Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50856 | −1.77382 | −0.886909 | − | 0.461945i | \(-0.847152\pi\) | ||||
−0.886909 | + | 0.461945i | \(0.847152\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.29286 | 2.14643 | ||||||||
\(5\) | −2.69434 | −1.20494 | −0.602472 | − | 0.798140i | \(-0.705817\pi\) | ||||
−0.602472 | + | 0.798140i | \(0.705817\pi\) | |||||||
\(6\) | 2.50856 | 1.02411 | ||||||||
\(7\) | 3.74400 | 1.41510 | 0.707550 | − | 0.706663i | \(-0.249800\pi\) | ||||
0.707550 | + | 0.706663i | \(0.249800\pi\) | |||||||
\(8\) | −5.75176 | −2.03355 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.75889 | 2.13735 | ||||||||
\(11\) | −1.71911 | −0.518332 | −0.259166 | − | 0.965833i | \(-0.583448\pi\) | ||||
−0.259166 | + | 0.965833i | \(0.583448\pi\) | |||||||
\(12\) | −4.29286 | −1.23924 | ||||||||
\(13\) | −0.139018 | −0.0385566 | −0.0192783 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192783 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(14\) | −9.39205 | −2.51013 | ||||||||
\(15\) | 2.69434 | 0.695674 | ||||||||
\(16\) | 5.84290 | 1.46072 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.50856 | −0.591272 | ||||||||
\(19\) | 5.54406 | 1.27189 | 0.635947 | − | 0.771732i | \(-0.280610\pi\) | ||||
0.635947 | + | 0.771732i | \(0.280610\pi\) | |||||||
\(20\) | −11.5664 | −2.58632 | ||||||||
\(21\) | −3.74400 | −0.817009 | ||||||||
\(22\) | 4.31249 | 0.919427 | ||||||||
\(23\) | 5.39210 | 1.12433 | 0.562165 | − | 0.827025i | \(-0.309968\pi\) | ||||
0.562165 | + | 0.827025i | \(0.309968\pi\) | |||||||
\(24\) | 5.75176 | 1.17407 | ||||||||
\(25\) | 2.25944 | 0.451888 | ||||||||
\(26\) | 0.348734 | 0.0683924 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 16.0725 | 3.03741 | ||||||||
\(29\) | 7.20257 | 1.33748 | 0.668741 | − | 0.743495i | \(-0.266833\pi\) | ||||
0.668741 | + | 0.743495i | \(0.266833\pi\) | |||||||
\(30\) | −6.75889 | −1.23400 | ||||||||
\(31\) | −6.35822 | −1.14197 | −0.570985 | − | 0.820961i | \(-0.693439\pi\) | ||||
−0.570985 | + | 0.820961i | \(0.693439\pi\) | |||||||
\(32\) | −3.15372 | −0.557504 | ||||||||
\(33\) | 1.71911 | 0.299259 | ||||||||
\(34\) | 2.50856 | 0.430214 | ||||||||
\(35\) | −10.0876 | −1.70512 | ||||||||
\(36\) | 4.29286 | 0.715476 | ||||||||
\(37\) | −9.56660 | −1.57274 | −0.786370 | − | 0.617756i | \(-0.788042\pi\) | ||||
−0.786370 | + | 0.617756i | \(0.788042\pi\) | |||||||
\(38\) | −13.9076 | −2.25611 | ||||||||
\(39\) | 0.139018 | 0.0222607 | ||||||||
\(40\) | 15.4972 | 2.45032 | ||||||||
\(41\) | 0.327658 | 0.0511716 | 0.0255858 | − | 0.999673i | \(-0.491855\pi\) | ||||
0.0255858 | + | 0.999673i | \(0.491855\pi\) | |||||||
\(42\) | 9.39205 | 1.44922 | ||||||||
\(43\) | 11.0164 | 1.67999 | 0.839996 | − | 0.542592i | \(-0.182557\pi\) | ||||
0.839996 | + | 0.542592i | \(0.182557\pi\) | |||||||
\(44\) | −7.37990 | −1.11256 | ||||||||
\(45\) | −2.69434 | −0.401648 | ||||||||
\(46\) | −13.5264 | −1.99436 | ||||||||
\(47\) | −8.65194 | −1.26202 | −0.631008 | − | 0.775777i | \(-0.717358\pi\) | ||||
−0.631008 | + | 0.775777i | \(0.717358\pi\) | |||||||
\(48\) | −5.84290 | −0.843349 | ||||||||
\(49\) | 7.01757 | 1.00251 | ||||||||
\(50\) | −5.66794 | −0.801568 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.596784 | −0.0827590 | ||||||||
\(53\) | 2.07677 | 0.285267 | 0.142633 | − | 0.989776i | \(-0.454443\pi\) | ||||
0.142633 | + | 0.989776i | \(0.454443\pi\) | |||||||
\(54\) | 2.50856 | 0.341371 | ||||||||
\(55\) | 4.63187 | 0.624561 | ||||||||
\(56\) | −21.5346 | −2.87768 | ||||||||
\(57\) | −5.54406 | −0.734329 | ||||||||
\(58\) | −18.0680 | −2.37245 | ||||||||
\(59\) | 2.59407 | 0.337719 | 0.168860 | − | 0.985640i | \(-0.445992\pi\) | ||||
0.168860 | + | 0.985640i | \(0.445992\pi\) | |||||||
\(60\) | 11.5664 | 1.49321 | ||||||||
\(61\) | 15.1344 | 1.93776 | 0.968882 | − | 0.247522i | \(-0.0796164\pi\) | ||||
0.968882 | + | 0.247522i | \(0.0796164\pi\) | |||||||
\(62\) | 15.9500 | 2.02565 | ||||||||
\(63\) | 3.74400 | 0.471700 | ||||||||
\(64\) | −3.77451 | −0.471814 | ||||||||
\(65\) | 0.374561 | 0.0464585 | ||||||||
\(66\) | −4.31249 | −0.530831 | ||||||||
\(67\) | 4.21389 | 0.514809 | 0.257404 | − | 0.966304i | \(-0.417133\pi\) | ||||
0.257404 | + | 0.966304i | \(0.417133\pi\) | |||||||
\(68\) | −4.29286 | −0.520585 | ||||||||
\(69\) | −5.39210 | −0.649133 | ||||||||
\(70\) | 25.3053 | 3.02456 | ||||||||
\(71\) | 8.71318 | 1.03406 | 0.517032 | − | 0.855966i | \(-0.327037\pi\) | ||||
0.517032 | + | 0.855966i | \(0.327037\pi\) | |||||||
\(72\) | −5.75176 | −0.677851 | ||||||||
\(73\) | 10.0129 | 1.17192 | 0.585962 | − | 0.810339i | \(-0.300717\pi\) | ||||
0.585962 | + | 0.810339i | \(0.300717\pi\) | |||||||
\(74\) | 23.9984 | 2.78975 | ||||||||
\(75\) | −2.25944 | −0.260898 | ||||||||
\(76\) | 23.7998 | 2.73003 | ||||||||
\(77\) | −6.43637 | −0.733492 | ||||||||
\(78\) | −0.348734 | −0.0394864 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −15.7427 | −1.76009 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.821949 | −0.0907691 | ||||||||
\(83\) | −16.7409 | −1.83755 | −0.918776 | − | 0.394779i | \(-0.870821\pi\) | ||||
−0.918776 | + | 0.394779i | \(0.870821\pi\) | |||||||
\(84\) | −16.0725 | −1.75365 | ||||||||
\(85\) | 2.69434 | 0.292242 | ||||||||
\(86\) | −27.6354 | −2.98000 | ||||||||
\(87\) | −7.20257 | −0.772196 | ||||||||
\(88\) | 9.88792 | 1.05406 | ||||||||
\(89\) | −0.176143 | −0.0186711 | −0.00933555 | − | 0.999956i | \(-0.502972\pi\) | ||||
−0.00933555 | + | 0.999956i | \(0.502972\pi\) | |||||||
\(90\) | 6.75889 | 0.712450 | ||||||||
\(91\) | −0.520484 | −0.0545615 | ||||||||
\(92\) | 23.1475 | 2.41329 | ||||||||
\(93\) | 6.35822 | 0.659317 | ||||||||
\(94\) | 21.7039 | 2.23858 | ||||||||
\(95\) | −14.9376 | −1.53256 | ||||||||
\(96\) | 3.15372 | 0.321875 | ||||||||
\(97\) | −9.72863 | −0.987793 | −0.493896 | − | 0.869521i | \(-0.664428\pi\) | ||||
−0.493896 | + | 0.869521i | \(0.664428\pi\) | |||||||
\(98\) | −17.6040 | −1.77827 | ||||||||
\(99\) | −1.71911 | −0.172777 | ||||||||
\(100\) | 9.69946 | 0.969946 | ||||||||
\(101\) | −3.07310 | −0.305785 | −0.152892 | − | 0.988243i | \(-0.548859\pi\) | ||||
−0.152892 | + | 0.988243i | \(0.548859\pi\) | |||||||
\(102\) | −2.50856 | −0.248384 | ||||||||
\(103\) | 15.7707 | 1.55393 | 0.776966 | − | 0.629542i | \(-0.216757\pi\) | ||||
0.776966 | + | 0.629542i | \(0.216757\pi\) | |||||||
\(104\) | 0.799597 | 0.0784069 | ||||||||
\(105\) | 10.0876 | 0.984449 | ||||||||
\(106\) | −5.20971 | −0.506011 | ||||||||
\(107\) | 0.106214 | 0.0102681 | 0.00513403 | − | 0.999987i | \(-0.498366\pi\) | ||||
0.00513403 | + | 0.999987i | \(0.498366\pi\) | |||||||
\(108\) | −4.29286 | −0.413080 | ||||||||
\(109\) | −19.5268 | −1.87033 | −0.935163 | − | 0.354219i | \(-0.884747\pi\) | ||||
−0.935163 | + | 0.354219i | \(0.884747\pi\) | |||||||
\(110\) | −11.6193 | −1.10786 | ||||||||
\(111\) | 9.56660 | 0.908021 | ||||||||
\(112\) | 21.8758 | 2.06707 | ||||||||
\(113\) | 10.4099 | 0.979277 | 0.489639 | − | 0.871925i | \(-0.337129\pi\) | ||||
0.489639 | + | 0.871925i | \(0.337129\pi\) | |||||||
\(114\) | 13.9076 | 1.30256 | ||||||||
\(115\) | −14.5281 | −1.35475 | ||||||||
\(116\) | 30.9196 | 2.87081 | ||||||||
\(117\) | −0.139018 | −0.0128522 | ||||||||
\(118\) | −6.50737 | −0.599052 | ||||||||
\(119\) | −3.74400 | −0.343212 | ||||||||
\(120\) | −15.4972 | −1.41469 | ||||||||
\(121\) | −8.04465 | −0.731332 | ||||||||
\(122\) | −37.9656 | −3.43724 | ||||||||
\(123\) | −0.327658 | −0.0295440 | ||||||||
\(124\) | −27.2949 | −2.45116 | ||||||||
\(125\) | 7.38398 | 0.660443 | ||||||||
\(126\) | −9.39205 | −0.836710 | ||||||||
\(127\) | −18.6065 | −1.65106 | −0.825532 | − | 0.564356i | \(-0.809125\pi\) | ||||
−0.825532 | + | 0.564356i | \(0.809125\pi\) | |||||||
\(128\) | 15.7760 | 1.39442 | ||||||||
\(129\) | −11.0164 | −0.969944 | ||||||||
\(130\) | −0.939607 | −0.0824090 | ||||||||
\(131\) | −5.45234 | −0.476373 | −0.238187 | − | 0.971219i | \(-0.576553\pi\) | ||||
−0.238187 | + | 0.971219i | \(0.576553\pi\) | |||||||
\(132\) | 7.37990 | 0.642338 | ||||||||
\(133\) | 20.7570 | 1.79986 | ||||||||
\(134\) | −10.5708 | −0.913177 | ||||||||
\(135\) | 2.69434 | 0.231891 | ||||||||
\(136\) | 5.75176 | 0.493209 | ||||||||
\(137\) | 3.81445 | 0.325890 | 0.162945 | − | 0.986635i | \(-0.447901\pi\) | ||||
0.162945 | + | 0.986635i | \(0.447901\pi\) | |||||||
\(138\) | 13.5264 | 1.15144 | ||||||||
\(139\) | −3.66939 | −0.311233 | −0.155617 | − | 0.987818i | \(-0.549736\pi\) | ||||
−0.155617 | + | 0.987818i | \(0.549736\pi\) | |||||||
\(140\) | −43.3046 | −3.65991 | ||||||||
\(141\) | 8.65194 | 0.728625 | ||||||||
\(142\) | −21.8575 | −1.83424 | ||||||||
\(143\) | 0.238987 | 0.0199851 | ||||||||
\(144\) | 5.84290 | 0.486908 | ||||||||
\(145\) | −19.4061 | −1.61159 | ||||||||
\(146\) | −25.1180 | −2.07878 | ||||||||
\(147\) | −7.01757 | −0.578799 | ||||||||
\(148\) | −41.0680 | −3.37577 | ||||||||
\(149\) | 10.2266 | 0.837799 | 0.418900 | − | 0.908032i | \(-0.362416\pi\) | ||||
0.418900 | + | 0.908032i | \(0.362416\pi\) | |||||||
\(150\) | 5.66794 | 0.462785 | ||||||||
\(151\) | −15.0719 | −1.22654 | −0.613268 | − | 0.789875i | \(-0.710146\pi\) | ||||
−0.613268 | + | 0.789875i | \(0.710146\pi\) | |||||||
\(152\) | −31.8881 | −2.58647 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 16.1460 | 1.30108 | ||||||||
\(155\) | 17.1312 | 1.37601 | ||||||||
\(156\) | 0.596784 | 0.0477809 | ||||||||
\(157\) | 2.91823 | 0.232900 | 0.116450 | − | 0.993197i | \(-0.462848\pi\) | ||||
0.116450 | + | 0.993197i | \(0.462848\pi\) | |||||||
\(158\) | −2.50856 | −0.199570 | ||||||||
\(159\) | −2.07677 | −0.164699 | ||||||||
\(160\) | 8.49718 | 0.671761 | ||||||||
\(161\) | 20.1880 | 1.59104 | ||||||||
\(162\) | −2.50856 | −0.197091 | ||||||||
\(163\) | −19.6064 | −1.53569 | −0.767845 | − | 0.640635i | \(-0.778671\pi\) | ||||
−0.767845 | + | 0.640635i | \(0.778671\pi\) | |||||||
\(164\) | 1.40659 | 0.109836 | ||||||||
\(165\) | −4.63187 | −0.360590 | ||||||||
\(166\) | 41.9955 | 3.25948 | ||||||||
\(167\) | −9.66602 | −0.747979 | −0.373990 | − | 0.927433i | \(-0.622010\pi\) | ||||
−0.373990 | + | 0.927433i | \(0.622010\pi\) | |||||||
\(168\) | 21.5346 | 1.66143 | ||||||||
\(169\) | −12.9807 | −0.998513 | ||||||||
\(170\) | −6.75889 | −0.518383 | ||||||||
\(171\) | 5.54406 | 0.423965 | ||||||||
\(172\) | 47.2920 | 3.60598 | ||||||||
\(173\) | 23.4494 | 1.78282 | 0.891411 | − | 0.453195i | \(-0.149716\pi\) | ||||
0.891411 | + | 0.453195i | \(0.149716\pi\) | |||||||
\(174\) | 18.0680 | 1.36973 | ||||||||
\(175\) | 8.45936 | 0.639468 | ||||||||
\(176\) | −10.0446 | −0.757140 | ||||||||
\(177\) | −2.59407 | −0.194982 | ||||||||
\(178\) | 0.441864 | 0.0331191 | ||||||||
\(179\) | 22.0195 | 1.64582 | 0.822909 | − | 0.568173i | \(-0.192350\pi\) | ||||
0.822909 | + | 0.568173i | \(0.192350\pi\) | |||||||
\(180\) | −11.5664 | −0.862108 | ||||||||
\(181\) | 8.02793 | 0.596712 | 0.298356 | − | 0.954455i | \(-0.403562\pi\) | ||||
0.298356 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(182\) | 1.30566 | 0.0967821 | ||||||||
\(183\) | −15.1344 | −1.11877 | ||||||||
\(184\) | −31.0140 | −2.28639 | ||||||||
\(185\) | 25.7756 | 1.89506 | ||||||||
\(186\) | −15.9500 | −1.16951 | ||||||||
\(187\) | 1.71911 | 0.125714 | ||||||||
\(188\) | −37.1415 | −2.70882 | ||||||||
\(189\) | −3.74400 | −0.272336 | ||||||||
\(190\) | 37.4717 | 2.71848 | ||||||||
\(191\) | −18.3556 | −1.32816 | −0.664082 | − | 0.747660i | \(-0.731177\pi\) | ||||
−0.664082 | + | 0.747660i | \(0.731177\pi\) | |||||||
\(192\) | 3.77451 | 0.272402 | ||||||||
\(193\) | −10.0684 | −0.724741 | −0.362370 | − | 0.932034i | \(-0.618032\pi\) | ||||
−0.362370 | + | 0.932034i | \(0.618032\pi\) | |||||||
\(194\) | 24.4048 | 1.75216 | ||||||||
\(195\) | −0.374561 | −0.0268229 | ||||||||
\(196\) | 30.1254 | 2.15181 | ||||||||
\(197\) | −15.7115 | −1.11940 | −0.559701 | − | 0.828695i | \(-0.689084\pi\) | ||||
−0.559701 | + | 0.828695i | \(0.689084\pi\) | |||||||
\(198\) | 4.31249 | 0.306476 | ||||||||
\(199\) | 10.4890 | 0.743543 | 0.371772 | − | 0.928324i | \(-0.378750\pi\) | ||||
0.371772 | + | 0.928324i | \(0.378750\pi\) | |||||||
\(200\) | −12.9958 | −0.918939 | ||||||||
\(201\) | −4.21389 | −0.297225 | ||||||||
\(202\) | 7.70904 | 0.542406 | ||||||||
\(203\) | 26.9664 | 1.89267 | ||||||||
\(204\) | 4.29286 | 0.300560 | ||||||||
\(205\) | −0.882821 | −0.0616589 | ||||||||
\(206\) | −39.5617 | −2.75639 | ||||||||
\(207\) | 5.39210 | 0.374777 | ||||||||
\(208\) | −0.812267 | −0.0563206 | ||||||||
\(209\) | −9.53087 | −0.659264 | ||||||||
\(210\) | −25.3053 | −1.74623 | ||||||||
\(211\) | 17.5312 | 1.20690 | 0.603449 | − | 0.797401i | \(-0.293793\pi\) | ||||
0.603449 | + | 0.797401i | \(0.293793\pi\) | |||||||
\(212\) | 8.91529 | 0.612305 | ||||||||
\(213\) | −8.71318 | −0.597017 | ||||||||
\(214\) | −0.266443 | −0.0182137 | ||||||||
\(215\) | −29.6820 | −2.02430 | ||||||||
\(216\) | 5.75176 | 0.391357 | ||||||||
\(217\) | −23.8052 | −1.61600 | ||||||||
\(218\) | 48.9840 | 3.31762 | ||||||||
\(219\) | −10.0129 | −0.676610 | ||||||||
\(220\) | 19.8839 | 1.34057 | ||||||||
\(221\) | 0.139018 | 0.00935136 | ||||||||
\(222\) | −23.9984 | −1.61066 | ||||||||
\(223\) | 1.07333 | 0.0718756 | 0.0359378 | − | 0.999354i | \(-0.488558\pi\) | ||||
0.0359378 | + | 0.999354i | \(0.488558\pi\) | |||||||
\(224\) | −11.8075 | −0.788924 | ||||||||
\(225\) | 2.25944 | 0.150629 | ||||||||
\(226\) | −26.1137 | −1.73706 | ||||||||
\(227\) | −6.66723 | −0.442520 | −0.221260 | − | 0.975215i | \(-0.571017\pi\) | ||||
−0.221260 | + | 0.975215i | \(0.571017\pi\) | |||||||
\(228\) | −23.7998 | −1.57618 | ||||||||
\(229\) | 20.5325 | 1.35683 | 0.678414 | − | 0.734680i | \(-0.262668\pi\) | ||||
0.678414 | + | 0.734680i | \(0.262668\pi\) | |||||||
\(230\) | 36.4446 | 2.40309 | ||||||||
\(231\) | 6.43637 | 0.423482 | ||||||||
\(232\) | −41.4274 | −2.71984 | ||||||||
\(233\) | −26.4189 | −1.73076 | −0.865378 | − | 0.501119i | \(-0.832922\pi\) | ||||
−0.865378 | + | 0.501119i | \(0.832922\pi\) | |||||||
\(234\) | 0.348734 | 0.0227975 | ||||||||
\(235\) | 23.3112 | 1.52066 | ||||||||
\(236\) | 11.1360 | 0.724890 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 9.39205 | 0.608796 | ||||||||
\(239\) | −12.3541 | −0.799120 | −0.399560 | − | 0.916707i | \(-0.630837\pi\) | ||||
−0.399560 | + | 0.916707i | \(0.630837\pi\) | |||||||
\(240\) | 15.7427 | 1.01619 | ||||||||
\(241\) | 4.32551 | 0.278630 | 0.139315 | − | 0.990248i | \(-0.455510\pi\) | ||||
0.139315 | + | 0.990248i | \(0.455510\pi\) | |||||||
\(242\) | 20.1805 | 1.29725 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 64.9699 | 4.15927 | ||||||||
\(245\) | −18.9077 | −1.20797 | ||||||||
\(246\) | 0.821949 | 0.0524056 | ||||||||
\(247\) | −0.770724 | −0.0490400 | ||||||||
\(248\) | 36.5709 | 2.32226 | ||||||||
\(249\) | 16.7409 | 1.06091 | ||||||||
\(250\) | −18.5231 | −1.17151 | ||||||||
\(251\) | 19.3106 | 1.21887 | 0.609436 | − | 0.792835i | \(-0.291396\pi\) | ||||
0.609436 | + | 0.792835i | \(0.291396\pi\) | |||||||
\(252\) | 16.0725 | 1.01247 | ||||||||
\(253\) | −9.26963 | −0.582777 | ||||||||
\(254\) | 46.6756 | 2.92868 | ||||||||
\(255\) | −2.69434 | −0.168726 | ||||||||
\(256\) | −32.0260 | −2.00162 | ||||||||
\(257\) | 23.6722 | 1.47663 | 0.738315 | − | 0.674456i | \(-0.235622\pi\) | ||||
0.738315 | + | 0.674456i | \(0.235622\pi\) | |||||||
\(258\) | 27.6354 | 1.72050 | ||||||||
\(259\) | −35.8174 | −2.22558 | ||||||||
\(260\) | 1.60794 | 0.0997199 | ||||||||
\(261\) | 7.20257 | 0.445828 | ||||||||
\(262\) | 13.6775 | 0.844999 | ||||||||
\(263\) | −9.98045 | −0.615421 | −0.307710 | − | 0.951480i | \(-0.599563\pi\) | ||||
−0.307710 | + | 0.951480i | \(0.599563\pi\) | |||||||
\(264\) | −9.88792 | −0.608559 | ||||||||
\(265\) | −5.59553 | −0.343730 | ||||||||
\(266\) | −52.0701 | −3.19262 | ||||||||
\(267\) | 0.176143 | 0.0107798 | ||||||||
\(268\) | 18.0896 | 1.10500 | ||||||||
\(269\) | 1.01465 | 0.0618644 | 0.0309322 | − | 0.999521i | \(-0.490152\pi\) | ||||
0.0309322 | + | 0.999521i | \(0.490152\pi\) | |||||||
\(270\) | −6.75889 | −0.411333 | ||||||||
\(271\) | −0.893528 | −0.0542780 | −0.0271390 | − | 0.999632i | \(-0.508640\pi\) | ||||
−0.0271390 | + | 0.999632i | \(0.508640\pi\) | |||||||
\(272\) | −5.84290 | −0.354278 | ||||||||
\(273\) | 0.520484 | 0.0315011 | ||||||||
\(274\) | −9.56875 | −0.578069 | ||||||||
\(275\) | −3.88424 | −0.234228 | ||||||||
\(276\) | −23.1475 | −1.39332 | ||||||||
\(277\) | −2.86557 | −0.172176 | −0.0860878 | − | 0.996288i | \(-0.527437\pi\) | ||||
−0.0860878 | + | 0.996288i | \(0.527437\pi\) | |||||||
\(278\) | 9.20486 | 0.552071 | ||||||||
\(279\) | −6.35822 | −0.380657 | ||||||||
\(280\) | 58.0214 | 3.46744 | ||||||||
\(281\) | −6.62580 | −0.395262 | −0.197631 | − | 0.980276i | \(-0.563325\pi\) | ||||
−0.197631 | + | 0.980276i | \(0.563325\pi\) | |||||||
\(282\) | −21.7039 | −1.29245 | ||||||||
\(283\) | −12.7835 | −0.759900 | −0.379950 | − | 0.925007i | \(-0.624059\pi\) | ||||
−0.379950 | + | 0.925007i | \(0.624059\pi\) | |||||||
\(284\) | 37.4044 | 2.21954 | ||||||||
\(285\) | 14.9376 | 0.884825 | ||||||||
\(286\) | −0.599514 | −0.0354500 | ||||||||
\(287\) | 1.22675 | 0.0724130 | ||||||||
\(288\) | −3.15372 | −0.185835 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 48.6814 | 2.85867 | ||||||||
\(291\) | 9.72863 | 0.570302 | ||||||||
\(292\) | 42.9840 | 2.51545 | ||||||||
\(293\) | 11.8071 | 0.689780 | 0.344890 | − | 0.938643i | \(-0.387916\pi\) | ||||
0.344890 | + | 0.938643i | \(0.387916\pi\) | |||||||
\(294\) | 17.6040 | 1.02668 | ||||||||
\(295\) | −6.98930 | −0.406933 | ||||||||
\(296\) | 55.0247 | 3.19825 | ||||||||
\(297\) | 1.71911 | 0.0997531 | ||||||||
\(298\) | −25.6541 | −1.48610 | ||||||||
\(299\) | −0.749598 | −0.0433504 | ||||||||
\(300\) | −9.69946 | −0.559999 | ||||||||
\(301\) | 41.2456 | 2.37736 | ||||||||
\(302\) | 37.8088 | 2.17565 | ||||||||
\(303\) | 3.07310 | 0.176545 | ||||||||
\(304\) | 32.3934 | 1.85789 | ||||||||
\(305\) | −40.7772 | −2.33490 | ||||||||
\(306\) | 2.50856 | 0.143405 | ||||||||
\(307\) | 18.2181 | 1.03976 | 0.519880 | − | 0.854239i | \(-0.325977\pi\) | ||||
0.519880 | + | 0.854239i | \(0.325977\pi\) | |||||||
\(308\) | −27.6304 | −1.57439 | ||||||||
\(309\) | −15.7707 | −0.897164 | ||||||||
\(310\) | −42.9745 | −2.44079 | ||||||||
\(311\) | 10.1159 | 0.573620 | 0.286810 | − | 0.957987i | \(-0.407405\pi\) | ||||
0.286810 | + | 0.957987i | \(0.407405\pi\) | |||||||
\(312\) | −0.799597 | −0.0452683 | ||||||||
\(313\) | −16.4058 | −0.927310 | −0.463655 | − | 0.886016i | \(-0.653462\pi\) | ||||
−0.463655 | + | 0.886016i | \(0.653462\pi\) | |||||||
\(314\) | −7.32055 | −0.413122 | ||||||||
\(315\) | −10.0876 | −0.568372 | ||||||||
\(316\) | 4.29286 | 0.241492 | ||||||||
\(317\) | 12.8397 | 0.721148 | 0.360574 | − | 0.932731i | \(-0.382581\pi\) | ||||
0.360574 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(318\) | 5.20971 | 0.292146 | ||||||||
\(319\) | −12.3820 | −0.693260 | ||||||||
\(320\) | 10.1698 | 0.568509 | ||||||||
\(321\) | −0.106214 | −0.00592827 | ||||||||
\(322\) | −50.6428 | −2.82222 | ||||||||
\(323\) | −5.54406 | −0.308480 | ||||||||
\(324\) | 4.29286 | 0.238492 | ||||||||
\(325\) | −0.314103 | −0.0174233 | ||||||||
\(326\) | 49.1837 | 2.72403 | ||||||||
\(327\) | 19.5268 | 1.07983 | ||||||||
\(328\) | −1.88461 | −0.104060 | ||||||||
\(329\) | −32.3929 | −1.78588 | ||||||||
\(330\) | 11.6193 | 0.639621 | ||||||||
\(331\) | 32.1823 | 1.76890 | 0.884451 | − | 0.466634i | \(-0.154533\pi\) | ||||
0.884451 | + | 0.466634i | \(0.154533\pi\) | |||||||
\(332\) | −71.8663 | −3.94417 | ||||||||
\(333\) | −9.56660 | −0.524246 | ||||||||
\(334\) | 24.2478 | 1.32678 | ||||||||
\(335\) | −11.3536 | −0.620316 | ||||||||
\(336\) | −21.8758 | −1.19342 | ||||||||
\(337\) | 31.9269 | 1.73917 | 0.869584 | − | 0.493786i | \(-0.164387\pi\) | ||||
0.869584 | + | 0.493786i | \(0.164387\pi\) | |||||||
\(338\) | 32.5628 | 1.77118 | ||||||||
\(339\) | −10.4099 | −0.565386 | ||||||||
\(340\) | 11.5664 | 0.627276 | ||||||||
\(341\) | 10.9305 | 0.591920 | ||||||||
\(342\) | −13.9076 | −0.752036 | ||||||||
\(343\) | 0.0657671 | 0.00355109 | ||||||||
\(344\) | −63.3639 | −3.41635 | ||||||||
\(345\) | 14.5281 | 0.782168 | ||||||||
\(346\) | −58.8241 | −3.16240 | ||||||||
\(347\) | 2.87151 | 0.154151 | 0.0770755 | − | 0.997025i | \(-0.475442\pi\) | ||||
0.0770755 | + | 0.997025i | \(0.475442\pi\) | |||||||
\(348\) | −30.9196 | −1.65746 | ||||||||
\(349\) | 21.8859 | 1.17152 | 0.585762 | − | 0.810483i | \(-0.300795\pi\) | ||||
0.585762 | + | 0.810483i | \(0.300795\pi\) | |||||||
\(350\) | −21.2208 | −1.13430 | ||||||||
\(351\) | 0.139018 | 0.00742023 | ||||||||
\(352\) | 5.42160 | 0.288972 | ||||||||
\(353\) | 30.1911 | 1.60691 | 0.803455 | − | 0.595365i | \(-0.202993\pi\) | ||||
0.803455 | + | 0.595365i | \(0.202993\pi\) | |||||||
\(354\) | 6.50737 | 0.345863 | ||||||||
\(355\) | −23.4762 | −1.24599 | ||||||||
\(356\) | −0.756155 | −0.0400761 | ||||||||
\(357\) | 3.74400 | 0.198154 | ||||||||
\(358\) | −55.2373 | −2.91938 | ||||||||
\(359\) | 28.3388 | 1.49567 | 0.747833 | − | 0.663887i | \(-0.231095\pi\) | ||||
0.747833 | + | 0.663887i | \(0.231095\pi\) | |||||||
\(360\) | 15.4972 | 0.816772 | ||||||||
\(361\) | 11.7366 | 0.617716 | ||||||||
\(362\) | −20.1385 | −1.05846 | ||||||||
\(363\) | 8.04465 | 0.422235 | ||||||||
\(364\) | −2.23436 | −0.117112 | ||||||||
\(365\) | −26.9781 | −1.41210 | ||||||||
\(366\) | 37.9656 | 1.98449 | ||||||||
\(367\) | −24.0440 | −1.25509 | −0.627543 | − | 0.778582i | \(-0.715940\pi\) | ||||
−0.627543 | + | 0.778582i | \(0.715940\pi\) | |||||||
\(368\) | 31.5055 | 1.64234 | ||||||||
\(369\) | 0.327658 | 0.0170572 | ||||||||
\(370\) | −64.6596 | −3.36149 | ||||||||
\(371\) | 7.77545 | 0.403681 | ||||||||
\(372\) | 27.2949 | 1.41518 | ||||||||
\(373\) | −5.63709 | −0.291878 | −0.145939 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145939 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(374\) | −4.31249 | −0.222994 | ||||||||
\(375\) | −7.38398 | −0.381307 | ||||||||
\(376\) | 49.7639 | 2.56638 | ||||||||
\(377\) | −1.00129 | −0.0515688 | ||||||||
\(378\) | 9.39205 | 0.483075 | ||||||||
\(379\) | 33.3778 | 1.71450 | 0.857250 | − | 0.514901i | \(-0.172171\pi\) | ||||
0.857250 | + | 0.514901i | \(0.172171\pi\) | |||||||
\(380\) | −64.1248 | −3.28953 | ||||||||
\(381\) | 18.6065 | 0.953242 | ||||||||
\(382\) | 46.0460 | 2.35592 | ||||||||
\(383\) | −11.5476 | −0.590054 | −0.295027 | − | 0.955489i | \(-0.595329\pi\) | ||||
−0.295027 | + | 0.955489i | \(0.595329\pi\) | |||||||
\(384\) | −15.7760 | −0.805066 | ||||||||
\(385\) | 17.3417 | 0.883816 | ||||||||
\(386\) | 25.2572 | 1.28556 | ||||||||
\(387\) | 11.0164 | 0.559997 | ||||||||
\(388\) | −41.7636 | −2.12023 | ||||||||
\(389\) | −7.53981 | −0.382283 | −0.191142 | − | 0.981562i | \(-0.561219\pi\) | ||||
−0.191142 | + | 0.981562i | \(0.561219\pi\) | |||||||
\(390\) | 0.939607 | 0.0475788 | ||||||||
\(391\) | −5.39210 | −0.272690 | ||||||||
\(392\) | −40.3633 | −2.03866 | ||||||||
\(393\) | 5.45234 | 0.275034 | ||||||||
\(394\) | 39.4133 | 1.98561 | ||||||||
\(395\) | −2.69434 | −0.135567 | ||||||||
\(396\) | −7.37990 | −0.370854 | ||||||||
\(397\) | −18.5849 | −0.932747 | −0.466373 | − | 0.884588i | \(-0.654440\pi\) | ||||
−0.466373 | + | 0.884588i | \(0.654440\pi\) | |||||||
\(398\) | −26.3122 | −1.31891 | ||||||||
\(399\) | −20.7570 | −1.03915 | ||||||||
\(400\) | 13.2017 | 0.660084 | ||||||||
\(401\) | 2.06309 | 0.103026 | 0.0515128 | − | 0.998672i | \(-0.483596\pi\) | ||||
0.0515128 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(402\) | 10.5708 | 0.527223 | ||||||||
\(403\) | 0.883906 | 0.0440305 | ||||||||
\(404\) | −13.1924 | −0.656344 | ||||||||
\(405\) | −2.69434 | −0.133883 | ||||||||
\(406\) | −67.6468 | −3.35726 | ||||||||
\(407\) | 16.4461 | 0.815201 | ||||||||
\(408\) | −5.75176 | −0.284754 | ||||||||
\(409\) | 11.2813 | 0.557824 | 0.278912 | − | 0.960317i | \(-0.410026\pi\) | ||||
0.278912 | + | 0.960317i | \(0.410026\pi\) | |||||||
\(410\) | 2.21461 | 0.109372 | ||||||||
\(411\) | −3.81445 | −0.188153 | ||||||||
\(412\) | 67.7013 | 3.33540 | ||||||||
\(413\) | 9.71221 | 0.477907 | ||||||||
\(414\) | −13.5264 | −0.664786 | ||||||||
\(415\) | 45.1056 | 2.21415 | ||||||||
\(416\) | 0.438423 | 0.0214955 | ||||||||
\(417\) | 3.66939 | 0.179691 | ||||||||
\(418\) | 23.9087 | 1.16941 | ||||||||
\(419\) | −13.1347 | −0.641671 | −0.320835 | − | 0.947135i | \(-0.603964\pi\) | ||||
−0.320835 | + | 0.947135i | \(0.603964\pi\) | |||||||
\(420\) | 43.3046 | 2.11305 | ||||||||
\(421\) | 37.6913 | 1.83696 | 0.918480 | − | 0.395467i | \(-0.129417\pi\) | ||||
0.918480 | + | 0.395467i | \(0.129417\pi\) | |||||||
\(422\) | −43.9780 | −2.14082 | ||||||||
\(423\) | −8.65194 | −0.420672 | ||||||||
\(424\) | −11.9451 | −0.580105 | ||||||||
\(425\) | −2.25944 | −0.109599 | ||||||||
\(426\) | 21.8575 | 1.05900 | ||||||||
\(427\) | 56.6633 | 2.74213 | ||||||||
\(428\) | 0.455960 | 0.0220397 | ||||||||
\(429\) | −0.238987 | −0.0115384 | ||||||||
\(430\) | 74.4590 | 3.59073 | ||||||||
\(431\) | 38.0414 | 1.83239 | 0.916194 | − | 0.400735i | \(-0.131245\pi\) | ||||
0.916194 | + | 0.400735i | \(0.131245\pi\) | |||||||
\(432\) | −5.84290 | −0.281116 | ||||||||
\(433\) | 35.0692 | 1.68532 | 0.842659 | − | 0.538448i | \(-0.180989\pi\) | ||||
0.842659 | + | 0.538448i | \(0.180989\pi\) | |||||||
\(434\) | 59.7167 | 2.86649 | ||||||||
\(435\) | 19.4061 | 0.930452 | ||||||||
\(436\) | −83.8256 | −4.01452 | ||||||||
\(437\) | 29.8941 | 1.43003 | ||||||||
\(438\) | 25.1180 | 1.20018 | ||||||||
\(439\) | 7.87788 | 0.375991 | 0.187995 | − | 0.982170i | \(-0.439801\pi\) | ||||
0.187995 | + | 0.982170i | \(0.439801\pi\) | |||||||
\(440\) | −26.6414 | −1.27008 | ||||||||
\(441\) | 7.01757 | 0.334170 | ||||||||
\(442\) | −0.348734 | −0.0165876 | ||||||||
\(443\) | 3.69444 | 0.175528 | 0.0877641 | − | 0.996141i | \(-0.472028\pi\) | ||||
0.0877641 | + | 0.996141i | \(0.472028\pi\) | |||||||
\(444\) | 41.0680 | 1.94900 | ||||||||
\(445\) | 0.474588 | 0.0224976 | ||||||||
\(446\) | −2.69251 | −0.127494 | ||||||||
\(447\) | −10.2266 | −0.483704 | ||||||||
\(448\) | −14.1318 | −0.667664 | ||||||||
\(449\) | −3.62828 | −0.171229 | −0.0856146 | − | 0.996328i | \(-0.527285\pi\) | ||||
−0.0856146 | + | 0.996328i | \(0.527285\pi\) | |||||||
\(450\) | −5.66794 | −0.267189 | ||||||||
\(451\) | −0.563282 | −0.0265239 | ||||||||
\(452\) | 44.6880 | 2.10195 | ||||||||
\(453\) | 15.0719 | 0.708141 | ||||||||
\(454\) | 16.7251 | 0.784949 | ||||||||
\(455\) | 1.40236 | 0.0657435 | ||||||||
\(456\) | 31.8881 | 1.49330 | ||||||||
\(457\) | −7.63909 | −0.357342 | −0.178671 | − | 0.983909i | \(-0.557180\pi\) | ||||
−0.178671 | + | 0.983909i | \(0.557180\pi\) | |||||||
\(458\) | −51.5070 | −2.40677 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −62.3671 | −2.90788 | ||||||||
\(461\) | 38.1537 | 1.77700 | 0.888498 | − | 0.458880i | \(-0.151749\pi\) | ||||
0.888498 | + | 0.458880i | \(0.151749\pi\) | |||||||
\(462\) | −16.1460 | −0.751179 | ||||||||
\(463\) | 4.62234 | 0.214818 | 0.107409 | − | 0.994215i | \(-0.465745\pi\) | ||||
0.107409 | + | 0.994215i | \(0.465745\pi\) | |||||||
\(464\) | 42.0838 | 1.95369 | ||||||||
\(465\) | −17.1312 | −0.794439 | ||||||||
\(466\) | 66.2732 | 3.07005 | ||||||||
\(467\) | 14.6418 | 0.677540 | 0.338770 | − | 0.940869i | \(-0.389989\pi\) | ||||
0.338770 | + | 0.940869i | \(0.389989\pi\) | |||||||
\(468\) | −0.596784 | −0.0275863 | ||||||||
\(469\) | 15.7768 | 0.728506 | ||||||||
\(470\) | −58.4775 | −2.69737 | ||||||||
\(471\) | −2.91823 | −0.134465 | ||||||||
\(472\) | −14.9205 | −0.686770 | ||||||||
\(473\) | −18.9385 | −0.870794 | ||||||||
\(474\) | 2.50856 | 0.115222 | ||||||||
\(475\) | 12.5265 | 0.574755 | ||||||||
\(476\) | −16.0725 | −0.736680 | ||||||||
\(477\) | 2.07677 | 0.0950890 | ||||||||
\(478\) | 30.9910 | 1.41749 | ||||||||
\(479\) | −16.7934 | −0.767311 | −0.383655 | − | 0.923476i | \(-0.625335\pi\) | ||||
−0.383655 | + | 0.923476i | \(0.625335\pi\) | |||||||
\(480\) | −8.49718 | −0.387841 | ||||||||
\(481\) | 1.32993 | 0.0606395 | ||||||||
\(482\) | −10.8508 | −0.494239 | ||||||||
\(483\) | −20.1880 | −0.918588 | ||||||||
\(484\) | −34.5345 | −1.56975 | ||||||||
\(485\) | 26.2122 | 1.19023 | ||||||||
\(486\) | 2.50856 | 0.113790 | ||||||||
\(487\) | −33.0770 | −1.49886 | −0.749432 | − | 0.662082i | \(-0.769673\pi\) | ||||
−0.749432 | + | 0.662082i | \(0.769673\pi\) | |||||||
\(488\) | −87.0495 | −3.94055 | ||||||||
\(489\) | 19.6064 | 0.886631 | ||||||||
\(490\) | 47.4310 | 2.14271 | ||||||||
\(491\) | −10.9250 | −0.493038 | −0.246519 | − | 0.969138i | \(-0.579287\pi\) | ||||
−0.246519 | + | 0.969138i | \(0.579287\pi\) | |||||||
\(492\) | −1.40659 | −0.0634140 | ||||||||
\(493\) | −7.20257 | −0.324387 | ||||||||
\(494\) | 1.93340 | 0.0869879 | ||||||||
\(495\) | 4.63187 | 0.208187 | ||||||||
\(496\) | −37.1504 | −1.66810 | ||||||||
\(497\) | 32.6222 | 1.46331 | ||||||||
\(498\) | −41.9955 | −1.88186 | ||||||||
\(499\) | 35.2632 | 1.57860 | 0.789299 | − | 0.614009i | \(-0.210444\pi\) | ||||
0.789299 | + | 0.614009i | \(0.210444\pi\) | |||||||
\(500\) | 31.6984 | 1.41759 | ||||||||
\(501\) | 9.66602 | 0.431846 | ||||||||
\(502\) | −48.4417 | −2.16206 | ||||||||
\(503\) | −0.658137 | −0.0293449 | −0.0146724 | − | 0.999892i | \(-0.504671\pi\) | ||||
−0.0146724 | + | 0.999892i | \(0.504671\pi\) | |||||||
\(504\) | −21.5346 | −0.959227 | ||||||||
\(505\) | 8.27995 | 0.368453 | ||||||||
\(506\) | 23.2534 | 1.03374 | ||||||||
\(507\) | 12.9807 | 0.576492 | ||||||||
\(508\) | −79.8752 | −3.54389 | ||||||||
\(509\) | 9.43187 | 0.418060 | 0.209030 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209030 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(510\) | 6.75889 | 0.299289 | ||||||||
\(511\) | 37.4884 | 1.65839 | ||||||||
\(512\) | 48.7870 | 2.15610 | ||||||||
\(513\) | −5.54406 | −0.244776 | ||||||||
\(514\) | −59.3830 | −2.61927 | ||||||||
\(515\) | −42.4915 | −1.87240 | ||||||||
\(516\) | −47.2920 | −2.08191 | ||||||||
\(517\) | 14.8737 | 0.654143 | ||||||||
\(518\) | 89.8499 | 3.94778 | ||||||||
\(519\) | −23.4494 | −1.02931 | ||||||||
\(520\) | −2.15438 | −0.0944759 | ||||||||
\(521\) | 35.4738 | 1.55413 | 0.777067 | − | 0.629418i | \(-0.216707\pi\) | ||||
0.777067 | + | 0.629418i | \(0.216707\pi\) | |||||||
\(522\) | −18.0680 | −0.790817 | ||||||||
\(523\) | 17.7537 | 0.776317 | 0.388158 | − | 0.921593i | \(-0.373111\pi\) | ||||
0.388158 | + | 0.921593i | \(0.373111\pi\) | |||||||
\(524\) | −23.4061 | −1.02250 | ||||||||
\(525\) | −8.45936 | −0.369197 | ||||||||
\(526\) | 25.0365 | 1.09164 | ||||||||
\(527\) | 6.35822 | 0.276968 | ||||||||
\(528\) | 10.0446 | 0.437135 | ||||||||
\(529\) | 6.07474 | 0.264119 | ||||||||
\(530\) | 14.0367 | 0.609715 | ||||||||
\(531\) | 2.59407 | 0.112573 | ||||||||
\(532\) | 89.1067 | 3.86327 | ||||||||
\(533\) | −0.0455504 | −0.00197301 | ||||||||
\(534\) | −0.441864 | −0.0191213 | ||||||||
\(535\) | −0.286175 | −0.0123724 | ||||||||
\(536\) | −24.2373 | −1.04689 | ||||||||
\(537\) | −22.0195 | −0.950213 | ||||||||
\(538\) | −2.54531 | −0.109736 | ||||||||
\(539\) | −12.0640 | −0.519633 | ||||||||
\(540\) | 11.5664 | 0.497738 | ||||||||
\(541\) | 1.45853 | 0.0627070 | 0.0313535 | − | 0.999508i | \(-0.490018\pi\) | ||||
0.0313535 | + | 0.999508i | \(0.490018\pi\) | |||||||
\(542\) | 2.24147 | 0.0962792 | ||||||||
\(543\) | −8.02793 | −0.344512 | ||||||||
\(544\) | 3.15372 | 0.135215 | ||||||||
\(545\) | 52.6117 | 2.25364 | ||||||||
\(546\) | −1.30566 | −0.0558772 | ||||||||
\(547\) | −27.0237 | −1.15545 | −0.577725 | − | 0.816232i | \(-0.696059\pi\) | ||||
−0.577725 | + | 0.816232i | \(0.696059\pi\) | |||||||
\(548\) | 16.3749 | 0.699499 | ||||||||
\(549\) | 15.1344 | 0.645921 | ||||||||
\(550\) | 9.74383 | 0.415478 | ||||||||
\(551\) | 39.9315 | 1.70114 | ||||||||
\(552\) | 31.0140 | 1.32005 | ||||||||
\(553\) | 3.74400 | 0.159211 | ||||||||
\(554\) | 7.18846 | 0.305408 | ||||||||
\(555\) | −25.7756 | −1.09411 | ||||||||
\(556\) | −15.7521 | −0.668040 | ||||||||
\(557\) | −34.8372 | −1.47610 | −0.738050 | − | 0.674746i | \(-0.764253\pi\) | ||||
−0.738050 | + | 0.674746i | \(0.764253\pi\) | |||||||
\(558\) | 15.9500 | 0.675215 | ||||||||
\(559\) | −1.53148 | −0.0647748 | ||||||||
\(560\) | −58.9408 | −2.49070 | ||||||||
\(561\) | −1.71911 | −0.0725810 | ||||||||
\(562\) | 16.6212 | 0.701123 | ||||||||
\(563\) | 28.5743 | 1.20426 | 0.602131 | − | 0.798397i | \(-0.294318\pi\) | ||||
0.602131 | + | 0.798397i | \(0.294318\pi\) | |||||||
\(564\) | 37.1415 | 1.56394 | ||||||||
\(565\) | −28.0477 | −1.17997 | ||||||||
\(566\) | 32.0681 | 1.34792 | ||||||||
\(567\) | 3.74400 | 0.157233 | ||||||||
\(568\) | −50.1161 | −2.10282 | ||||||||
\(569\) | 28.5706 | 1.19774 | 0.598871 | − | 0.800846i | \(-0.295616\pi\) | ||||
0.598871 | + | 0.800846i | \(0.295616\pi\) | |||||||
\(570\) | −37.4717 | −1.56952 | ||||||||
\(571\) | −4.76657 | −0.199475 | −0.0997373 | − | 0.995014i | \(-0.531800\pi\) | ||||
−0.0997373 | + | 0.995014i | \(0.531800\pi\) | |||||||
\(572\) | 1.02594 | 0.0428967 | ||||||||
\(573\) | 18.3556 | 0.766816 | ||||||||
\(574\) | −3.07738 | −0.128447 | ||||||||
\(575\) | 12.1831 | 0.508072 | ||||||||
\(576\) | −3.77451 | −0.157271 | ||||||||
\(577\) | 8.93976 | 0.372167 | 0.186084 | − | 0.982534i | \(-0.440420\pi\) | ||||
0.186084 | + | 0.982534i | \(0.440420\pi\) | |||||||
\(578\) | −2.50856 | −0.104342 | ||||||||
\(579\) | 10.0684 | 0.418429 | ||||||||
\(580\) | −83.3077 | −3.45916 | ||||||||
\(581\) | −62.6780 | −2.60032 | ||||||||
\(582\) | −24.4048 | −1.01161 | ||||||||
\(583\) | −3.57021 | −0.147863 | ||||||||
\(584\) | −57.5918 | −2.38317 | ||||||||
\(585\) | 0.374561 | 0.0154862 | ||||||||
\(586\) | −29.6188 | −1.22354 | ||||||||
\(587\) | −27.6439 | −1.14099 | −0.570493 | − | 0.821303i | \(-0.693248\pi\) | ||||
−0.570493 | + | 0.821303i | \(0.693248\pi\) | |||||||
\(588\) | −30.1254 | −1.24235 | ||||||||
\(589\) | −35.2503 | −1.45247 | ||||||||
\(590\) | 17.5330 | 0.721824 | ||||||||
\(591\) | 15.7115 | 0.646287 | ||||||||
\(592\) | −55.8966 | −2.29734 | ||||||||
\(593\) | 24.3651 | 1.00055 | 0.500277 | − | 0.865866i | \(-0.333232\pi\) | ||||
0.500277 | + | 0.865866i | \(0.333232\pi\) | |||||||
\(594\) | −4.31249 | −0.176944 | ||||||||
\(595\) | 10.0876 | 0.413551 | ||||||||
\(596\) | 43.9015 | 1.79828 | ||||||||
\(597\) | −10.4890 | −0.429285 | ||||||||
\(598\) | 1.88041 | 0.0768957 | ||||||||
\(599\) | −38.3834 | −1.56830 | −0.784151 | − | 0.620570i | \(-0.786901\pi\) | ||||
−0.784151 | + | 0.620570i | \(0.786901\pi\) | |||||||
\(600\) | 12.9958 | 0.530550 | ||||||||
\(601\) | 10.1591 | 0.414399 | 0.207200 | − | 0.978299i | \(-0.433565\pi\) | ||||
0.207200 | + | 0.978299i | \(0.433565\pi\) | |||||||
\(602\) | −103.467 | −4.21700 | ||||||||
\(603\) | 4.21389 | 0.171603 | ||||||||
\(604\) | −64.7016 | −2.63267 | ||||||||
\(605\) | 21.6750 | 0.881213 | ||||||||
\(606\) | −7.70904 | −0.313158 | ||||||||
\(607\) | 36.5524 | 1.48362 | 0.741809 | − | 0.670611i | \(-0.233968\pi\) | ||||
0.741809 | + | 0.670611i | \(0.233968\pi\) | |||||||
\(608\) | −17.4844 | −0.709086 | ||||||||
\(609\) | −26.9664 | −1.09273 | ||||||||
\(610\) | 102.292 | 4.14168 | ||||||||
\(611\) | 1.20277 | 0.0486591 | ||||||||
\(612\) | −4.29286 | −0.173528 | ||||||||
\(613\) | −25.7134 | −1.03855 | −0.519276 | − | 0.854606i | \(-0.673798\pi\) | ||||
−0.519276 | + | 0.854606i | \(0.673798\pi\) | |||||||
\(614\) | −45.7011 | −1.84434 | ||||||||
\(615\) | 0.882821 | 0.0355988 | ||||||||
\(616\) | 37.0204 | 1.49160 | ||||||||
\(617\) | −23.4453 | −0.943871 | −0.471935 | − | 0.881633i | \(-0.656444\pi\) | ||||
−0.471935 | + | 0.881633i | \(0.656444\pi\) | |||||||
\(618\) | 39.5617 | 1.59140 | ||||||||
\(619\) | 35.7309 | 1.43615 | 0.718074 | − | 0.695967i | \(-0.245024\pi\) | ||||
0.718074 | + | 0.695967i | \(0.245024\pi\) | |||||||
\(620\) | 73.5416 | 2.95350 | ||||||||
\(621\) | −5.39210 | −0.216378 | ||||||||
\(622\) | −25.3763 | −1.01750 | ||||||||
\(623\) | −0.659479 | −0.0264215 | ||||||||
\(624\) | 0.812267 | 0.0325167 | ||||||||
\(625\) | −31.1921 | −1.24769 | ||||||||
\(626\) | 41.1548 | 1.64488 | ||||||||
\(627\) | 9.53087 | 0.380626 | ||||||||
\(628\) | 12.5275 | 0.499904 | ||||||||
\(629\) | 9.56660 | 0.381445 | ||||||||
\(630\) | 25.3053 | 1.00819 | ||||||||
\(631\) | 16.7832 | 0.668129 | 0.334065 | − | 0.942550i | \(-0.391580\pi\) | ||||
0.334065 | + | 0.942550i | \(0.391580\pi\) | |||||||
\(632\) | −5.75176 | −0.228793 | ||||||||
\(633\) | −17.5312 | −0.696803 | ||||||||
\(634\) | −32.2091 | −1.27919 | ||||||||
\(635\) | 50.1323 | 1.98944 | ||||||||
\(636\) | −8.91529 | −0.353514 | ||||||||
\(637\) | −0.975567 | −0.0386534 | ||||||||
\(638\) | 31.0610 | 1.22972 | ||||||||
\(639\) | 8.71318 | 0.344688 | ||||||||
\(640\) | −42.5058 | −1.68019 | ||||||||
\(641\) | −29.9402 | −1.18257 | −0.591283 | − | 0.806464i | \(-0.701378\pi\) | ||||
−0.591283 | + | 0.806464i | \(0.701378\pi\) | |||||||
\(642\) | 0.266443 | 0.0105157 | ||||||||
\(643\) | 7.06091 | 0.278455 | 0.139228 | − | 0.990260i | \(-0.455538\pi\) | ||||
0.139228 | + | 0.990260i | \(0.455538\pi\) | |||||||
\(644\) | 86.6643 | 3.41505 | ||||||||
\(645\) | 29.6820 | 1.16873 | ||||||||
\(646\) | 13.9076 | 0.547187 | ||||||||
\(647\) | 17.0182 | 0.669054 | 0.334527 | − | 0.942386i | \(-0.391423\pi\) | ||||
0.334527 | + | 0.942386i | \(0.391423\pi\) | |||||||
\(648\) | −5.75176 | −0.225950 | ||||||||
\(649\) | −4.45950 | −0.175051 | ||||||||
\(650\) | 0.787945 | 0.0309057 | ||||||||
\(651\) | 23.8052 | 0.932999 | ||||||||
\(652\) | −84.1674 | −3.29625 | ||||||||
\(653\) | 29.1632 | 1.14124 | 0.570622 | − | 0.821213i | \(-0.306702\pi\) | ||||
0.570622 | + | 0.821213i | \(0.306702\pi\) | |||||||
\(654\) | −48.9840 | −1.91543 | ||||||||
\(655\) | 14.6904 | 0.574003 | ||||||||
\(656\) | 1.91447 | 0.0747476 | ||||||||
\(657\) | 10.0129 | 0.390641 | ||||||||
\(658\) | 81.2594 | 3.16782 | ||||||||
\(659\) | 21.4490 | 0.835535 | 0.417768 | − | 0.908554i | \(-0.362813\pi\) | ||||
0.417768 | + | 0.908554i | \(0.362813\pi\) | |||||||
\(660\) | −19.8839 | −0.773981 | ||||||||
\(661\) | −26.4673 | −1.02946 | −0.514730 | − | 0.857352i | \(-0.672108\pi\) | ||||
−0.514730 | + | 0.857352i | \(0.672108\pi\) | |||||||
\(662\) | −80.7312 | −3.13771 | ||||||||
\(663\) | −0.139018 | −0.00539901 | ||||||||
\(664\) | 96.2896 | 3.73676 | ||||||||
\(665\) | −55.9263 | −2.16873 | ||||||||
\(666\) | 23.9984 | 0.929917 | ||||||||
\(667\) | 38.8370 | 1.50377 | ||||||||
\(668\) | −41.4948 | −1.60548 | ||||||||
\(669\) | −1.07333 | −0.0414974 | ||||||||
\(670\) | 28.4812 | 1.10033 | ||||||||
\(671\) | −26.0178 | −1.00441 | ||||||||
\(672\) | 11.8075 | 0.455486 | ||||||||
\(673\) | 5.99232 | 0.230987 | 0.115493 | − | 0.993308i | \(-0.463155\pi\) | ||||
0.115493 | + | 0.993308i | \(0.463155\pi\) | |||||||
\(674\) | −80.0903 | −3.08496 | ||||||||
\(675\) | −2.25944 | −0.0869660 | ||||||||
\(676\) | −55.7242 | −2.14324 | ||||||||
\(677\) | −32.1490 | −1.23559 | −0.617794 | − | 0.786340i | \(-0.711973\pi\) | ||||
−0.617794 | + | 0.786340i | \(0.711973\pi\) | |||||||
\(678\) | 26.1137 | 1.00289 | ||||||||
\(679\) | −36.4240 | −1.39783 | ||||||||
\(680\) | −15.4972 | −0.594289 | ||||||||
\(681\) | 6.66723 | 0.255489 | ||||||||
\(682\) | −27.4198 | −1.04996 | ||||||||
\(683\) | −30.6438 | −1.17255 | −0.586276 | − | 0.810111i | \(-0.699407\pi\) | ||||
−0.586276 | + | 0.810111i | \(0.699407\pi\) | |||||||
\(684\) | 23.7998 | 0.910010 | ||||||||
\(685\) | −10.2774 | −0.392679 | ||||||||
\(686\) | −0.164981 | −0.00629899 | ||||||||
\(687\) | −20.5325 | −0.783365 | ||||||||
\(688\) | 64.3679 | 2.45400 | ||||||||
\(689\) | −0.288709 | −0.0109989 | ||||||||
\(690\) | −36.4446 | −1.38742 | ||||||||
\(691\) | −6.24184 | −0.237451 | −0.118725 | − | 0.992927i | \(-0.537881\pi\) | ||||
−0.118725 | + | 0.992927i | \(0.537881\pi\) | |||||||
\(692\) | 100.665 | 3.82670 | ||||||||
\(693\) | −6.43637 | −0.244497 | ||||||||
\(694\) | −7.20336 | −0.273436 | ||||||||
\(695\) | 9.88655 | 0.375018 | ||||||||
\(696\) | 41.4274 | 1.57030 | ||||||||
\(697\) | −0.327658 | −0.0124109 | ||||||||
\(698\) | −54.9019 | −2.07807 | ||||||||
\(699\) | 26.4189 | 0.999253 | ||||||||
\(700\) | 36.3148 | 1.37257 | ||||||||
\(701\) | 25.8694 | 0.977072 | 0.488536 | − | 0.872544i | \(-0.337531\pi\) | ||||
0.488536 | + | 0.872544i | \(0.337531\pi\) | |||||||
\(702\) | −0.348734 | −0.0131621 | ||||||||
\(703\) | −53.0378 | −2.00036 | ||||||||
\(704\) | 6.48881 | 0.244556 | ||||||||
\(705\) | −23.3112 | −0.877952 | ||||||||
\(706\) | −75.7361 | −2.85037 | ||||||||
\(707\) | −11.5057 | −0.432716 | ||||||||
\(708\) | −11.1360 | −0.418515 | ||||||||
\(709\) | −30.6086 | −1.14953 | −0.574766 | − | 0.818318i | \(-0.694907\pi\) | ||||
−0.574766 | + | 0.818318i | \(0.694907\pi\) | |||||||
\(710\) | 58.8915 | 2.21016 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 1.01313 | 0.0379687 | ||||||||
\(713\) | −34.2842 | −1.28395 | ||||||||
\(714\) | −9.39205 | −0.351488 | ||||||||
\(715\) | −0.643912 | −0.0240810 | ||||||||
\(716\) | 94.5267 | 3.53263 | ||||||||
\(717\) | 12.3541 | 0.461372 | ||||||||
\(718\) | −71.0895 | −2.65304 | ||||||||
\(719\) | 11.5708 | 0.431518 | 0.215759 | − | 0.976447i | \(-0.430777\pi\) | ||||
0.215759 | + | 0.976447i | \(0.430777\pi\) | |||||||
\(720\) | −15.7427 | −0.586696 | ||||||||
\(721\) | 59.0455 | 2.19897 | ||||||||
\(722\) | −29.4419 | −1.09572 | ||||||||
\(723\) | −4.32551 | −0.160867 | ||||||||
\(724\) | 34.4628 | 1.28080 | ||||||||
\(725\) | 16.2738 | 0.604393 | ||||||||
\(726\) | −20.1805 | −0.748967 | ||||||||
\(727\) | −24.7108 | −0.916473 | −0.458237 | − | 0.888830i | \(-0.651519\pi\) | ||||
−0.458237 | + | 0.888830i | \(0.651519\pi\) | |||||||
\(728\) | 2.99369 | 0.110954 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 67.6762 | 2.50481 | ||||||||
\(731\) | −11.0164 | −0.407458 | ||||||||
\(732\) | −64.9699 | −2.40136 | ||||||||
\(733\) | 51.8781 | 1.91616 | 0.958080 | − | 0.286500i | \(-0.0924918\pi\) | ||||
0.958080 | + | 0.286500i | \(0.0924918\pi\) | |||||||
\(734\) | 60.3157 | 2.22629 | ||||||||
\(735\) | 18.9077 | 0.697420 | ||||||||
\(736\) | −17.0052 | −0.626819 | ||||||||
\(737\) | −7.24416 | −0.266842 | ||||||||
\(738\) | −0.821949 | −0.0302564 | ||||||||
\(739\) | 44.8867 | 1.65118 | 0.825592 | − | 0.564267i | \(-0.190841\pi\) | ||||
0.825592 | + | 0.564267i | \(0.190841\pi\) | |||||||
\(740\) | 110.651 | 4.06761 | ||||||||
\(741\) | 0.770724 | 0.0283132 | ||||||||
\(742\) | −19.5052 | −0.716057 | ||||||||
\(743\) | 30.8520 | 1.13185 | 0.565926 | − | 0.824456i | \(-0.308519\pi\) | ||||
0.565926 | + | 0.824456i | \(0.308519\pi\) | |||||||
\(744\) | −36.5709 | −1.34076 | ||||||||
\(745\) | −27.5540 | −1.00950 | ||||||||
\(746\) | 14.1410 | 0.517737 | ||||||||
\(747\) | −16.7409 | −0.612517 | ||||||||
\(748\) | 7.37990 | 0.269836 | ||||||||
\(749\) | 0.397665 | 0.0145303 | ||||||||
\(750\) | 18.5231 | 0.676369 | ||||||||
\(751\) | 19.7178 | 0.719513 | 0.359757 | − | 0.933046i | \(-0.382860\pi\) | ||||
0.359757 | + | 0.933046i | \(0.382860\pi\) | |||||||
\(752\) | −50.5524 | −1.84346 | ||||||||
\(753\) | −19.3106 | −0.703716 | ||||||||
\(754\) | 2.51178 | 0.0914737 | ||||||||
\(755\) | 40.6089 | 1.47791 | ||||||||
\(756\) | −16.0725 | −0.584550 | ||||||||
\(757\) | 15.8870 | 0.577424 | 0.288712 | − | 0.957416i | \(-0.406773\pi\) | ||||
0.288712 | + | 0.957416i | \(0.406773\pi\) | |||||||
\(758\) | −83.7300 | −3.04121 | ||||||||
\(759\) | 9.26963 | 0.336466 | ||||||||
\(760\) | 85.9172 | 3.11654 | ||||||||
\(761\) | 25.0751 | 0.908972 | 0.454486 | − | 0.890754i | \(-0.349823\pi\) | ||||
0.454486 | + | 0.890754i | \(0.349823\pi\) | |||||||
\(762\) | −46.6756 | −1.69088 | ||||||||
\(763\) | −73.1083 | −2.64670 | ||||||||
\(764\) | −78.7979 | −2.85081 | ||||||||
\(765\) | 2.69434 | 0.0974139 | ||||||||
\(766\) | 28.9677 | 1.04665 | ||||||||
\(767\) | −0.360622 | −0.0130213 | ||||||||
\(768\) | 32.0260 | 1.15564 | ||||||||
\(769\) | 17.2244 | 0.621127 | 0.310564 | − | 0.950553i | \(-0.399482\pi\) | ||||
0.310564 | + | 0.950553i | \(0.399482\pi\) | |||||||
\(770\) | −43.5027 | −1.56773 | ||||||||
\(771\) | −23.6722 | −0.852533 | ||||||||
\(772\) | −43.2223 | −1.55560 | ||||||||
\(773\) | 24.4961 | 0.881063 | 0.440531 | − | 0.897737i | \(-0.354790\pi\) | ||||
0.440531 | + | 0.897737i | \(0.354790\pi\) | |||||||
\(774\) | −27.6354 | −0.993333 | ||||||||
\(775\) | −14.3660 | −0.516043 | ||||||||
\(776\) | 55.9567 | 2.00873 | ||||||||
\(777\) | 35.8174 | 1.28494 | ||||||||
\(778\) | 18.9140 | 0.678101 | ||||||||
\(779\) | 1.81656 | 0.0650849 | ||||||||
\(780\) | −1.60794 | −0.0575733 | ||||||||
\(781\) | −14.9789 | −0.535989 | ||||||||
\(782\) | 13.5264 | 0.483703 | ||||||||
\(783\) | −7.20257 | −0.257399 | ||||||||
\(784\) | 41.0029 | 1.46439 | ||||||||
\(785\) | −7.86269 | −0.280632 | ||||||||
\(786\) | −13.6775 | −0.487860 | ||||||||
\(787\) | −31.2735 | −1.11478 | −0.557389 | − | 0.830251i | \(-0.688197\pi\) | ||||
−0.557389 | + | 0.830251i | \(0.688197\pi\) | |||||||
\(788\) | −67.4474 | −2.40271 | ||||||||
\(789\) | 9.98045 | 0.355313 | ||||||||
\(790\) | 6.75889 | 0.240471 | ||||||||
\(791\) | 38.9746 | 1.38578 | ||||||||
\(792\) | 9.88792 | 0.351352 | ||||||||
\(793\) | −2.10396 | −0.0747137 | ||||||||
\(794\) | 46.6211 | 1.65452 | ||||||||
\(795\) | 5.59553 | 0.198453 | ||||||||
\(796\) | 45.0276 | 1.59596 | ||||||||
\(797\) | −50.7016 | −1.79594 | −0.897972 | − | 0.440053i | \(-0.854959\pi\) | ||||
−0.897972 | + | 0.440053i | \(0.854959\pi\) | |||||||
\(798\) | 52.0701 | 1.84326 | ||||||||
\(799\) | 8.65194 | 0.306084 | ||||||||
\(800\) | −7.12565 | −0.251930 | ||||||||
\(801\) | −0.176143 | −0.00622370 | ||||||||
\(802\) | −5.17537 | −0.182749 | ||||||||
\(803\) | −17.2133 | −0.607445 | ||||||||
\(804\) | −18.0896 | −0.637972 | ||||||||
\(805\) | −54.3934 | −1.91711 | ||||||||
\(806\) | −2.21733 | −0.0781021 | ||||||||
\(807\) | −1.01465 | −0.0357174 | ||||||||
\(808\) | 17.6757 | 0.621829 | ||||||||
\(809\) | 4.30764 | 0.151449 | 0.0757243 | − | 0.997129i | \(-0.475873\pi\) | ||||
0.0757243 | + | 0.997129i | \(0.475873\pi\) | |||||||
\(810\) | 6.75889 | 0.237483 | ||||||||
\(811\) | −9.54767 | −0.335264 | −0.167632 | − | 0.985850i | \(-0.553612\pi\) | ||||
−0.167632 | + | 0.985850i | \(0.553612\pi\) | |||||||
\(812\) | 115.763 | 4.06248 | ||||||||
\(813\) | 0.893528 | 0.0313374 | ||||||||
\(814\) | −41.2559 | −1.44602 | ||||||||
\(815\) | 52.8262 | 1.85042 | ||||||||
\(816\) | 5.84290 | 0.204542 | ||||||||
\(817\) | 61.0758 | 2.13677 | ||||||||
\(818\) | −28.2998 | −0.989478 | ||||||||
\(819\) | −0.520484 | −0.0181872 | ||||||||
\(820\) | −3.78982 | −0.132346 | ||||||||
\(821\) | 39.9747 | 1.39513 | 0.697564 | − | 0.716523i | \(-0.254267\pi\) | ||||
0.697564 | + | 0.716523i | \(0.254267\pi\) | |||||||
\(822\) | 9.56875 | 0.333748 | ||||||||
\(823\) | −19.6790 | −0.685968 | −0.342984 | − | 0.939341i | \(-0.611438\pi\) | ||||
−0.342984 | + | 0.939341i | \(0.611438\pi\) | |||||||
\(824\) | −90.7092 | −3.16000 | ||||||||
\(825\) | 3.88424 | 0.135232 | ||||||||
\(826\) | −24.3636 | −0.847719 | ||||||||
\(827\) | 31.9137 | 1.10975 | 0.554873 | − | 0.831935i | \(-0.312767\pi\) | ||||
0.554873 | + | 0.831935i | \(0.312767\pi\) | |||||||
\(828\) | 23.1475 | 0.804431 | ||||||||
\(829\) | −10.6270 | −0.369092 | −0.184546 | − | 0.982824i | \(-0.559081\pi\) | ||||
−0.184546 | + | 0.982824i | \(0.559081\pi\) | |||||||
\(830\) | −113.150 | −3.92749 | ||||||||
\(831\) | 2.86557 | 0.0994057 | ||||||||
\(832\) | 0.524724 | 0.0181915 | ||||||||
\(833\) | −7.01757 | −0.243144 | ||||||||
\(834\) | −9.20486 | −0.318738 | ||||||||
\(835\) | 26.0435 | 0.901273 | ||||||||
\(836\) | −40.9146 | −1.41506 | ||||||||
\(837\) | 6.35822 | 0.219772 | ||||||||
\(838\) | 32.9491 | 1.13821 | ||||||||
\(839\) | 10.1406 | 0.350091 | 0.175046 | − | 0.984560i | \(-0.443993\pi\) | ||||
0.175046 | + | 0.984560i | \(0.443993\pi\) | |||||||
\(840\) | −58.0214 | −2.00193 | ||||||||
\(841\) | 22.8769 | 0.788860 | ||||||||
\(842\) | −94.5507 | −3.25843 | ||||||||
\(843\) | 6.62580 | 0.228205 | ||||||||
\(844\) | 75.2590 | 2.59052 | ||||||||
\(845\) | 34.9743 | 1.20315 | ||||||||
\(846\) | 21.7039 | 0.746195 | ||||||||
\(847\) | −30.1192 | −1.03491 | ||||||||
\(848\) | 12.1344 | 0.416696 | ||||||||
\(849\) | 12.7835 | 0.438729 | ||||||||
\(850\) | 5.66794 | 0.194409 | ||||||||
\(851\) | −51.5841 | −1.76828 | ||||||||
\(852\) | −37.4044 | −1.28145 | ||||||||
\(853\) | −19.6341 | −0.672260 | −0.336130 | − | 0.941816i | \(-0.609118\pi\) | ||||
−0.336130 | + | 0.941816i | \(0.609118\pi\) | |||||||
\(854\) | −142.143 | −4.86404 | ||||||||
\(855\) | −14.9376 | −0.510854 | ||||||||
\(856\) | −0.610915 | −0.0208807 | ||||||||
\(857\) | −21.5317 | −0.735508 | −0.367754 | − | 0.929923i | \(-0.619873\pi\) | ||||
−0.367754 | + | 0.929923i | \(0.619873\pi\) | |||||||
\(858\) | 0.599514 | 0.0204671 | ||||||||
\(859\) | 30.3366 | 1.03507 | 0.517535 | − | 0.855662i | \(-0.326850\pi\) | ||||
0.517535 | + | 0.855662i | \(0.326850\pi\) | |||||||
\(860\) | −127.421 | −4.34500 | ||||||||
\(861\) | −1.22675 | −0.0418077 | ||||||||
\(862\) | −95.4289 | −3.25032 | ||||||||
\(863\) | 35.4483 | 1.20667 | 0.603337 | − | 0.797486i | \(-0.293837\pi\) | ||||
0.603337 | + | 0.797486i | \(0.293837\pi\) | |||||||
\(864\) | 3.15372 | 0.107292 | ||||||||
\(865\) | −63.1805 | −2.14820 | ||||||||
\(866\) | −87.9730 | −2.98945 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −102.192 | −3.46863 | ||||||||
\(869\) | −1.71911 | −0.0583169 | ||||||||
\(870\) | −48.6814 | −1.65045 | ||||||||
\(871\) | −0.585807 | −0.0198493 | ||||||||
\(872\) | 112.313 | 3.80341 | ||||||||
\(873\) | −9.72863 | −0.329264 | ||||||||
\(874\) | −74.9911 | −2.53661 | ||||||||
\(875\) | 27.6457 | 0.934594 | ||||||||
\(876\) | −42.9840 | −1.45229 | ||||||||
\(877\) | −17.4436 | −0.589029 | −0.294514 | − | 0.955647i | \(-0.595158\pi\) | ||||
−0.294514 | + | 0.955647i | \(0.595158\pi\) | |||||||
\(878\) | −19.7621 | −0.666939 | ||||||||
\(879\) | −11.8071 | −0.398245 | ||||||||
\(880\) | 27.0635 | 0.912311 | ||||||||
\(881\) | −12.5196 | −0.421794 | −0.210897 | − | 0.977508i | \(-0.567639\pi\) | ||||
−0.210897 | + | 0.977508i | \(0.567639\pi\) | |||||||
\(882\) | −17.6040 | −0.592756 | ||||||||
\(883\) | −22.4719 | −0.756241 | −0.378120 | − | 0.925756i | \(-0.623429\pi\) | ||||
−0.378120 | + | 0.925756i | \(0.623429\pi\) | |||||||
\(884\) | 0.596784 | 0.0200720 | ||||||||
\(885\) | 6.98930 | 0.234943 | ||||||||
\(886\) | −9.26771 | −0.311355 | ||||||||
\(887\) | 26.2816 | 0.882448 | 0.441224 | − | 0.897397i | \(-0.354544\pi\) | ||||
0.441224 | + | 0.897397i | \(0.354544\pi\) | |||||||
\(888\) | −55.0247 | −1.84651 | ||||||||
\(889\) | −69.6630 | −2.33642 | ||||||||
\(890\) | −1.19053 | −0.0399066 | ||||||||
\(891\) | −1.71911 | −0.0575925 | ||||||||
\(892\) | 4.60766 | 0.154276 | ||||||||
\(893\) | −47.9669 | −1.60515 | ||||||||
\(894\) | 25.6541 | 0.858002 | ||||||||
\(895\) | −59.3280 | −1.98312 | ||||||||
\(896\) | 59.0654 | 1.97324 | ||||||||
\(897\) | 0.749598 | 0.0250284 | ||||||||
\(898\) | 9.10175 | 0.303729 | ||||||||
\(899\) | −45.7955 | −1.52736 | ||||||||
\(900\) | 9.69946 | 0.323315 | ||||||||
\(901\) | −2.07677 | −0.0691874 | ||||||||
\(902\) | 1.41302 | 0.0470485 | ||||||||
\(903\) | −41.2456 | −1.37257 | ||||||||
\(904\) | −59.8750 | −1.99141 | ||||||||
\(905\) | −21.6299 | −0.719004 | ||||||||
\(906\) | −37.8088 | −1.25611 | ||||||||
\(907\) | −1.93038 | −0.0640972 | −0.0320486 | − | 0.999486i | \(-0.510203\pi\) | ||||
−0.0320486 | + | 0.999486i | \(0.510203\pi\) | |||||||
\(908\) | −28.6215 | −0.949837 | ||||||||
\(909\) | −3.07310 | −0.101928 | ||||||||
\(910\) | −3.51789 | −0.116617 | ||||||||
\(911\) | 23.1841 | 0.768123 | 0.384061 | − | 0.923308i | \(-0.374525\pi\) | ||||
0.384061 | + | 0.923308i | \(0.374525\pi\) | |||||||
\(912\) | −32.3934 | −1.07265 | ||||||||
\(913\) | 28.7795 | 0.952463 | ||||||||
\(914\) | 19.1631 | 0.633859 | ||||||||
\(915\) | 40.7772 | 1.34805 | ||||||||
\(916\) | 88.1432 | 2.91233 | ||||||||
\(917\) | −20.4136 | −0.674116 | ||||||||
\(918\) | −2.50856 | −0.0827947 | ||||||||
\(919\) | −30.5628 | −1.00817 | −0.504087 | − | 0.863653i | \(-0.668171\pi\) | ||||
−0.504087 | + | 0.863653i | \(0.668171\pi\) | |||||||
\(920\) | 83.5622 | 2.75497 | ||||||||
\(921\) | −18.2181 | −0.600306 | ||||||||
\(922\) | −95.7108 | −3.15207 | ||||||||
\(923\) | −1.21129 | −0.0398700 | ||||||||
\(924\) | 27.6304 | 0.908973 | ||||||||
\(925\) | −21.6152 | −0.710703 | ||||||||
\(926\) | −11.5954 | −0.381049 | ||||||||
\(927\) | 15.7707 | 0.517978 | ||||||||
\(928\) | −22.7149 | −0.745652 | ||||||||
\(929\) | 7.06537 | 0.231807 | 0.115904 | − | 0.993260i | \(-0.463024\pi\) | ||||
0.115904 | + | 0.993260i | \(0.463024\pi\) | |||||||
\(930\) | 42.9745 | 1.40919 | ||||||||
\(931\) | 38.9058 | 1.27509 | ||||||||
\(932\) | −113.412 | −3.71494 | ||||||||
\(933\) | −10.1159 | −0.331180 | ||||||||
\(934\) | −36.7297 | −1.20183 | ||||||||
\(935\) | −4.63187 | −0.151478 | ||||||||
\(936\) | 0.799597 | 0.0261356 | ||||||||
\(937\) | −16.4990 | −0.538999 | −0.269500 | − | 0.963000i | \(-0.586858\pi\) | ||||
−0.269500 | + | 0.963000i | \(0.586858\pi\) | |||||||
\(938\) | −39.5771 | −1.29224 | ||||||||
\(939\) | 16.4058 | 0.535382 | ||||||||
\(940\) | 100.072 | 3.26398 | ||||||||
\(941\) | 4.21742 | 0.137484 | 0.0687420 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687420 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(942\) | 7.32055 | 0.238516 | ||||||||
\(943\) | 1.76677 | 0.0575338 | ||||||||
\(944\) | 15.1569 | 0.493315 | ||||||||
\(945\) | 10.0876 | 0.328150 | ||||||||
\(946\) | 47.5083 | 1.54463 | ||||||||
\(947\) | 8.56505 | 0.278327 | 0.139163 | − | 0.990269i | \(-0.455559\pi\) | ||||
0.139163 | + | 0.990269i | \(0.455559\pi\) | |||||||
\(948\) | −4.29286 | −0.139425 | ||||||||
\(949\) | −1.39197 | −0.0451854 | ||||||||
\(950\) | −31.4234 | −1.01951 | ||||||||
\(951\) | −12.8397 | −0.416355 | ||||||||
\(952\) | 21.5346 | 0.697940 | ||||||||
\(953\) | −59.0273 | −1.91208 | −0.956041 | − | 0.293231i | \(-0.905269\pi\) | ||||
−0.956041 | + | 0.293231i | \(0.905269\pi\) | |||||||
\(954\) | −5.20971 | −0.168670 | ||||||||
\(955\) | 49.4561 | 1.60036 | ||||||||
\(956\) | −53.0344 | −1.71525 | ||||||||
\(957\) | 12.3820 | 0.400254 | ||||||||
\(958\) | 42.1272 | 1.36107 | ||||||||
\(959\) | 14.2813 | 0.461167 | ||||||||
\(960\) | −10.1698 | −0.328229 | ||||||||
\(961\) | 9.42695 | 0.304095 | ||||||||
\(962\) | −3.33620 | −0.107563 | ||||||||
\(963\) | 0.106214 | 0.00342269 | ||||||||
\(964\) | 18.5688 | 0.598060 | ||||||||
\(965\) | 27.1277 | 0.873271 | ||||||||
\(966\) | 50.6428 | 1.62941 | ||||||||
\(967\) | −15.1871 | −0.488385 | −0.244193 | − | 0.969727i | \(-0.578523\pi\) | ||||
−0.244193 | + | 0.969727i | \(0.578523\pi\) | |||||||
\(968\) | 46.2709 | 1.48720 | ||||||||
\(969\) | 5.54406 | 0.178101 | ||||||||
\(970\) | −65.7547 | −2.11126 | ||||||||
\(971\) | −47.5157 | −1.52485 | −0.762426 | − | 0.647076i | \(-0.775992\pi\) | ||||
−0.762426 | + | 0.647076i | \(0.775992\pi\) | |||||||
\(972\) | −4.29286 | −0.137693 | ||||||||
\(973\) | −13.7382 | −0.440426 | ||||||||
\(974\) | 82.9756 | 2.65871 | ||||||||
\(975\) | 0.314103 | 0.0100593 | ||||||||
\(976\) | 88.4288 | 2.83054 | ||||||||
\(977\) | −32.4199 | −1.03720 | −0.518602 | − | 0.855016i | \(-0.673547\pi\) | ||||
−0.518602 | + | 0.855016i | \(0.673547\pi\) | |||||||
\(978\) | −49.1837 | −1.57272 | ||||||||
\(979\) | 0.302809 | 0.00967783 | ||||||||
\(980\) | −81.1679 | −2.59281 | ||||||||
\(981\) | −19.5268 | −0.623442 | ||||||||
\(982\) | 27.4059 | 0.874559 | ||||||||
\(983\) | 3.04172 | 0.0970157 | 0.0485078 | − | 0.998823i | \(-0.484553\pi\) | ||||
0.0485078 | + | 0.998823i | \(0.484553\pi\) | |||||||
\(984\) | 1.88461 | 0.0600792 | ||||||||
\(985\) | 42.3322 | 1.34881 | ||||||||
\(986\) | 18.0680 | 0.575404 | ||||||||
\(987\) | 32.3929 | 1.03108 | ||||||||
\(988\) | −3.30860 | −0.105261 | ||||||||
\(989\) | 59.4018 | 1.88887 | ||||||||
\(990\) | −11.6193 | −0.369286 | ||||||||
\(991\) | 32.8602 | 1.04384 | 0.521920 | − | 0.852995i | \(-0.325216\pi\) | ||||
0.521920 | + | 0.852995i | \(0.325216\pi\) | |||||||
\(992\) | 20.0520 | 0.636653 | ||||||||
\(993\) | −32.1823 | −1.02128 | ||||||||
\(994\) | −81.8346 | −2.59564 | ||||||||
\(995\) | −28.2608 | −0.895927 | ||||||||
\(996\) | 71.8663 | 2.27717 | ||||||||
\(997\) | 22.0507 | 0.698352 | 0.349176 | − | 0.937057i | \(-0.386462\pi\) | ||||
0.349176 | + | 0.937057i | \(0.386462\pi\) | |||||||
\(998\) | −88.4598 | −2.80014 | ||||||||
\(999\) | 9.56660 | 0.302674 |
(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 | 4029.2.a.l.1.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.4 | ✓ | 32 | 1.1 | even | 1 | trivial |