Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(81\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.26929 | −1.88753 | −0.943764 | − | 0.330620i | \(-0.892742\pi\) | ||||
−0.943764 | + | 0.330620i | \(0.892742\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.66866 | −0.746249 | −0.373125 | − | 0.927781i | \(-0.621714\pi\) | ||||
−0.373125 | + | 0.927781i | \(0.621714\pi\) | |||||||
\(6\) | 3.26929 | 1.33468 | ||||||||
\(7\) | −1.36572 | −0.516192 | −0.258096 | − | 0.966119i | \(-0.583095\pi\) | ||||
−0.258096 | + | 0.966119i | \(0.583095\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.68829 | 2.56276 | ||||||||
\(10\) | 1.66866 | 0.527678 | ||||||||
\(11\) | −2.47020 | −0.744793 | −0.372397 | − | 0.928074i | \(-0.621464\pi\) | ||||
−0.372397 | + | 0.928074i | \(0.621464\pi\) | |||||||
\(12\) | −3.26929 | −0.943764 | ||||||||
\(13\) | −4.48260 | −1.24325 | −0.621625 | − | 0.783315i | \(-0.713527\pi\) | ||||
−0.621625 | + | 0.783315i | \(0.713527\pi\) | |||||||
\(14\) | 1.36572 | 0.365003 | ||||||||
\(15\) | 5.45535 | 1.40857 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.81792 | 1.41105 | 0.705526 | − | 0.708684i | \(-0.250711\pi\) | ||||
0.705526 | + | 0.708684i | \(0.250711\pi\) | |||||||
\(18\) | −7.68829 | −1.81215 | ||||||||
\(19\) | −1.65821 | −0.380420 | −0.190210 | − | 0.981743i | \(-0.560917\pi\) | ||||
−0.190210 | + | 0.981743i | \(0.560917\pi\) | |||||||
\(20\) | −1.66866 | −0.373125 | ||||||||
\(21\) | 4.46493 | 0.974327 | ||||||||
\(22\) | 2.47020 | 0.526648 | ||||||||
\(23\) | 1.86242 | 0.388341 | 0.194171 | − | 0.980968i | \(-0.437798\pi\) | ||||
0.194171 | + | 0.980968i | \(0.437798\pi\) | |||||||
\(24\) | 3.26929 | 0.667342 | ||||||||
\(25\) | −2.21556 | −0.443112 | ||||||||
\(26\) | 4.48260 | 0.879111 | ||||||||
\(27\) | −15.3274 | −2.94976 | ||||||||
\(28\) | −1.36572 | −0.258096 | ||||||||
\(29\) | 0.722005 | 0.134073 | 0.0670365 | − | 0.997751i | \(-0.478646\pi\) | ||||
0.0670365 | + | 0.997751i | \(0.478646\pi\) | |||||||
\(30\) | −5.45535 | −0.996007 | ||||||||
\(31\) | −6.88253 | −1.23614 | −0.618069 | − | 0.786124i | \(-0.712085\pi\) | ||||
−0.618069 | + | 0.786124i | \(0.712085\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.07581 | 1.40582 | ||||||||
\(34\) | −5.81792 | −0.997765 | ||||||||
\(35\) | 2.27892 | 0.385208 | ||||||||
\(36\) | 7.68829 | 1.28138 | ||||||||
\(37\) | −1.76064 | −0.289448 | −0.144724 | − | 0.989472i | \(-0.546229\pi\) | ||||
−0.144724 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(38\) | 1.65821 | 0.268997 | ||||||||
\(39\) | 14.6550 | 2.34667 | ||||||||
\(40\) | 1.66866 | 0.263839 | ||||||||
\(41\) | −1.52448 | −0.238083 | −0.119042 | − | 0.992889i | \(-0.537982\pi\) | ||||
−0.119042 | + | 0.992889i | \(0.537982\pi\) | |||||||
\(42\) | −4.46493 | −0.688953 | ||||||||
\(43\) | 5.84573 | 0.891466 | 0.445733 | − | 0.895166i | \(-0.352943\pi\) | ||||
0.445733 | + | 0.895166i | \(0.352943\pi\) | |||||||
\(44\) | −2.47020 | −0.372397 | ||||||||
\(45\) | −12.8292 | −1.91246 | ||||||||
\(46\) | −1.86242 | −0.274599 | ||||||||
\(47\) | 1.50351 | 0.219310 | 0.109655 | − | 0.993970i | \(-0.465025\pi\) | ||||
0.109655 | + | 0.993970i | \(0.465025\pi\) | |||||||
\(48\) | −3.26929 | −0.471882 | ||||||||
\(49\) | −5.13482 | −0.733546 | ||||||||
\(50\) | 2.21556 | 0.313328 | ||||||||
\(51\) | −19.0205 | −2.66340 | ||||||||
\(52\) | −4.48260 | −0.621625 | ||||||||
\(53\) | 11.9036 | 1.63508 | 0.817540 | − | 0.575872i | \(-0.195337\pi\) | ||||
0.817540 | + | 0.575872i | \(0.195337\pi\) | |||||||
\(54\) | 15.3274 | 2.08579 | ||||||||
\(55\) | 4.12193 | 0.555801 | ||||||||
\(56\) | 1.36572 | 0.182501 | ||||||||
\(57\) | 5.42118 | 0.718053 | ||||||||
\(58\) | −0.722005 | −0.0948040 | ||||||||
\(59\) | −4.33407 | −0.564248 | −0.282124 | − | 0.959378i | \(-0.591039\pi\) | ||||
−0.282124 | + | 0.959378i | \(0.591039\pi\) | |||||||
\(60\) | 5.45535 | 0.704283 | ||||||||
\(61\) | −0.735274 | −0.0941422 | −0.0470711 | − | 0.998892i | \(-0.514989\pi\) | ||||
−0.0470711 | + | 0.998892i | \(0.514989\pi\) | |||||||
\(62\) | 6.88253 | 0.874082 | ||||||||
\(63\) | −10.5000 | −1.32288 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.47996 | 0.927775 | ||||||||
\(66\) | −8.07581 | −0.994064 | ||||||||
\(67\) | −7.66184 | −0.936043 | −0.468021 | − | 0.883717i | \(-0.655033\pi\) | ||||
−0.468021 | + | 0.883717i | \(0.655033\pi\) | |||||||
\(68\) | 5.81792 | 0.705526 | ||||||||
\(69\) | −6.08880 | −0.733005 | ||||||||
\(70\) | −2.27892 | −0.272383 | ||||||||
\(71\) | −8.32609 | −0.988125 | −0.494063 | − | 0.869426i | \(-0.664489\pi\) | ||||
−0.494063 | + | 0.869426i | \(0.664489\pi\) | |||||||
\(72\) | −7.68829 | −0.906073 | ||||||||
\(73\) | −5.17284 | −0.605435 | −0.302718 | − | 0.953080i | \(-0.597894\pi\) | ||||
−0.302718 | + | 0.953080i | \(0.597894\pi\) | |||||||
\(74\) | 1.76064 | 0.204671 | ||||||||
\(75\) | 7.24332 | 0.836387 | ||||||||
\(76\) | −1.65821 | −0.190210 | ||||||||
\(77\) | 3.37359 | 0.384457 | ||||||||
\(78\) | −14.6550 | −1.65935 | ||||||||
\(79\) | 14.9132 | 1.67786 | 0.838931 | − | 0.544237i | \(-0.183181\pi\) | ||||
0.838931 | + | 0.544237i | \(0.183181\pi\) | |||||||
\(80\) | −1.66866 | −0.186562 | ||||||||
\(81\) | 27.0449 | 3.00499 | ||||||||
\(82\) | 1.52448 | 0.168350 | ||||||||
\(83\) | −2.21733 | −0.243383 | −0.121692 | − | 0.992568i | \(-0.538832\pi\) | ||||
−0.121692 | + | 0.992568i | \(0.538832\pi\) | |||||||
\(84\) | 4.46493 | 0.487164 | ||||||||
\(85\) | −9.70815 | −1.05300 | ||||||||
\(86\) | −5.84573 | −0.630361 | ||||||||
\(87\) | −2.36045 | −0.253067 | ||||||||
\(88\) | 2.47020 | 0.263324 | ||||||||
\(89\) | 1.54388 | 0.163651 | 0.0818256 | − | 0.996647i | \(-0.473925\pi\) | ||||
0.0818256 | + | 0.996647i | \(0.473925\pi\) | |||||||
\(90\) | 12.8292 | 1.35231 | ||||||||
\(91\) | 6.12196 | 0.641756 | ||||||||
\(92\) | 1.86242 | 0.194171 | ||||||||
\(93\) | 22.5010 | 2.33325 | ||||||||
\(94\) | −1.50351 | −0.155075 | ||||||||
\(95\) | 2.76700 | 0.283888 | ||||||||
\(96\) | 3.26929 | 0.333671 | ||||||||
\(97\) | 11.7066 | 1.18862 | 0.594311 | − | 0.804235i | \(-0.297425\pi\) | ||||
0.594311 | + | 0.804235i | \(0.297425\pi\) | |||||||
\(98\) | 5.13482 | 0.518695 | ||||||||
\(99\) | −18.9916 | −1.90873 | ||||||||
\(100\) | −2.21556 | −0.221556 | ||||||||
\(101\) | −13.7383 | −1.36701 | −0.683505 | − | 0.729946i | \(-0.739545\pi\) | ||||
−0.683505 | + | 0.729946i | \(0.739545\pi\) | |||||||
\(102\) | 19.0205 | 1.88331 | ||||||||
\(103\) | 8.06265 | 0.794437 | 0.397218 | − | 0.917724i | \(-0.369976\pi\) | ||||
0.397218 | + | 0.917724i | \(0.369976\pi\) | |||||||
\(104\) | 4.48260 | 0.439555 | ||||||||
\(105\) | −7.45046 | −0.727091 | ||||||||
\(106\) | −11.9036 | −1.15618 | ||||||||
\(107\) | −7.66056 | −0.740574 | −0.370287 | − | 0.928917i | \(-0.620741\pi\) | ||||
−0.370287 | + | 0.928917i | \(0.620741\pi\) | |||||||
\(108\) | −15.3274 | −1.47488 | ||||||||
\(109\) | 13.0031 | 1.24547 | 0.622736 | − | 0.782432i | \(-0.286021\pi\) | ||||
0.622736 | + | 0.782432i | \(0.286021\pi\) | |||||||
\(110\) | −4.12193 | −0.393011 | ||||||||
\(111\) | 5.75606 | 0.546341 | ||||||||
\(112\) | −1.36572 | −0.129048 | ||||||||
\(113\) | 13.0881 | 1.23122 | 0.615611 | − | 0.788050i | \(-0.288909\pi\) | ||||
0.615611 | + | 0.788050i | \(0.288909\pi\) | |||||||
\(114\) | −5.42118 | −0.507740 | ||||||||
\(115\) | −3.10775 | −0.289799 | ||||||||
\(116\) | 0.722005 | 0.0670365 | ||||||||
\(117\) | −34.4635 | −3.18616 | ||||||||
\(118\) | 4.33407 | 0.398984 | ||||||||
\(119\) | −7.94563 | −0.728374 | ||||||||
\(120\) | −5.45535 | −0.498003 | ||||||||
\(121\) | −4.89811 | −0.445283 | ||||||||
\(122\) | 0.735274 | 0.0665686 | ||||||||
\(123\) | 4.98396 | 0.449389 | ||||||||
\(124\) | −6.88253 | −0.618069 | ||||||||
\(125\) | 12.0403 | 1.07692 | ||||||||
\(126\) | 10.5000 | 0.935416 | ||||||||
\(127\) | 16.8834 | 1.49816 | 0.749082 | − | 0.662477i | \(-0.230495\pi\) | ||||
0.749082 | + | 0.662477i | \(0.230495\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −19.1114 | −1.68267 | ||||||||
\(130\) | −7.47996 | −0.656036 | ||||||||
\(131\) | −9.54322 | −0.833795 | −0.416898 | − | 0.908953i | \(-0.636883\pi\) | ||||
−0.416898 | + | 0.908953i | \(0.636883\pi\) | |||||||
\(132\) | 8.07581 | 0.702909 | ||||||||
\(133\) | 2.26465 | 0.196370 | ||||||||
\(134\) | 7.66184 | 0.661882 | ||||||||
\(135\) | 25.5763 | 2.20125 | ||||||||
\(136\) | −5.81792 | −0.498882 | ||||||||
\(137\) | 20.2600 | 1.73092 | 0.865462 | − | 0.500974i | \(-0.167025\pi\) | ||||
0.865462 | + | 0.500974i | \(0.167025\pi\) | |||||||
\(138\) | 6.08880 | 0.518313 | ||||||||
\(139\) | −3.80448 | −0.322692 | −0.161346 | − | 0.986898i | \(-0.551584\pi\) | ||||
−0.161346 | + | 0.986898i | \(0.551584\pi\) | |||||||
\(140\) | 2.27892 | 0.192604 | ||||||||
\(141\) | −4.91542 | −0.413953 | ||||||||
\(142\) | 8.32609 | 0.698710 | ||||||||
\(143\) | 11.0729 | 0.925965 | ||||||||
\(144\) | 7.68829 | 0.640691 | ||||||||
\(145\) | −1.20478 | −0.100052 | ||||||||
\(146\) | 5.17284 | 0.428107 | ||||||||
\(147\) | 16.7872 | 1.38459 | ||||||||
\(148\) | −1.76064 | −0.144724 | ||||||||
\(149\) | 3.03242 | 0.248426 | 0.124213 | − | 0.992256i | \(-0.460359\pi\) | ||||
0.124213 | + | 0.992256i | \(0.460359\pi\) | |||||||
\(150\) | −7.24332 | −0.591415 | ||||||||
\(151\) | −15.7481 | −1.28156 | −0.640781 | − | 0.767724i | \(-0.721389\pi\) | ||||
−0.640781 | + | 0.767724i | \(0.721389\pi\) | |||||||
\(152\) | 1.65821 | 0.134499 | ||||||||
\(153\) | 44.7298 | 3.61619 | ||||||||
\(154\) | −3.37359 | −0.271852 | ||||||||
\(155\) | 11.4846 | 0.922467 | ||||||||
\(156\) | 14.6550 | 1.17334 | ||||||||
\(157\) | 1.34112 | 0.107033 | 0.0535165 | − | 0.998567i | \(-0.482957\pi\) | ||||
0.0535165 | + | 0.998567i | \(0.482957\pi\) | |||||||
\(158\) | −14.9132 | −1.18643 | ||||||||
\(159\) | −38.9163 | −3.08626 | ||||||||
\(160\) | 1.66866 | 0.131919 | ||||||||
\(161\) | −2.54354 | −0.200459 | ||||||||
\(162\) | −27.0449 | −2.12485 | ||||||||
\(163\) | 0.0974129 | 0.00762997 | 0.00381498 | − | 0.999993i | \(-0.498786\pi\) | ||||
0.00381498 | + | 0.999993i | \(0.498786\pi\) | |||||||
\(164\) | −1.52448 | −0.119042 | ||||||||
\(165\) | −13.4758 | −1.04909 | ||||||||
\(166\) | 2.21733 | 0.172098 | ||||||||
\(167\) | −2.57137 | −0.198979 | −0.0994895 | − | 0.995039i | \(-0.531721\pi\) | ||||
−0.0994895 | + | 0.995039i | \(0.531721\pi\) | |||||||
\(168\) | −4.46493 | −0.344477 | ||||||||
\(169\) | 7.09374 | 0.545672 | ||||||||
\(170\) | 9.70815 | 0.744581 | ||||||||
\(171\) | −12.7488 | −0.974925 | ||||||||
\(172\) | 5.84573 | 0.445733 | ||||||||
\(173\) | 0.993081 | 0.0755026 | 0.0377513 | − | 0.999287i | \(-0.487981\pi\) | ||||
0.0377513 | + | 0.999287i | \(0.487981\pi\) | |||||||
\(174\) | 2.36045 | 0.178945 | ||||||||
\(175\) | 3.02583 | 0.228731 | ||||||||
\(176\) | −2.47020 | −0.186198 | ||||||||
\(177\) | 14.1694 | 1.06503 | ||||||||
\(178\) | −1.54388 | −0.115719 | ||||||||
\(179\) | 8.73610 | 0.652967 | 0.326483 | − | 0.945203i | \(-0.394136\pi\) | ||||
0.326483 | + | 0.945203i | \(0.394136\pi\) | |||||||
\(180\) | −12.8292 | −0.956230 | ||||||||
\(181\) | 6.69399 | 0.497560 | 0.248780 | − | 0.968560i | \(-0.419970\pi\) | ||||
0.248780 | + | 0.968560i | \(0.419970\pi\) | |||||||
\(182\) | −6.12196 | −0.453790 | ||||||||
\(183\) | 2.40383 | 0.177696 | ||||||||
\(184\) | −1.86242 | −0.137299 | ||||||||
\(185\) | 2.93792 | 0.216000 | ||||||||
\(186\) | −22.5010 | −1.64985 | ||||||||
\(187\) | −14.3714 | −1.05094 | ||||||||
\(188\) | 1.50351 | 0.109655 | ||||||||
\(189\) | 20.9329 | 1.52264 | ||||||||
\(190\) | −2.76700 | −0.200739 | ||||||||
\(191\) | −0.143869 | −0.0104100 | −0.00520500 | − | 0.999986i | \(-0.501657\pi\) | ||||
−0.00520500 | + | 0.999986i | \(0.501657\pi\) | |||||||
\(192\) | −3.26929 | −0.235941 | ||||||||
\(193\) | 6.68854 | 0.481452 | 0.240726 | − | 0.970593i | \(-0.422615\pi\) | ||||
0.240726 | + | 0.970593i | \(0.422615\pi\) | |||||||
\(194\) | −11.7066 | −0.840483 | ||||||||
\(195\) | −24.4542 | −1.75120 | ||||||||
\(196\) | −5.13482 | −0.366773 | ||||||||
\(197\) | 16.3505 | 1.16492 | 0.582461 | − | 0.812859i | \(-0.302090\pi\) | ||||
0.582461 | + | 0.812859i | \(0.302090\pi\) | |||||||
\(198\) | 18.9916 | 1.34967 | ||||||||
\(199\) | 21.9579 | 1.55655 | 0.778275 | − | 0.627923i | \(-0.216095\pi\) | ||||
0.778275 | + | 0.627923i | \(0.216095\pi\) | |||||||
\(200\) | 2.21556 | 0.156664 | ||||||||
\(201\) | 25.0488 | 1.76681 | ||||||||
\(202\) | 13.7383 | 0.966622 | ||||||||
\(203\) | −0.986055 | −0.0692075 | ||||||||
\(204\) | −19.0205 | −1.33170 | ||||||||
\(205\) | 2.54384 | 0.177669 | ||||||||
\(206\) | −8.06265 | −0.561752 | ||||||||
\(207\) | 14.3188 | 0.995227 | ||||||||
\(208\) | −4.48260 | −0.310813 | ||||||||
\(209\) | 4.09611 | 0.283334 | ||||||||
\(210\) | 7.45046 | 0.514131 | ||||||||
\(211\) | 21.8203 | 1.50217 | 0.751085 | − | 0.660205i | \(-0.229531\pi\) | ||||
0.751085 | + | 0.660205i | \(0.229531\pi\) | |||||||
\(212\) | 11.9036 | 0.817540 | ||||||||
\(213\) | 27.2204 | 1.86511 | ||||||||
\(214\) | 7.66056 | 0.523665 | ||||||||
\(215\) | −9.75456 | −0.665256 | ||||||||
\(216\) | 15.3274 | 1.04290 | ||||||||
\(217\) | 9.39958 | 0.638085 | ||||||||
\(218\) | −13.0031 | −0.880682 | ||||||||
\(219\) | 16.9115 | 1.14278 | ||||||||
\(220\) | 4.12193 | 0.277901 | ||||||||
\(221\) | −26.0794 | −1.75429 | ||||||||
\(222\) | −5.75606 | −0.386322 | ||||||||
\(223\) | 1.42229 | 0.0952434 | 0.0476217 | − | 0.998865i | \(-0.484836\pi\) | ||||
0.0476217 | + | 0.998865i | \(0.484836\pi\) | |||||||
\(224\) | 1.36572 | 0.0912507 | ||||||||
\(225\) | −17.0339 | −1.13559 | ||||||||
\(226\) | −13.0881 | −0.870605 | ||||||||
\(227\) | 7.93675 | 0.526780 | 0.263390 | − | 0.964689i | \(-0.415159\pi\) | ||||
0.263390 | + | 0.964689i | \(0.415159\pi\) | |||||||
\(228\) | 5.42118 | 0.359027 | ||||||||
\(229\) | 4.46832 | 0.295275 | 0.147638 | − | 0.989042i | \(-0.452833\pi\) | ||||
0.147638 | + | 0.989042i | \(0.452833\pi\) | |||||||
\(230\) | 3.10775 | 0.204919 | ||||||||
\(231\) | −11.0293 | −0.725673 | ||||||||
\(232\) | −0.722005 | −0.0474020 | ||||||||
\(233\) | 6.84289 | 0.448293 | 0.224146 | − | 0.974555i | \(-0.428041\pi\) | ||||
0.224146 | + | 0.974555i | \(0.428041\pi\) | |||||||
\(234\) | 34.4635 | 2.25295 | ||||||||
\(235\) | −2.50886 | −0.163660 | ||||||||
\(236\) | −4.33407 | −0.282124 | ||||||||
\(237\) | −48.7555 | −3.16701 | ||||||||
\(238\) | 7.94563 | 0.515038 | ||||||||
\(239\) | 10.4623 | 0.676752 | 0.338376 | − | 0.941011i | \(-0.390122\pi\) | ||||
0.338376 | + | 0.941011i | \(0.390122\pi\) | |||||||
\(240\) | 5.45535 | 0.352142 | ||||||||
\(241\) | 10.0608 | 0.648072 | 0.324036 | − | 0.946045i | \(-0.394960\pi\) | ||||
0.324036 | + | 0.946045i | \(0.394960\pi\) | |||||||
\(242\) | 4.89811 | 0.314863 | ||||||||
\(243\) | −42.4356 | −2.72224 | ||||||||
\(244\) | −0.735274 | −0.0470711 | ||||||||
\(245\) | 8.56829 | 0.547408 | ||||||||
\(246\) | −4.98396 | −0.317766 | ||||||||
\(247\) | 7.43310 | 0.472957 | ||||||||
\(248\) | 6.88253 | 0.437041 | ||||||||
\(249\) | 7.24910 | 0.459393 | ||||||||
\(250\) | −12.0403 | −0.761498 | ||||||||
\(251\) | −9.02061 | −0.569376 | −0.284688 | − | 0.958620i | \(-0.591890\pi\) | ||||
−0.284688 | + | 0.958620i | \(0.591890\pi\) | |||||||
\(252\) | −10.5000 | −0.661439 | ||||||||
\(253\) | −4.60055 | −0.289234 | ||||||||
\(254\) | −16.8834 | −1.05936 | ||||||||
\(255\) | 31.7388 | 1.98756 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.2390 | −1.82388 | −0.911939 | − | 0.410325i | \(-0.865415\pi\) | ||||
−0.911939 | + | 0.410325i | \(0.865415\pi\) | |||||||
\(258\) | 19.1114 | 1.18983 | ||||||||
\(259\) | 2.40454 | 0.149411 | ||||||||
\(260\) | 7.47996 | 0.463887 | ||||||||
\(261\) | 5.55099 | 0.343597 | ||||||||
\(262\) | 9.54322 | 0.589582 | ||||||||
\(263\) | −15.9830 | −0.985552 | −0.492776 | − | 0.870156i | \(-0.664018\pi\) | ||||
−0.492776 | + | 0.870156i | \(0.664018\pi\) | |||||||
\(264\) | −8.07581 | −0.497032 | ||||||||
\(265\) | −19.8630 | −1.22018 | ||||||||
\(266\) | −2.26465 | −0.138854 | ||||||||
\(267\) | −5.04741 | −0.308896 | ||||||||
\(268\) | −7.66184 | −0.468021 | ||||||||
\(269\) | 5.57090 | 0.339664 | 0.169832 | − | 0.985473i | \(-0.445678\pi\) | ||||
0.169832 | + | 0.985473i | \(0.445678\pi\) | |||||||
\(270\) | −25.5763 | −1.55652 | ||||||||
\(271\) | −4.83280 | −0.293572 | −0.146786 | − | 0.989168i | \(-0.546893\pi\) | ||||
−0.146786 | + | 0.989168i | \(0.546893\pi\) | |||||||
\(272\) | 5.81792 | 0.352763 | ||||||||
\(273\) | −20.0145 | −1.21133 | ||||||||
\(274\) | −20.2600 | −1.22395 | ||||||||
\(275\) | 5.47288 | 0.330027 | ||||||||
\(276\) | −6.08880 | −0.366503 | ||||||||
\(277\) | 5.59881 | 0.336400 | 0.168200 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168200 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(278\) | 3.80448 | 0.228178 | ||||||||
\(279\) | −52.9148 | −3.16793 | ||||||||
\(280\) | −2.27892 | −0.136192 | ||||||||
\(281\) | 13.3974 | 0.799220 | 0.399610 | − | 0.916685i | \(-0.369145\pi\) | ||||
0.399610 | + | 0.916685i | \(0.369145\pi\) | |||||||
\(282\) | 4.91542 | 0.292709 | ||||||||
\(283\) | 8.28139 | 0.492277 | 0.246139 | − | 0.969235i | \(-0.420838\pi\) | ||||
0.246139 | + | 0.969235i | \(0.420838\pi\) | |||||||
\(284\) | −8.32609 | −0.494063 | ||||||||
\(285\) | −9.04613 | −0.535846 | ||||||||
\(286\) | −11.0729 | −0.654756 | ||||||||
\(287\) | 2.08200 | 0.122897 | ||||||||
\(288\) | −7.68829 | −0.453037 | ||||||||
\(289\) | 16.8482 | 0.991069 | ||||||||
\(290\) | 1.20478 | 0.0707474 | ||||||||
\(291\) | −38.2722 | −2.24356 | ||||||||
\(292\) | −5.17284 | −0.302718 | ||||||||
\(293\) | −11.8937 | −0.694839 | −0.347420 | − | 0.937710i | \(-0.612942\pi\) | ||||
−0.347420 | + | 0.937710i | \(0.612942\pi\) | |||||||
\(294\) | −16.7872 | −0.979052 | ||||||||
\(295\) | 7.23211 | 0.421070 | ||||||||
\(296\) | 1.76064 | 0.102335 | ||||||||
\(297\) | 37.8617 | 2.19696 | ||||||||
\(298\) | −3.03242 | −0.175664 | ||||||||
\(299\) | −8.34849 | −0.482806 | ||||||||
\(300\) | 7.24332 | 0.418193 | ||||||||
\(301\) | −7.98361 | −0.460168 | ||||||||
\(302\) | 15.7481 | 0.906201 | ||||||||
\(303\) | 44.9145 | 2.58027 | ||||||||
\(304\) | −1.65821 | −0.0951049 | ||||||||
\(305\) | 1.22693 | 0.0702536 | ||||||||
\(306\) | −44.7298 | −2.55703 | ||||||||
\(307\) | 13.8965 | 0.793116 | 0.396558 | − | 0.918010i | \(-0.370205\pi\) | ||||
0.396558 | + | 0.918010i | \(0.370205\pi\) | |||||||
\(308\) | 3.37359 | 0.192228 | ||||||||
\(309\) | −26.3592 | −1.49952 | ||||||||
\(310\) | −11.4846 | −0.652283 | ||||||||
\(311\) | −16.3562 | −0.927473 | −0.463736 | − | 0.885973i | \(-0.653492\pi\) | ||||
−0.463736 | + | 0.885973i | \(0.653492\pi\) | |||||||
\(312\) | −14.6550 | −0.829673 | ||||||||
\(313\) | 6.46571 | 0.365464 | 0.182732 | − | 0.983163i | \(-0.441506\pi\) | ||||
0.182732 | + | 0.983163i | \(0.441506\pi\) | |||||||
\(314\) | −1.34112 | −0.0756837 | ||||||||
\(315\) | 17.5210 | 0.987197 | ||||||||
\(316\) | 14.9132 | 0.838931 | ||||||||
\(317\) | −2.63051 | −0.147744 | −0.0738721 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738721 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(318\) | 38.9163 | 2.18232 | ||||||||
\(319\) | −1.78350 | −0.0998567 | ||||||||
\(320\) | −1.66866 | −0.0932811 | ||||||||
\(321\) | 25.0446 | 1.39785 | ||||||||
\(322\) | 2.54354 | 0.141746 | ||||||||
\(323\) | −9.64734 | −0.536792 | ||||||||
\(324\) | 27.0449 | 1.50249 | ||||||||
\(325\) | 9.93148 | 0.550899 | ||||||||
\(326\) | −0.0974129 | −0.00539520 | ||||||||
\(327\) | −42.5110 | −2.35087 | ||||||||
\(328\) | 1.52448 | 0.0841751 | ||||||||
\(329\) | −2.05337 | −0.113206 | ||||||||
\(330\) | 13.4758 | 0.741819 | ||||||||
\(331\) | 14.4302 | 0.793158 | 0.396579 | − | 0.918001i | \(-0.370197\pi\) | ||||
0.396579 | + | 0.918001i | \(0.370197\pi\) | |||||||
\(332\) | −2.21733 | −0.121692 | ||||||||
\(333\) | −13.5363 | −0.741786 | ||||||||
\(334\) | 2.57137 | 0.140699 | ||||||||
\(335\) | 12.7850 | 0.698521 | ||||||||
\(336\) | 4.46493 | 0.243582 | ||||||||
\(337\) | 10.8467 | 0.590856 | 0.295428 | − | 0.955365i | \(-0.404538\pi\) | ||||
0.295428 | + | 0.955365i | \(0.404538\pi\) | |||||||
\(338\) | −7.09374 | −0.385848 | ||||||||
\(339\) | −42.7887 | −2.32397 | ||||||||
\(340\) | −9.70815 | −0.526498 | ||||||||
\(341\) | 17.0012 | 0.920668 | ||||||||
\(342\) | 12.7488 | 0.689376 | ||||||||
\(343\) | 16.5727 | 0.894843 | ||||||||
\(344\) | −5.84573 | −0.315181 | ||||||||
\(345\) | 10.1602 | 0.547005 | ||||||||
\(346\) | −0.993081 | −0.0533884 | ||||||||
\(347\) | −33.0799 | −1.77582 | −0.887910 | − | 0.460017i | \(-0.847843\pi\) | ||||
−0.887910 | + | 0.460017i | \(0.847843\pi\) | |||||||
\(348\) | −2.36045 | −0.126533 | ||||||||
\(349\) | 6.71026 | 0.359192 | 0.179596 | − | 0.983740i | \(-0.442521\pi\) | ||||
0.179596 | + | 0.983740i | \(0.442521\pi\) | |||||||
\(350\) | −3.02583 | −0.161737 | ||||||||
\(351\) | 68.7066 | 3.66729 | ||||||||
\(352\) | 2.47020 | 0.131662 | ||||||||
\(353\) | 30.9815 | 1.64898 | 0.824489 | − | 0.565878i | \(-0.191463\pi\) | ||||
0.824489 | + | 0.565878i | \(0.191463\pi\) | |||||||
\(354\) | −14.1694 | −0.753093 | ||||||||
\(355\) | 13.8934 | 0.737388 | ||||||||
\(356\) | 1.54388 | 0.0818256 | ||||||||
\(357\) | 25.9766 | 1.37483 | ||||||||
\(358\) | −8.73610 | −0.461717 | ||||||||
\(359\) | 6.40867 | 0.338237 | 0.169118 | − | 0.985596i | \(-0.445908\pi\) | ||||
0.169118 | + | 0.985596i | \(0.445908\pi\) | |||||||
\(360\) | 12.8292 | 0.676156 | ||||||||
\(361\) | −16.2503 | −0.855281 | ||||||||
\(362\) | −6.69399 | −0.351828 | ||||||||
\(363\) | 16.0134 | 0.840484 | ||||||||
\(364\) | 6.12196 | 0.320878 | ||||||||
\(365\) | 8.63173 | 0.451806 | ||||||||
\(366\) | −2.40383 | −0.125650 | ||||||||
\(367\) | −15.9079 | −0.830386 | −0.415193 | − | 0.909733i | \(-0.636286\pi\) | ||||
−0.415193 | + | 0.909733i | \(0.636286\pi\) | |||||||
\(368\) | 1.86242 | 0.0970853 | ||||||||
\(369\) | −11.7206 | −0.610151 | ||||||||
\(370\) | −2.93792 | −0.152735 | ||||||||
\(371\) | −16.2569 | −0.844016 | ||||||||
\(372\) | 22.5010 | 1.16662 | ||||||||
\(373\) | 21.3965 | 1.10787 | 0.553934 | − | 0.832560i | \(-0.313126\pi\) | ||||
0.553934 | + | 0.832560i | \(0.313126\pi\) | |||||||
\(374\) | 14.3714 | 0.743129 | ||||||||
\(375\) | −39.3634 | −2.03272 | ||||||||
\(376\) | −1.50351 | −0.0775377 | ||||||||
\(377\) | −3.23646 | −0.166686 | ||||||||
\(378\) | −20.9329 | −1.07667 | ||||||||
\(379\) | −26.8603 | −1.37972 | −0.689861 | − | 0.723942i | \(-0.742328\pi\) | ||||
−0.689861 | + | 0.723942i | \(0.742328\pi\) | |||||||
\(380\) | 2.76700 | 0.141944 | ||||||||
\(381\) | −55.1970 | −2.82783 | ||||||||
\(382\) | 0.143869 | 0.00736098 | ||||||||
\(383\) | −6.05516 | −0.309404 | −0.154702 | − | 0.987961i | \(-0.549442\pi\) | ||||
−0.154702 | + | 0.987961i | \(0.549442\pi\) | |||||||
\(384\) | 3.26929 | 0.166835 | ||||||||
\(385\) | −5.62939 | −0.286900 | ||||||||
\(386\) | −6.68854 | −0.340438 | ||||||||
\(387\) | 44.9437 | 2.28462 | ||||||||
\(388\) | 11.7066 | 0.594311 | ||||||||
\(389\) | −20.2788 | −1.02818 | −0.514088 | − | 0.857737i | \(-0.671870\pi\) | ||||
−0.514088 | + | 0.857737i | \(0.671870\pi\) | |||||||
\(390\) | 24.4542 | 1.23829 | ||||||||
\(391\) | 10.8354 | 0.547970 | ||||||||
\(392\) | 5.13482 | 0.259348 | ||||||||
\(393\) | 31.1996 | 1.57381 | ||||||||
\(394\) | −16.3505 | −0.823724 | ||||||||
\(395\) | −24.8851 | −1.25210 | ||||||||
\(396\) | −18.9916 | −0.954364 | ||||||||
\(397\) | −12.6736 | −0.636071 | −0.318036 | − | 0.948079i | \(-0.603023\pi\) | ||||
−0.318036 | + | 0.948079i | \(0.603023\pi\) | |||||||
\(398\) | −21.9579 | −1.10065 | ||||||||
\(399\) | −7.40379 | −0.370653 | ||||||||
\(400\) | −2.21556 | −0.110778 | ||||||||
\(401\) | −1.51459 | −0.0756352 | −0.0378176 | − | 0.999285i | \(-0.512041\pi\) | ||||
−0.0378176 | + | 0.999285i | \(0.512041\pi\) | |||||||
\(402\) | −25.0488 | −1.24932 | ||||||||
\(403\) | 30.8516 | 1.53683 | ||||||||
\(404\) | −13.7383 | −0.683505 | ||||||||
\(405\) | −45.1288 | −2.24247 | ||||||||
\(406\) | 0.986055 | 0.0489371 | ||||||||
\(407\) | 4.34914 | 0.215579 | ||||||||
\(408\) | 19.0205 | 0.941655 | ||||||||
\(409\) | 32.1903 | 1.59171 | 0.795854 | − | 0.605489i | \(-0.207022\pi\) | ||||
0.795854 | + | 0.605489i | \(0.207022\pi\) | |||||||
\(410\) | −2.54384 | −0.125631 | ||||||||
\(411\) | −66.2358 | −3.26717 | ||||||||
\(412\) | 8.06265 | 0.397218 | ||||||||
\(413\) | 5.91911 | 0.291260 | ||||||||
\(414\) | −14.3188 | −0.703732 | ||||||||
\(415\) | 3.69998 | 0.181625 | ||||||||
\(416\) | 4.48260 | 0.219778 | ||||||||
\(417\) | 12.4380 | 0.609090 | ||||||||
\(418\) | −4.09611 | −0.200347 | ||||||||
\(419\) | 38.4497 | 1.87839 | 0.939195 | − | 0.343385i | \(-0.111574\pi\) | ||||
0.939195 | + | 0.343385i | \(0.111574\pi\) | |||||||
\(420\) | −7.45046 | −0.363545 | ||||||||
\(421\) | −23.6302 | −1.15166 | −0.575832 | − | 0.817568i | \(-0.695322\pi\) | ||||
−0.575832 | + | 0.817568i | \(0.695322\pi\) | |||||||
\(422\) | −21.8203 | −1.06219 | ||||||||
\(423\) | 11.5594 | 0.562039 | ||||||||
\(424\) | −11.9036 | −0.578088 | ||||||||
\(425\) | −12.8900 | −0.625255 | ||||||||
\(426\) | −27.2204 | −1.31884 | ||||||||
\(427\) | 1.00418 | 0.0485955 | ||||||||
\(428\) | −7.66056 | −0.370287 | ||||||||
\(429\) | −36.2007 | −1.74778 | ||||||||
\(430\) | 9.75456 | 0.470407 | ||||||||
\(431\) | −15.9285 | −0.767248 | −0.383624 | − | 0.923489i | \(-0.625324\pi\) | ||||
−0.383624 | + | 0.923489i | \(0.625324\pi\) | |||||||
\(432\) | −15.3274 | −0.737440 | ||||||||
\(433\) | 27.3235 | 1.31308 | 0.656541 | − | 0.754290i | \(-0.272019\pi\) | ||||
0.656541 | + | 0.754290i | \(0.272019\pi\) | |||||||
\(434\) | −9.39958 | −0.451194 | ||||||||
\(435\) | 3.93880 | 0.188851 | ||||||||
\(436\) | 13.0031 | 0.622736 | ||||||||
\(437\) | −3.08829 | −0.147733 | ||||||||
\(438\) | −16.9115 | −0.808065 | ||||||||
\(439\) | −20.7917 | −0.992335 | −0.496168 | − | 0.868227i | \(-0.665260\pi\) | ||||
−0.496168 | + | 0.868227i | \(0.665260\pi\) | |||||||
\(440\) | −4.12193 | −0.196505 | ||||||||
\(441\) | −39.4780 | −1.87990 | ||||||||
\(442\) | 26.0794 | 1.24047 | ||||||||
\(443\) | −22.9946 | −1.09251 | −0.546253 | − | 0.837620i | \(-0.683946\pi\) | ||||
−0.546253 | + | 0.837620i | \(0.683946\pi\) | |||||||
\(444\) | 5.75606 | 0.273171 | ||||||||
\(445\) | −2.57622 | −0.122125 | ||||||||
\(446\) | −1.42229 | −0.0673472 | ||||||||
\(447\) | −9.91388 | −0.468911 | ||||||||
\(448\) | −1.36572 | −0.0645240 | ||||||||
\(449\) | 13.2910 | 0.627240 | 0.313620 | − | 0.949548i | \(-0.398458\pi\) | ||||
0.313620 | + | 0.949548i | \(0.398458\pi\) | |||||||
\(450\) | 17.0339 | 0.802984 | ||||||||
\(451\) | 3.76576 | 0.177323 | ||||||||
\(452\) | 13.0881 | 0.615611 | ||||||||
\(453\) | 51.4852 | 2.41898 | ||||||||
\(454\) | −7.93675 | −0.372490 | ||||||||
\(455\) | −10.2155 | −0.478910 | ||||||||
\(456\) | −5.42118 | −0.253870 | ||||||||
\(457\) | 16.1759 | 0.756677 | 0.378338 | − | 0.925667i | \(-0.376496\pi\) | ||||
0.378338 | + | 0.925667i | \(0.376496\pi\) | |||||||
\(458\) | −4.46832 | −0.208791 | ||||||||
\(459\) | −89.1735 | −4.16226 | ||||||||
\(460\) | −3.10775 | −0.144900 | ||||||||
\(461\) | −7.74907 | −0.360910 | −0.180455 | − | 0.983583i | \(-0.557757\pi\) | ||||
−0.180455 | + | 0.983583i | \(0.557757\pi\) | |||||||
\(462\) | 11.0293 | 0.513128 | ||||||||
\(463\) | 4.35584 | 0.202433 | 0.101216 | − | 0.994864i | \(-0.467727\pi\) | ||||
0.101216 | + | 0.994864i | \(0.467727\pi\) | |||||||
\(464\) | 0.722005 | 0.0335183 | ||||||||
\(465\) | −37.5466 | −1.74118 | ||||||||
\(466\) | −6.84289 | −0.316991 | ||||||||
\(467\) | −12.3000 | −0.569177 | −0.284589 | − | 0.958650i | \(-0.591857\pi\) | ||||
−0.284589 | + | 0.958650i | \(0.591857\pi\) | |||||||
\(468\) | −34.4635 | −1.59308 | ||||||||
\(469\) | 10.4639 | 0.483178 | ||||||||
\(470\) | 2.50886 | 0.115725 | ||||||||
\(471\) | −4.38451 | −0.202028 | ||||||||
\(472\) | 4.33407 | 0.199492 | ||||||||
\(473\) | −14.4401 | −0.663958 | ||||||||
\(474\) | 48.7555 | 2.23942 | ||||||||
\(475\) | 3.67387 | 0.168569 | ||||||||
\(476\) | −7.94563 | −0.364187 | ||||||||
\(477\) | 91.5180 | 4.19032 | ||||||||
\(478\) | −10.4623 | −0.478536 | ||||||||
\(479\) | −37.8644 | −1.73007 | −0.865035 | − | 0.501712i | \(-0.832704\pi\) | ||||
−0.865035 | + | 0.501712i | \(0.832704\pi\) | |||||||
\(480\) | −5.45535 | −0.249002 | ||||||||
\(481\) | 7.89227 | 0.359856 | ||||||||
\(482\) | −10.0608 | −0.458256 | ||||||||
\(483\) | 8.31557 | 0.378372 | ||||||||
\(484\) | −4.89811 | −0.222641 | ||||||||
\(485\) | −19.5343 | −0.887008 | ||||||||
\(486\) | 42.4356 | 1.92492 | ||||||||
\(487\) | 43.1079 | 1.95340 | 0.976702 | − | 0.214600i | \(-0.0688448\pi\) | ||||
0.976702 | + | 0.214600i | \(0.0688448\pi\) | |||||||
\(488\) | 0.735274 | 0.0332843 | ||||||||
\(489\) | −0.318471 | −0.0144018 | ||||||||
\(490\) | −8.56829 | −0.387076 | ||||||||
\(491\) | −10.8096 | −0.487832 | −0.243916 | − | 0.969796i | \(-0.578432\pi\) | ||||
−0.243916 | + | 0.969796i | \(0.578432\pi\) | |||||||
\(492\) | 4.98396 | 0.224694 | ||||||||
\(493\) | 4.20057 | 0.189184 | ||||||||
\(494\) | −7.43310 | −0.334431 | ||||||||
\(495\) | 31.6906 | 1.42439 | ||||||||
\(496\) | −6.88253 | −0.309035 | ||||||||
\(497\) | 11.3711 | 0.510063 | ||||||||
\(498\) | −7.24910 | −0.324840 | ||||||||
\(499\) | −11.2787 | −0.504902 | −0.252451 | − | 0.967610i | \(-0.581237\pi\) | ||||
−0.252451 | + | 0.967610i | \(0.581237\pi\) | |||||||
\(500\) | 12.0403 | 0.538461 | ||||||||
\(501\) | 8.40658 | 0.375578 | ||||||||
\(502\) | 9.02061 | 0.402609 | ||||||||
\(503\) | 14.1787 | 0.632198 | 0.316099 | − | 0.948726i | \(-0.397627\pi\) | ||||
0.316099 | + | 0.948726i | \(0.397627\pi\) | |||||||
\(504\) | 10.5000 | 0.467708 | ||||||||
\(505\) | 22.9246 | 1.02013 | ||||||||
\(506\) | 4.60055 | 0.204519 | ||||||||
\(507\) | −23.1915 | −1.02997 | ||||||||
\(508\) | 16.8834 | 0.749082 | ||||||||
\(509\) | 5.81771 | 0.257865 | 0.128933 | − | 0.991653i | \(-0.458845\pi\) | ||||
0.128933 | + | 0.991653i | \(0.458845\pi\) | |||||||
\(510\) | −31.7388 | −1.40542 | ||||||||
\(511\) | 7.06463 | 0.312521 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 25.4161 | 1.12215 | ||||||||
\(514\) | 29.2390 | 1.28968 | ||||||||
\(515\) | −13.4539 | −0.592848 | ||||||||
\(516\) | −19.1114 | −0.841333 | ||||||||
\(517\) | −3.71398 | −0.163340 | ||||||||
\(518\) | −2.40454 | −0.105649 | ||||||||
\(519\) | −3.24667 | −0.142513 | ||||||||
\(520\) | −7.47996 | −0.328018 | ||||||||
\(521\) | −37.8255 | −1.65717 | −0.828584 | − | 0.559865i | \(-0.810853\pi\) | ||||
−0.828584 | + | 0.559865i | \(0.810853\pi\) | |||||||
\(522\) | −5.55099 | −0.242960 | ||||||||
\(523\) | 24.4422 | 1.06878 | 0.534391 | − | 0.845237i | \(-0.320541\pi\) | ||||
0.534391 | + | 0.845237i | \(0.320541\pi\) | |||||||
\(524\) | −9.54322 | −0.416898 | ||||||||
\(525\) | −9.89232 | −0.431736 | ||||||||
\(526\) | 15.9830 | 0.696890 | ||||||||
\(527\) | −40.0420 | −1.74426 | ||||||||
\(528\) | 8.07581 | 0.351455 | ||||||||
\(529\) | −19.5314 | −0.849191 | ||||||||
\(530\) | 19.8630 | 0.862795 | ||||||||
\(531\) | −33.3216 | −1.44603 | ||||||||
\(532\) | 2.26465 | 0.0981849 | ||||||||
\(533\) | 6.83362 | 0.295997 | ||||||||
\(534\) | 5.04741 | 0.218423 | ||||||||
\(535\) | 12.7829 | 0.552653 | ||||||||
\(536\) | 7.66184 | 0.330941 | ||||||||
\(537\) | −28.5609 | −1.23249 | ||||||||
\(538\) | −5.57090 | −0.240178 | ||||||||
\(539\) | 12.6840 | 0.546340 | ||||||||
\(540\) | 25.5763 | 1.10063 | ||||||||
\(541\) | −32.7214 | −1.40680 | −0.703402 | − | 0.710792i | \(-0.748337\pi\) | ||||
−0.703402 | + | 0.710792i | \(0.748337\pi\) | |||||||
\(542\) | 4.83280 | 0.207587 | ||||||||
\(543\) | −21.8846 | −0.939159 | ||||||||
\(544\) | −5.81792 | −0.249441 | ||||||||
\(545\) | −21.6978 | −0.929433 | ||||||||
\(546\) | 20.0145 | 0.856542 | ||||||||
\(547\) | −23.3503 | −0.998386 | −0.499193 | − | 0.866491i | \(-0.666370\pi\) | ||||
−0.499193 | + | 0.866491i | \(0.666370\pi\) | |||||||
\(548\) | 20.2600 | 0.865462 | ||||||||
\(549\) | −5.65300 | −0.241264 | ||||||||
\(550\) | −5.47288 | −0.233364 | ||||||||
\(551\) | −1.19724 | −0.0510040 | ||||||||
\(552\) | 6.08880 | 0.259156 | ||||||||
\(553\) | −20.3672 | −0.866100 | ||||||||
\(554\) | −5.59881 | −0.237871 | ||||||||
\(555\) | −9.60493 | −0.407707 | ||||||||
\(556\) | −3.80448 | −0.161346 | ||||||||
\(557\) | −15.3137 | −0.648861 | −0.324430 | − | 0.945910i | \(-0.605173\pi\) | ||||
−0.324430 | + | 0.945910i | \(0.605173\pi\) | |||||||
\(558\) | 52.9148 | 2.24006 | ||||||||
\(559\) | −26.2041 | −1.10832 | ||||||||
\(560\) | 2.27892 | 0.0963020 | ||||||||
\(561\) | 46.9844 | 1.98368 | ||||||||
\(562\) | −13.3974 | −0.565134 | ||||||||
\(563\) | −18.2403 | −0.768735 | −0.384367 | − | 0.923180i | \(-0.625580\pi\) | ||||
−0.384367 | + | 0.923180i | \(0.625580\pi\) | |||||||
\(564\) | −4.91542 | −0.206977 | ||||||||
\(565\) | −21.8396 | −0.918798 | ||||||||
\(566\) | −8.28139 | −0.348093 | ||||||||
\(567\) | −36.9357 | −1.55115 | ||||||||
\(568\) | 8.32609 | 0.349355 | ||||||||
\(569\) | −31.6645 | −1.32744 | −0.663721 | − | 0.747980i | \(-0.731024\pi\) | ||||
−0.663721 | + | 0.747980i | \(0.731024\pi\) | |||||||
\(570\) | 9.04613 | 0.378901 | ||||||||
\(571\) | 11.2700 | 0.471634 | 0.235817 | − | 0.971798i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971798i | \(0.424223\pi\) | |||||||
\(572\) | 11.0729 | 0.462982 | ||||||||
\(573\) | 0.470350 | 0.0196492 | ||||||||
\(574\) | −2.08200 | −0.0869011 | ||||||||
\(575\) | −4.12630 | −0.172079 | ||||||||
\(576\) | 7.68829 | 0.320345 | ||||||||
\(577\) | −15.9919 | −0.665752 | −0.332876 | − | 0.942971i | \(-0.608019\pi\) | ||||
−0.332876 | + | 0.942971i | \(0.608019\pi\) | |||||||
\(578\) | −16.8482 | −0.700792 | ||||||||
\(579\) | −21.8668 | −0.908754 | ||||||||
\(580\) | −1.20478 | −0.0500260 | ||||||||
\(581\) | 3.02824 | 0.125633 | ||||||||
\(582\) | 38.2722 | 1.58643 | ||||||||
\(583\) | −29.4042 | −1.21780 | ||||||||
\(584\) | 5.17284 | 0.214054 | ||||||||
\(585\) | 57.5081 | 2.37767 | ||||||||
\(586\) | 11.8937 | 0.491325 | ||||||||
\(587\) | −7.78822 | −0.321454 | −0.160727 | − | 0.986999i | \(-0.551384\pi\) | ||||
−0.160727 | + | 0.986999i | \(0.551384\pi\) | |||||||
\(588\) | 16.7872 | 0.692294 | ||||||||
\(589\) | 11.4127 | 0.470251 | ||||||||
\(590\) | −7.23211 | −0.297741 | ||||||||
\(591\) | −53.4545 | −2.19882 | ||||||||
\(592\) | −1.76064 | −0.0723620 | ||||||||
\(593\) | 3.64630 | 0.149736 | 0.0748678 | − | 0.997193i | \(-0.476147\pi\) | ||||
0.0748678 | + | 0.997193i | \(0.476147\pi\) | |||||||
\(594\) | −37.8617 | −1.55349 | ||||||||
\(595\) | 13.2586 | 0.543549 | ||||||||
\(596\) | 3.03242 | 0.124213 | ||||||||
\(597\) | −71.7867 | −2.93803 | ||||||||
\(598\) | 8.34849 | 0.341395 | ||||||||
\(599\) | −32.5173 | −1.32862 | −0.664310 | − | 0.747457i | \(-0.731275\pi\) | ||||
−0.664310 | + | 0.747457i | \(0.731275\pi\) | |||||||
\(600\) | −7.24332 | −0.295707 | ||||||||
\(601\) | 5.72376 | 0.233477 | 0.116738 | − | 0.993163i | \(-0.462756\pi\) | ||||
0.116738 | + | 0.993163i | \(0.462756\pi\) | |||||||
\(602\) | 7.98361 | 0.325388 | ||||||||
\(603\) | −58.9064 | −2.39885 | ||||||||
\(604\) | −15.7481 | −0.640781 | ||||||||
\(605\) | 8.17330 | 0.332292 | ||||||||
\(606\) | −44.9145 | −1.82453 | ||||||||
\(607\) | −8.87069 | −0.360050 | −0.180025 | − | 0.983662i | \(-0.557618\pi\) | ||||
−0.180025 | + | 0.983662i | \(0.557618\pi\) | |||||||
\(608\) | 1.65821 | 0.0672493 | ||||||||
\(609\) | 3.22370 | 0.130631 | ||||||||
\(610\) | −1.22693 | −0.0496768 | ||||||||
\(611\) | −6.73965 | −0.272657 | ||||||||
\(612\) | 44.7298 | 1.80810 | ||||||||
\(613\) | −40.9503 | −1.65397 | −0.826984 | − | 0.562226i | \(-0.809945\pi\) | ||||
−0.826984 | + | 0.562226i | \(0.809945\pi\) | |||||||
\(614\) | −13.8965 | −0.560818 | ||||||||
\(615\) | −8.31656 | −0.335356 | ||||||||
\(616\) | −3.37359 | −0.135926 | ||||||||
\(617\) | 6.38180 | 0.256922 | 0.128461 | − | 0.991715i | \(-0.458996\pi\) | ||||
0.128461 | + | 0.991715i | \(0.458996\pi\) | |||||||
\(618\) | 26.3592 | 1.06032 | ||||||||
\(619\) | −15.8492 | −0.637032 | −0.318516 | − | 0.947918i | \(-0.603184\pi\) | ||||
−0.318516 | + | 0.947918i | \(0.603184\pi\) | |||||||
\(620\) | 11.4846 | 0.461234 | ||||||||
\(621\) | −28.5460 | −1.14551 | ||||||||
\(622\) | 16.3562 | 0.655822 | ||||||||
\(623\) | −2.10851 | −0.0844755 | ||||||||
\(624\) | 14.6550 | 0.586668 | ||||||||
\(625\) | −9.01349 | −0.360539 | ||||||||
\(626\) | −6.46571 | −0.258422 | ||||||||
\(627\) | −13.3914 | −0.534801 | ||||||||
\(628\) | 1.34112 | 0.0535165 | ||||||||
\(629\) | −10.2433 | −0.408426 | ||||||||
\(630\) | −17.5210 | −0.698053 | ||||||||
\(631\) | 17.7673 | 0.707306 | 0.353653 | − | 0.935377i | \(-0.384939\pi\) | ||||
0.353653 | + | 0.935377i | \(0.384939\pi\) | |||||||
\(632\) | −14.9132 | −0.593214 | ||||||||
\(633\) | −71.3369 | −2.83539 | ||||||||
\(634\) | 2.63051 | 0.104471 | ||||||||
\(635\) | −28.1728 | −1.11800 | ||||||||
\(636\) | −38.9163 | −1.54313 | ||||||||
\(637\) | 23.0174 | 0.911981 | ||||||||
\(638\) | 1.78350 | 0.0706094 | ||||||||
\(639\) | −64.0134 | −2.53233 | ||||||||
\(640\) | 1.66866 | 0.0659597 | ||||||||
\(641\) | 41.2143 | 1.62787 | 0.813933 | − | 0.580959i | \(-0.197322\pi\) | ||||
0.813933 | + | 0.580959i | \(0.197322\pi\) | |||||||
\(642\) | −25.0446 | −0.988432 | ||||||||
\(643\) | −16.6183 | −0.655360 | −0.327680 | − | 0.944789i | \(-0.606267\pi\) | ||||
−0.327680 | + | 0.944789i | \(0.606267\pi\) | |||||||
\(644\) | −2.54354 | −0.100229 | ||||||||
\(645\) | 31.8905 | 1.25569 | ||||||||
\(646\) | 9.64734 | 0.379569 | ||||||||
\(647\) | 14.0065 | 0.550652 | 0.275326 | − | 0.961351i | \(-0.411214\pi\) | ||||
0.275326 | + | 0.961351i | \(0.411214\pi\) | |||||||
\(648\) | −27.0449 | −1.06242 | ||||||||
\(649\) | 10.7060 | 0.420248 | ||||||||
\(650\) | −9.93148 | −0.389545 | ||||||||
\(651\) | −30.7300 | −1.20440 | ||||||||
\(652\) | 0.0974129 | 0.00381498 | ||||||||
\(653\) | −22.2727 | −0.871599 | −0.435799 | − | 0.900044i | \(-0.643534\pi\) | ||||
−0.435799 | + | 0.900044i | \(0.643534\pi\) | |||||||
\(654\) | 42.5110 | 1.66231 | ||||||||
\(655\) | 15.9244 | 0.622219 | ||||||||
\(656\) | −1.52448 | −0.0595208 | ||||||||
\(657\) | −39.7703 | −1.55159 | ||||||||
\(658\) | 2.05337 | 0.0800487 | ||||||||
\(659\) | −48.9389 | −1.90639 | −0.953195 | − | 0.302356i | \(-0.902227\pi\) | ||||
−0.953195 | + | 0.302356i | \(0.902227\pi\) | |||||||
\(660\) | −13.4758 | −0.524545 | ||||||||
\(661\) | −33.8685 | −1.31733 | −0.658666 | − | 0.752435i | \(-0.728879\pi\) | ||||
−0.658666 | + | 0.752435i | \(0.728879\pi\) | |||||||
\(662\) | −14.4302 | −0.560848 | ||||||||
\(663\) | 85.2613 | 3.31128 | ||||||||
\(664\) | 2.21733 | 0.0860490 | ||||||||
\(665\) | −3.77893 | −0.146541 | ||||||||
\(666\) | 13.5363 | 0.524522 | ||||||||
\(667\) | 1.34468 | 0.0520661 | ||||||||
\(668\) | −2.57137 | −0.0994895 | ||||||||
\(669\) | −4.64987 | −0.179775 | ||||||||
\(670\) | −12.7850 | −0.493929 | ||||||||
\(671\) | 1.81628 | 0.0701165 | ||||||||
\(672\) | −4.46493 | −0.172238 | ||||||||
\(673\) | −11.9786 | −0.461741 | −0.230870 | − | 0.972984i | \(-0.574157\pi\) | ||||
−0.230870 | + | 0.972984i | \(0.574157\pi\) | |||||||
\(674\) | −10.8467 | −0.417798 | ||||||||
\(675\) | 33.9588 | 1.30707 | ||||||||
\(676\) | 7.09374 | 0.272836 | ||||||||
\(677\) | 29.7177 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(678\) | 42.7887 | 1.64329 | ||||||||
\(679\) | −15.9879 | −0.613557 | ||||||||
\(680\) | 9.70815 | 0.372291 | ||||||||
\(681\) | −25.9476 | −0.994313 | ||||||||
\(682\) | −17.0012 | −0.651010 | ||||||||
\(683\) | −10.5606 | −0.404091 | −0.202046 | − | 0.979376i | \(-0.564759\pi\) | ||||
−0.202046 | + | 0.979376i | \(0.564759\pi\) | |||||||
\(684\) | −12.7488 | −0.487463 | ||||||||
\(685\) | −33.8070 | −1.29170 | ||||||||
\(686\) | −16.5727 | −0.632749 | ||||||||
\(687\) | −14.6083 | −0.557340 | ||||||||
\(688\) | 5.84573 | 0.222866 | ||||||||
\(689\) | −53.3590 | −2.03281 | ||||||||
\(690\) | −10.1602 | −0.386791 | ||||||||
\(691\) | 21.5855 | 0.821153 | 0.410576 | − | 0.911826i | \(-0.365328\pi\) | ||||
0.410576 | + | 0.911826i | \(0.365328\pi\) | |||||||
\(692\) | 0.993081 | 0.0377513 | ||||||||
\(693\) | 25.9371 | 0.985271 | ||||||||
\(694\) | 33.0799 | 1.25569 | ||||||||
\(695\) | 6.34840 | 0.240809 | ||||||||
\(696\) | 2.36045 | 0.0894726 | ||||||||
\(697\) | −8.86928 | −0.335948 | ||||||||
\(698\) | −6.71026 | −0.253987 | ||||||||
\(699\) | −22.3714 | −0.846165 | ||||||||
\(700\) | 3.02583 | 0.114366 | ||||||||
\(701\) | −5.82014 | −0.219824 | −0.109912 | − | 0.993941i | \(-0.535057\pi\) | ||||
−0.109912 | + | 0.993941i | \(0.535057\pi\) | |||||||
\(702\) | −68.7066 | −2.59316 | ||||||||
\(703\) | 2.91952 | 0.110112 | ||||||||
\(704\) | −2.47020 | −0.0930992 | ||||||||
\(705\) | 8.20219 | 0.308912 | ||||||||
\(706\) | −30.9815 | −1.16600 | ||||||||
\(707\) | 18.7626 | 0.705640 | ||||||||
\(708\) | 14.1694 | 0.532517 | ||||||||
\(709\) | 9.31063 | 0.349668 | 0.174834 | − | 0.984598i | \(-0.444061\pi\) | ||||
0.174834 | + | 0.984598i | \(0.444061\pi\) | |||||||
\(710\) | −13.8934 | −0.521412 | ||||||||
\(711\) | 114.657 | 4.29996 | ||||||||
\(712\) | −1.54388 | −0.0578595 | ||||||||
\(713\) | −12.8182 | −0.480044 | ||||||||
\(714\) | −25.9766 | −0.972150 | ||||||||
\(715\) | −18.4770 | −0.691000 | ||||||||
\(716\) | 8.73610 | 0.326483 | ||||||||
\(717\) | −34.2044 | −1.27739 | ||||||||
\(718\) | −6.40867 | −0.239169 | ||||||||
\(719\) | 12.0313 | 0.448692 | 0.224346 | − | 0.974510i | \(-0.427975\pi\) | ||||
0.224346 | + | 0.974510i | \(0.427975\pi\) | |||||||
\(720\) | −12.8292 | −0.478115 | ||||||||
\(721\) | −11.0113 | −0.410082 | ||||||||
\(722\) | 16.2503 | 0.604775 | ||||||||
\(723\) | −32.8917 | −1.22325 | ||||||||
\(724\) | 6.69399 | 0.248780 | ||||||||
\(725\) | −1.59965 | −0.0594094 | ||||||||
\(726\) | −16.0134 | −0.594312 | ||||||||
\(727\) | −50.7447 | −1.88202 | −0.941008 | − | 0.338383i | \(-0.890120\pi\) | ||||
−0.941008 | + | 0.338383i | \(0.890120\pi\) | |||||||
\(728\) | −6.12196 | −0.226895 | ||||||||
\(729\) | 57.5997 | 2.13332 | ||||||||
\(730\) | −8.63173 | −0.319475 | ||||||||
\(731\) | 34.0100 | 1.25791 | ||||||||
\(732\) | 2.40383 | 0.0888481 | ||||||||
\(733\) | −29.4276 | −1.08693 | −0.543466 | − | 0.839431i | \(-0.682888\pi\) | ||||
−0.543466 | + | 0.839431i | \(0.682888\pi\) | |||||||
\(734\) | 15.9079 | 0.587172 | ||||||||
\(735\) | −28.0123 | −1.03325 | ||||||||
\(736\) | −1.86242 | −0.0686497 | ||||||||
\(737\) | 18.9263 | 0.697158 | ||||||||
\(738\) | 11.7206 | 0.431442 | ||||||||
\(739\) | −14.2276 | −0.523369 | −0.261685 | − | 0.965153i | \(-0.584278\pi\) | ||||
−0.261685 | + | 0.965153i | \(0.584278\pi\) | |||||||
\(740\) | 2.93792 | 0.108000 | ||||||||
\(741\) | −24.3010 | −0.892720 | ||||||||
\(742\) | 16.2569 | 0.596809 | ||||||||
\(743\) | −44.0338 | −1.61544 | −0.807722 | − | 0.589564i | \(-0.799300\pi\) | ||||
−0.807722 | + | 0.589564i | \(0.799300\pi\) | |||||||
\(744\) | −22.5010 | −0.824927 | ||||||||
\(745\) | −5.06009 | −0.185387 | ||||||||
\(746\) | −21.3965 | −0.783382 | ||||||||
\(747\) | −17.0475 | −0.623734 | ||||||||
\(748\) | −14.3714 | −0.525471 | ||||||||
\(749\) | 10.4621 | 0.382278 | ||||||||
\(750\) | 39.3634 | 1.43735 | ||||||||
\(751\) | 37.7758 | 1.37846 | 0.689230 | − | 0.724543i | \(-0.257949\pi\) | ||||
0.689230 | + | 0.724543i | \(0.257949\pi\) | |||||||
\(752\) | 1.50351 | 0.0548274 | ||||||||
\(753\) | 29.4910 | 1.07471 | ||||||||
\(754\) | 3.23646 | 0.117865 | ||||||||
\(755\) | 26.2783 | 0.956364 | ||||||||
\(756\) | 20.9329 | 0.761321 | ||||||||
\(757\) | −34.7261 | −1.26214 | −0.631070 | − | 0.775726i | \(-0.717384\pi\) | ||||
−0.631070 | + | 0.775726i | \(0.717384\pi\) | |||||||
\(758\) | 26.8603 | 0.975611 | ||||||||
\(759\) | 15.0406 | 0.545937 | ||||||||
\(760\) | −2.76700 | −0.100370 | ||||||||
\(761\) | 25.2423 | 0.915032 | 0.457516 | − | 0.889201i | \(-0.348739\pi\) | ||||
0.457516 | + | 0.889201i | \(0.348739\pi\) | |||||||
\(762\) | 55.1970 | 1.99958 | ||||||||
\(763\) | −17.7586 | −0.642903 | ||||||||
\(764\) | −0.143869 | −0.00520500 | ||||||||
\(765\) | −74.6391 | −2.69858 | ||||||||
\(766\) | 6.05516 | 0.218782 | ||||||||
\(767\) | 19.4279 | 0.701502 | ||||||||
\(768\) | −3.26929 | −0.117971 | ||||||||
\(769\) | 3.84225 | 0.138555 | 0.0692775 | − | 0.997597i | \(-0.477931\pi\) | ||||
0.0692775 | + | 0.997597i | \(0.477931\pi\) | |||||||
\(770\) | 5.62939 | 0.202869 | ||||||||
\(771\) | 95.5909 | 3.44262 | ||||||||
\(772\) | 6.68854 | 0.240726 | ||||||||
\(773\) | −16.8917 | −0.607552 | −0.303776 | − | 0.952744i | \(-0.598247\pi\) | ||||
−0.303776 | + | 0.952744i | \(0.598247\pi\) | |||||||
\(774\) | −44.9437 | −1.61547 | ||||||||
\(775\) | 15.2487 | 0.547748 | ||||||||
\(776\) | −11.7066 | −0.420241 | ||||||||
\(777\) | −7.86115 | −0.282017 | ||||||||
\(778\) | 20.2788 | 0.727030 | ||||||||
\(779\) | 2.52790 | 0.0905716 | ||||||||
\(780\) | −24.4542 | −0.875600 | ||||||||
\(781\) | 20.5671 | 0.735949 | ||||||||
\(782\) | −10.8354 | −0.387473 | ||||||||
\(783\) | −11.0665 | −0.395483 | ||||||||
\(784\) | −5.13482 | −0.183386 | ||||||||
\(785\) | −2.23788 | −0.0798732 | ||||||||
\(786\) | −31.1996 | −1.11285 | ||||||||
\(787\) | 42.8806 | 1.52853 | 0.764264 | − | 0.644903i | \(-0.223102\pi\) | ||||
0.764264 | + | 0.644903i | \(0.223102\pi\) | |||||||
\(788\) | 16.3505 | 0.582461 | ||||||||
\(789\) | 52.2530 | 1.86026 | ||||||||
\(790\) | 24.8851 | 0.885371 | ||||||||
\(791\) | −17.8746 | −0.635547 | ||||||||
\(792\) | 18.9916 | 0.674837 | ||||||||
\(793\) | 3.29594 | 0.117042 | ||||||||
\(794\) | 12.6736 | 0.449770 | ||||||||
\(795\) | 64.9381 | 2.30312 | ||||||||
\(796\) | 21.9579 | 0.778275 | ||||||||
\(797\) | −20.1368 | −0.713281 | −0.356640 | − | 0.934242i | \(-0.616078\pi\) | ||||
−0.356640 | + | 0.934242i | \(0.616078\pi\) | |||||||
\(798\) | 7.40379 | 0.262091 | ||||||||
\(799\) | 8.74731 | 0.309458 | ||||||||
\(800\) | 2.21556 | 0.0783319 | ||||||||
\(801\) | 11.8698 | 0.419399 | ||||||||
\(802\) | 1.51459 | 0.0534822 | ||||||||
\(803\) | 12.7780 | 0.450924 | ||||||||
\(804\) | 25.0488 | 0.883403 | ||||||||
\(805\) | 4.24431 | 0.149592 | ||||||||
\(806\) | −30.8516 | −1.08670 | ||||||||
\(807\) | −18.2129 | −0.641125 | ||||||||
\(808\) | 13.7383 | 0.483311 | ||||||||
\(809\) | −3.79078 | −0.133277 | −0.0666384 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666384 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(810\) | 45.1288 | 1.58567 | ||||||||
\(811\) | −4.16895 | −0.146392 | −0.0731959 | − | 0.997318i | \(-0.523320\pi\) | ||||
−0.0731959 | + | 0.997318i | \(0.523320\pi\) | |||||||
\(812\) | −0.986055 | −0.0346037 | ||||||||
\(813\) | 15.7998 | 0.554125 | ||||||||
\(814\) | −4.34914 | −0.152437 | ||||||||
\(815\) | −0.162549 | −0.00569386 | ||||||||
\(816\) | −19.0205 | −0.665850 | ||||||||
\(817\) | −9.69346 | −0.339131 | ||||||||
\(818\) | −32.1903 | −1.12551 | ||||||||
\(819\) | 47.0674 | 1.64467 | ||||||||
\(820\) | 2.54384 | 0.0888347 | ||||||||
\(821\) | 5.70995 | 0.199278 | 0.0996392 | − | 0.995024i | \(-0.468231\pi\) | ||||
0.0996392 | + | 0.995024i | \(0.468231\pi\) | |||||||
\(822\) | 66.2358 | 2.31024 | ||||||||
\(823\) | −17.8561 | −0.622426 | −0.311213 | − | 0.950340i | \(-0.600735\pi\) | ||||
−0.311213 | + | 0.950340i | \(0.600735\pi\) | |||||||
\(824\) | −8.06265 | −0.280876 | ||||||||
\(825\) | −17.8925 | −0.622935 | ||||||||
\(826\) | −5.91911 | −0.205952 | ||||||||
\(827\) | −35.1971 | −1.22392 | −0.611962 | − | 0.790887i | \(-0.709619\pi\) | ||||
−0.611962 | + | 0.790887i | \(0.709619\pi\) | |||||||
\(828\) | 14.3188 | 0.497613 | ||||||||
\(829\) | 30.7097 | 1.06659 | 0.533296 | − | 0.845929i | \(-0.320953\pi\) | ||||
0.533296 | + | 0.845929i | \(0.320953\pi\) | |||||||
\(830\) | −3.69998 | −0.128428 | ||||||||
\(831\) | −18.3042 | −0.634965 | ||||||||
\(832\) | −4.48260 | −0.155406 | ||||||||
\(833\) | −29.8740 | −1.03507 | ||||||||
\(834\) | −12.4380 | −0.430692 | ||||||||
\(835\) | 4.29076 | 0.148488 | ||||||||
\(836\) | 4.09611 | 0.141667 | ||||||||
\(837\) | 105.491 | 3.64631 | ||||||||
\(838\) | −38.4497 | −1.32822 | ||||||||
\(839\) | 19.9074 | 0.687281 | 0.343640 | − | 0.939101i | \(-0.388340\pi\) | ||||
0.343640 | + | 0.939101i | \(0.388340\pi\) | |||||||
\(840\) | 7.45046 | 0.257065 | ||||||||
\(841\) | −28.4787 | −0.982024 | ||||||||
\(842\) | 23.6302 | 0.814349 | ||||||||
\(843\) | −43.8000 | −1.50855 | ||||||||
\(844\) | 21.8203 | 0.751085 | ||||||||
\(845\) | −11.8371 | −0.407207 | ||||||||
\(846\) | −11.5594 | −0.397421 | ||||||||
\(847\) | 6.68943 | 0.229852 | ||||||||
\(848\) | 11.9036 | 0.408770 | ||||||||
\(849\) | −27.0743 | −0.929188 | ||||||||
\(850\) | 12.8900 | 0.442122 | ||||||||
\(851\) | −3.27906 | −0.112405 | ||||||||
\(852\) | 27.2204 | 0.932557 | ||||||||
\(853\) | −18.8117 | −0.644101 | −0.322051 | − | 0.946722i | \(-0.604372\pi\) | ||||
−0.322051 | + | 0.946722i | \(0.604372\pi\) | |||||||
\(854\) | −1.00418 | −0.0343622 | ||||||||
\(855\) | 21.2735 | 0.727537 | ||||||||
\(856\) | 7.66056 | 0.261832 | ||||||||
\(857\) | 42.9068 | 1.46567 | 0.732834 | − | 0.680408i | \(-0.238197\pi\) | ||||
0.732834 | + | 0.680408i | \(0.238197\pi\) | |||||||
\(858\) | 36.2007 | 1.23587 | ||||||||
\(859\) | −12.2051 | −0.416434 | −0.208217 | − | 0.978083i | \(-0.566766\pi\) | ||||
−0.208217 | + | 0.978083i | \(0.566766\pi\) | |||||||
\(860\) | −9.75456 | −0.332628 | ||||||||
\(861\) | −6.80668 | −0.231971 | ||||||||
\(862\) | 15.9285 | 0.542526 | ||||||||
\(863\) | 44.5428 | 1.51625 | 0.758127 | − | 0.652106i | \(-0.226115\pi\) | ||||
0.758127 | + | 0.652106i | \(0.226115\pi\) | |||||||
\(864\) | 15.3274 | 0.521448 | ||||||||
\(865\) | −1.65712 | −0.0563437 | ||||||||
\(866\) | −27.3235 | −0.928490 | ||||||||
\(867\) | −55.0817 | −1.87067 | ||||||||
\(868\) | 9.39958 | 0.319042 | ||||||||
\(869\) | −36.8385 | −1.24966 | ||||||||
\(870\) | −3.93880 | −0.133538 | ||||||||
\(871\) | 34.3450 | 1.16374 | ||||||||
\(872\) | −13.0031 | −0.440341 | ||||||||
\(873\) | 90.0035 | 3.04616 | ||||||||
\(874\) | 3.08829 | 0.104463 | ||||||||
\(875\) | −16.4437 | −0.555898 | ||||||||
\(876\) | 16.9115 | 0.571388 | ||||||||
\(877\) | −3.44974 | −0.116489 | −0.0582447 | − | 0.998302i | \(-0.518550\pi\) | ||||
−0.0582447 | + | 0.998302i | \(0.518550\pi\) | |||||||
\(878\) | 20.7917 | 0.701687 | ||||||||
\(879\) | 38.8841 | 1.31153 | ||||||||
\(880\) | 4.12193 | 0.138950 | ||||||||
\(881\) | −13.9242 | −0.469117 | −0.234559 | − | 0.972102i | \(-0.575364\pi\) | ||||
−0.234559 | + | 0.972102i | \(0.575364\pi\) | |||||||
\(882\) | 39.4780 | 1.32929 | ||||||||
\(883\) | 8.45867 | 0.284657 | 0.142328 | − | 0.989819i | \(-0.454541\pi\) | ||||
0.142328 | + | 0.989819i | \(0.454541\pi\) | |||||||
\(884\) | −26.0794 | −0.877146 | ||||||||
\(885\) | −23.6439 | −0.794781 | ||||||||
\(886\) | 22.9946 | 0.772518 | ||||||||
\(887\) | 39.7557 | 1.33486 | 0.667432 | − | 0.744671i | \(-0.267393\pi\) | ||||
0.667432 | + | 0.744671i | \(0.267393\pi\) | |||||||
\(888\) | −5.75606 | −0.193161 | ||||||||
\(889\) | −23.0580 | −0.773341 | ||||||||
\(890\) | 2.57622 | 0.0863551 | ||||||||
\(891\) | −66.8063 | −2.23810 | ||||||||
\(892\) | 1.42229 | 0.0476217 | ||||||||
\(893\) | −2.49314 | −0.0834298 | ||||||||
\(894\) | 9.91388 | 0.331570 | ||||||||
\(895\) | −14.5776 | −0.487276 | ||||||||
\(896\) | 1.36572 | 0.0456254 | ||||||||
\(897\) | 27.2937 | 0.911309 | ||||||||
\(898\) | −13.2910 | −0.443526 | ||||||||
\(899\) | −4.96922 | −0.165733 | ||||||||
\(900\) | −17.0339 | −0.567796 | ||||||||
\(901\) | 69.2540 | 2.30718 | ||||||||
\(902\) | −3.76576 | −0.125386 | ||||||||
\(903\) | 26.1008 | 0.868579 | ||||||||
\(904\) | −13.0881 | −0.435303 | ||||||||
\(905\) | −11.1700 | −0.371304 | ||||||||
\(906\) | −51.4852 | −1.71048 | ||||||||
\(907\) | 54.7806 | 1.81896 | 0.909481 | − | 0.415746i | \(-0.136480\pi\) | ||||
0.909481 | + | 0.415746i | \(0.136480\pi\) | |||||||
\(908\) | 7.93675 | 0.263390 | ||||||||
\(909\) | −105.624 | −3.50332 | ||||||||
\(910\) | 10.2155 | 0.338641 | ||||||||
\(911\) | 52.1209 | 1.72684 | 0.863422 | − | 0.504483i | \(-0.168317\pi\) | ||||
0.863422 | + | 0.504483i | \(0.168317\pi\) | |||||||
\(912\) | 5.42118 | 0.179513 | ||||||||
\(913\) | 5.47724 | 0.181270 | ||||||||
\(914\) | −16.1759 | −0.535051 | ||||||||
\(915\) | −4.01118 | −0.132606 | ||||||||
\(916\) | 4.46832 | 0.147638 | ||||||||
\(917\) | 13.0333 | 0.430399 | ||||||||
\(918\) | 89.1735 | 2.94316 | ||||||||
\(919\) | −51.6274 | −1.70303 | −0.851515 | − | 0.524331i | \(-0.824316\pi\) | ||||
−0.851515 | + | 0.524331i | \(0.824316\pi\) | |||||||
\(920\) | 3.10775 | 0.102460 | ||||||||
\(921\) | −45.4318 | −1.49703 | ||||||||
\(922\) | 7.74907 | 0.255202 | ||||||||
\(923\) | 37.3226 | 1.22849 | ||||||||
\(924\) | −11.0293 | −0.362836 | ||||||||
\(925\) | 3.90081 | 0.128258 | ||||||||
\(926\) | −4.35584 | −0.143142 | ||||||||
\(927\) | 61.9880 | 2.03595 | ||||||||
\(928\) | −0.722005 | −0.0237010 | ||||||||
\(929\) | 4.27176 | 0.140152 | 0.0700760 | − | 0.997542i | \(-0.477676\pi\) | ||||
0.0700760 | + | 0.997542i | \(0.477676\pi\) | |||||||
\(930\) | 37.5466 | 1.23120 | ||||||||
\(931\) | 8.51462 | 0.279055 | ||||||||
\(932\) | 6.84289 | 0.224146 | ||||||||
\(933\) | 53.4731 | 1.75063 | ||||||||
\(934\) | 12.3000 | 0.402469 | ||||||||
\(935\) | 23.9811 | 0.784265 | ||||||||
\(936\) | 34.4635 | 1.12648 | ||||||||
\(937\) | 11.8825 | 0.388183 | 0.194092 | − | 0.980983i | \(-0.437824\pi\) | ||||
0.194092 | + | 0.980983i | \(0.437824\pi\) | |||||||
\(938\) | −10.4639 | −0.341658 | ||||||||
\(939\) | −21.1383 | −0.689823 | ||||||||
\(940\) | −2.50886 | −0.0818299 | ||||||||
\(941\) | 27.8061 | 0.906453 | 0.453226 | − | 0.891395i | \(-0.350273\pi\) | ||||
0.453226 | + | 0.891395i | \(0.350273\pi\) | |||||||
\(942\) | 4.38451 | 0.142855 | ||||||||
\(943\) | −2.83922 | −0.0924576 | ||||||||
\(944\) | −4.33407 | −0.141062 | ||||||||
\(945\) | −34.9299 | −1.13627 | ||||||||
\(946\) | 14.4401 | 0.469489 | ||||||||
\(947\) | 46.3284 | 1.50547 | 0.752736 | − | 0.658323i | \(-0.228734\pi\) | ||||
0.752736 | + | 0.658323i | \(0.228734\pi\) | |||||||
\(948\) | −48.7555 | −1.58351 | ||||||||
\(949\) | 23.1878 | 0.752708 | ||||||||
\(950\) | −3.67387 | −0.119196 | ||||||||
\(951\) | 8.59992 | 0.278872 | ||||||||
\(952\) | 7.94563 | 0.257519 | ||||||||
\(953\) | 35.1394 | 1.13828 | 0.569139 | − | 0.822242i | \(-0.307277\pi\) | ||||
0.569139 | + | 0.822242i | \(0.307277\pi\) | |||||||
\(954\) | −91.5180 | −2.96300 | ||||||||
\(955\) | 0.240069 | 0.00776845 | ||||||||
\(956\) | 10.4623 | 0.338376 | ||||||||
\(957\) | 5.83078 | 0.188482 | ||||||||
\(958\) | 37.8644 | 1.22334 | ||||||||
\(959\) | −27.6693 | −0.893490 | ||||||||
\(960\) | 5.45535 | 0.176071 | ||||||||
\(961\) | 16.3692 | 0.528038 | ||||||||
\(962\) | −7.89227 | −0.254457 | ||||||||
\(963\) | −58.8966 | −1.89792 | ||||||||
\(964\) | 10.0608 | 0.324036 | ||||||||
\(965\) | −11.1609 | −0.359283 | ||||||||
\(966\) | −8.31557 | −0.267549 | ||||||||
\(967\) | −31.2537 | −1.00505 | −0.502526 | − | 0.864562i | \(-0.667596\pi\) | ||||
−0.502526 | + | 0.864562i | \(0.667596\pi\) | |||||||
\(968\) | 4.89811 | 0.157431 | ||||||||
\(969\) | 31.5400 | 1.01321 | ||||||||
\(970\) | 19.5343 | 0.627210 | ||||||||
\(971\) | −39.6882 | −1.27366 | −0.636828 | − | 0.771006i | \(-0.719754\pi\) | ||||
−0.636828 | + | 0.771006i | \(0.719754\pi\) | |||||||
\(972\) | −42.4356 | −1.36112 | ||||||||
\(973\) | 5.19584 | 0.166571 | ||||||||
\(974\) | −43.1079 | −1.38127 | ||||||||
\(975\) | −32.4689 | −1.03984 | ||||||||
\(976\) | −0.735274 | −0.0235356 | ||||||||
\(977\) | −47.9201 | −1.53310 | −0.766550 | − | 0.642184i | \(-0.778028\pi\) | ||||
−0.766550 | + | 0.642184i | \(0.778028\pi\) | |||||||
\(978\) | 0.318471 | 0.0101836 | ||||||||
\(979\) | −3.81370 | −0.121886 | ||||||||
\(980\) | 8.56829 | 0.273704 | ||||||||
\(981\) | 99.9717 | 3.19185 | ||||||||
\(982\) | 10.8096 | 0.344950 | ||||||||
\(983\) | 2.90148 | 0.0925428 | 0.0462714 | − | 0.998929i | \(-0.485266\pi\) | ||||
0.0462714 | + | 0.998929i | \(0.485266\pi\) | |||||||
\(984\) | −4.98396 | −0.158883 | ||||||||
\(985\) | −27.2834 | −0.869322 | ||||||||
\(986\) | −4.20057 | −0.133773 | ||||||||
\(987\) | 6.71307 | 0.213679 | ||||||||
\(988\) | 7.43310 | 0.236479 | ||||||||
\(989\) | 10.8872 | 0.346193 | ||||||||
\(990\) | −31.6906 | −1.00719 | ||||||||
\(991\) | 27.1166 | 0.861388 | 0.430694 | − | 0.902498i | \(-0.358269\pi\) | ||||
0.430694 | + | 0.902498i | \(0.358269\pi\) | |||||||
\(992\) | 6.88253 | 0.218520 | ||||||||
\(993\) | −47.1767 | −1.49711 | ||||||||
\(994\) | −11.3711 | −0.360669 | ||||||||
\(995\) | −36.6403 | −1.16157 | ||||||||
\(996\) | 7.24910 | 0.229697 | ||||||||
\(997\) | −20.0165 | −0.633930 | −0.316965 | − | 0.948437i | \(-0.602664\pi\) | ||||
−0.316965 | + | 0.948437i | \(0.602664\pi\) | |||||||
\(998\) | 11.2787 | 0.357020 | ||||||||
\(999\) | 26.9861 | 0.853801 |
(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 | 8026.2.a.b.1.1 | ✓ | 81 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.b.1.1 | ✓ | 81 | 1.1 | even | 1 | trivial |