Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −1.67728 | −0.968379 | −0.484189 | − | 0.874963i | \(-0.660885\pi\) | ||||
−0.484189 | + | 0.874963i | \(0.660885\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.83767 | 0.821831 | 0.410915 | − | 0.911673i | \(-0.365209\pi\) | ||||
0.410915 | + | 0.911673i | \(0.365209\pi\) | |||||||
\(6\) | 1.67728 | 0.684747 | ||||||||
\(7\) | 4.34649 | 1.64282 | 0.821409 | − | 0.570340i | \(-0.193188\pi\) | ||||
0.821409 | + | 0.570340i | \(0.193188\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.186728 | −0.0622425 | ||||||||
\(10\) | −1.83767 | −0.581122 | ||||||||
\(11\) | −3.12207 | −0.941340 | −0.470670 | − | 0.882309i | \(-0.655988\pi\) | ||||
−0.470670 | + | 0.882309i | \(0.655988\pi\) | |||||||
\(12\) | −1.67728 | −0.484189 | ||||||||
\(13\) | −1.45926 | −0.404725 | −0.202362 | − | 0.979311i | \(-0.564862\pi\) | ||||
−0.202362 | + | 0.979311i | \(0.564862\pi\) | |||||||
\(14\) | −4.34649 | −1.16165 | ||||||||
\(15\) | −3.08229 | −0.795843 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.19635 | 1.74537 | 0.872686 | − | 0.488282i | \(-0.162376\pi\) | ||||
0.872686 | + | 0.488282i | \(0.162376\pi\) | |||||||
\(18\) | 0.186728 | 0.0440121 | ||||||||
\(19\) | −1.42373 | −0.326625 | −0.163313 | − | 0.986574i | \(-0.552218\pi\) | ||||
−0.163313 | + | 0.986574i | \(0.552218\pi\) | |||||||
\(20\) | 1.83767 | 0.410915 | ||||||||
\(21\) | −7.29028 | −1.59087 | ||||||||
\(22\) | 3.12207 | 0.665628 | ||||||||
\(23\) | −3.84407 | −0.801545 | −0.400772 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400772 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(24\) | 1.67728 | 0.342374 | ||||||||
\(25\) | −1.62297 | −0.324594 | ||||||||
\(26\) | 1.45926 | 0.286184 | ||||||||
\(27\) | 5.34504 | 1.02865 | ||||||||
\(28\) | 4.34649 | 0.821409 | ||||||||
\(29\) | −2.37377 | −0.440797 | −0.220399 | − | 0.975410i | \(-0.570736\pi\) | ||||
−0.220399 | + | 0.975410i | \(0.570736\pi\) | |||||||
\(30\) | 3.08229 | 0.562746 | ||||||||
\(31\) | −9.37454 | −1.68372 | −0.841858 | − | 0.539699i | \(-0.818538\pi\) | ||||
−0.841858 | + | 0.539699i | \(0.818538\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.23659 | 0.911574 | ||||||||
\(34\) | −7.19635 | −1.23416 | ||||||||
\(35\) | 7.98741 | 1.35012 | ||||||||
\(36\) | −0.186728 | −0.0311213 | ||||||||
\(37\) | 3.02156 | 0.496741 | 0.248370 | − | 0.968665i | \(-0.420105\pi\) | ||||
0.248370 | + | 0.968665i | \(0.420105\pi\) | |||||||
\(38\) | 1.42373 | 0.230959 | ||||||||
\(39\) | 2.44758 | 0.391927 | ||||||||
\(40\) | −1.83767 | −0.290561 | ||||||||
\(41\) | 4.86747 | 0.760171 | 0.380086 | − | 0.924951i | \(-0.375894\pi\) | ||||
0.380086 | + | 0.924951i | \(0.375894\pi\) | |||||||
\(42\) | 7.29028 | 1.12492 | ||||||||
\(43\) | 0.736530 | 0.112320 | 0.0561599 | − | 0.998422i | \(-0.482114\pi\) | ||||
0.0561599 | + | 0.998422i | \(0.482114\pi\) | |||||||
\(44\) | −3.12207 | −0.470670 | ||||||||
\(45\) | −0.343143 | −0.0511528 | ||||||||
\(46\) | 3.84407 | 0.566778 | ||||||||
\(47\) | 6.51698 | 0.950599 | 0.475300 | − | 0.879824i | \(-0.342340\pi\) | ||||
0.475300 | + | 0.879824i | \(0.342340\pi\) | |||||||
\(48\) | −1.67728 | −0.242095 | ||||||||
\(49\) | 11.8920 | 1.69885 | ||||||||
\(50\) | 1.62297 | 0.229523 | ||||||||
\(51\) | −12.0703 | −1.69018 | ||||||||
\(52\) | −1.45926 | −0.202362 | ||||||||
\(53\) | 10.3671 | 1.42403 | 0.712017 | − | 0.702162i | \(-0.247782\pi\) | ||||
0.712017 | + | 0.702162i | \(0.247782\pi\) | |||||||
\(54\) | −5.34504 | −0.727368 | ||||||||
\(55\) | −5.73734 | −0.773622 | ||||||||
\(56\) | −4.34649 | −0.580824 | ||||||||
\(57\) | 2.38799 | 0.316297 | ||||||||
\(58\) | 2.37377 | 0.311691 | ||||||||
\(59\) | −1.43766 | −0.187168 | −0.0935839 | − | 0.995611i | \(-0.529832\pi\) | ||||
−0.0935839 | + | 0.995611i | \(0.529832\pi\) | |||||||
\(60\) | −3.08229 | −0.397922 | ||||||||
\(61\) | 11.7254 | 1.50129 | 0.750643 | − | 0.660708i | \(-0.229744\pi\) | ||||
0.750643 | + | 0.660708i | \(0.229744\pi\) | |||||||
\(62\) | 9.37454 | 1.19057 | ||||||||
\(63\) | −0.811609 | −0.102253 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.68163 | −0.332615 | ||||||||
\(66\) | −5.23659 | −0.644580 | ||||||||
\(67\) | 13.3564 | 1.63174 | 0.815871 | − | 0.578235i | \(-0.196258\pi\) | ||||
0.815871 | + | 0.578235i | \(0.196258\pi\) | |||||||
\(68\) | 7.19635 | 0.872686 | ||||||||
\(69\) | 6.44759 | 0.776199 | ||||||||
\(70\) | −7.98741 | −0.954678 | ||||||||
\(71\) | −4.30326 | −0.510703 | −0.255352 | − | 0.966848i | \(-0.582191\pi\) | ||||
−0.255352 | + | 0.966848i | \(0.582191\pi\) | |||||||
\(72\) | 0.186728 | 0.0220061 | ||||||||
\(73\) | −0.705872 | −0.0826161 | −0.0413080 | − | 0.999146i | \(-0.513152\pi\) | ||||
−0.0413080 | + | 0.999146i | \(0.513152\pi\) | |||||||
\(74\) | −3.02156 | −0.351249 | ||||||||
\(75\) | 2.72218 | 0.314330 | ||||||||
\(76\) | −1.42373 | −0.163313 | ||||||||
\(77\) | −13.5701 | −1.54645 | ||||||||
\(78\) | −2.44758 | −0.277134 | ||||||||
\(79\) | 2.30224 | 0.259022 | 0.129511 | − | 0.991578i | \(-0.458659\pi\) | ||||
0.129511 | + | 0.991578i | \(0.458659\pi\) | |||||||
\(80\) | 1.83767 | 0.205458 | ||||||||
\(81\) | −8.40495 | −0.933883 | ||||||||
\(82\) | −4.86747 | −0.537522 | ||||||||
\(83\) | 3.07087 | 0.337072 | 0.168536 | − | 0.985696i | \(-0.446096\pi\) | ||||
0.168536 | + | 0.985696i | \(0.446096\pi\) | |||||||
\(84\) | −7.29028 | −0.795435 | ||||||||
\(85\) | 13.2245 | 1.43440 | ||||||||
\(86\) | −0.736530 | −0.0794221 | ||||||||
\(87\) | 3.98147 | 0.426859 | ||||||||
\(88\) | 3.12207 | 0.332814 | ||||||||
\(89\) | 1.00500 | 0.106530 | 0.0532650 | − | 0.998580i | \(-0.483037\pi\) | ||||
0.0532650 | + | 0.998580i | \(0.483037\pi\) | |||||||
\(90\) | 0.343143 | 0.0361705 | ||||||||
\(91\) | −6.34264 | −0.664889 | ||||||||
\(92\) | −3.84407 | −0.400772 | ||||||||
\(93\) | 15.7237 | 1.63048 | ||||||||
\(94\) | −6.51698 | −0.672175 | ||||||||
\(95\) | −2.61634 | −0.268431 | ||||||||
\(96\) | 1.67728 | 0.171187 | ||||||||
\(97\) | 2.04288 | 0.207423 | 0.103711 | − | 0.994607i | \(-0.466928\pi\) | ||||
0.103711 | + | 0.994607i | \(0.466928\pi\) | |||||||
\(98\) | −11.8920 | −1.20127 | ||||||||
\(99\) | 0.582977 | 0.0585914 | ||||||||
\(100\) | −1.62297 | −0.162297 | ||||||||
\(101\) | 1.31398 | 0.130746 | 0.0653729 | − | 0.997861i | \(-0.479176\pi\) | ||||
0.0653729 | + | 0.997861i | \(0.479176\pi\) | |||||||
\(102\) | 12.0703 | 1.19514 | ||||||||
\(103\) | −10.6517 | −1.04955 | −0.524773 | − | 0.851242i | \(-0.675850\pi\) | ||||
−0.524773 | + | 0.851242i | \(0.675850\pi\) | |||||||
\(104\) | 1.45926 | 0.143092 | ||||||||
\(105\) | −13.3971 | −1.30743 | ||||||||
\(106\) | −10.3671 | −1.00694 | ||||||||
\(107\) | 13.8864 | 1.34245 | 0.671226 | − | 0.741253i | \(-0.265768\pi\) | ||||
0.671226 | + | 0.741253i | \(0.265768\pi\) | |||||||
\(108\) | 5.34504 | 0.514327 | ||||||||
\(109\) | −8.73711 | −0.836863 | −0.418432 | − | 0.908248i | \(-0.637420\pi\) | ||||
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(110\) | 5.73734 | 0.547034 | ||||||||
\(111\) | −5.06800 | −0.481033 | ||||||||
\(112\) | 4.34649 | 0.410705 | ||||||||
\(113\) | 4.24731 | 0.399553 | 0.199776 | − | 0.979841i | \(-0.435978\pi\) | ||||
0.199776 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(114\) | −2.38799 | −0.223656 | ||||||||
\(115\) | −7.06414 | −0.658734 | ||||||||
\(116\) | −2.37377 | −0.220399 | ||||||||
\(117\) | 0.272483 | 0.0251911 | ||||||||
\(118\) | 1.43766 | 0.132348 | ||||||||
\(119\) | 31.2788 | 2.86733 | ||||||||
\(120\) | 3.08229 | 0.281373 | ||||||||
\(121\) | −1.25266 | −0.113879 | ||||||||
\(122\) | −11.7254 | −1.06157 | ||||||||
\(123\) | −8.16412 | −0.736134 | ||||||||
\(124\) | −9.37454 | −0.841858 | ||||||||
\(125\) | −12.1708 | −1.08859 | ||||||||
\(126\) | 0.811609 | 0.0723039 | ||||||||
\(127\) | 12.3152 | 1.09280 | 0.546401 | − | 0.837524i | \(-0.315998\pi\) | ||||
0.546401 | + | 0.837524i | \(0.315998\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.23537 | −0.108768 | ||||||||
\(130\) | 2.68163 | 0.235195 | ||||||||
\(131\) | −3.54201 | −0.309467 | −0.154733 | − | 0.987956i | \(-0.549452\pi\) | ||||
−0.154733 | + | 0.987956i | \(0.549452\pi\) | |||||||
\(132\) | 5.23659 | 0.455787 | ||||||||
\(133\) | −6.18821 | −0.536586 | ||||||||
\(134\) | −13.3564 | −1.15382 | ||||||||
\(135\) | 9.82241 | 0.845379 | ||||||||
\(136\) | −7.19635 | −0.617082 | ||||||||
\(137\) | −15.8198 | −1.35158 | −0.675788 | − | 0.737096i | \(-0.736197\pi\) | ||||
−0.675788 | + | 0.737096i | \(0.736197\pi\) | |||||||
\(138\) | −6.44759 | −0.548856 | ||||||||
\(139\) | −7.38172 | −0.626110 | −0.313055 | − | 0.949735i | \(-0.601352\pi\) | ||||
−0.313055 | + | 0.949735i | \(0.601352\pi\) | |||||||
\(140\) | 7.98741 | 0.675059 | ||||||||
\(141\) | −10.9308 | −0.920540 | ||||||||
\(142\) | 4.30326 | 0.361122 | ||||||||
\(143\) | 4.55590 | 0.380984 | ||||||||
\(144\) | −0.186728 | −0.0155606 | ||||||||
\(145\) | −4.36220 | −0.362261 | ||||||||
\(146\) | 0.705872 | 0.0584184 | ||||||||
\(147\) | −19.9462 | −1.64513 | ||||||||
\(148\) | 3.02156 | 0.248370 | ||||||||
\(149\) | 12.4129 | 1.01690 | 0.508451 | − | 0.861091i | \(-0.330218\pi\) | ||||
0.508451 | + | 0.861091i | \(0.330218\pi\) | |||||||
\(150\) | −2.72218 | −0.222265 | ||||||||
\(151\) | 12.7569 | 1.03814 | 0.519072 | − | 0.854731i | \(-0.326278\pi\) | ||||
0.519072 | + | 0.854731i | \(0.326278\pi\) | |||||||
\(152\) | 1.42373 | 0.115480 | ||||||||
\(153\) | −1.34376 | −0.108636 | ||||||||
\(154\) | 13.5701 | 1.09351 | ||||||||
\(155\) | −17.2273 | −1.38373 | ||||||||
\(156\) | 2.44758 | 0.195963 | ||||||||
\(157\) | 3.67743 | 0.293491 | 0.146746 | − | 0.989174i | \(-0.453120\pi\) | ||||
0.146746 | + | 0.989174i | \(0.453120\pi\) | |||||||
\(158\) | −2.30224 | −0.183156 | ||||||||
\(159\) | −17.3886 | −1.37900 | ||||||||
\(160\) | −1.83767 | −0.145281 | ||||||||
\(161\) | −16.7082 | −1.31679 | ||||||||
\(162\) | 8.40495 | 0.660355 | ||||||||
\(163\) | −16.4579 | −1.28909 | −0.644543 | − | 0.764568i | \(-0.722952\pi\) | ||||
−0.644543 | + | 0.764568i | \(0.722952\pi\) | |||||||
\(164\) | 4.86747 | 0.380086 | ||||||||
\(165\) | 9.62313 | 0.749159 | ||||||||
\(166\) | −3.07087 | −0.238346 | ||||||||
\(167\) | 15.8349 | 1.22534 | 0.612672 | − | 0.790337i | \(-0.290095\pi\) | ||||
0.612672 | + | 0.790337i | \(0.290095\pi\) | |||||||
\(168\) | 7.29028 | 0.562458 | ||||||||
\(169\) | −10.8706 | −0.836198 | ||||||||
\(170\) | −13.2245 | −1.01427 | ||||||||
\(171\) | 0.265849 | 0.0203300 | ||||||||
\(172\) | 0.736530 | 0.0561599 | ||||||||
\(173\) | 23.6349 | 1.79692 | 0.898462 | − | 0.439050i | \(-0.144685\pi\) | ||||
0.898462 | + | 0.439050i | \(0.144685\pi\) | |||||||
\(174\) | −3.98147 | −0.301835 | ||||||||
\(175\) | −7.05422 | −0.533249 | ||||||||
\(176\) | −3.12207 | −0.235335 | ||||||||
\(177\) | 2.41136 | 0.181249 | ||||||||
\(178\) | −1.00500 | −0.0753281 | ||||||||
\(179\) | 22.0369 | 1.64712 | 0.823558 | − | 0.567233i | \(-0.191986\pi\) | ||||
0.823558 | + | 0.567233i | \(0.191986\pi\) | |||||||
\(180\) | −0.343143 | −0.0255764 | ||||||||
\(181\) | −17.3531 | −1.28984 | −0.644921 | − | 0.764249i | \(-0.723110\pi\) | ||||
−0.644921 | + | 0.764249i | \(0.723110\pi\) | |||||||
\(182\) | 6.34264 | 0.470148 | ||||||||
\(183\) | −19.6668 | −1.45381 | ||||||||
\(184\) | 3.84407 | 0.283389 | ||||||||
\(185\) | 5.55262 | 0.408237 | ||||||||
\(186\) | −15.7237 | −1.15292 | ||||||||
\(187\) | −22.4675 | −1.64299 | ||||||||
\(188\) | 6.51698 | 0.475300 | ||||||||
\(189\) | 23.2321 | 1.68989 | ||||||||
\(190\) | 2.61634 | 0.189809 | ||||||||
\(191\) | −9.73826 | −0.704636 | −0.352318 | − | 0.935880i | \(-0.614606\pi\) | ||||
−0.352318 | + | 0.935880i | \(0.614606\pi\) | |||||||
\(192\) | −1.67728 | −0.121047 | ||||||||
\(193\) | 4.54525 | 0.327174 | 0.163587 | − | 0.986529i | \(-0.447694\pi\) | ||||
0.163587 | + | 0.986529i | \(0.447694\pi\) | |||||||
\(194\) | −2.04288 | −0.146670 | ||||||||
\(195\) | 4.49785 | 0.322098 | ||||||||
\(196\) | 11.8920 | 0.849426 | ||||||||
\(197\) | 5.21493 | 0.371548 | 0.185774 | − | 0.982592i | \(-0.440521\pi\) | ||||
0.185774 | + | 0.982592i | \(0.440521\pi\) | |||||||
\(198\) | −0.582977 | −0.0414304 | ||||||||
\(199\) | −4.15238 | −0.294355 | −0.147177 | − | 0.989110i | \(-0.547019\pi\) | ||||
−0.147177 | + | 0.989110i | \(0.547019\pi\) | |||||||
\(200\) | 1.62297 | 0.114761 | ||||||||
\(201\) | −22.4024 | −1.58014 | ||||||||
\(202\) | −1.31398 | −0.0924513 | ||||||||
\(203\) | −10.3175 | −0.724150 | ||||||||
\(204\) | −12.0703 | −0.845090 | ||||||||
\(205\) | 8.94480 | 0.624732 | ||||||||
\(206\) | 10.6517 | 0.742141 | ||||||||
\(207\) | 0.717794 | 0.0498902 | ||||||||
\(208\) | −1.45926 | −0.101181 | ||||||||
\(209\) | 4.44498 | 0.307466 | ||||||||
\(210\) | 13.3971 | 0.924490 | ||||||||
\(211\) | 3.90589 | 0.268893 | 0.134446 | − | 0.990921i | \(-0.457074\pi\) | ||||
0.134446 | + | 0.990921i | \(0.457074\pi\) | |||||||
\(212\) | 10.3671 | 0.712017 | ||||||||
\(213\) | 7.21778 | 0.494554 | ||||||||
\(214\) | −13.8864 | −0.949257 | ||||||||
\(215\) | 1.35350 | 0.0923079 | ||||||||
\(216\) | −5.34504 | −0.363684 | ||||||||
\(217\) | −40.7463 | −2.76604 | ||||||||
\(218\) | 8.73711 | 0.591752 | ||||||||
\(219\) | 1.18395 | 0.0800036 | ||||||||
\(220\) | −5.73734 | −0.386811 | ||||||||
\(221\) | −10.5013 | −0.706395 | ||||||||
\(222\) | 5.06800 | 0.340142 | ||||||||
\(223\) | 13.2702 | 0.888639 | 0.444320 | − | 0.895868i | \(-0.353446\pi\) | ||||
0.444320 | + | 0.895868i | \(0.353446\pi\) | |||||||
\(224\) | −4.34649 | −0.290412 | ||||||||
\(225\) | 0.303053 | 0.0202036 | ||||||||
\(226\) | −4.24731 | −0.282527 | ||||||||
\(227\) | 18.2184 | 1.20920 | 0.604599 | − | 0.796530i | \(-0.293333\pi\) | ||||
0.604599 | + | 0.796530i | \(0.293333\pi\) | |||||||
\(228\) | 2.38799 | 0.158149 | ||||||||
\(229\) | 5.36759 | 0.354701 | 0.177350 | − | 0.984148i | \(-0.443247\pi\) | ||||
0.177350 | + | 0.984148i | \(0.443247\pi\) | |||||||
\(230\) | 7.06414 | 0.465795 | ||||||||
\(231\) | 22.7608 | 1.49755 | ||||||||
\(232\) | 2.37377 | 0.155845 | ||||||||
\(233\) | 3.10684 | 0.203536 | 0.101768 | − | 0.994808i | \(-0.467550\pi\) | ||||
0.101768 | + | 0.994808i | \(0.467550\pi\) | |||||||
\(234\) | −0.272483 | −0.0178128 | ||||||||
\(235\) | 11.9761 | 0.781232 | ||||||||
\(236\) | −1.43766 | −0.0935839 | ||||||||
\(237\) | −3.86150 | −0.250831 | ||||||||
\(238\) | −31.2788 | −2.02751 | ||||||||
\(239\) | −25.1587 | −1.62738 | −0.813691 | − | 0.581298i | \(-0.802545\pi\) | ||||
−0.813691 | + | 0.581298i | \(0.802545\pi\) | |||||||
\(240\) | −3.08229 | −0.198961 | ||||||||
\(241\) | −3.12108 | −0.201046 | −0.100523 | − | 0.994935i | \(-0.532052\pi\) | ||||
−0.100523 | + | 0.994935i | \(0.532052\pi\) | |||||||
\(242\) | 1.25266 | 0.0805243 | ||||||||
\(243\) | −1.93765 | −0.124300 | ||||||||
\(244\) | 11.7254 | 0.750643 | ||||||||
\(245\) | 21.8535 | 1.39617 | ||||||||
\(246\) | 8.16412 | 0.520525 | ||||||||
\(247\) | 2.07758 | 0.132193 | ||||||||
\(248\) | 9.37454 | 0.595284 | ||||||||
\(249\) | −5.15071 | −0.326413 | ||||||||
\(250\) | 12.1708 | 0.769751 | ||||||||
\(251\) | 10.5090 | 0.663324 | 0.331662 | − | 0.943398i | \(-0.392391\pi\) | ||||
0.331662 | + | 0.943398i | \(0.392391\pi\) | |||||||
\(252\) | −0.811609 | −0.0511266 | ||||||||
\(253\) | 12.0015 | 0.754526 | ||||||||
\(254\) | −12.3152 | −0.772727 | ||||||||
\(255\) | −22.1812 | −1.38904 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.06010 | 0.565154 | 0.282577 | − | 0.959245i | \(-0.408811\pi\) | ||||
0.282577 | + | 0.959245i | \(0.408811\pi\) | |||||||
\(258\) | 1.23537 | 0.0769107 | ||||||||
\(259\) | 13.1332 | 0.816055 | ||||||||
\(260\) | −2.68163 | −0.166308 | ||||||||
\(261\) | 0.443247 | 0.0274363 | ||||||||
\(262\) | 3.54201 | 0.218826 | ||||||||
\(263\) | 5.18207 | 0.319540 | 0.159770 | − | 0.987154i | \(-0.448925\pi\) | ||||
0.159770 | + | 0.987154i | \(0.448925\pi\) | |||||||
\(264\) | −5.23659 | −0.322290 | ||||||||
\(265\) | 19.0513 | 1.17031 | ||||||||
\(266\) | 6.18821 | 0.379424 | ||||||||
\(267\) | −1.68567 | −0.103161 | ||||||||
\(268\) | 13.3564 | 0.815871 | ||||||||
\(269\) | 28.2615 | 1.72313 | 0.861567 | − | 0.507644i | \(-0.169483\pi\) | ||||
0.861567 | + | 0.507644i | \(0.169483\pi\) | |||||||
\(270\) | −9.82241 | −0.597773 | ||||||||
\(271\) | −14.5932 | −0.886474 | −0.443237 | − | 0.896404i | \(-0.646170\pi\) | ||||
−0.443237 | + | 0.896404i | \(0.646170\pi\) | |||||||
\(272\) | 7.19635 | 0.436343 | ||||||||
\(273\) | 10.6384 | 0.643865 | ||||||||
\(274\) | 15.8198 | 0.955709 | ||||||||
\(275\) | 5.06703 | 0.305554 | ||||||||
\(276\) | 6.44759 | 0.388099 | ||||||||
\(277\) | −2.58668 | −0.155418 | −0.0777092 | − | 0.996976i | \(-0.524761\pi\) | ||||
−0.0777092 | + | 0.996976i | \(0.524761\pi\) | |||||||
\(278\) | 7.38172 | 0.442726 | ||||||||
\(279\) | 1.75048 | 0.104799 | ||||||||
\(280\) | −7.98741 | −0.477339 | ||||||||
\(281\) | 26.4215 | 1.57617 | 0.788086 | − | 0.615565i | \(-0.211072\pi\) | ||||
0.788086 | + | 0.615565i | \(0.211072\pi\) | |||||||
\(282\) | 10.9308 | 0.650920 | ||||||||
\(283\) | −31.4457 | −1.86925 | −0.934626 | − | 0.355633i | \(-0.884265\pi\) | ||||
−0.934626 | + | 0.355633i | \(0.884265\pi\) | |||||||
\(284\) | −4.30326 | −0.255352 | ||||||||
\(285\) | 4.38834 | 0.259943 | ||||||||
\(286\) | −4.55590 | −0.269396 | ||||||||
\(287\) | 21.1564 | 1.24882 | ||||||||
\(288\) | 0.186728 | 0.0110030 | ||||||||
\(289\) | 34.7875 | 2.04632 | ||||||||
\(290\) | 4.36220 | 0.256157 | ||||||||
\(291\) | −3.42648 | −0.200864 | ||||||||
\(292\) | −0.705872 | −0.0413080 | ||||||||
\(293\) | 11.6519 | 0.680710 | 0.340355 | − | 0.940297i | \(-0.389453\pi\) | ||||
0.340355 | + | 0.940297i | \(0.389453\pi\) | |||||||
\(294\) | 19.9462 | 1.16328 | ||||||||
\(295\) | −2.64195 | −0.153820 | ||||||||
\(296\) | −3.02156 | −0.175624 | ||||||||
\(297\) | −16.6876 | −0.968313 | ||||||||
\(298\) | −12.4129 | −0.719059 | ||||||||
\(299\) | 5.60949 | 0.324405 | ||||||||
\(300\) | 2.72218 | 0.157165 | ||||||||
\(301\) | 3.20132 | 0.184521 | ||||||||
\(302\) | −12.7569 | −0.734079 | ||||||||
\(303\) | −2.20391 | −0.126612 | ||||||||
\(304\) | −1.42373 | −0.0816563 | ||||||||
\(305\) | 21.5474 | 1.23380 | ||||||||
\(306\) | 1.34376 | 0.0768175 | ||||||||
\(307\) | 4.32158 | 0.246646 | 0.123323 | − | 0.992367i | \(-0.460645\pi\) | ||||
0.123323 | + | 0.992367i | \(0.460645\pi\) | |||||||
\(308\) | −13.5701 | −0.773225 | ||||||||
\(309\) | 17.8659 | 1.01636 | ||||||||
\(310\) | 17.2273 | 0.978445 | ||||||||
\(311\) | 7.17597 | 0.406912 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(312\) | −2.44758 | −0.138567 | ||||||||
\(313\) | 30.1467 | 1.70399 | 0.851997 | − | 0.523547i | \(-0.175392\pi\) | ||||
0.851997 | + | 0.523547i | \(0.175392\pi\) | |||||||
\(314\) | −3.67743 | −0.207530 | ||||||||
\(315\) | −1.49147 | −0.0840348 | ||||||||
\(316\) | 2.30224 | 0.129511 | ||||||||
\(317\) | 19.4532 | 1.09260 | 0.546301 | − | 0.837589i | \(-0.316036\pi\) | ||||
0.546301 | + | 0.837589i | \(0.316036\pi\) | |||||||
\(318\) | 17.3886 | 0.975103 | ||||||||
\(319\) | 7.41107 | 0.414940 | ||||||||
\(320\) | 1.83767 | 0.102729 | ||||||||
\(321\) | −23.2915 | −1.30000 | ||||||||
\(322\) | 16.7082 | 0.931113 | ||||||||
\(323\) | −10.2456 | −0.570083 | ||||||||
\(324\) | −8.40495 | −0.466942 | ||||||||
\(325\) | 2.36833 | 0.131371 | ||||||||
\(326\) | 16.4579 | 0.911521 | ||||||||
\(327\) | 14.6546 | 0.810401 | ||||||||
\(328\) | −4.86747 | −0.268761 | ||||||||
\(329\) | 28.3260 | 1.56166 | ||||||||
\(330\) | −9.62313 | −0.529736 | ||||||||
\(331\) | −5.69857 | −0.313222 | −0.156611 | − | 0.987660i | \(-0.550057\pi\) | ||||
−0.156611 | + | 0.987660i | \(0.550057\pi\) | |||||||
\(332\) | 3.07087 | 0.168536 | ||||||||
\(333\) | −0.564208 | −0.0309184 | ||||||||
\(334\) | −15.8349 | −0.866450 | ||||||||
\(335\) | 24.5446 | 1.34102 | ||||||||
\(336\) | −7.29028 | −0.397718 | ||||||||
\(337\) | 19.6853 | 1.07233 | 0.536163 | − | 0.844115i | \(-0.319873\pi\) | ||||
0.536163 | + | 0.844115i | \(0.319873\pi\) | |||||||
\(338\) | 10.8706 | 0.591281 | ||||||||
\(339\) | −7.12393 | −0.386919 | ||||||||
\(340\) | 13.2245 | 0.717200 | ||||||||
\(341\) | 29.2680 | 1.58495 | ||||||||
\(342\) | −0.265849 | −0.0143755 | ||||||||
\(343\) | 21.2628 | 1.14809 | ||||||||
\(344\) | −0.736530 | −0.0397110 | ||||||||
\(345\) | 11.8485 | 0.637904 | ||||||||
\(346\) | −23.6349 | −1.27062 | ||||||||
\(347\) | 3.33574 | 0.179072 | 0.0895360 | − | 0.995984i | \(-0.471462\pi\) | ||||
0.0895360 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(348\) | 3.98147 | 0.213429 | ||||||||
\(349\) | 27.9614 | 1.49674 | 0.748370 | − | 0.663282i | \(-0.230837\pi\) | ||||
0.748370 | + | 0.663282i | \(0.230837\pi\) | |||||||
\(350\) | 7.05422 | 0.377064 | ||||||||
\(351\) | −7.79978 | −0.416321 | ||||||||
\(352\) | 3.12207 | 0.166407 | ||||||||
\(353\) | −8.89445 | −0.473404 | −0.236702 | − | 0.971582i | \(-0.576066\pi\) | ||||
−0.236702 | + | 0.971582i | \(0.576066\pi\) | |||||||
\(354\) | −2.41136 | −0.128163 | ||||||||
\(355\) | −7.90797 | −0.419712 | ||||||||
\(356\) | 1.00500 | 0.0532650 | ||||||||
\(357\) | −52.4634 | −2.77666 | ||||||||
\(358\) | −22.0369 | −1.16469 | ||||||||
\(359\) | −3.62239 | −0.191182 | −0.0955911 | − | 0.995421i | \(-0.530474\pi\) | ||||
−0.0955911 | + | 0.995421i | \(0.530474\pi\) | |||||||
\(360\) | 0.343143 | 0.0180853 | ||||||||
\(361\) | −16.9730 | −0.893316 | ||||||||
\(362\) | 17.3531 | 0.912056 | ||||||||
\(363\) | 2.10107 | 0.110278 | ||||||||
\(364\) | −6.34264 | −0.332445 | ||||||||
\(365\) | −1.29716 | −0.0678964 | ||||||||
\(366\) | 19.6668 | 1.02800 | ||||||||
\(367\) | −15.4468 | −0.806318 | −0.403159 | − | 0.915130i | \(-0.632088\pi\) | ||||
−0.403159 | + | 0.915130i | \(0.632088\pi\) | |||||||
\(368\) | −3.84407 | −0.200386 | ||||||||
\(369\) | −0.908891 | −0.0473150 | ||||||||
\(370\) | −5.55262 | −0.288667 | ||||||||
\(371\) | 45.0606 | 2.33943 | ||||||||
\(372\) | 15.7237 | 0.815238 | ||||||||
\(373\) | 36.8227 | 1.90661 | 0.953304 | − | 0.302012i | \(-0.0976583\pi\) | ||||
0.953304 | + | 0.302012i | \(0.0976583\pi\) | |||||||
\(374\) | 22.4675 | 1.16177 | ||||||||
\(375\) | 20.4139 | 1.05417 | ||||||||
\(376\) | −6.51698 | −0.336088 | ||||||||
\(377\) | 3.46393 | 0.178402 | ||||||||
\(378\) | −23.2321 | −1.19493 | ||||||||
\(379\) | 27.4556 | 1.41030 | 0.705149 | − | 0.709059i | \(-0.250880\pi\) | ||||
0.705149 | + | 0.709059i | \(0.250880\pi\) | |||||||
\(380\) | −2.61634 | −0.134215 | ||||||||
\(381\) | −20.6561 | −1.05825 | ||||||||
\(382\) | 9.73826 | 0.498253 | ||||||||
\(383\) | −35.4972 | −1.81382 | −0.906910 | − | 0.421325i | \(-0.861565\pi\) | ||||
−0.906910 | + | 0.421325i | \(0.861565\pi\) | |||||||
\(384\) | 1.67728 | 0.0855934 | ||||||||
\(385\) | −24.9373 | −1.27092 | ||||||||
\(386\) | −4.54525 | −0.231347 | ||||||||
\(387\) | −0.137530 | −0.00699107 | ||||||||
\(388\) | 2.04288 | 0.103711 | ||||||||
\(389\) | 18.8076 | 0.953581 | 0.476790 | − | 0.879017i | \(-0.341800\pi\) | ||||
0.476790 | + | 0.879017i | \(0.341800\pi\) | |||||||
\(390\) | −4.49785 | −0.227757 | ||||||||
\(391\) | −27.6633 | −1.39899 | ||||||||
\(392\) | −11.8920 | −0.600635 | ||||||||
\(393\) | 5.94095 | 0.299681 | ||||||||
\(394\) | −5.21493 | −0.262724 | ||||||||
\(395\) | 4.23075 | 0.212872 | ||||||||
\(396\) | 0.582977 | 0.0292957 | ||||||||
\(397\) | −3.51960 | −0.176644 | −0.0883219 | − | 0.996092i | \(-0.528150\pi\) | ||||
−0.0883219 | + | 0.996092i | \(0.528150\pi\) | |||||||
\(398\) | 4.15238 | 0.208140 | ||||||||
\(399\) | 10.3794 | 0.519619 | ||||||||
\(400\) | −1.62297 | −0.0811485 | ||||||||
\(401\) | −22.0266 | −1.09996 | −0.549978 | − | 0.835179i | \(-0.685364\pi\) | ||||
−0.549978 | + | 0.835179i | \(0.685364\pi\) | |||||||
\(402\) | 22.4024 | 1.11733 | ||||||||
\(403\) | 13.6798 | 0.681442 | ||||||||
\(404\) | 1.31398 | 0.0653729 | ||||||||
\(405\) | −15.4455 | −0.767494 | ||||||||
\(406\) | 10.3175 | 0.512051 | ||||||||
\(407\) | −9.43352 | −0.467602 | ||||||||
\(408\) | 12.0703 | 0.597569 | ||||||||
\(409\) | −10.1073 | −0.499774 | −0.249887 | − | 0.968275i | \(-0.580393\pi\) | ||||
−0.249887 | + | 0.968275i | \(0.580393\pi\) | |||||||
\(410\) | −8.94480 | −0.441752 | ||||||||
\(411\) | 26.5342 | 1.30884 | ||||||||
\(412\) | −10.6517 | −0.524773 | ||||||||
\(413\) | −6.24878 | −0.307483 | ||||||||
\(414\) | −0.717794 | −0.0352777 | ||||||||
\(415\) | 5.64325 | 0.277016 | ||||||||
\(416\) | 1.45926 | 0.0715459 | ||||||||
\(417\) | 12.3812 | 0.606311 | ||||||||
\(418\) | −4.44498 | −0.217411 | ||||||||
\(419\) | −21.2937 | −1.04026 | −0.520132 | − | 0.854086i | \(-0.674117\pi\) | ||||
−0.520132 | + | 0.854086i | \(0.674117\pi\) | |||||||
\(420\) | −13.3971 | −0.653713 | ||||||||
\(421\) | 21.9547 | 1.07001 | 0.535003 | − | 0.844850i | \(-0.320310\pi\) | ||||
0.535003 | + | 0.844850i | \(0.320310\pi\) | |||||||
\(422\) | −3.90589 | −0.190136 | ||||||||
\(423\) | −1.21690 | −0.0591677 | ||||||||
\(424\) | −10.3671 | −0.503472 | ||||||||
\(425\) | −11.6795 | −0.566537 | ||||||||
\(426\) | −7.21778 | −0.349703 | ||||||||
\(427\) | 50.9644 | 2.46634 | ||||||||
\(428\) | 13.8864 | 0.671226 | ||||||||
\(429\) | −7.64153 | −0.368937 | ||||||||
\(430\) | −1.35350 | −0.0652715 | ||||||||
\(431\) | 23.0292 | 1.10928 | 0.554639 | − | 0.832091i | \(-0.312856\pi\) | ||||
0.554639 | + | 0.832091i | \(0.312856\pi\) | |||||||
\(432\) | 5.34504 | 0.257163 | ||||||||
\(433\) | −35.0000 | −1.68199 | −0.840995 | − | 0.541042i | \(-0.818030\pi\) | ||||
−0.840995 | + | 0.541042i | \(0.818030\pi\) | |||||||
\(434\) | 40.7463 | 1.95589 | ||||||||
\(435\) | 7.31663 | 0.350806 | ||||||||
\(436\) | −8.73711 | −0.418432 | ||||||||
\(437\) | 5.47291 | 0.261805 | ||||||||
\(438\) | −1.18395 | −0.0565711 | ||||||||
\(439\) | 2.60724 | 0.124437 | 0.0622185 | − | 0.998063i | \(-0.480182\pi\) | ||||
0.0622185 | + | 0.998063i | \(0.480182\pi\) | |||||||
\(440\) | 5.73734 | 0.273517 | ||||||||
\(441\) | −2.22056 | −0.105741 | ||||||||
\(442\) | 10.5013 | 0.499497 | ||||||||
\(443\) | 1.00138 | 0.0475772 | 0.0237886 | − | 0.999717i | \(-0.492427\pi\) | ||||
0.0237886 | + | 0.999717i | \(0.492427\pi\) | |||||||
\(444\) | −5.06800 | −0.240517 | ||||||||
\(445\) | 1.84686 | 0.0875497 | ||||||||
\(446\) | −13.2702 | −0.628363 | ||||||||
\(447\) | −20.8199 | −0.984747 | ||||||||
\(448\) | 4.34649 | 0.205352 | ||||||||
\(449\) | −6.14747 | −0.290117 | −0.145059 | − | 0.989423i | \(-0.546337\pi\) | ||||
−0.145059 | + | 0.989423i | \(0.546337\pi\) | |||||||
\(450\) | −0.303053 | −0.0142861 | ||||||||
\(451\) | −15.1966 | −0.715580 | ||||||||
\(452\) | 4.24731 | 0.199776 | ||||||||
\(453\) | −21.3970 | −1.00532 | ||||||||
\(454\) | −18.2184 | −0.855032 | ||||||||
\(455\) | −11.6557 | −0.546426 | ||||||||
\(456\) | −2.38799 | −0.111828 | ||||||||
\(457\) | 41.1661 | 1.92567 | 0.962835 | − | 0.270090i | \(-0.0870535\pi\) | ||||
0.962835 | + | 0.270090i | \(0.0870535\pi\) | |||||||
\(458\) | −5.36759 | −0.250811 | ||||||||
\(459\) | 38.4648 | 1.79538 | ||||||||
\(460\) | −7.06414 | −0.329367 | ||||||||
\(461\) | 13.8367 | 0.644438 | 0.322219 | − | 0.946665i | \(-0.395571\pi\) | ||||
0.322219 | + | 0.946665i | \(0.395571\pi\) | |||||||
\(462\) | −22.7608 | −1.05893 | ||||||||
\(463\) | −29.6863 | −1.37964 | −0.689820 | − | 0.723980i | \(-0.742311\pi\) | ||||
−0.689820 | + | 0.723980i | \(0.742311\pi\) | |||||||
\(464\) | −2.37377 | −0.110199 | ||||||||
\(465\) | 28.8950 | 1.33997 | ||||||||
\(466\) | −3.10684 | −0.143922 | ||||||||
\(467\) | 3.39795 | 0.157238 | 0.0786192 | − | 0.996905i | \(-0.474949\pi\) | ||||
0.0786192 | + | 0.996905i | \(0.474949\pi\) | |||||||
\(468\) | 0.272483 | 0.0125955 | ||||||||
\(469\) | 58.0533 | 2.68065 | ||||||||
\(470\) | −11.9761 | −0.552414 | ||||||||
\(471\) | −6.16809 | −0.284211 | ||||||||
\(472\) | 1.43766 | 0.0661738 | ||||||||
\(473\) | −2.29950 | −0.105731 | ||||||||
\(474\) | 3.86150 | 0.177365 | ||||||||
\(475\) | 2.31067 | 0.106021 | ||||||||
\(476\) | 31.2788 | 1.43366 | ||||||||
\(477\) | −1.93583 | −0.0886354 | ||||||||
\(478\) | 25.1587 | 1.15073 | ||||||||
\(479\) | 7.60708 | 0.347576 | 0.173788 | − | 0.984783i | \(-0.444399\pi\) | ||||
0.173788 | + | 0.984783i | \(0.444399\pi\) | |||||||
\(480\) | 3.08229 | 0.140687 | ||||||||
\(481\) | −4.40922 | −0.201043 | ||||||||
\(482\) | 3.12108 | 0.142161 | ||||||||
\(483\) | 28.0244 | 1.27515 | ||||||||
\(484\) | −1.25266 | −0.0569393 | ||||||||
\(485\) | 3.75413 | 0.170466 | ||||||||
\(486\) | 1.93765 | 0.0878936 | ||||||||
\(487\) | −19.9468 | −0.903874 | −0.451937 | − | 0.892050i | \(-0.649267\pi\) | ||||
−0.451937 | + | 0.892050i | \(0.649267\pi\) | |||||||
\(488\) | −11.7254 | −0.530785 | ||||||||
\(489\) | 27.6046 | 1.24832 | ||||||||
\(490\) | −21.8535 | −0.987240 | ||||||||
\(491\) | −30.5819 | −1.38014 | −0.690072 | − | 0.723741i | \(-0.742421\pi\) | ||||
−0.690072 | + | 0.723741i | \(0.742421\pi\) | |||||||
\(492\) | −8.16412 | −0.368067 | ||||||||
\(493\) | −17.0824 | −0.769355 | ||||||||
\(494\) | −2.07758 | −0.0934748 | ||||||||
\(495\) | 1.07132 | 0.0481522 | ||||||||
\(496\) | −9.37454 | −0.420929 | ||||||||
\(497\) | −18.7041 | −0.838992 | ||||||||
\(498\) | 5.15071 | 0.230809 | ||||||||
\(499\) | 6.35824 | 0.284634 | 0.142317 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142317 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(500\) | −12.1708 | −0.544296 | ||||||||
\(501\) | −26.5597 | −1.18660 | ||||||||
\(502\) | −10.5090 | −0.469041 | ||||||||
\(503\) | −17.8518 | −0.795974 | −0.397987 | − | 0.917391i | \(-0.630291\pi\) | ||||
−0.397987 | + | 0.917391i | \(0.630291\pi\) | |||||||
\(504\) | 0.811609 | 0.0361519 | ||||||||
\(505\) | 2.41466 | 0.107451 | ||||||||
\(506\) | −12.0015 | −0.533531 | ||||||||
\(507\) | 18.2330 | 0.809756 | ||||||||
\(508\) | 12.3152 | 0.546401 | ||||||||
\(509\) | 0.228865 | 0.0101442 | 0.00507212 | − | 0.999987i | \(-0.498385\pi\) | ||||
0.00507212 | + | 0.999987i | \(0.498385\pi\) | |||||||
\(510\) | 22.1812 | 0.982201 | ||||||||
\(511\) | −3.06806 | −0.135723 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.60988 | −0.335984 | ||||||||
\(514\) | −9.06010 | −0.399624 | ||||||||
\(515\) | −19.5743 | −0.862549 | ||||||||
\(516\) | −1.23537 | −0.0543840 | ||||||||
\(517\) | −20.3465 | −0.894837 | ||||||||
\(518\) | −13.1332 | −0.577038 | ||||||||
\(519\) | −39.6423 | −1.74010 | ||||||||
\(520\) | 2.68163 | 0.117597 | ||||||||
\(521\) | 9.84109 | 0.431146 | 0.215573 | − | 0.976488i | \(-0.430838\pi\) | ||||
0.215573 | + | 0.976488i | \(0.430838\pi\) | |||||||
\(522\) | −0.443247 | −0.0194004 | ||||||||
\(523\) | 24.5350 | 1.07284 | 0.536421 | − | 0.843951i | \(-0.319776\pi\) | ||||
0.536421 | + | 0.843951i | \(0.319776\pi\) | |||||||
\(524\) | −3.54201 | −0.154733 | ||||||||
\(525\) | 11.8319 | 0.516387 | ||||||||
\(526\) | −5.18207 | −0.225949 | ||||||||
\(527\) | −67.4625 | −2.93871 | ||||||||
\(528\) | 5.23659 | 0.227893 | ||||||||
\(529\) | −8.22310 | −0.357526 | ||||||||
\(530\) | −19.0513 | −0.827538 | ||||||||
\(531\) | 0.268451 | 0.0116498 | ||||||||
\(532\) | −6.18821 | −0.268293 | ||||||||
\(533\) | −7.10289 | −0.307660 | ||||||||
\(534\) | 1.68567 | 0.0729461 | ||||||||
\(535\) | 25.5187 | 1.10327 | ||||||||
\(536\) | −13.3564 | −0.576908 | ||||||||
\(537\) | −36.9621 | −1.59503 | ||||||||
\(538\) | −28.2615 | −1.21844 | ||||||||
\(539\) | −37.1276 | −1.59920 | ||||||||
\(540\) | 9.82241 | 0.422689 | ||||||||
\(541\) | −26.6316 | −1.14498 | −0.572490 | − | 0.819911i | \(-0.694023\pi\) | ||||
−0.572490 | + | 0.819911i | \(0.694023\pi\) | |||||||
\(542\) | 14.5932 | 0.626832 | ||||||||
\(543\) | 29.1060 | 1.24906 | ||||||||
\(544\) | −7.19635 | −0.308541 | ||||||||
\(545\) | −16.0559 | −0.687760 | ||||||||
\(546\) | −10.6384 | −0.455281 | ||||||||
\(547\) | −32.0583 | −1.37071 | −0.685356 | − | 0.728208i | \(-0.740354\pi\) | ||||
−0.685356 | + | 0.728208i | \(0.740354\pi\) | |||||||
\(548\) | −15.8198 | −0.675788 | ||||||||
\(549\) | −2.18946 | −0.0934438 | ||||||||
\(550\) | −5.06703 | −0.216059 | ||||||||
\(551\) | 3.37959 | 0.143976 | ||||||||
\(552\) | −6.44759 | −0.274428 | ||||||||
\(553\) | 10.0066 | 0.425526 | ||||||||
\(554\) | 2.58668 | 0.109897 | ||||||||
\(555\) | −9.31331 | −0.395328 | ||||||||
\(556\) | −7.38172 | −0.313055 | ||||||||
\(557\) | 4.65383 | 0.197189 | 0.0985946 | − | 0.995128i | \(-0.468565\pi\) | ||||
0.0985946 | + | 0.995128i | \(0.468565\pi\) | |||||||
\(558\) | −1.75048 | −0.0741039 | ||||||||
\(559\) | −1.07479 | −0.0454586 | ||||||||
\(560\) | 7.98741 | 0.337530 | ||||||||
\(561\) | 37.6844 | 1.59103 | ||||||||
\(562\) | −26.4215 | −1.11452 | ||||||||
\(563\) | −31.4027 | −1.32347 | −0.661734 | − | 0.749739i | \(-0.730179\pi\) | ||||
−0.661734 | + | 0.749739i | \(0.730179\pi\) | |||||||
\(564\) | −10.9308 | −0.460270 | ||||||||
\(565\) | 7.80514 | 0.328365 | ||||||||
\(566\) | 31.4457 | 1.32176 | ||||||||
\(567\) | −36.5320 | −1.53420 | ||||||||
\(568\) | 4.30326 | 0.180561 | ||||||||
\(569\) | −10.8116 | −0.453247 | −0.226624 | − | 0.973982i | \(-0.572769\pi\) | ||||
−0.226624 | + | 0.973982i | \(0.572769\pi\) | |||||||
\(570\) | −4.38834 | −0.183807 | ||||||||
\(571\) | 20.3541 | 0.851793 | 0.425897 | − | 0.904772i | \(-0.359959\pi\) | ||||
0.425897 | + | 0.904772i | \(0.359959\pi\) | |||||||
\(572\) | 4.55590 | 0.190492 | ||||||||
\(573\) | 16.3338 | 0.682355 | ||||||||
\(574\) | −21.1564 | −0.883051 | ||||||||
\(575\) | 6.23882 | 0.260177 | ||||||||
\(576\) | −0.186728 | −0.00778031 | ||||||||
\(577\) | 3.85462 | 0.160470 | 0.0802350 | − | 0.996776i | \(-0.474433\pi\) | ||||
0.0802350 | + | 0.996776i | \(0.474433\pi\) | |||||||
\(578\) | −34.7875 | −1.44697 | ||||||||
\(579\) | −7.62366 | −0.316829 | ||||||||
\(580\) | −4.36220 | −0.181130 | ||||||||
\(581\) | 13.3475 | 0.553748 | ||||||||
\(582\) | 3.42648 | 0.142032 | ||||||||
\(583\) | −32.3669 | −1.34050 | ||||||||
\(584\) | 0.705872 | 0.0292092 | ||||||||
\(585\) | 0.500734 | 0.0207028 | ||||||||
\(586\) | −11.6519 | −0.481334 | ||||||||
\(587\) | −44.6604 | −1.84333 | −0.921666 | − | 0.387985i | \(-0.873171\pi\) | ||||
−0.921666 | + | 0.387985i | \(0.873171\pi\) | |||||||
\(588\) | −19.9462 | −0.822566 | ||||||||
\(589\) | 13.3468 | 0.549945 | ||||||||
\(590\) | 2.64195 | 0.108767 | ||||||||
\(591\) | −8.74690 | −0.359799 | ||||||||
\(592\) | 3.02156 | 0.124185 | ||||||||
\(593\) | −14.3581 | −0.589616 | −0.294808 | − | 0.955557i | \(-0.595256\pi\) | ||||
−0.294808 | + | 0.955557i | \(0.595256\pi\) | |||||||
\(594\) | 16.6876 | 0.684700 | ||||||||
\(595\) | 57.4802 | 2.35646 | ||||||||
\(596\) | 12.4129 | 0.508451 | ||||||||
\(597\) | 6.96472 | 0.285047 | ||||||||
\(598\) | −5.60949 | −0.229389 | ||||||||
\(599\) | 13.1241 | 0.536238 | 0.268119 | − | 0.963386i | \(-0.413598\pi\) | ||||
0.268119 | + | 0.963386i | \(0.413598\pi\) | |||||||
\(600\) | −2.72218 | −0.111132 | ||||||||
\(601\) | −41.0911 | −1.67614 | −0.838071 | − | 0.545561i | \(-0.816317\pi\) | ||||
−0.838071 | + | 0.545561i | \(0.816317\pi\) | |||||||
\(602\) | −3.20132 | −0.130476 | ||||||||
\(603\) | −2.49400 | −0.101564 | ||||||||
\(604\) | 12.7569 | 0.519072 | ||||||||
\(605\) | −2.30198 | −0.0935889 | ||||||||
\(606\) | 2.20391 | 0.0895279 | ||||||||
\(607\) | −30.1460 | −1.22359 | −0.611793 | − | 0.791018i | \(-0.709552\pi\) | ||||
−0.611793 | + | 0.791018i | \(0.709552\pi\) | |||||||
\(608\) | 1.42373 | 0.0577398 | ||||||||
\(609\) | 17.3054 | 0.701251 | ||||||||
\(610\) | −21.5474 | −0.872430 | ||||||||
\(611\) | −9.50994 | −0.384731 | ||||||||
\(612\) | −1.34376 | −0.0543181 | ||||||||
\(613\) | 21.9736 | 0.887506 | 0.443753 | − | 0.896149i | \(-0.353647\pi\) | ||||
0.443753 | + | 0.896149i | \(0.353647\pi\) | |||||||
\(614\) | −4.32158 | −0.174405 | ||||||||
\(615\) | −15.0030 | −0.604977 | ||||||||
\(616\) | 13.5701 | 0.546753 | ||||||||
\(617\) | 41.8499 | 1.68481 | 0.842406 | − | 0.538843i | \(-0.181138\pi\) | ||||
0.842406 | + | 0.538843i | \(0.181138\pi\) | |||||||
\(618\) | −17.8659 | −0.718673 | ||||||||
\(619\) | 25.3005 | 1.01691 | 0.508457 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508457 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(620\) | −17.2273 | −0.691865 | ||||||||
\(621\) | −20.5467 | −0.824511 | ||||||||
\(622\) | −7.17597 | −0.287730 | ||||||||
\(623\) | 4.36823 | 0.175009 | ||||||||
\(624\) | 2.44758 | 0.0979817 | ||||||||
\(625\) | −14.2511 | −0.570044 | ||||||||
\(626\) | −30.1467 | −1.20491 | ||||||||
\(627\) | −7.45548 | −0.297743 | ||||||||
\(628\) | 3.67743 | 0.146746 | ||||||||
\(629\) | 21.7442 | 0.866997 | ||||||||
\(630\) | 1.49147 | 0.0594216 | ||||||||
\(631\) | 42.3384 | 1.68546 | 0.842732 | − | 0.538333i | \(-0.180946\pi\) | ||||
0.842732 | + | 0.538333i | \(0.180946\pi\) | |||||||
\(632\) | −2.30224 | −0.0915781 | ||||||||
\(633\) | −6.55128 | −0.260390 | ||||||||
\(634\) | −19.4532 | −0.772586 | ||||||||
\(635\) | 22.6314 | 0.898098 | ||||||||
\(636\) | −17.3886 | −0.689502 | ||||||||
\(637\) | −17.3534 | −0.687567 | ||||||||
\(638\) | −7.41107 | −0.293407 | ||||||||
\(639\) | 0.803537 | 0.0317874 | ||||||||
\(640\) | −1.83767 | −0.0726403 | ||||||||
\(641\) | 24.1514 | 0.953923 | 0.476962 | − | 0.878924i | \(-0.341738\pi\) | ||||
0.476962 | + | 0.878924i | \(0.341738\pi\) | |||||||
\(642\) | 23.2915 | 0.919240 | ||||||||
\(643\) | 23.3124 | 0.919350 | 0.459675 | − | 0.888087i | \(-0.347966\pi\) | ||||
0.459675 | + | 0.888087i | \(0.347966\pi\) | |||||||
\(644\) | −16.7082 | −0.658396 | ||||||||
\(645\) | −2.27020 | −0.0893890 | ||||||||
\(646\) | 10.2456 | 0.403109 | ||||||||
\(647\) | −1.24820 | −0.0490720 | −0.0245360 | − | 0.999699i | \(-0.507811\pi\) | ||||
−0.0245360 | + | 0.999699i | \(0.507811\pi\) | |||||||
\(648\) | 8.40495 | 0.330178 | ||||||||
\(649\) | 4.48849 | 0.176188 | ||||||||
\(650\) | −2.36833 | −0.0928935 | ||||||||
\(651\) | 68.3430 | 2.67857 | ||||||||
\(652\) | −16.4579 | −0.644543 | ||||||||
\(653\) | 33.6494 | 1.31680 | 0.658401 | − | 0.752668i | \(-0.271233\pi\) | ||||
0.658401 | + | 0.752668i | \(0.271233\pi\) | |||||||
\(654\) | −14.6546 | −0.573040 | ||||||||
\(655\) | −6.50904 | −0.254329 | ||||||||
\(656\) | 4.86747 | 0.190043 | ||||||||
\(657\) | 0.131806 | 0.00514223 | ||||||||
\(658\) | −28.3260 | −1.10426 | ||||||||
\(659\) | 48.7758 | 1.90004 | 0.950018 | − | 0.312194i | \(-0.101064\pi\) | ||||
0.950018 | + | 0.312194i | \(0.101064\pi\) | |||||||
\(660\) | 9.62313 | 0.374580 | ||||||||
\(661\) | −26.4182 | −1.02755 | −0.513774 | − | 0.857926i | \(-0.671753\pi\) | ||||
−0.513774 | + | 0.857926i | \(0.671753\pi\) | |||||||
\(662\) | 5.69857 | 0.221481 | ||||||||
\(663\) | 17.6137 | 0.684058 | ||||||||
\(664\) | −3.07087 | −0.119173 | ||||||||
\(665\) | −11.3719 | −0.440983 | ||||||||
\(666\) | 0.564208 | 0.0218626 | ||||||||
\(667\) | 9.12493 | 0.353319 | ||||||||
\(668\) | 15.8349 | 0.612672 | ||||||||
\(669\) | −22.2579 | −0.860539 | ||||||||
\(670\) | −24.5446 | −0.948241 | ||||||||
\(671\) | −36.6076 | −1.41322 | ||||||||
\(672\) | 7.29028 | 0.281229 | ||||||||
\(673\) | −28.2232 | −1.08793 | −0.543963 | − | 0.839109i | \(-0.683077\pi\) | ||||
−0.543963 | + | 0.839109i | \(0.683077\pi\) | |||||||
\(674\) | −19.6853 | −0.758249 | ||||||||
\(675\) | −8.67484 | −0.333895 | ||||||||
\(676\) | −10.8706 | −0.418099 | ||||||||
\(677\) | 12.7377 | 0.489548 | 0.244774 | − | 0.969580i | \(-0.421286\pi\) | ||||
0.244774 | + | 0.969580i | \(0.421286\pi\) | |||||||
\(678\) | 7.12393 | 0.273593 | ||||||||
\(679\) | 8.87934 | 0.340758 | ||||||||
\(680\) | −13.2245 | −0.507137 | ||||||||
\(681\) | −30.5574 | −1.17096 | ||||||||
\(682\) | −29.2680 | −1.12073 | ||||||||
\(683\) | 23.7035 | 0.906990 | 0.453495 | − | 0.891259i | \(-0.350177\pi\) | ||||
0.453495 | + | 0.891259i | \(0.350177\pi\) | |||||||
\(684\) | 0.265849 | 0.0101650 | ||||||||
\(685\) | −29.0716 | −1.11077 | ||||||||
\(686\) | −21.2628 | −0.811819 | ||||||||
\(687\) | −9.00297 | −0.343485 | ||||||||
\(688\) | 0.736530 | 0.0280799 | ||||||||
\(689\) | −15.1283 | −0.576342 | ||||||||
\(690\) | −11.8485 | −0.451066 | ||||||||
\(691\) | 30.9708 | 1.17818 | 0.589092 | − | 0.808066i | \(-0.299486\pi\) | ||||
0.589092 | + | 0.808066i | \(0.299486\pi\) | |||||||
\(692\) | 23.6349 | 0.898462 | ||||||||
\(693\) | 2.53390 | 0.0962550 | ||||||||
\(694\) | −3.33574 | −0.126623 | ||||||||
\(695\) | −13.5652 | −0.514556 | ||||||||
\(696\) | −3.98147 | −0.150917 | ||||||||
\(697\) | 35.0280 | 1.32678 | ||||||||
\(698\) | −27.9614 | −1.05835 | ||||||||
\(699\) | −5.21105 | −0.197100 | ||||||||
\(700\) | −7.05422 | −0.266625 | ||||||||
\(701\) | −14.6477 | −0.553235 | −0.276618 | − | 0.960980i | \(-0.589214\pi\) | ||||
−0.276618 | + | 0.960980i | \(0.589214\pi\) | |||||||
\(702\) | 7.79978 | 0.294384 | ||||||||
\(703\) | −4.30187 | −0.162248 | ||||||||
\(704\) | −3.12207 | −0.117668 | ||||||||
\(705\) | −20.0872 | −0.756528 | ||||||||
\(706\) | 8.89445 | 0.334747 | ||||||||
\(707\) | 5.71120 | 0.214792 | ||||||||
\(708\) | 2.41136 | 0.0906246 | ||||||||
\(709\) | −9.08757 | −0.341291 | −0.170645 | − | 0.985333i | \(-0.554585\pi\) | ||||
−0.170645 | + | 0.985333i | \(0.554585\pi\) | |||||||
\(710\) | 7.90797 | 0.296781 | ||||||||
\(711\) | −0.429891 | −0.0161222 | ||||||||
\(712\) | −1.00500 | −0.0376641 | ||||||||
\(713\) | 36.0364 | 1.34957 | ||||||||
\(714\) | 52.4634 | 1.96339 | ||||||||
\(715\) | 8.37224 | 0.313104 | ||||||||
\(716\) | 22.0369 | 0.823558 | ||||||||
\(717\) | 42.1982 | 1.57592 | ||||||||
\(718\) | 3.62239 | 0.135186 | ||||||||
\(719\) | 0.828510 | 0.0308982 | 0.0154491 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154491 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(720\) | −0.343143 | −0.0127882 | ||||||||
\(721\) | −46.2976 | −1.72421 | ||||||||
\(722\) | 16.9730 | 0.631670 | ||||||||
\(723\) | 5.23493 | 0.194689 | ||||||||
\(724\) | −17.3531 | −0.644921 | ||||||||
\(725\) | 3.85255 | 0.143080 | ||||||||
\(726\) | −2.10107 | −0.0779781 | ||||||||
\(727\) | −12.8346 | −0.476008 | −0.238004 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238004 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(728\) | 6.34264 | 0.235074 | ||||||||
\(729\) | 28.4648 | 1.05425 | ||||||||
\(730\) | 1.29716 | 0.0480100 | ||||||||
\(731\) | 5.30033 | 0.196040 | ||||||||
\(732\) | −19.6668 | −0.726907 | ||||||||
\(733\) | −0.216462 | −0.00799520 | −0.00399760 | − | 0.999992i | \(-0.501272\pi\) | ||||
−0.00399760 | + | 0.999992i | \(0.501272\pi\) | |||||||
\(734\) | 15.4468 | 0.570153 | ||||||||
\(735\) | −36.6544 | −1.35202 | ||||||||
\(736\) | 3.84407 | 0.141694 | ||||||||
\(737\) | −41.6996 | −1.53602 | ||||||||
\(738\) | 0.908891 | 0.0334567 | ||||||||
\(739\) | −37.4402 | −1.37726 | −0.688629 | − | 0.725114i | \(-0.741787\pi\) | ||||
−0.688629 | + | 0.725114i | \(0.741787\pi\) | |||||||
\(740\) | 5.55262 | 0.204118 | ||||||||
\(741\) | −3.48469 | −0.128013 | ||||||||
\(742\) | −45.0606 | −1.65423 | ||||||||
\(743\) | 10.2539 | 0.376180 | 0.188090 | − | 0.982152i | \(-0.439770\pi\) | ||||
0.188090 | + | 0.982152i | \(0.439770\pi\) | |||||||
\(744\) | −15.7237 | −0.576460 | ||||||||
\(745\) | 22.8108 | 0.835722 | ||||||||
\(746\) | −36.8227 | −1.34818 | ||||||||
\(747\) | −0.573416 | −0.0209802 | ||||||||
\(748\) | −22.4675 | −0.821494 | ||||||||
\(749\) | 60.3572 | 2.20540 | ||||||||
\(750\) | −20.4139 | −0.745411 | ||||||||
\(751\) | −12.9672 | −0.473182 | −0.236591 | − | 0.971609i | \(-0.576030\pi\) | ||||
−0.236591 | + | 0.971609i | \(0.576030\pi\) | |||||||
\(752\) | 6.51698 | 0.237650 | ||||||||
\(753\) | −17.6266 | −0.642349 | ||||||||
\(754\) | −3.46393 | −0.126149 | ||||||||
\(755\) | 23.4430 | 0.853179 | ||||||||
\(756\) | 23.2321 | 0.844945 | ||||||||
\(757\) | 8.66530 | 0.314946 | 0.157473 | − | 0.987523i | \(-0.449665\pi\) | ||||
0.157473 | + | 0.987523i | \(0.449665\pi\) | |||||||
\(758\) | −27.4556 | −0.997232 | ||||||||
\(759\) | −20.1298 | −0.730667 | ||||||||
\(760\) | 2.61634 | 0.0949046 | ||||||||
\(761\) | 29.0039 | 1.05139 | 0.525695 | − | 0.850673i | \(-0.323805\pi\) | ||||
0.525695 | + | 0.850673i | \(0.323805\pi\) | |||||||
\(762\) | 20.6561 | 0.748293 | ||||||||
\(763\) | −37.9757 | −1.37481 | ||||||||
\(764\) | −9.73826 | −0.352318 | ||||||||
\(765\) | −2.46938 | −0.0892806 | ||||||||
\(766\) | 35.4972 | 1.28256 | ||||||||
\(767\) | 2.09792 | 0.0757514 | ||||||||
\(768\) | −1.67728 | −0.0605237 | ||||||||
\(769\) | 15.6349 | 0.563809 | 0.281904 | − | 0.959443i | \(-0.409034\pi\) | ||||
0.281904 | + | 0.959443i | \(0.409034\pi\) | |||||||
\(770\) | 24.9373 | 0.898677 | ||||||||
\(771\) | −15.1963 | −0.547283 | ||||||||
\(772\) | 4.54525 | 0.163587 | ||||||||
\(773\) | −28.8921 | −1.03918 | −0.519589 | − | 0.854416i | \(-0.673915\pi\) | ||||
−0.519589 | + | 0.854416i | \(0.673915\pi\) | |||||||
\(774\) | 0.137530 | 0.00494343 | ||||||||
\(775\) | 15.2146 | 0.546525 | ||||||||
\(776\) | −2.04288 | −0.0733350 | ||||||||
\(777\) | −22.0280 | −0.790250 | ||||||||
\(778\) | −18.8076 | −0.674283 | ||||||||
\(779\) | −6.92995 | −0.248291 | ||||||||
\(780\) | 4.49785 | 0.161049 | ||||||||
\(781\) | 13.4351 | 0.480745 | ||||||||
\(782\) | 27.6633 | 0.989238 | ||||||||
\(783\) | −12.6879 | −0.453427 | ||||||||
\(784\) | 11.8920 | 0.424713 | ||||||||
\(785\) | 6.75791 | 0.241200 | ||||||||
\(786\) | −5.94095 | −0.211907 | ||||||||
\(787\) | 41.8647 | 1.49231 | 0.746157 | − | 0.665769i | \(-0.231897\pi\) | ||||
0.746157 | + | 0.665769i | \(0.231897\pi\) | |||||||
\(788\) | 5.21493 | 0.185774 | ||||||||
\(789\) | −8.69180 | −0.309436 | ||||||||
\(790\) | −4.23075 | −0.150523 | ||||||||
\(791\) | 18.4609 | 0.656393 | ||||||||
\(792\) | −0.582977 | −0.0207152 | ||||||||
\(793\) | −17.1104 | −0.607608 | ||||||||
\(794\) | 3.51960 | 0.124906 | ||||||||
\(795\) | −31.9545 | −1.13331 | ||||||||
\(796\) | −4.15238 | −0.147177 | ||||||||
\(797\) | −6.45030 | −0.228481 | −0.114241 | − | 0.993453i | \(-0.536444\pi\) | ||||
−0.114241 | + | 0.993453i | \(0.536444\pi\) | |||||||
\(798\) | −10.3794 | −0.367426 | ||||||||
\(799\) | 46.8985 | 1.65915 | ||||||||
\(800\) | 1.62297 | 0.0573807 | ||||||||
\(801\) | −0.187662 | −0.00663070 | ||||||||
\(802\) | 22.0266 | 0.777786 | ||||||||
\(803\) | 2.20378 | 0.0777698 | ||||||||
\(804\) | −22.4024 | −0.790072 | ||||||||
\(805\) | −30.7042 | −1.08218 | ||||||||
\(806\) | −13.6798 | −0.481852 | ||||||||
\(807\) | −47.4025 | −1.66865 | ||||||||
\(808\) | −1.31398 | −0.0462256 | ||||||||
\(809\) | 2.67478 | 0.0940404 | 0.0470202 | − | 0.998894i | \(-0.485027\pi\) | ||||
0.0470202 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(810\) | 15.4455 | 0.542700 | ||||||||
\(811\) | −4.39196 | −0.154222 | −0.0771112 | − | 0.997022i | \(-0.524570\pi\) | ||||
−0.0771112 | + | 0.997022i | \(0.524570\pi\) | |||||||
\(812\) | −10.3175 | −0.362075 | ||||||||
\(813\) | 24.4769 | 0.858443 | ||||||||
\(814\) | 9.43352 | 0.330645 | ||||||||
\(815\) | −30.2443 | −1.05941 | ||||||||
\(816\) | −12.0703 | −0.422545 | ||||||||
\(817\) | −1.04862 | −0.0366865 | ||||||||
\(818\) | 10.1073 | 0.353393 | ||||||||
\(819\) | 1.18435 | 0.0413844 | ||||||||
\(820\) | 8.94480 | 0.312366 | ||||||||
\(821\) | 56.8577 | 1.98435 | 0.992174 | − | 0.124866i | \(-0.0398500\pi\) | ||||
0.992174 | + | 0.124866i | \(0.0398500\pi\) | |||||||
\(822\) | −26.5342 | −0.925488 | ||||||||
\(823\) | 0.654208 | 0.0228042 | 0.0114021 | − | 0.999935i | \(-0.496371\pi\) | ||||
0.0114021 | + | 0.999935i | \(0.496371\pi\) | |||||||
\(824\) | 10.6517 | 0.371070 | ||||||||
\(825\) | −8.49884 | −0.295892 | ||||||||
\(826\) | 6.24878 | 0.217423 | ||||||||
\(827\) | −43.3740 | −1.50826 | −0.754131 | − | 0.656725i | \(-0.771941\pi\) | ||||
−0.754131 | + | 0.656725i | \(0.771941\pi\) | |||||||
\(828\) | 0.717794 | 0.0249451 | ||||||||
\(829\) | −53.6506 | −1.86336 | −0.931682 | − | 0.363276i | \(-0.881658\pi\) | ||||
−0.931682 | + | 0.363276i | \(0.881658\pi\) | |||||||
\(830\) | −5.64325 | −0.195880 | ||||||||
\(831\) | 4.33859 | 0.150504 | ||||||||
\(832\) | −1.45926 | −0.0505906 | ||||||||
\(833\) | 85.5787 | 2.96513 | ||||||||
\(834\) | −12.3812 | −0.428727 | ||||||||
\(835\) | 29.0994 | 1.00703 | ||||||||
\(836\) | 4.44498 | 0.153733 | ||||||||
\(837\) | −50.1073 | −1.73196 | ||||||||
\(838\) | 21.2937 | 0.735577 | ||||||||
\(839\) | 0.0927105 | 0.00320072 | 0.00160036 | − | 0.999999i | \(-0.499491\pi\) | ||||
0.00160036 | + | 0.999999i | \(0.499491\pi\) | |||||||
\(840\) | 13.3971 | 0.462245 | ||||||||
\(841\) | −23.3652 | −0.805698 | ||||||||
\(842\) | −21.9547 | −0.756609 | ||||||||
\(843\) | −44.3162 | −1.52633 | ||||||||
\(844\) | 3.90589 | 0.134446 | ||||||||
\(845\) | −19.9765 | −0.687213 | ||||||||
\(846\) | 1.21690 | 0.0418379 | ||||||||
\(847\) | −5.44469 | −0.187082 | ||||||||
\(848\) | 10.3671 | 0.356008 | ||||||||
\(849\) | 52.7432 | 1.81014 | ||||||||
\(850\) | 11.6795 | 0.400602 | ||||||||
\(851\) | −11.6151 | −0.398160 | ||||||||
\(852\) | 7.21778 | 0.247277 | ||||||||
\(853\) | −6.21319 | −0.212736 | −0.106368 | − | 0.994327i | \(-0.533922\pi\) | ||||
−0.106368 | + | 0.994327i | \(0.533922\pi\) | |||||||
\(854\) | −50.9644 | −1.74397 | ||||||||
\(855\) | 0.488543 | 0.0167078 | ||||||||
\(856\) | −13.8864 | −0.474629 | ||||||||
\(857\) | 32.6506 | 1.11532 | 0.557662 | − | 0.830068i | \(-0.311698\pi\) | ||||
0.557662 | + | 0.830068i | \(0.311698\pi\) | |||||||
\(858\) | 7.64153 | 0.260878 | ||||||||
\(859\) | −33.1027 | −1.12945 | −0.564725 | − | 0.825279i | \(-0.691018\pi\) | ||||
−0.564725 | + | 0.825279i | \(0.691018\pi\) | |||||||
\(860\) | 1.35350 | 0.0461539 | ||||||||
\(861\) | −35.4852 | −1.20933 | ||||||||
\(862\) | −23.0292 | −0.784378 | ||||||||
\(863\) | 26.7250 | 0.909730 | 0.454865 | − | 0.890561i | \(-0.349688\pi\) | ||||
0.454865 | + | 0.890561i | \(0.349688\pi\) | |||||||
\(864\) | −5.34504 | −0.181842 | ||||||||
\(865\) | 43.4331 | 1.47677 | ||||||||
\(866\) | 35.0000 | 1.18935 | ||||||||
\(867\) | −58.3483 | −1.98161 | ||||||||
\(868\) | −40.7463 | −1.38302 | ||||||||
\(869\) | −7.18775 | −0.243828 | ||||||||
\(870\) | −7.31663 | −0.248057 | ||||||||
\(871\) | −19.4904 | −0.660406 | ||||||||
\(872\) | 8.73711 | 0.295876 | ||||||||
\(873\) | −0.381461 | −0.0129105 | ||||||||
\(874\) | −5.47291 | −0.185124 | ||||||||
\(875\) | −52.9004 | −1.78836 | ||||||||
\(876\) | 1.18395 | 0.0400018 | ||||||||
\(877\) | −32.1216 | −1.08467 | −0.542334 | − | 0.840163i | \(-0.682459\pi\) | ||||
−0.542334 | + | 0.840163i | \(0.682459\pi\) | |||||||
\(878\) | −2.60724 | −0.0879902 | ||||||||
\(879\) | −19.5435 | −0.659185 | ||||||||
\(880\) | −5.73734 | −0.193406 | ||||||||
\(881\) | 42.1131 | 1.41883 | 0.709413 | − | 0.704793i | \(-0.248960\pi\) | ||||
0.709413 | + | 0.704793i | \(0.248960\pi\) | |||||||
\(882\) | 2.22056 | 0.0747700 | ||||||||
\(883\) | −47.8462 | −1.61015 | −0.805077 | − | 0.593171i | \(-0.797876\pi\) | ||||
−0.805077 | + | 0.593171i | \(0.797876\pi\) | |||||||
\(884\) | −10.5013 | −0.353197 | ||||||||
\(885\) | 4.43129 | 0.148956 | ||||||||
\(886\) | −1.00138 | −0.0336421 | ||||||||
\(887\) | 2.52223 | 0.0846881 | 0.0423440 | − | 0.999103i | \(-0.486517\pi\) | ||||
0.0423440 | + | 0.999103i | \(0.486517\pi\) | |||||||
\(888\) | 5.06800 | 0.170071 | ||||||||
\(889\) | 53.5281 | 1.79527 | ||||||||
\(890\) | −1.84686 | −0.0619070 | ||||||||
\(891\) | 26.2409 | 0.879102 | ||||||||
\(892\) | 13.2702 | 0.444320 | ||||||||
\(893\) | −9.27840 | −0.310490 | ||||||||
\(894\) | 20.8199 | 0.696321 | ||||||||
\(895\) | 40.4965 | 1.35365 | ||||||||
\(896\) | −4.34649 | −0.145206 | ||||||||
\(897\) | −9.40869 | −0.314147 | ||||||||
\(898\) | 6.14747 | 0.205144 | ||||||||
\(899\) | 22.2530 | 0.742177 | ||||||||
\(900\) | 0.303053 | 0.0101018 | ||||||||
\(901\) | 74.6054 | 2.48547 | ||||||||
\(902\) | 15.1966 | 0.505991 | ||||||||
\(903\) | −5.36951 | −0.178686 | ||||||||
\(904\) | −4.24731 | −0.141263 | ||||||||
\(905\) | −31.8892 | −1.06003 | ||||||||
\(906\) | 21.3970 | 0.710866 | ||||||||
\(907\) | −35.9006 | −1.19206 | −0.596030 | − | 0.802962i | \(-0.703256\pi\) | ||||
−0.596030 | + | 0.802962i | \(0.703256\pi\) | |||||||
\(908\) | 18.2184 | 0.604599 | ||||||||
\(909\) | −0.245356 | −0.00813795 | ||||||||
\(910\) | 11.6557 | 0.386382 | ||||||||
\(911\) | −30.8123 | −1.02086 | −0.510428 | − | 0.859921i | \(-0.670513\pi\) | ||||
−0.510428 | + | 0.859921i | \(0.670513\pi\) | |||||||
\(912\) | 2.38799 | 0.0790743 | ||||||||
\(913\) | −9.58748 | −0.317299 | ||||||||
\(914\) | −41.1661 | −1.36165 | ||||||||
\(915\) | −36.1411 | −1.19479 | ||||||||
\(916\) | 5.36759 | 0.177350 | ||||||||
\(917\) | −15.3953 | −0.508398 | ||||||||
\(918\) | −38.4648 | −1.26953 | ||||||||
\(919\) | 15.8214 | 0.521901 | 0.260951 | − | 0.965352i | \(-0.415964\pi\) | ||||
0.260951 | + | 0.965352i | \(0.415964\pi\) | |||||||
\(920\) | 7.06414 | 0.232898 | ||||||||
\(921\) | −7.24851 | −0.238847 | ||||||||
\(922\) | −13.8367 | −0.455687 | ||||||||
\(923\) | 6.27956 | 0.206694 | ||||||||
\(924\) | 22.7608 | 0.748775 | ||||||||
\(925\) | −4.90390 | −0.161239 | ||||||||
\(926\) | 29.6863 | 0.975553 | ||||||||
\(927\) | 1.98897 | 0.0653263 | ||||||||
\(928\) | 2.37377 | 0.0779227 | ||||||||
\(929\) | 15.3625 | 0.504028 | 0.252014 | − | 0.967724i | \(-0.418907\pi\) | ||||
0.252014 | + | 0.967724i | \(0.418907\pi\) | |||||||
\(930\) | −28.8950 | −0.947505 | ||||||||
\(931\) | −16.9309 | −0.554888 | ||||||||
\(932\) | 3.10684 | 0.101768 | ||||||||
\(933\) | −12.0361 | −0.394045 | ||||||||
\(934\) | −3.39795 | −0.111184 | ||||||||
\(935\) | −41.2879 | −1.35026 | ||||||||
\(936\) | −0.272483 | −0.00890639 | ||||||||
\(937\) | −27.6452 | −0.903129 | −0.451564 | − | 0.892239i | \(-0.649134\pi\) | ||||
−0.451564 | + | 0.892239i | \(0.649134\pi\) | |||||||
\(938\) | −58.0533 | −1.89551 | ||||||||
\(939\) | −50.5645 | −1.65011 | ||||||||
\(940\) | 11.9761 | 0.390616 | ||||||||
\(941\) | 2.21511 | 0.0722104 | 0.0361052 | − | 0.999348i | \(-0.488505\pi\) | ||||
0.0361052 | + | 0.999348i | \(0.488505\pi\) | |||||||
\(942\) | 6.16809 | 0.200967 | ||||||||
\(943\) | −18.7109 | −0.609311 | ||||||||
\(944\) | −1.43766 | −0.0467919 | ||||||||
\(945\) | 42.6930 | 1.38880 | ||||||||
\(946\) | 2.29950 | 0.0747632 | ||||||||
\(947\) | −37.0382 | −1.20358 | −0.601790 | − | 0.798655i | \(-0.705545\pi\) | ||||
−0.601790 | + | 0.798655i | \(0.705545\pi\) | |||||||
\(948\) | −3.86150 | −0.125416 | ||||||||
\(949\) | 1.03005 | 0.0334368 | ||||||||
\(950\) | −2.31067 | −0.0749679 | ||||||||
\(951\) | −32.6285 | −1.05805 | ||||||||
\(952\) | −31.2788 | −1.01375 | ||||||||
\(953\) | 7.13854 | 0.231240 | 0.115620 | − | 0.993294i | \(-0.463115\pi\) | ||||
0.115620 | + | 0.993294i | \(0.463115\pi\) | |||||||
\(954\) | 1.93583 | 0.0626747 | ||||||||
\(955\) | −17.8957 | −0.579092 | ||||||||
\(956\) | −25.1587 | −0.813691 | ||||||||
\(957\) | −12.4304 | −0.401819 | ||||||||
\(958\) | −7.60708 | −0.245773 | ||||||||
\(959\) | −68.7606 | −2.22039 | ||||||||
\(960\) | −3.08229 | −0.0994804 | ||||||||
\(961\) | 56.8820 | 1.83490 | ||||||||
\(962\) | 4.40922 | 0.142159 | ||||||||
\(963\) | −2.59298 | −0.0835576 | ||||||||
\(964\) | −3.12108 | −0.100523 | ||||||||
\(965\) | 8.35267 | 0.268882 | ||||||||
\(966\) | −28.0244 | −0.901670 | ||||||||
\(967\) | 45.2291 | 1.45447 | 0.727235 | − | 0.686389i | \(-0.240805\pi\) | ||||
0.727235 | + | 0.686389i | \(0.240805\pi\) | |||||||
\(968\) | 1.25266 | 0.0402622 | ||||||||
\(969\) | 17.1848 | 0.552056 | ||||||||
\(970\) | −3.75413 | −0.120538 | ||||||||
\(971\) | −7.45868 | −0.239360 | −0.119680 | − | 0.992812i | \(-0.538187\pi\) | ||||
−0.119680 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(972\) | −1.93765 | −0.0621501 | ||||||||
\(973\) | −32.0846 | −1.02858 | ||||||||
\(974\) | 19.9468 | 0.639135 | ||||||||
\(975\) | −3.97236 | −0.127217 | ||||||||
\(976\) | 11.7254 | 0.375321 | ||||||||
\(977\) | 21.4897 | 0.687517 | 0.343759 | − | 0.939058i | \(-0.388300\pi\) | ||||
0.343759 | + | 0.939058i | \(0.388300\pi\) | |||||||
\(978\) | −27.6046 | −0.882698 | ||||||||
\(979\) | −3.13769 | −0.100281 | ||||||||
\(980\) | 21.8535 | 0.698084 | ||||||||
\(981\) | 1.63146 | 0.0520885 | ||||||||
\(982\) | 30.5819 | 0.975909 | ||||||||
\(983\) | −31.5013 | −1.00474 | −0.502368 | − | 0.864654i | \(-0.667538\pi\) | ||||
−0.502368 | + | 0.864654i | \(0.667538\pi\) | |||||||
\(984\) | 8.16412 | 0.260263 | ||||||||
\(985\) | 9.58331 | 0.305350 | ||||||||
\(986\) | 17.0824 | 0.544016 | ||||||||
\(987\) | −47.5106 | −1.51228 | ||||||||
\(988\) | 2.07758 | 0.0660967 | ||||||||
\(989\) | −2.83128 | −0.0900293 | ||||||||
\(990\) | −1.07132 | −0.0340487 | ||||||||
\(991\) | −6.81616 | −0.216522 | −0.108261 | − | 0.994122i | \(-0.534528\pi\) | ||||
−0.108261 | + | 0.994122i | \(0.534528\pi\) | |||||||
\(992\) | 9.37454 | 0.297642 | ||||||||
\(993\) | 9.55810 | 0.303317 | ||||||||
\(994\) | 18.7041 | 0.593257 | ||||||||
\(995\) | −7.63071 | −0.241910 | ||||||||
\(996\) | −5.15071 | −0.163207 | ||||||||
\(997\) | −16.4227 | −0.520112 | −0.260056 | − | 0.965593i | \(-0.583741\pi\) | ||||
−0.260056 | + | 0.965593i | \(0.583741\pi\) | |||||||
\(998\) | −6.35824 | −0.201267 | ||||||||
\(999\) | 16.1503 | 0.510974 |
(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 | 4006.2.a.h.1.13 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.h.1.13 | ✓ | 42 | 1.1 | even | 1 | trivial |