\pi\) | ||||
−0.567070 | + | 0.823669i | \(0.691923\pi\) | |||||||
\(132\) | 0.737328 | 0.0641761 | ||||||||
\(133\) | −1.03965 | −0.0901494 | ||||||||
\(134\) | −11.5399 | −0.996892 | ||||||||
\(135\) | 16.4348 | 1.41448 | ||||||||
\(136\) | 3.23599 | 0.277484 | ||||||||
\(137\) | 8.38749 | 0.716592 | 0.358296 | − | 0.933608i | \(-0.383358\pi\) | ||||
0.358296 | + | 0.933608i | \(0.383358\pi\) | |||||||
\(138\) | 0.0764274 | 0.00650593 | ||||||||
\(139\) | −18.9541 | −1.60767 | −0.803834 | − | 0.594854i | \(-0.797210\pi\) | ||||
−0.803834 | + | 0.594854i | \(0.797210\pi\) | |||||||
\(140\) | 4.55020 | 0.384562 | ||||||||
\(141\) | 7.70604 | 0.648965 | ||||||||
\(142\) | −8.52973 | −0.715799 | ||||||||
\(143\) | 1.89072 | 0.158110 | ||||||||
\(144\) | −2.54068 | −0.211723 | ||||||||
\(145\) | −13.9908 | −1.16187 | ||||||||
\(146\) | −3.18541 | −0.263626 | ||||||||
\(147\) | −4.01159 | −0.330870 | ||||||||
\(148\) | −5.39162 | −0.443188 | ||||||||
\(149\) | −15.3632 | −1.25860 | −0.629302 | − | 0.777161i | \(-0.716659\pi\) | ||||
−0.629302 | + | 0.777161i | \(0.716659\pi\) | |||||||
\(150\) | 9.59333 | 0.783292 | ||||||||
\(151\) | 16.1717 | 1.31603 | 0.658016 | − | 0.753004i | \(-0.271396\pi\) | ||||
0.658016 | + | 0.753004i | \(0.271396\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −8.22162 | −0.664678 | ||||||||
\(154\) | −1.13107 | −0.0911444 | ||||||||
\(155\) | 3.85470 | 0.309617 | ||||||||
\(156\) | 1.17783 | 0.0943021 | ||||||||
\(157\) | 20.0070 | 1.59673 | 0.798365 | − | 0.602174i | \(-0.205699\pi\) | ||||
0.798365 | + | 0.602174i | \(0.205699\pi\) | |||||||
\(158\) | −9.57466 | −0.761719 | ||||||||
\(159\) | 4.51847 | 0.358338 | ||||||||
\(160\) | −4.37664 | −0.346004 | ||||||||
\(161\) | −0.117241 | −0.00923986 | ||||||||
\(162\) | 5.07707 | 0.398892 | ||||||||
\(163\) | 7.50860 | 0.588119 | 0.294060 | − | 0.955787i | \(-0.404994\pi\) | ||||
0.294060 | + | 0.955787i | \(0.404994\pi\) | |||||||
\(164\) | −3.58857 | −0.280220 | ||||||||
\(165\) | −3.22702 | −0.251223 | ||||||||
\(166\) | 12.4902 | 0.969427 | ||||||||
\(167\) | 10.5744 | 0.818270 | 0.409135 | − | 0.912474i | \(-0.365831\pi\) | ||||
0.409135 | + | 0.912474i | \(0.365831\pi\) | |||||||
\(168\) | −0.704609 | −0.0543617 | ||||||||
\(169\) | −9.97971 | −0.767670 | ||||||||
\(170\) | −14.1628 | −1.08624 | ||||||||
\(171\) | −2.54068 | −0.194290 | ||||||||
\(172\) | 4.67245 | 0.356271 | ||||||||
\(173\) | 17.9144 | 1.36201 | 0.681004 | − | 0.732279i | \(-0.261543\pi\) | ||||
0.681004 | + | 0.732279i | \(0.261543\pi\) | |||||||
\(174\) | 2.16650 | 0.164242 | ||||||||
\(175\) | −14.7163 | −1.11245 | ||||||||
\(176\) | 1.08793 | 0.0820059 | ||||||||
\(177\) | −4.11823 | −0.309545 | ||||||||
\(178\) | −12.6888 | −0.951063 | ||||||||
\(179\) | −22.4848 | −1.68060 | −0.840298 | − | 0.542124i | \(-0.817620\pi\) | ||||
−0.840298 | + | 0.542124i | \(0.817620\pi\) | |||||||
\(180\) | 11.1196 | 0.828809 | ||||||||
\(181\) | 1.63017 | 0.121169 | 0.0605847 | − | 0.998163i | \(-0.480703\pi\) | ||||
0.0605847 | + | 0.998163i | \(0.480703\pi\) | |||||||
\(182\) | −1.80681 | −0.133930 | ||||||||
\(183\) | −2.58511 | −0.191097 | ||||||||
\(184\) | 0.112769 | 0.00831344 | ||||||||
\(185\) | 23.5972 | 1.73490 | ||||||||
\(186\) | −0.596909 | −0.0437675 | ||||||||
\(187\) | 3.52054 | 0.257447 | ||||||||
\(188\) | 11.3703 | 0.829264 | ||||||||
\(189\) | 3.90401 | 0.283975 | ||||||||
\(190\) | −4.37664 | −0.317515 | ||||||||
\(191\) | −3.20936 | −0.232221 | −0.116111 | − | 0.993236i | \(-0.537043\pi\) | ||||
−0.116111 | + | 0.993236i | \(0.537043\pi\) | |||||||
\(192\) | 0.677734 | 0.0489112 | ||||||||
\(193\) | −13.6373 | −0.981636 | −0.490818 | − | 0.871262i | \(-0.663302\pi\) | ||||
−0.490818 | + | 0.871262i | \(0.663302\pi\) | |||||||
\(194\) | 9.17511 | 0.658734 | ||||||||
\(195\) | −5.15496 | −0.369154 | ||||||||
\(196\) | −5.91912 | −0.422794 | ||||||||
\(197\) | −24.4141 | −1.73944 | −0.869718 | − | 0.493549i | \(-0.835699\pi\) | ||||
−0.869718 | + | 0.493549i | \(0.835699\pi\) | |||||||
\(198\) | −2.76408 | −0.196435 | ||||||||
\(199\) | 4.83687 | 0.342877 | 0.171438 | − | 0.985195i | \(-0.445159\pi\) | ||||
0.171438 | + | 0.985195i | \(0.445159\pi\) | |||||||
\(200\) | 14.1550 | 1.00091 | ||||||||
\(201\) | −7.82095 | −0.551647 | ||||||||
\(202\) | −14.1641 | −0.996584 | ||||||||
\(203\) | −3.32345 | −0.233260 | ||||||||
\(204\) | 2.19314 | 0.153551 | ||||||||
\(205\) | 15.7059 | 1.09695 | ||||||||
\(206\) | −3.16377 | −0.220430 | ||||||||
\(207\) | −0.286510 | −0.0199138 | ||||||||
\(208\) | 1.73790 | 0.120502 | ||||||||
\(209\) | 1.08793 | 0.0752538 | ||||||||
\(210\) | 3.08382 | 0.212804 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 6.66703 | 0.457893 | ||||||||
\(213\) | −5.78088 | −0.396100 | ||||||||
\(214\) | 2.48968 | 0.170191 | ||||||||
\(215\) | −20.4496 | −1.39465 | ||||||||
\(216\) | −3.75510 | −0.255502 | ||||||||
\(217\) | 0.915668 | 0.0621596 | ||||||||
\(218\) | 7.05283 | 0.477678 | ||||||||
\(219\) | −2.15886 | −0.145882 | ||||||||
\(220\) | −4.76149 | −0.321019 | ||||||||
\(221\) | 5.62383 | 0.378300 | ||||||||
\(222\) | −3.65408 | −0.245246 | ||||||||
\(223\) | 3.93852 | 0.263743 | 0.131871 | − | 0.991267i | \(-0.457901\pi\) | ||||
0.131871 | + | 0.991267i | \(0.457901\pi\) | |||||||
\(224\) | −1.03965 | −0.0694648 | ||||||||
\(225\) | −35.9633 | −2.39755 | ||||||||
\(226\) | −16.5892 | −1.10350 | ||||||||
\(227\) | 2.97691 | 0.197585 | 0.0987923 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987923 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(228\) | 0.677734 | 0.0448840 | ||||||||
\(229\) | −24.6325 | −1.62776 | −0.813882 | − | 0.581030i | \(-0.802650\pi\) | ||||
−0.813882 | + | 0.581030i | \(0.802650\pi\) | |||||||
\(230\) | −0.493550 | −0.0325437 | ||||||||
\(231\) | −0.766566 | −0.0504363 | ||||||||
\(232\) | 3.19669 | 0.209873 | ||||||||
\(233\) | 3.21421 | 0.210570 | 0.105285 | − | 0.994442i | \(-0.466424\pi\) | ||||
0.105285 | + | 0.994442i | \(0.466424\pi\) | |||||||
\(234\) | −4.41544 | −0.288646 | ||||||||
\(235\) | −49.7638 | −3.24623 | ||||||||
\(236\) | −6.07647 | −0.395545 | ||||||||
\(237\) | −6.48907 | −0.421510 | ||||||||
\(238\) | −3.36431 | −0.218076 | ||||||||
\(239\) | 1.83792 | 0.118885 | 0.0594427 | − | 0.998232i | \(-0.481068\pi\) | ||||
0.0594427 | + | 0.998232i | \(0.481068\pi\) | |||||||
\(240\) | −2.96620 | −0.191467 | ||||||||
\(241\) | 2.01575 | 0.129846 | 0.0649228 | − | 0.997890i | \(-0.479320\pi\) | ||||
0.0649228 | + | 0.997890i | \(0.479320\pi\) | |||||||
\(242\) | −9.81641 | −0.631022 | ||||||||
\(243\) | 14.7062 | 0.943404 | ||||||||
\(244\) | −3.81434 | −0.244188 | ||||||||
\(245\) | 25.9059 | 1.65507 | ||||||||
\(246\) | −2.43209 | −0.155065 | ||||||||
\(247\) | 1.73790 | 0.110580 | ||||||||
\(248\) | −0.880743 | −0.0559272 | ||||||||
\(249\) | 8.46503 | 0.536449 | ||||||||
\(250\) | −40.0682 | −2.53414 | ||||||||
\(251\) | 1.53715 | 0.0970240 | 0.0485120 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485120 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(252\) | 2.64142 | 0.166394 | ||||||||
\(253\) | 0.122685 | 0.00771313 | ||||||||
\(254\) | −3.51464 | −0.220528 | ||||||||
\(255\) | −9.59861 | −0.601088 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.8071 | −0.861264 | −0.430632 | − | 0.902528i | \(-0.641709\pi\) | ||||
−0.430632 | + | 0.902528i | \(0.641709\pi\) | |||||||
\(258\) | 3.16668 | 0.197149 | ||||||||
\(259\) | 5.60542 | 0.348304 | ||||||||
\(260\) | −7.60617 | −0.471714 | ||||||||
\(261\) | −8.12174 | −0.502723 | ||||||||
\(262\) | −12.9808 | −0.801958 | ||||||||
\(263\) | −10.5628 | −0.651330 | −0.325665 | − | 0.945485i | \(-0.605588\pi\) | ||||
−0.325665 | + | 0.945485i | \(0.605588\pi\) | |||||||
\(264\) | 0.737328 | 0.0453794 | ||||||||
\(265\) | −29.1792 | −1.79246 | ||||||||
\(266\) | −1.03965 | −0.0637453 | ||||||||
\(267\) | −8.59961 | −0.526287 | ||||||||
\(268\) | −11.5399 | −0.704909 | ||||||||
\(269\) | 16.6982 | 1.01811 | 0.509055 | − | 0.860734i | \(-0.329995\pi\) | ||||
0.509055 | + | 0.860734i | \(0.329995\pi\) | |||||||
\(270\) | 16.4348 | 1.00019 | ||||||||
\(271\) | −2.72534 | −0.165553 | −0.0827763 | − | 0.996568i | \(-0.526379\pi\) | ||||
−0.0827763 | + | 0.996568i | \(0.526379\pi\) | |||||||
\(272\) | 3.23599 | 0.196211 | ||||||||
\(273\) | −1.22454 | −0.0741125 | ||||||||
\(274\) | 8.38749 | 0.506707 | ||||||||
\(275\) | 15.3997 | 0.928636 | ||||||||
\(276\) | 0.0764274 | 0.00460039 | ||||||||
\(277\) | 29.0179 | 1.74352 | 0.871759 | − | 0.489935i | \(-0.162980\pi\) | ||||
0.871759 | + | 0.489935i | \(0.162980\pi\) | |||||||
\(278\) | −18.9541 | −1.13679 | ||||||||
\(279\) | 2.23768 | 0.133967 | ||||||||
\(280\) | 4.55020 | 0.271926 | ||||||||
\(281\) | 1.00727 | 0.0600888 | 0.0300444 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300444 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(282\) | 7.70604 | 0.458888 | ||||||||
\(283\) | −33.1531 | −1.97075 | −0.985373 | − | 0.170414i | \(-0.945490\pi\) | ||||
−0.985373 | + | 0.170414i | \(0.945490\pi\) | |||||||
\(284\) | −8.52973 | −0.506146 | ||||||||
\(285\) | −2.96620 | −0.175703 | ||||||||
\(286\) | 1.89072 | 0.111800 | ||||||||
\(287\) | 3.73087 | 0.220226 | ||||||||
\(288\) | −2.54068 | −0.149711 | ||||||||
\(289\) | −6.52834 | −0.384020 | ||||||||
\(290\) | −13.9908 | −0.821565 | ||||||||
\(291\) | 6.21828 | 0.364522 | ||||||||
\(292\) | −3.18541 | −0.186412 | ||||||||
\(293\) | 11.2238 | 0.655701 | 0.327850 | − | 0.944730i | \(-0.393676\pi\) | ||||
0.327850 | + | 0.944730i | \(0.393676\pi\) | |||||||
\(294\) | −4.01159 | −0.233961 | ||||||||
\(295\) | 26.5946 | 1.54840 | ||||||||
\(296\) | −5.39162 | −0.313381 | ||||||||
\(297\) | −4.08530 | −0.237053 | ||||||||
\(298\) | −15.3632 | −0.889967 | ||||||||
\(299\) | 0.195981 | 0.0113339 | ||||||||
\(300\) | 9.59333 | 0.553871 | ||||||||
\(301\) | −4.85773 | −0.279995 | ||||||||
\(302\) | 16.1717 | 0.930575 | ||||||||
\(303\) | −9.59950 | −0.551477 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 16.6940 | 0.955896 | ||||||||
\(306\) | −8.22162 | −0.469999 | ||||||||
\(307\) | −1.17249 | −0.0669175 | −0.0334588 | − | 0.999440i | \(-0.510652\pi\) | ||||
−0.0334588 | + | 0.999440i | \(0.510652\pi\) | |||||||
\(308\) | −1.13107 | −0.0644488 | ||||||||
\(309\) | −2.14419 | −0.121979 | ||||||||
\(310\) | 3.85470 | 0.218932 | ||||||||
\(311\) | −12.4924 | −0.708377 | −0.354188 | − | 0.935174i | \(-0.615243\pi\) | ||||
−0.354188 | + | 0.935174i | \(0.615243\pi\) | |||||||
\(312\) | 1.17783 | 0.0666817 | ||||||||
\(313\) | 6.41799 | 0.362766 | 0.181383 | − | 0.983412i | \(-0.441943\pi\) | ||||
0.181383 | + | 0.983412i | \(0.441943\pi\) | |||||||
\(314\) | 20.0070 | 1.12906 | ||||||||
\(315\) | −11.5606 | −0.651365 | ||||||||
\(316\) | −9.57466 | −0.538616 | ||||||||
\(317\) | 16.0619 | 0.902129 | 0.451064 | − | 0.892491i | \(-0.351044\pi\) | ||||
0.451064 | + | 0.892491i | \(0.351044\pi\) | |||||||
\(318\) | 4.51847 | 0.253383 | ||||||||
\(319\) | 3.47777 | 0.194718 | ||||||||
\(320\) | −4.37664 | −0.244662 | ||||||||
\(321\) | 1.68734 | 0.0941780 | ||||||||
\(322\) | −0.117241 | −0.00653357 | ||||||||
\(323\) | 3.23599 | 0.180056 | ||||||||
\(324\) | 5.07707 | 0.282059 | ||||||||
\(325\) | 24.6000 | 1.36456 | ||||||||
\(326\) | 7.50860 | 0.415863 | ||||||||
\(327\) | 4.77994 | 0.264331 | ||||||||
\(328\) | −3.58857 | −0.198146 | ||||||||
\(329\) | −11.8212 | −0.651723 | ||||||||
\(330\) | −3.22702 | −0.177642 | ||||||||
\(331\) | −29.6379 | −1.62905 | −0.814524 | − | 0.580130i | \(-0.803002\pi\) | ||||
−0.814524 | + | 0.580130i | \(0.803002\pi\) | |||||||
\(332\) | 12.4902 | 0.685489 | ||||||||
\(333\) | 13.6984 | 0.750665 | ||||||||
\(334\) | 10.5744 | 0.578604 | ||||||||
\(335\) | 50.5058 | 2.75943 | ||||||||
\(336\) | −0.704609 | −0.0384396 | ||||||||
\(337\) | −4.45504 | −0.242682 | −0.121341 | − | 0.992611i | \(-0.538719\pi\) | ||||
−0.121341 | + | 0.992611i | \(0.538719\pi\) | |||||||
\(338\) | −9.97971 | −0.542824 | ||||||||
\(339\) | −11.2431 | −0.610640 | ||||||||
\(340\) | −14.1628 | −0.768086 | ||||||||
\(341\) | −0.958188 | −0.0518888 | ||||||||
\(342\) | −2.54068 | −0.137384 | ||||||||
\(343\) | 13.4314 | 0.725228 | ||||||||
\(344\) | 4.67245 | 0.251922 | ||||||||
\(345\) | −0.334495 | −0.0180086 | ||||||||
\(346\) | 17.9144 | 0.963086 | ||||||||
\(347\) | 2.94754 | 0.158232 | 0.0791162 | − | 0.996865i | \(-0.474790\pi\) | ||||
0.0791162 | + | 0.996865i | \(0.474790\pi\) | |||||||
\(348\) | 2.16650 | 0.116137 | ||||||||
\(349\) | 12.1898 | 0.652504 | 0.326252 | − | 0.945283i | \(-0.394214\pi\) | ||||
0.326252 | + | 0.945283i | \(0.394214\pi\) | |||||||
\(350\) | −14.7163 | −0.786620 | ||||||||
\(351\) | −6.52599 | −0.348332 | ||||||||
\(352\) | 1.08793 | 0.0579869 | ||||||||
\(353\) | 1.80519 | 0.0960807 | 0.0480403 | − | 0.998845i | \(-0.484702\pi\) | ||||
0.0480403 | + | 0.998845i | \(0.484702\pi\) | |||||||
\(354\) | −4.11823 | −0.218882 | ||||||||
\(355\) | 37.3316 | 1.98135 | ||||||||
\(356\) | −12.6888 | −0.672503 | ||||||||
\(357\) | −2.28011 | −0.120676 | ||||||||
\(358\) | −22.4848 | −1.18836 | ||||||||
\(359\) | 3.38306 | 0.178551 | 0.0892754 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892754 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(360\) | 11.1196 | 0.586056 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 1.63017 | 0.0856798 | ||||||||
\(363\) | −6.65291 | −0.349187 | ||||||||
\(364\) | −1.80681 | −0.0947028 | ||||||||
\(365\) | 13.9414 | 0.729726 | ||||||||
\(366\) | −2.58511 | −0.135126 | ||||||||
\(367\) | −30.5652 | −1.59549 | −0.797746 | − | 0.602993i | \(-0.793975\pi\) | ||||
−0.797746 | + | 0.602993i | \(0.793975\pi\) | |||||||
\(368\) | 0.112769 | 0.00587849 | ||||||||
\(369\) | 9.11739 | 0.474632 | ||||||||
\(370\) | 23.5972 | 1.22676 | ||||||||
\(371\) | −6.93140 | −0.359860 | ||||||||
\(372\) | −0.596909 | −0.0309483 | ||||||||
\(373\) | −19.5072 | −1.01004 | −0.505022 | − | 0.863106i | \(-0.668516\pi\) | ||||
−0.505022 | + | 0.863106i | \(0.668516\pi\) | |||||||
\(374\) | 3.52054 | 0.182043 | ||||||||
\(375\) | −27.1556 | −1.40231 | ||||||||
\(376\) | 11.3703 | 0.586378 | ||||||||
\(377\) | 5.55552 | 0.286124 | ||||||||
\(378\) | 3.90401 | 0.200801 | ||||||||
\(379\) | −25.9549 | −1.33321 | −0.666607 | − | 0.745409i | \(-0.732254\pi\) | ||||
−0.666607 | + | 0.745409i | \(0.732254\pi\) | |||||||
\(380\) | −4.37664 | −0.224517 | ||||||||
\(381\) | −2.38199 | −0.122033 | ||||||||
\(382\) | −3.20936 | −0.164205 | ||||||||
\(383\) | 30.3912 | 1.55292 | 0.776460 | − | 0.630167i | \(-0.217013\pi\) | ||||
0.776460 | + | 0.630167i | \(0.217013\pi\) | |||||||
\(384\) | 0.677734 | 0.0345855 | ||||||||
\(385\) | 4.95030 | 0.252291 | ||||||||
\(386\) | −13.6373 | −0.694122 | ||||||||
\(387\) | −11.8712 | −0.603446 | ||||||||
\(388\) | 9.17511 | 0.465796 | ||||||||
\(389\) | 10.7419 | 0.544636 | 0.272318 | − | 0.962207i | \(-0.412210\pi\) | ||||
0.272318 | + | 0.962207i | \(0.412210\pi\) | |||||||
\(390\) | −5.15496 | −0.261031 | ||||||||
\(391\) | 0.364920 | 0.0184548 | ||||||||
\(392\) | −5.91912 | −0.298961 | ||||||||
\(393\) | −8.79755 | −0.443778 | ||||||||
\(394\) | −24.4141 | −1.22997 | ||||||||
\(395\) | 41.9049 | 2.10846 | ||||||||
\(396\) | −2.76408 | −0.138900 | ||||||||
\(397\) | −9.73475 | −0.488573 | −0.244287 | − | 0.969703i | \(-0.578554\pi\) | ||||
−0.244287 | + | 0.969703i | \(0.578554\pi\) | |||||||
\(398\) | 4.83687 | 0.242451 | ||||||||
\(399\) | −0.704609 | −0.0352746 | ||||||||
\(400\) | 14.1550 | 0.707751 | ||||||||
\(401\) | 8.63370 | 0.431146 | 0.215573 | − | 0.976488i | \(-0.430838\pi\) | ||||
0.215573 | + | 0.976488i | \(0.430838\pi\) | |||||||
\(402\) | −7.82095 | −0.390074 | ||||||||
\(403\) | −1.53064 | −0.0762467 | ||||||||
\(404\) | −14.1641 | −0.704691 | ||||||||
\(405\) | −22.2205 | −1.10415 | ||||||||
\(406\) | −3.32345 | −0.164940 | ||||||||
\(407\) | −5.86571 | −0.290752 | ||||||||
\(408\) | 2.19314 | 0.108577 | ||||||||
\(409\) | 0.907335 | 0.0448648 | 0.0224324 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224324 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(410\) | 15.7059 | 0.775658 | ||||||||
\(411\) | 5.68449 | 0.280395 | ||||||||
\(412\) | −3.16377 | −0.155868 | ||||||||
\(413\) | 6.31743 | 0.310860 | ||||||||
\(414\) | −0.286510 | −0.0140812 | ||||||||
\(415\) | −54.6651 | −2.68341 | ||||||||
\(416\) | 1.73790 | 0.0852075 | ||||||||
\(417\) | −12.8459 | −0.629064 | ||||||||
\(418\) | 1.08793 | 0.0532125 | ||||||||
\(419\) | −19.6319 | −0.959080 | −0.479540 | − | 0.877520i | \(-0.659196\pi\) | ||||
−0.479540 | + | 0.877520i | \(0.659196\pi\) | |||||||
\(420\) | 3.08382 | 0.150475 | ||||||||
\(421\) | −27.2987 | −1.33046 | −0.665229 | − | 0.746640i | \(-0.731666\pi\) | ||||
−0.665229 | + | 0.746640i | \(0.731666\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −28.8883 | −1.40460 | ||||||||
\(424\) | 6.66703 | 0.323779 | ||||||||
\(425\) | 45.8055 | 2.22190 | ||||||||
\(426\) | −5.78088 | −0.280085 | ||||||||
\(427\) | 3.96559 | 0.191908 | ||||||||
\(428\) | 2.48968 | 0.120343 | ||||||||
\(429\) | 1.28140 | 0.0618667 | ||||||||
\(430\) | −20.4496 | −0.986169 | ||||||||
\(431\) | 6.94829 | 0.334687 | 0.167344 | − | 0.985899i | \(-0.446481\pi\) | ||||
0.167344 | + | 0.985899i | \(0.446481\pi\) | |||||||
\(432\) | −3.75510 | −0.180668 | ||||||||
\(433\) | −28.7277 | −1.38056 | −0.690282 | − | 0.723540i | \(-0.742514\pi\) | ||||
−0.690282 | + | 0.723540i | \(0.742514\pi\) | |||||||
\(434\) | 0.915668 | 0.0439535 | ||||||||
\(435\) | −9.48201 | −0.454627 | ||||||||
\(436\) | 7.05283 | 0.337769 | ||||||||
\(437\) | 0.112769 | 0.00539447 | ||||||||
\(438\) | −2.15886 | −0.103154 | ||||||||
\(439\) | 22.0835 | 1.05399 | 0.526993 | − | 0.849870i | \(-0.323319\pi\) | ||||
0.526993 | + | 0.849870i | \(0.323319\pi\) | |||||||
\(440\) | −4.76149 | −0.226995 | ||||||||
\(441\) | 15.0386 | 0.716122 | ||||||||
\(442\) | 5.62383 | 0.267498 | ||||||||
\(443\) | 3.42410 | 0.162684 | 0.0813420 | − | 0.996686i | \(-0.474079\pi\) | ||||
0.0813420 | + | 0.996686i | \(0.474079\pi\) | |||||||
\(444\) | −3.65408 | −0.173415 | ||||||||
\(445\) | 55.5342 | 2.63257 | ||||||||
\(446\) | 3.93852 | 0.186494 | ||||||||
\(447\) | −10.4122 | −0.492479 | ||||||||
\(448\) | −1.03965 | −0.0491190 | ||||||||
\(449\) | −6.45014 | −0.304401 | −0.152200 | − | 0.988350i | \(-0.548636\pi\) | ||||
−0.152200 | + | 0.988350i | \(0.548636\pi\) | |||||||
\(450\) | −35.9633 | −1.69533 | ||||||||
\(451\) | −3.90412 | −0.183838 | ||||||||
\(452\) | −16.5892 | −0.780291 | ||||||||
\(453\) | 10.9601 | 0.514950 | ||||||||
\(454\) | 2.97691 | 0.139713 | ||||||||
\(455\) | 7.90778 | 0.370723 | ||||||||
\(456\) | 0.677734 | 0.0317378 | ||||||||
\(457\) | 17.0170 | 0.796023 | 0.398012 | − | 0.917380i | \(-0.369700\pi\) | ||||
0.398012 | + | 0.917380i | \(0.369700\pi\) | |||||||
\(458\) | −24.6325 | −1.15100 | ||||||||
\(459\) | −12.1515 | −0.567183 | ||||||||
\(460\) | −0.493550 | −0.0230119 | ||||||||
\(461\) | −6.85354 | −0.319201 | −0.159601 | − | 0.987182i | \(-0.551021\pi\) | ||||
−0.159601 | + | 0.987182i | \(0.551021\pi\) | |||||||
\(462\) | −0.766566 | −0.0356639 | ||||||||
\(463\) | −13.7414 | −0.638615 | −0.319308 | − | 0.947651i | \(-0.603450\pi\) | ||||
−0.319308 | + | 0.947651i | \(0.603450\pi\) | |||||||
\(464\) | 3.19669 | 0.148402 | ||||||||
\(465\) | 2.61246 | 0.121150 | ||||||||
\(466\) | 3.21421 | 0.148896 | ||||||||
\(467\) | 33.1199 | 1.53261 | 0.766303 | − | 0.642480i | \(-0.222094\pi\) | ||||
0.766303 | + | 0.642480i | \(0.222094\pi\) | |||||||
\(468\) | −4.41544 | −0.204104 | ||||||||
\(469\) | 11.9975 | 0.553991 | ||||||||
\(470\) | −49.7638 | −2.29543 | ||||||||
\(471\) | 13.5594 | 0.624784 | ||||||||
\(472\) | −6.07647 | −0.279692 | ||||||||
\(473\) | 5.08330 | 0.233731 | ||||||||
\(474\) | −6.48907 | −0.298053 | ||||||||
\(475\) | 14.1550 | 0.649477 | ||||||||
\(476\) | −3.36431 | −0.154203 | ||||||||
\(477\) | −16.9388 | −0.775572 | ||||||||
\(478\) | 1.83792 | 0.0840646 | ||||||||
\(479\) | 10.3502 | 0.472913 | 0.236456 | − | 0.971642i | \(-0.424014\pi\) | ||||
0.236456 | + | 0.971642i | \(0.424014\pi\) | |||||||
\(480\) | −2.96620 | −0.135388 | ||||||||
\(481\) | −9.37009 | −0.427239 | ||||||||
\(482\) | 2.01575 | 0.0918147 | ||||||||
\(483\) | −0.0794580 | −0.00361546 | ||||||||
\(484\) | −9.81641 | −0.446200 | ||||||||
\(485\) | −40.1562 | −1.82340 | ||||||||
\(486\) | 14.7062 | 0.667087 | ||||||||
\(487\) | −8.92066 | −0.404234 | −0.202117 | − | 0.979361i | \(-0.564782\pi\) | ||||
−0.202117 | + | 0.979361i | \(0.564782\pi\) | |||||||
\(488\) | −3.81434 | −0.172667 | ||||||||
\(489\) | 5.08883 | 0.230125 | ||||||||
\(490\) | 25.9059 | 1.17031 | ||||||||
\(491\) | 26.0318 | 1.17480 | 0.587400 | − | 0.809297i | \(-0.300152\pi\) | ||||
0.587400 | + | 0.809297i | \(0.300152\pi\) | |||||||
\(492\) | −2.43209 | −0.109647 | ||||||||
\(493\) | 10.3445 | 0.465891 | ||||||||
\(494\) | 1.73790 | 0.0781918 | ||||||||
\(495\) | 12.0974 | 0.543738 | ||||||||
\(496\) | −0.880743 | −0.0395465 | ||||||||
\(497\) | 8.86796 | 0.397783 | ||||||||
\(498\) | 8.46503 | 0.379327 | ||||||||
\(499\) | −4.96533 | −0.222279 | −0.111139 | − | 0.993805i | \(-0.535450\pi\) | ||||
−0.111139 | + | 0.993805i | \(0.535450\pi\) | |||||||
\(500\) | −40.0682 | −1.79191 | ||||||||
\(501\) | 7.16661 | 0.320181 | ||||||||
\(502\) | 1.53715 | 0.0686063 | ||||||||
\(503\) | −15.5829 | −0.694808 | −0.347404 | − | 0.937716i | \(-0.612937\pi\) | ||||
−0.347404 | + | 0.937716i | \(0.612937\pi\) | |||||||
\(504\) | 2.64142 | 0.117658 | ||||||||
\(505\) | 61.9913 | 2.75858 | ||||||||
\(506\) | 0.122685 | 0.00545401 | ||||||||
\(507\) | −6.76358 | −0.300381 | ||||||||
\(508\) | −3.51464 | −0.155937 | ||||||||
\(509\) | −18.7446 | −0.830842 | −0.415421 | − | 0.909629i | \(-0.636366\pi\) | ||||
−0.415421 | + | 0.909629i | \(0.636366\pi\) | |||||||
\(510\) | −9.59861 | −0.425033 | ||||||||
\(511\) | 3.31172 | 0.146502 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.75510 | −0.165792 | ||||||||
\(514\) | −13.8071 | −0.609005 | ||||||||
\(515\) | 13.8467 | 0.610159 | ||||||||
\(516\) | 3.16668 | 0.139405 | ||||||||
\(517\) | 12.3701 | 0.544037 | ||||||||
\(518\) | 5.60542 | 0.246288 | ||||||||
\(519\) | 12.1412 | 0.532940 | ||||||||
\(520\) | −7.60617 | −0.333553 | ||||||||
\(521\) | 4.43158 | 0.194151 | 0.0970755 | − | 0.995277i | \(-0.469051\pi\) | ||||
0.0970755 | + | 0.995277i | \(0.469051\pi\) | |||||||
\(522\) | −8.12174 | −0.355479 | ||||||||
\(523\) | −0.307784 | −0.0134585 | −0.00672923 | − | 0.999977i | \(-0.502142\pi\) | ||||
−0.00672923 | + | 0.999977i | \(0.502142\pi\) | |||||||
\(524\) | −12.9808 | −0.567070 | ||||||||
\(525\) | −9.97374 | −0.435290 | ||||||||
\(526\) | −10.5628 | −0.460560 | ||||||||
\(527\) | −2.85008 | −0.124151 | ||||||||
\(528\) | 0.737328 | 0.0320881 | ||||||||
\(529\) | −22.9873 | −0.999447 | ||||||||
\(530\) | −29.1792 | −1.26746 | ||||||||
\(531\) | 15.4384 | 0.669968 | ||||||||
\(532\) | −1.03965 | −0.0450747 | ||||||||
\(533\) | −6.23657 | −0.270136 | ||||||||
\(534\) | −8.59961 | −0.372141 | ||||||||
\(535\) | −10.8964 | −0.471094 | ||||||||
\(536\) | −11.5399 | −0.498446 | ||||||||
\(537\) | −15.2387 | −0.657600 | ||||||||
\(538\) | 16.6982 | 0.719912 | ||||||||
\(539\) | −6.43960 | −0.277373 | ||||||||
\(540\) | 16.4348 | 0.707239 | ||||||||
\(541\) | 4.14272 | 0.178109 | 0.0890546 | − | 0.996027i | \(-0.471615\pi\) | ||||
0.0890546 | + | 0.996027i | \(0.471615\pi\) | |||||||
\(542\) | −2.72534 | −0.117063 | ||||||||
\(543\) | 1.10482 | 0.0474124 | ||||||||
\(544\) | 3.23599 | 0.138742 | ||||||||
\(545\) | −30.8677 | −1.32223 | ||||||||
\(546\) | −1.22454 | −0.0524054 | ||||||||
\(547\) | −29.3319 | −1.25414 | −0.627070 | − | 0.778963i | \(-0.715746\pi\) | ||||
−0.627070 | + | 0.778963i | \(0.715746\pi\) | |||||||
\(548\) | 8.38749 | 0.358296 | ||||||||
\(549\) | 9.69100 | 0.413602 | ||||||||
\(550\) | 15.3997 | 0.656645 | ||||||||
\(551\) | 3.19669 | 0.136183 | ||||||||
\(552\) | 0.0764274 | 0.00325296 | ||||||||
\(553\) | 9.95433 | 0.423301 | ||||||||
\(554\) | 29.0179 | 1.23285 | ||||||||
\(555\) | 15.9926 | 0.678849 | ||||||||
\(556\) | −18.9541 | −0.803834 | ||||||||
\(557\) | 11.4328 | 0.484422 | 0.242211 | − | 0.970224i | \(-0.422127\pi\) | ||||
0.242211 | + | 0.970224i | \(0.422127\pi\) | |||||||
\(558\) | 2.23768 | 0.0947287 | ||||||||
\(559\) | 8.12025 | 0.343450 | ||||||||
\(560\) | 4.55020 | 0.192281 | ||||||||
\(561\) | 2.38599 | 0.100737 | ||||||||
\(562\) | 1.00727 | 0.0424892 | ||||||||
\(563\) | −43.2521 | −1.82286 | −0.911430 | − | 0.411455i | \(-0.865021\pi\) | ||||
−0.911430 | + | 0.411455i | \(0.865021\pi\) | |||||||
\(564\) | 7.70604 | 0.324483 | ||||||||
\(565\) | 72.6051 | 3.05452 | ||||||||
\(566\) | −33.1531 | −1.39353 | ||||||||
\(567\) | −5.27840 | −0.221672 | ||||||||
\(568\) | −8.52973 | −0.357899 | ||||||||
\(569\) | −24.0639 | −1.00881 | −0.504406 | − | 0.863466i | \(-0.668289\pi\) | ||||
−0.504406 | + | 0.863466i | \(0.668289\pi\) | |||||||
\(570\) | −2.96620 | −0.124240 | ||||||||
\(571\) | 8.73645 | 0.365609 | 0.182805 | − | 0.983149i | \(-0.441482\pi\) | ||||
0.182805 | + | 0.983149i | \(0.441482\pi\) | |||||||
\(572\) | 1.89072 | 0.0790548 | ||||||||
\(573\) | −2.17509 | −0.0908658 | ||||||||
\(574\) | 3.73087 | 0.155723 | ||||||||
\(575\) | 1.59625 | 0.0665681 | ||||||||
\(576\) | −2.54068 | −0.105862 | ||||||||
\(577\) | 34.3770 | 1.43113 | 0.715567 | − | 0.698544i | \(-0.246169\pi\) | ||||
0.715567 | + | 0.698544i | \(0.246169\pi\) | |||||||
\(578\) | −6.52834 | −0.271543 | ||||||||
\(579\) | −9.24248 | −0.384104 | ||||||||
\(580\) | −13.9908 | −0.580934 | ||||||||
\(581\) | −12.9855 | −0.538729 | ||||||||
\(582\) | 6.21828 | 0.257756 | ||||||||
\(583\) | 7.25327 | 0.300400 | ||||||||
\(584\) | −3.18541 | −0.131813 | ||||||||
\(585\) | 19.3248 | 0.798983 | ||||||||
\(586\) | 11.2238 | 0.463650 | ||||||||
\(587\) | 22.1454 | 0.914039 | 0.457020 | − | 0.889457i | \(-0.348917\pi\) | ||||
0.457020 | + | 0.889457i | \(0.348917\pi\) | |||||||
\(588\) | −4.01159 | −0.165435 | ||||||||
\(589\) | −0.880743 | −0.0362904 | ||||||||
\(590\) | 26.5946 | 1.09488 | ||||||||
\(591\) | −16.5463 | −0.680624 | ||||||||
\(592\) | −5.39162 | −0.221594 | ||||||||
\(593\) | 27.9209 | 1.14657 | 0.573287 | − | 0.819355i | \(-0.305668\pi\) | ||||
0.573287 | + | 0.819355i | \(0.305668\pi\) | |||||||
\(594\) | −4.08530 | −0.167622 | ||||||||
\(595\) | 14.7244 | 0.603642 | ||||||||
\(596\) | −15.3632 | −0.629302 | ||||||||
\(597\) | 3.27811 | 0.134164 | ||||||||
\(598\) | 0.195981 | 0.00801427 | ||||||||
\(599\) | 1.89628 | 0.0774798 | 0.0387399 | − | 0.999249i | \(-0.487666\pi\) | ||||
0.0387399 | + | 0.999249i | \(0.487666\pi\) | |||||||
\(600\) | 9.59333 | 0.391646 | ||||||||
\(601\) | −20.6199 | −0.841102 | −0.420551 | − | 0.907269i | \(-0.638163\pi\) | ||||
−0.420551 | + | 0.907269i | \(0.638163\pi\) | |||||||
\(602\) | −4.85773 | −0.197986 | ||||||||
\(603\) | 29.3190 | 1.19396 | ||||||||
\(604\) | 16.1717 | 0.658016 | ||||||||
\(605\) | 42.9629 | 1.74669 | ||||||||
\(606\) | −9.59950 | −0.389953 | ||||||||
\(607\) | −28.1411 | −1.14221 | −0.571107 | − | 0.820876i | \(-0.693486\pi\) | ||||
−0.571107 | + | 0.820876i | \(0.693486\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −2.25241 | −0.0912723 | ||||||||
\(610\) | 16.6940 | 0.675920 | ||||||||
\(611\) | 19.7604 | 0.799422 | ||||||||
\(612\) | −8.22162 | −0.332339 | ||||||||
\(613\) | 1.60168 | 0.0646911 | 0.0323455 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323455 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(614\) | −1.17249 | −0.0473178 | ||||||||
\(615\) | 10.6444 | 0.429224 | ||||||||
\(616\) | −1.13107 | −0.0455722 | ||||||||
\(617\) | −22.0485 | −0.887640 | −0.443820 | − | 0.896116i | \(-0.646377\pi\) | ||||
−0.443820 | + | 0.896116i | \(0.646377\pi\) | |||||||
\(618\) | −2.14419 | −0.0862522 | ||||||||
\(619\) | −29.7628 | −1.19627 | −0.598135 | − | 0.801396i | \(-0.704091\pi\) | ||||
−0.598135 | + | 0.801396i | \(0.704091\pi\) | |||||||
\(620\) | 3.85470 | 0.154808 | ||||||||
\(621\) | −0.423459 | −0.0169928 | ||||||||
\(622\) | −12.4924 | −0.500898 | ||||||||
\(623\) | 13.1919 | 0.528523 | ||||||||
\(624\) | 1.17783 | 0.0471511 | ||||||||
\(625\) | 104.589 | 4.18357 | ||||||||
\(626\) | 6.41799 | 0.256515 | ||||||||
\(627\) | 0.737328 | 0.0294460 | ||||||||
\(628\) | 20.0070 | 0.798365 | ||||||||
\(629\) | −17.4472 | −0.695667 | ||||||||
\(630\) | −11.5606 | −0.460584 | ||||||||
\(631\) | −9.89467 | −0.393901 | −0.196950 | − | 0.980413i | \(-0.563104\pi\) | ||||
−0.196950 | + | 0.980413i | \(0.563104\pi\) | |||||||
\(632\) | −9.57466 | −0.380859 | ||||||||
\(633\) | −0.677734 | −0.0269375 | ||||||||
\(634\) | 16.0619 | 0.637901 | ||||||||
\(635\) | 15.3823 | 0.610429 | ||||||||
\(636\) | 4.51847 | 0.179169 | ||||||||
\(637\) | −10.2868 | −0.407579 | ||||||||
\(638\) | 3.47777 | 0.137686 | ||||||||
\(639\) | 21.6713 | 0.857303 | ||||||||
\(640\) | −4.37664 | −0.173002 | ||||||||
\(641\) | 37.3617 | 1.47570 | 0.737849 | − | 0.674965i | \(-0.235841\pi\) | ||||
0.737849 | + | 0.674965i | \(0.235841\pi\) | |||||||
\(642\) | 1.68734 | 0.0665939 | ||||||||
\(643\) | −27.7726 | −1.09524 | −0.547622 | − | 0.836726i | \(-0.684467\pi\) | ||||
−0.547622 | + | 0.836726i | \(0.684467\pi\) | |||||||
\(644\) | −0.117241 | −0.00461993 | ||||||||
\(645\) | −13.8594 | −0.545714 | ||||||||
\(646\) | 3.23599 | 0.127319 | ||||||||
\(647\) | −29.6180 | −1.16440 | −0.582202 | − | 0.813044i | \(-0.697809\pi\) | ||||
−0.582202 | + | 0.813044i | \(0.697809\pi\) | |||||||
\(648\) | 5.07707 | 0.199446 | ||||||||
\(649\) | −6.61079 | −0.259496 | ||||||||
\(650\) | 24.6000 | 0.964891 | ||||||||
\(651\) | 0.620579 | 0.0243224 | ||||||||
\(652\) | 7.50860 | 0.294060 | ||||||||
\(653\) | 17.4693 | 0.683626 | 0.341813 | − | 0.939768i | \(-0.388959\pi\) | ||||
0.341813 | + | 0.939768i | \(0.388959\pi\) | |||||||
\(654\) | 4.77994 | 0.186911 | ||||||||
\(655\) | 56.8125 | 2.21985 | ||||||||
\(656\) | −3.58857 | −0.140110 | ||||||||
\(657\) | 8.09309 | 0.315741 | ||||||||
\(658\) | −11.8212 | −0.460838 | ||||||||
\(659\) | 13.7271 | 0.534733 | 0.267367 | − | 0.963595i | \(-0.413847\pi\) | ||||
0.267367 | + | 0.963595i | \(0.413847\pi\) | |||||||
\(660\) | −3.22702 | −0.125612 | ||||||||
\(661\) | 31.9960 | 1.24450 | 0.622249 | − | 0.782819i | \(-0.286219\pi\) | ||||
0.622249 | + | 0.782819i | \(0.286219\pi\) | |||||||
\(662\) | −29.6379 | −1.15191 | ||||||||
\(663\) | 3.81146 | 0.148025 | ||||||||
\(664\) | 12.4902 | 0.484714 | ||||||||
\(665\) | 4.55020 | 0.176449 | ||||||||
\(666\) | 13.6984 | 0.530800 | ||||||||
\(667\) | 0.360487 | 0.0139581 | ||||||||
\(668\) | 10.5744 | 0.409135 | ||||||||
\(669\) | 2.66927 | 0.103200 | ||||||||
\(670\) | 50.5058 | 1.95121 | ||||||||
\(671\) | −4.14974 | −0.160199 | ||||||||
\(672\) | −0.704609 | −0.0271809 | ||||||||
\(673\) | 4.33516 | 0.167108 | 0.0835541 | − | 0.996503i | \(-0.473373\pi\) | ||||
0.0835541 | + | 0.996503i | \(0.473373\pi\) | |||||||
\(674\) | −4.45504 | −0.171602 | ||||||||
\(675\) | −53.1535 | −2.04588 | ||||||||
\(676\) | −9.97971 | −0.383835 | ||||||||
\(677\) | 30.9367 | 1.18899 | 0.594497 | − | 0.804098i | \(-0.297351\pi\) | ||||
0.594497 | + | 0.804098i | \(0.297351\pi\) | |||||||
\(678\) | −11.2431 | −0.431788 | ||||||||
\(679\) | −9.53894 | −0.366071 | ||||||||
\(680\) | −14.1628 | −0.543118 | ||||||||
\(681\) | 2.01755 | 0.0773128 | ||||||||
\(682\) | −0.958188 | −0.0366909 | ||||||||
\(683\) | 14.5295 | 0.555957 | 0.277978 | − | 0.960587i | \(-0.410336\pi\) | ||||
0.277978 | + | 0.960587i | \(0.410336\pi\) | |||||||
\(684\) | −2.54068 | −0.0971452 | ||||||||
\(685\) | −36.7091 | −1.40258 | ||||||||
\(686\) | 13.4314 | 0.512814 | ||||||||
\(687\) | −16.6943 | −0.636927 | ||||||||
\(688\) | 4.67245 | 0.178135 | ||||||||
\(689\) | 11.5866 | 0.441415 | ||||||||
\(690\) | −0.334495 | −0.0127340 | ||||||||
\(691\) | −14.3955 | −0.547632 | −0.273816 | − | 0.961782i | \(-0.588286\pi\) | ||||
−0.273816 | + | 0.961782i | \(0.588286\pi\) | |||||||
\(692\) | 17.9144 | 0.681004 | ||||||||
\(693\) | 2.87369 | 0.109162 | ||||||||
\(694\) | 2.94754 | 0.111887 | ||||||||
\(695\) | 82.9554 | 3.14668 | ||||||||
\(696\) | 2.16650 | 0.0821210 | ||||||||
\(697\) | −11.6126 | −0.439858 | ||||||||
\(698\) | 12.1898 | 0.461390 | ||||||||
\(699\) | 2.17838 | 0.0823940 | ||||||||
\(700\) | −14.7163 | −0.556224 | ||||||||
\(701\) | 5.95449 | 0.224898 | 0.112449 | − | 0.993657i | \(-0.464131\pi\) | ||||
0.112449 | + | 0.993657i | \(0.464131\pi\) | |||||||
\(702\) | −6.52599 | −0.246308 | ||||||||
\(703\) | −5.39162 | −0.203349 | ||||||||
\(704\) | 1.08793 | 0.0410030 | ||||||||
\(705\) | −33.7266 | −1.27022 | ||||||||
\(706\) | 1.80519 | 0.0679393 | ||||||||
\(707\) | 14.7258 | 0.553820 | ||||||||
\(708\) | −4.11823 | −0.154773 | ||||||||
\(709\) | −18.9234 | −0.710682 | −0.355341 | − | 0.934737i | \(-0.615635\pi\) | ||||
−0.355341 | + | 0.934737i | \(0.615635\pi\) | |||||||
\(710\) | 37.3316 | 1.40103 | ||||||||
\(711\) | 24.3261 | 0.912300 | ||||||||
\(712\) | −12.6888 | −0.475532 | ||||||||
\(713\) | −0.0993205 | −0.00371958 | ||||||||
\(714\) | −2.28011 | −0.0853310 | ||||||||
\(715\) | −8.27499 | −0.309467 | ||||||||
\(716\) | −22.4848 | −0.840298 | ||||||||
\(717\) | 1.24562 | 0.0465186 | ||||||||
\(718\) | 3.38306 | 0.126255 | ||||||||
\(719\) | −9.62073 | −0.358793 | −0.179396 | − | 0.983777i | \(-0.557414\pi\) | ||||
−0.179396 | + | 0.983777i | \(0.557414\pi\) | |||||||
\(720\) | 11.1196 | 0.414404 | ||||||||
\(721\) | 3.28923 | 0.122497 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 1.36614 | 0.0508073 | ||||||||
\(724\) | 1.63017 | 0.0605847 | ||||||||
\(725\) | 45.2491 | 1.68051 | ||||||||
\(726\) | −6.65291 | −0.246913 | ||||||||
\(727\) | −43.6033 | −1.61716 | −0.808579 | − | 0.588387i | \(-0.799763\pi\) | ||||
−0.808579 | + | 0.588387i | \(0.799763\pi\) | |||||||
\(728\) | −1.80681 | −0.0669650 | ||||||||
\(729\) | −5.26431 | −0.194974 | ||||||||
\(730\) | 13.9414 | 0.515994 | ||||||||
\(731\) | 15.1200 | 0.559234 | ||||||||
\(732\) | −2.58511 | −0.0955483 | ||||||||
\(733\) | 26.9647 | 0.995964 | 0.497982 | − | 0.867187i | \(-0.334075\pi\) | ||||
0.497982 | + | 0.867187i | \(0.334075\pi\) | |||||||
\(734\) | −30.5652 | −1.12818 | ||||||||
\(735\) | 17.5573 | 0.647610 | ||||||||
\(736\) | 0.112769 | 0.00415672 | ||||||||
\(737\) | −12.5546 | −0.462454 | ||||||||
\(738\) | 9.11739 | 0.335616 | ||||||||
\(739\) | −13.8465 | −0.509353 | −0.254677 | − | 0.967026i | \(-0.581969\pi\) | ||||
−0.254677 | + | 0.967026i | \(0.581969\pi\) | |||||||
\(740\) | 23.5972 | 0.867450 | ||||||||
\(741\) | 1.17783 | 0.0432688 | ||||||||
\(742\) | −6.93140 | −0.254460 | ||||||||
\(743\) | 17.1248 | 0.628248 | 0.314124 | − | 0.949382i | \(-0.398289\pi\) | ||||
0.314124 | + | 0.949382i | \(0.398289\pi\) | |||||||
\(744\) | −0.596909 | −0.0218838 | ||||||||
\(745\) | 67.2393 | 2.46346 | ||||||||
\(746\) | −19.5072 | −0.714210 | ||||||||
\(747\) | −31.7336 | −1.16107 | ||||||||
\(748\) | 3.52054 | 0.128724 | ||||||||
\(749\) | −2.58840 | −0.0945782 | ||||||||
\(750\) | −27.1556 | −0.991582 | ||||||||
\(751\) | 32.5624 | 1.18822 | 0.594109 | − | 0.804384i | \(-0.297505\pi\) | ||||
0.594109 | + | 0.804384i | \(0.297505\pi\) | |||||||
\(752\) | 11.3703 | 0.414632 | ||||||||
\(753\) | 1.04178 | 0.0379645 | ||||||||
\(754\) | 5.55552 | 0.202320 | ||||||||
\(755\) | −70.7776 | −2.57586 | ||||||||
\(756\) | 3.90401 | 0.141987 | ||||||||
\(757\) | −25.7400 | −0.935535 | −0.467767 | − | 0.883852i | \(-0.654942\pi\) | ||||
−0.467767 | + | 0.883852i | \(0.654942\pi\) | |||||||
\(758\) | −25.9549 | −0.942725 | ||||||||
\(759\) | 0.0831477 | 0.00301807 | ||||||||
\(760\) | −4.37664 | −0.158758 | ||||||||
\(761\) | 11.3198 | 0.410344 | 0.205172 | − | 0.978726i | \(-0.434225\pi\) | ||||
0.205172 | + | 0.978726i | \(0.434225\pi\) | |||||||
\(762\) | −2.38199 | −0.0862904 | ||||||||
\(763\) | −7.33250 | −0.265454 | ||||||||
\(764\) | −3.20936 | −0.116111 | ||||||||
\(765\) | 35.9831 | 1.30097 | ||||||||
\(766\) | 30.3912 | 1.09808 | ||||||||
\(767\) | −10.5603 | −0.381310 | ||||||||
\(768\) | 0.677734 | 0.0244556 | ||||||||
\(769\) | 35.1897 | 1.26897 | 0.634487 | − | 0.772933i | \(-0.281211\pi\) | ||||
0.634487 | + | 0.772933i | \(0.281211\pi\) | |||||||
\(770\) | 4.95030 | 0.178396 | ||||||||
\(771\) | −9.35754 | −0.337004 | ||||||||
\(772\) | −13.6373 | −0.490818 | ||||||||
\(773\) | 15.8358 | 0.569576 | 0.284788 | − | 0.958591i | \(-0.408077\pi\) | ||||
0.284788 | + | 0.958591i | \(0.408077\pi\) | |||||||
\(774\) | −11.8712 | −0.426701 | ||||||||
\(775\) | −12.4669 | −0.447825 | ||||||||
\(776\) | 9.17511 | 0.329367 | ||||||||
\(777\) | 3.79898 | 0.136288 | ||||||||
\(778\) | 10.7419 | 0.385116 | ||||||||
\(779\) | −3.58857 | −0.128574 | ||||||||
\(780\) | −5.15496 | −0.184577 | ||||||||
\(781\) | −9.27976 | −0.332056 | ||||||||
\(782\) | 0.364920 | 0.0130495 | ||||||||
\(783\) | −12.0039 | −0.428984 | ||||||||
\(784\) | −5.91912 | −0.211397 | ||||||||
\(785\) | −87.5634 | −3.12527 | ||||||||
\(786\) | −8.79755 | −0.313798 | ||||||||
\(787\) | −34.6096 | −1.23370 | −0.616849 | − | 0.787081i | \(-0.711591\pi\) | ||||
−0.616849 | + | 0.787081i | \(0.711591\pi\) | |||||||
\(788\) | −24.4141 | −0.869718 | ||||||||
\(789\) | −7.15876 | −0.254859 | ||||||||
\(790\) | 41.9049 | 1.49091 | ||||||||
\(791\) | 17.2470 | 0.613234 | ||||||||
\(792\) | −2.76408 | −0.0982174 | ||||||||
\(793\) | −6.62894 | −0.235400 | ||||||||
\(794\) | −9.73475 | −0.345473 | ||||||||
\(795\) | −19.7757 | −0.701373 | ||||||||
\(796\) | 4.83687 | 0.171438 | ||||||||
\(797\) | 22.2230 | 0.787179 | 0.393589 | − | 0.919286i | \(-0.371233\pi\) | ||||
0.393589 | + | 0.919286i | \(0.371233\pi\) | |||||||
\(798\) | −0.704609 | −0.0249429 | ||||||||
\(799\) | 36.7942 | 1.30169 | ||||||||
\(800\) | 14.1550 | 0.500455 | ||||||||
\(801\) | 32.2381 | 1.13908 | ||||||||
\(802\) | 8.63370 | 0.304867 | ||||||||
\(803\) | −3.46550 | −0.122295 | ||||||||
\(804\) | −7.82095 | −0.275824 | ||||||||
\(805\) | 0.513121 | 0.0180851 | ||||||||
\(806\) | −1.53064 | −0.0539146 | ||||||||
\(807\) | 11.3170 | 0.398376 | ||||||||
\(808\) | −14.1641 | −0.498292 | ||||||||
\(809\) | 14.4195 | 0.506962 | 0.253481 | − | 0.967340i | \(-0.418424\pi\) | ||||
0.253481 | + | 0.967340i | \(0.418424\pi\) | |||||||
\(810\) | −22.2205 | −0.780750 | ||||||||
\(811\) | 55.7753 | 1.95854 | 0.979268 | − | 0.202569i | \(-0.0649291\pi\) | ||||
0.979268 | + | 0.202569i | \(0.0649291\pi\) | |||||||
\(812\) | −3.32345 | −0.116630 | ||||||||
\(813\) | −1.84706 | −0.0647791 | ||||||||
\(814\) | −5.86571 | −0.205593 | ||||||||
\(815\) | −32.8625 | −1.15112 | ||||||||
\(816\) | 2.19314 | 0.0767754 | ||||||||
\(817\) | 4.67245 | 0.163468 | ||||||||
\(818\) | 0.907335 | 0.0317242 | ||||||||
\(819\) | 4.59053 | 0.160406 | ||||||||
\(820\) | 15.7059 | 0.548473 | ||||||||
\(821\) | −52.6843 | −1.83870 | −0.919348 | − | 0.393446i | \(-0.871283\pi\) | ||||
−0.919348 | + | 0.393446i | \(0.871283\pi\) | |||||||
\(822\) | 5.68449 | 0.198269 | ||||||||
\(823\) | −10.9292 | −0.380969 | −0.190484 | − | 0.981690i | \(-0.561006\pi\) | ||||
−0.190484 | + | 0.981690i | \(0.561006\pi\) | |||||||
\(824\) | −3.16377 | −0.110215 | ||||||||
\(825\) | 10.4369 | 0.363366 | ||||||||
\(826\) | 6.31743 | 0.219812 | ||||||||
\(827\) | −28.5567 | −0.993012 | −0.496506 | − | 0.868033i | \(-0.665384\pi\) | ||||
−0.496506 | + | 0.868033i | \(0.665384\pi\) | |||||||
\(828\) | −0.286510 | −0.00995690 | ||||||||
\(829\) | 31.2443 | 1.08516 | 0.542580 | − | 0.840004i | \(-0.317448\pi\) | ||||
0.542580 | + | 0.840004i | \(0.317448\pi\) | |||||||
\(830\) | −54.6651 | −1.89745 | ||||||||
\(831\) | 19.6664 | 0.682221 | ||||||||
\(832\) | 1.73790 | 0.0602508 | ||||||||
\(833\) | −19.1542 | −0.663655 | ||||||||
\(834\) | −12.8459 | −0.444815 | ||||||||
\(835\) | −46.2803 | −1.60159 | ||||||||
\(836\) | 1.08793 | 0.0376269 | ||||||||
\(837\) | 3.30728 | 0.114316 | ||||||||
\(838\) | −19.6319 | −0.678172 | ||||||||
\(839\) | −25.6234 | −0.884616 | −0.442308 | − | 0.896863i | \(-0.645840\pi\) | ||||
−0.442308 | + | 0.896863i | \(0.645840\pi\) | |||||||
\(840\) | 3.08382 | 0.106402 | ||||||||
\(841\) | −18.7812 | −0.647628 | ||||||||
\(842\) | −27.2987 | −0.940775 | ||||||||
\(843\) | 0.682662 | 0.0235121 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 43.6776 | 1.50256 | ||||||||
\(846\) | −28.8883 | −0.993199 | ||||||||
\(847\) | 10.2057 | 0.350671 | ||||||||
\(848\) | 6.66703 | 0.228947 | ||||||||
\(849\) | −22.4690 | −0.771132 | ||||||||
\(850\) | 45.8055 | 1.57112 | ||||||||
\(851\) | −0.608007 | −0.0208422 | ||||||||
\(852\) | −5.78088 | −0.198050 | ||||||||
\(853\) | 22.0570 | 0.755219 | 0.377609 | − | 0.925965i | \(-0.376746\pi\) | ||||
0.377609 | + | 0.925965i | \(0.376746\pi\) | |||||||
\(854\) | 3.96559 | 0.135700 | ||||||||
\(855\) | 11.1196 | 0.380284 | ||||||||
\(856\) | 2.48968 | 0.0850954 | ||||||||
\(857\) | 24.5272 | 0.837834 | 0.418917 | − | 0.908024i | \(-0.362410\pi\) | ||||
0.418917 | + | 0.908024i | \(0.362410\pi\) | |||||||
\(858\) | 1.28140 | 0.0437463 | ||||||||
\(859\) | −28.2679 | −0.964489 | −0.482244 | − | 0.876037i | \(-0.660178\pi\) | ||||
−0.482244 | + | 0.876037i | \(0.660178\pi\) | |||||||
\(860\) | −20.4496 | −0.697327 | ||||||||
\(861\) | 2.52854 | 0.0861723 | ||||||||
\(862\) | 6.94829 | 0.236660 | ||||||||
\(863\) | 28.0607 | 0.955198 | 0.477599 | − | 0.878578i | \(-0.341507\pi\) | ||||
0.477599 | + | 0.878578i | \(0.341507\pi\) | |||||||
\(864\) | −3.75510 | −0.127751 | ||||||||
\(865\) | −78.4051 | −2.66585 | ||||||||
\(866\) | −28.7277 | −0.976207 | ||||||||
\(867\) | −4.42448 | −0.150263 | ||||||||
\(868\) | 0.915668 | 0.0310798 | ||||||||
\(869\) | −10.4166 | −0.353358 | ||||||||
\(870\) | −9.48201 | −0.321470 | ||||||||
\(871\) | −20.0551 | −0.679541 | ||||||||
\(872\) | 7.05283 | 0.238839 | ||||||||
\(873\) | −23.3110 | −0.788957 | ||||||||
\(874\) | 0.112769 | 0.00381447 | ||||||||
\(875\) | 41.6571 | 1.40827 | ||||||||
\(876\) | −2.15886 | −0.0729410 | ||||||||
\(877\) | −25.9774 | −0.877195 | −0.438597 | − | 0.898684i | \(-0.644525\pi\) | ||||
−0.438597 | + | 0.898684i | \(0.644525\pi\) | |||||||
\(878\) | 22.0835 | 0.745281 | ||||||||
\(879\) | 7.60674 | 0.256569 | ||||||||
\(880\) | −4.76149 | −0.160510 | ||||||||
\(881\) | 50.2449 | 1.69279 | 0.846397 | − | 0.532553i | \(-0.178767\pi\) | ||||
0.846397 | + | 0.532553i | \(0.178767\pi\) | |||||||
\(882\) | 15.0386 | 0.506375 | ||||||||
\(883\) | 11.2831 | 0.379707 | 0.189854 | − | 0.981812i | \(-0.439199\pi\) | ||||
0.189854 | + | 0.981812i | \(0.439199\pi\) | |||||||
\(884\) | 5.62383 | 0.189150 | ||||||||
\(885\) | 18.0240 | 0.605871 | ||||||||
\(886\) | 3.42410 | 0.115035 | ||||||||
\(887\) | −44.7976 | −1.50416 | −0.752078 | − | 0.659074i | \(-0.770948\pi\) | ||||
−0.752078 | + | 0.659074i | \(0.770948\pi\) | |||||||
\(888\) | −3.65408 | −0.122623 | ||||||||
\(889\) | 3.65401 | 0.122552 | ||||||||
\(890\) | 55.5342 | 1.86151 | ||||||||
\(891\) | 5.52350 | 0.185044 | ||||||||
\(892\) | 3.93852 | 0.131871 | ||||||||
\(893\) | 11.3703 | 0.380493 | ||||||||
\(894\) | −10.4122 | −0.348235 | ||||||||
\(895\) | 98.4082 | 3.28942 | ||||||||
\(896\) | −1.03965 | −0.0347324 | ||||||||
\(897\) | 0.132823 | 0.00443483 | ||||||||
\(898\) | −6.45014 | −0.215244 | ||||||||
\(899\) | −2.81546 | −0.0939008 | ||||||||
\(900\) | −35.9633 | −1.19878 | ||||||||
\(901\) | 21.5745 | 0.718749 | ||||||||
\(902\) | −3.90412 | −0.129993 | ||||||||
\(903\) | −3.29225 | −0.109559 | ||||||||
\(904\) | −16.5892 | −0.551749 | ||||||||
\(905\) | −7.13467 | −0.237164 | ||||||||
\(906\) | 10.9601 | 0.364124 | ||||||||
\(907\) | 5.01363 | 0.166475 | 0.0832374 | − | 0.996530i | \(-0.473474\pi\) | ||||
0.0832374 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(908\) | 2.97691 | 0.0987923 | ||||||||
\(909\) | 35.9864 | 1.19359 | ||||||||
\(910\) | 7.90778 | 0.262140 | ||||||||
\(911\) | −55.3502 | −1.83384 | −0.916918 | − | 0.399077i | \(-0.869331\pi\) | ||||
−0.916918 | + | 0.399077i | \(0.869331\pi\) | |||||||
\(912\) | 0.677734 | 0.0224420 | ||||||||
\(913\) | 13.5885 | 0.449713 | ||||||||
\(914\) | 17.0170 | 0.562873 | ||||||||
\(915\) | 11.3141 | 0.374032 | ||||||||
\(916\) | −24.6325 | −0.813882 | ||||||||
\(917\) | 13.4956 | 0.445663 | ||||||||
\(918\) | −12.1515 | −0.401059 | ||||||||
\(919\) | −15.0345 | −0.495943 | −0.247971 | − | 0.968767i | \(-0.579764\pi\) | ||||
−0.247971 | + | 0.968767i | \(0.579764\pi\) | |||||||
\(920\) | −0.493550 | −0.0162719 | ||||||||
\(921\) | −0.794636 | −0.0261841 | ||||||||
\(922\) | −6.85354 | −0.225709 | ||||||||
\(923\) | −14.8238 | −0.487932 | ||||||||
\(924\) | −0.766566 | −0.0252182 | ||||||||
\(925\) | −76.3184 | −2.50933 | ||||||||
\(926\) | −13.7414 | −0.451569 | ||||||||
\(927\) | 8.03812 | 0.264007 | ||||||||
\(928\) | 3.19669 | 0.104936 | ||||||||
\(929\) | 56.2773 | 1.84640 | 0.923198 | − | 0.384324i | \(-0.125565\pi\) | ||||
0.923198 | + | 0.384324i | \(0.125565\pi\) | |||||||
\(930\) | 2.61246 | 0.0856659 | ||||||||
\(931\) | −5.91912 | −0.193991 | ||||||||
\(932\) | 3.21421 | 0.105285 | ||||||||
\(933\) | −8.46650 | −0.277181 | ||||||||
\(934\) | 33.1199 | 1.08372 | ||||||||
\(935\) | −15.4081 | −0.503900 | ||||||||
\(936\) | −4.41544 | −0.144323 | ||||||||
\(937\) | −28.8804 | −0.943481 | −0.471740 | − | 0.881737i | \(-0.656374\pi\) | ||||
−0.471740 | + | 0.881737i | \(0.656374\pi\) | |||||||
\(938\) | 11.9975 | 0.391731 | ||||||||
\(939\) | 4.34969 | 0.141947 | ||||||||
\(940\) | −49.7638 | −1.62311 | ||||||||
\(941\) | −0.483464 | −0.0157605 | −0.00788024 | − | 0.999969i | \(-0.502508\pi\) | ||||
−0.00788024 | + | 0.999969i | \(0.502508\pi\) | |||||||
\(942\) | 13.5594 | 0.441789 | ||||||||
\(943\) | −0.404679 | −0.0131782 | ||||||||
\(944\) | −6.07647 | −0.197772 | ||||||||
\(945\) | −17.0865 | −0.555823 | ||||||||
\(946\) | 5.08330 | 0.165272 | ||||||||
\(947\) | 4.38320 | 0.142435 | 0.0712174 | − | 0.997461i | \(-0.477312\pi\) | ||||
0.0712174 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(948\) | −6.48907 | −0.210755 | ||||||||
\(949\) | −5.53592 | −0.179703 | ||||||||
\(950\) | 14.1550 | 0.459249 | ||||||||
\(951\) | 10.8857 | 0.352994 | ||||||||
\(952\) | −3.36431 | −0.109038 | ||||||||
\(953\) | 40.0977 | 1.29889 | 0.649446 | − | 0.760408i | \(-0.275001\pi\) | ||||
0.649446 | + | 0.760408i | \(0.275001\pi\) | |||||||
\(954\) | −16.9388 | −0.548413 | ||||||||
\(955\) | 14.0462 | 0.454525 | ||||||||
\(956\) | 1.83792 | 0.0594427 | ||||||||
\(957\) | 2.35700 | 0.0761911 | ||||||||
\(958\) | 10.3502 | 0.334400 | ||||||||
\(959\) | −8.72009 | −0.281586 | ||||||||
\(960\) | −2.96620 | −0.0957337 | ||||||||
\(961\) | −30.2243 | −0.974977 | ||||||||
\(962\) | −9.37009 | −0.302104 | ||||||||
\(963\) | −6.32546 | −0.203835 | ||||||||
\(964\) | 2.01575 | 0.0649228 | ||||||||
\(965\) | 59.6857 | 1.92135 | ||||||||
\(966\) | −0.0794580 | −0.00255652 | ||||||||
\(967\) | 33.0590 | 1.06311 | 0.531553 | − | 0.847025i | \(-0.321608\pi\) | ||||
0.531553 | + | 0.847025i | \(0.321608\pi\) | |||||||
\(968\) | −9.81641 | −0.315511 | ||||||||
\(969\) | 2.19314 | 0.0704539 | ||||||||
\(970\) | −40.1562 | −1.28934 | ||||||||
\(971\) | −0.210526 | −0.00675609 | −0.00337804 | − | 0.999994i | \(-0.501075\pi\) | ||||
−0.00337804 | + | 0.999994i | \(0.501075\pi\) | |||||||
\(972\) | 14.7062 | 0.471702 | ||||||||
\(973\) | 19.7057 | 0.631737 | ||||||||
\(974\) | −8.92066 | −0.285836 | ||||||||
\(975\) | 16.6722 | 0.533939 | ||||||||
\(976\) | −3.81434 | −0.122094 | ||||||||
\(977\) | 5.30124 | 0.169602 | 0.0848009 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0848009 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(978\) | 5.08883 | 0.162723 | ||||||||
\(979\) | −13.8045 | −0.441194 | ||||||||
\(980\) | 25.9059 | 0.827533 | ||||||||
\(981\) | −17.9190 | −0.572109 | ||||||||
\(982\) | 26.0318 | 0.830709 | ||||||||
\(983\) | 39.0136 | 1.24434 | 0.622170 | − | 0.782882i | \(-0.286251\pi\) | ||||
0.622170 | + | 0.782882i | \(0.286251\pi\) | |||||||
\(984\) | −2.43209 | −0.0775323 | ||||||||
\(985\) | 106.852 | 3.40459 | ||||||||
\(986\) | 10.3445 | 0.329435 | ||||||||
\(987\) | −8.01161 | −0.255012 | ||||||||
\(988\) | 1.73790 | 0.0552899 | ||||||||
\(989\) | 0.526907 | 0.0167547 | ||||||||
\(990\) | 12.0974 | 0.384481 | ||||||||
\(991\) | 7.95223 | 0.252611 | 0.126305 | − | 0.991991i | \(-0.459688\pi\) | ||||
0.126305 | + | 0.991991i | \(0.459688\pi\) | |||||||
\(992\) | −0.880743 | −0.0279636 | ||||||||
\(993\) | −20.0866 | −0.637430 | ||||||||
\(994\) | 8.86796 | 0.281275 | ||||||||
\(995\) | −21.1693 | −0.671111 | ||||||||
\(996\) | 8.46503 | 0.268225 | ||||||||
\(997\) | −43.0933 | −1.36478 | −0.682389 | − | 0.730989i | \(-0.739059\pi\) | ||||
−0.682389 | + | 0.730989i | \(0.739059\pi\) | |||||||
\(998\) | −4.96533 | −0.157175 | ||||||||
\(999\) | 20.2461 | 0.640558 |
(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 | 8018.2.a.d.1.19 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.19 | ✓ | 30 | 1.1 | even | 1 | trivial |