Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −2.78808 | −1.60970 | −0.804849 | − | 0.593480i | \(-0.797754\pi\) | ||||
−0.804849 | + | 0.593480i | \(0.797754\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.68662 | 0.754277 | 0.377139 | − | 0.926157i | \(-0.376908\pi\) | ||||
0.377139 | + | 0.926157i | \(0.376908\pi\) | |||||||
\(6\) | −2.78808 | −1.13823 | ||||||||
\(7\) | −0.478055 | −0.180688 | −0.0903440 | − | 0.995911i | \(-0.528797\pi\) | ||||
−0.0903440 | + | 0.995911i | \(0.528797\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.77338 | 1.59113 | ||||||||
\(10\) | 1.68662 | 0.533355 | ||||||||
\(11\) | 2.20706 | 0.665455 | 0.332727 | − | 0.943023i | \(-0.392031\pi\) | ||||
0.332727 | + | 0.943023i | \(0.392031\pi\) | |||||||
\(12\) | −2.78808 | −0.804849 | ||||||||
\(13\) | 5.56059 | 1.54223 | 0.771115 | − | 0.636696i | \(-0.219699\pi\) | ||||
0.771115 | + | 0.636696i | \(0.219699\pi\) | |||||||
\(14\) | −0.478055 | −0.127766 | ||||||||
\(15\) | −4.70241 | −1.21416 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.64824 | 0.399758 | 0.199879 | − | 0.979821i | \(-0.435945\pi\) | ||||
0.199879 | + | 0.979821i | \(0.435945\pi\) | |||||||
\(18\) | 4.77338 | 1.12510 | ||||||||
\(19\) | 4.26835 | 0.979227 | 0.489614 | − | 0.871939i | \(-0.337138\pi\) | ||||
0.489614 | + | 0.871939i | \(0.337138\pi\) | |||||||
\(20\) | 1.68662 | 0.377139 | ||||||||
\(21\) | 1.33286 | 0.290853 | ||||||||
\(22\) | 2.20706 | 0.470548 | ||||||||
\(23\) | −6.71615 | −1.40041 | −0.700207 | − | 0.713940i | \(-0.746909\pi\) | ||||
−0.700207 | + | 0.713940i | \(0.746909\pi\) | |||||||
\(24\) | −2.78808 | −0.569114 | ||||||||
\(25\) | −2.15533 | −0.431066 | ||||||||
\(26\) | 5.56059 | 1.09052 | ||||||||
\(27\) | −4.94431 | −0.951533 | ||||||||
\(28\) | −0.478055 | −0.0903440 | ||||||||
\(29\) | 3.62683 | 0.673485 | 0.336743 | − | 0.941597i | \(-0.390675\pi\) | ||||
0.336743 | + | 0.941597i | \(0.390675\pi\) | |||||||
\(30\) | −4.70241 | −0.858539 | ||||||||
\(31\) | 2.87716 | 0.516752 | 0.258376 | − | 0.966044i | \(-0.416813\pi\) | ||||
0.258376 | + | 0.966044i | \(0.416813\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.15347 | −1.07118 | ||||||||
\(34\) | 1.64824 | 0.282671 | ||||||||
\(35\) | −0.806296 | −0.136289 | ||||||||
\(36\) | 4.77338 | 0.795563 | ||||||||
\(37\) | 1.83077 | 0.300977 | 0.150489 | − | 0.988612i | \(-0.451915\pi\) | ||||
0.150489 | + | 0.988612i | \(0.451915\pi\) | |||||||
\(38\) | 4.26835 | 0.692418 | ||||||||
\(39\) | −15.5034 | −2.48252 | ||||||||
\(40\) | 1.68662 | 0.266677 | ||||||||
\(41\) | 6.78226 | 1.05921 | 0.529606 | − | 0.848244i | \(-0.322340\pi\) | ||||
0.529606 | + | 0.848244i | \(0.322340\pi\) | |||||||
\(42\) | 1.33286 | 0.205664 | ||||||||
\(43\) | 1.02674 | 0.156576 | 0.0782882 | − | 0.996931i | \(-0.475055\pi\) | ||||
0.0782882 | + | 0.996931i | \(0.475055\pi\) | |||||||
\(44\) | 2.20706 | 0.332727 | ||||||||
\(45\) | 8.05085 | 1.20015 | ||||||||
\(46\) | −6.71615 | −0.990242 | ||||||||
\(47\) | 10.3458 | 1.50909 | 0.754543 | − | 0.656251i | \(-0.227859\pi\) | ||||
0.754543 | + | 0.656251i | \(0.227859\pi\) | |||||||
\(48\) | −2.78808 | −0.402424 | ||||||||
\(49\) | −6.77146 | −0.967352 | ||||||||
\(50\) | −2.15533 | −0.304809 | ||||||||
\(51\) | −4.59543 | −0.643489 | ||||||||
\(52\) | 5.56059 | 0.771115 | ||||||||
\(53\) | 12.9134 | 1.77379 | 0.886894 | − | 0.461974i | \(-0.152859\pi\) | ||||
0.886894 | + | 0.461974i | \(0.152859\pi\) | |||||||
\(54\) | −4.94431 | −0.672835 | ||||||||
\(55\) | 3.72247 | 0.501938 | ||||||||
\(56\) | −0.478055 | −0.0638828 | ||||||||
\(57\) | −11.9005 | −1.57626 | ||||||||
\(58\) | 3.62683 | 0.476226 | ||||||||
\(59\) | 6.42878 | 0.836955 | 0.418478 | − | 0.908227i | \(-0.362564\pi\) | ||||
0.418478 | + | 0.908227i | \(0.362564\pi\) | |||||||
\(60\) | −4.70241 | −0.607079 | ||||||||
\(61\) | 4.33547 | 0.555100 | 0.277550 | − | 0.960711i | \(-0.410478\pi\) | ||||
0.277550 | + | 0.960711i | \(0.410478\pi\) | |||||||
\(62\) | 2.87716 | 0.365399 | ||||||||
\(63\) | −2.28194 | −0.287497 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.37857 | 1.16327 | ||||||||
\(66\) | −6.15347 | −0.757439 | ||||||||
\(67\) | −9.68788 | −1.18356 | −0.591781 | − | 0.806098i | \(-0.701575\pi\) | ||||
−0.591781 | + | 0.806098i | \(0.701575\pi\) | |||||||
\(68\) | 1.64824 | 0.199879 | ||||||||
\(69\) | 18.7251 | 2.25424 | ||||||||
\(70\) | −0.806296 | −0.0963708 | ||||||||
\(71\) | 4.36042 | 0.517486 | 0.258743 | − | 0.965946i | \(-0.416692\pi\) | ||||
0.258743 | + | 0.965946i | \(0.416692\pi\) | |||||||
\(72\) | 4.77338 | 0.562548 | ||||||||
\(73\) | −0.189903 | −0.0222265 | −0.0111132 | − | 0.999938i | \(-0.503538\pi\) | ||||
−0.0111132 | + | 0.999938i | \(0.503538\pi\) | |||||||
\(74\) | 1.83077 | 0.212823 | ||||||||
\(75\) | 6.00922 | 0.693885 | ||||||||
\(76\) | 4.26835 | 0.489614 | ||||||||
\(77\) | −1.05510 | −0.120240 | ||||||||
\(78\) | −15.5034 | −1.75541 | ||||||||
\(79\) | −12.0283 | −1.35329 | −0.676647 | − | 0.736308i | \(-0.736567\pi\) | ||||
−0.676647 | + | 0.736308i | \(0.736567\pi\) | |||||||
\(80\) | 1.68662 | 0.188569 | ||||||||
\(81\) | −0.535012 | −0.0594458 | ||||||||
\(82\) | 6.78226 | 0.748975 | ||||||||
\(83\) | 5.45551 | 0.598820 | 0.299410 | − | 0.954125i | \(-0.403210\pi\) | ||||
0.299410 | + | 0.954125i | \(0.403210\pi\) | |||||||
\(84\) | 1.33286 | 0.145426 | ||||||||
\(85\) | 2.77995 | 0.301528 | ||||||||
\(86\) | 1.02674 | 0.110716 | ||||||||
\(87\) | −10.1119 | −1.08411 | ||||||||
\(88\) | 2.20706 | 0.235274 | ||||||||
\(89\) | −12.7133 | −1.34761 | −0.673803 | − | 0.738911i | \(-0.735341\pi\) | ||||
−0.673803 | + | 0.738911i | \(0.735341\pi\) | |||||||
\(90\) | 8.05085 | 0.848634 | ||||||||
\(91\) | −2.65827 | −0.278662 | ||||||||
\(92\) | −6.71615 | −0.700207 | ||||||||
\(93\) | −8.02173 | −0.831815 | ||||||||
\(94\) | 10.3458 | 1.06708 | ||||||||
\(95\) | 7.19907 | 0.738609 | ||||||||
\(96\) | −2.78808 | −0.284557 | ||||||||
\(97\) | −5.00870 | −0.508556 | −0.254278 | − | 0.967131i | \(-0.581838\pi\) | ||||
−0.254278 | + | 0.967131i | \(0.581838\pi\) | |||||||
\(98\) | −6.77146 | −0.684021 | ||||||||
\(99\) | 10.5351 | 1.05882 | ||||||||
\(100\) | −2.15533 | −0.215533 | ||||||||
\(101\) | −6.47702 | −0.644488 | −0.322244 | − | 0.946657i | \(-0.604437\pi\) | ||||
−0.322244 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(102\) | −4.59543 | −0.455015 | ||||||||
\(103\) | −3.67441 | −0.362051 | −0.181025 | − | 0.983478i | \(-0.557942\pi\) | ||||
−0.181025 | + | 0.983478i | \(0.557942\pi\) | |||||||
\(104\) | 5.56059 | 0.545261 | ||||||||
\(105\) | 2.24801 | 0.219384 | ||||||||
\(106\) | 12.9134 | 1.25426 | ||||||||
\(107\) | −16.3658 | −1.58214 | −0.791071 | − | 0.611724i | \(-0.790476\pi\) | ||||
−0.791071 | + | 0.611724i | \(0.790476\pi\) | |||||||
\(108\) | −4.94431 | −0.475766 | ||||||||
\(109\) | −0.447873 | −0.0428984 | −0.0214492 | − | 0.999770i | \(-0.506828\pi\) | ||||
−0.0214492 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(110\) | 3.72247 | 0.354923 | ||||||||
\(111\) | −5.10433 | −0.484482 | ||||||||
\(112\) | −0.478055 | −0.0451720 | ||||||||
\(113\) | 2.96760 | 0.279168 | 0.139584 | − | 0.990210i | \(-0.455423\pi\) | ||||
0.139584 | + | 0.990210i | \(0.455423\pi\) | |||||||
\(114\) | −11.9005 | −1.11458 | ||||||||
\(115\) | −11.3276 | −1.05630 | ||||||||
\(116\) | 3.62683 | 0.336743 | ||||||||
\(117\) | 26.5428 | 2.45388 | ||||||||
\(118\) | 6.42878 | 0.591817 | ||||||||
\(119\) | −0.787952 | −0.0722314 | ||||||||
\(120\) | −4.70241 | −0.429270 | ||||||||
\(121\) | −6.12887 | −0.557170 | ||||||||
\(122\) | 4.33547 | 0.392515 | ||||||||
\(123\) | −18.9095 | −1.70501 | ||||||||
\(124\) | 2.87716 | 0.258376 | ||||||||
\(125\) | −12.0683 | −1.07942 | ||||||||
\(126\) | −2.28194 | −0.203291 | ||||||||
\(127\) | −5.87319 | −0.521161 | −0.260581 | − | 0.965452i | \(-0.583914\pi\) | ||||
−0.260581 | + | 0.965452i | \(0.583914\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.86263 | −0.252041 | ||||||||
\(130\) | 9.37857 | 0.822555 | ||||||||
\(131\) | −16.5788 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(132\) | −6.15347 | −0.535590 | ||||||||
\(133\) | −2.04051 | −0.176935 | ||||||||
\(134\) | −9.68788 | −0.836905 | ||||||||
\(135\) | −8.33915 | −0.717719 | ||||||||
\(136\) | 1.64824 | 0.141336 | ||||||||
\(137\) | 6.99325 | 0.597473 | 0.298737 | − | 0.954336i | \(-0.403435\pi\) | ||||
0.298737 | + | 0.954336i | \(0.403435\pi\) | |||||||
\(138\) | 18.7251 | 1.59399 | ||||||||
\(139\) | 0.329142 | 0.0279175 | 0.0139587 | − | 0.999903i | \(-0.495557\pi\) | ||||
0.0139587 | + | 0.999903i | \(0.495557\pi\) | |||||||
\(140\) | −0.806296 | −0.0681444 | ||||||||
\(141\) | −28.8448 | −2.42917 | ||||||||
\(142\) | 4.36042 | 0.365918 | ||||||||
\(143\) | 12.2726 | 1.02628 | ||||||||
\(144\) | 4.77338 | 0.397781 | ||||||||
\(145\) | 6.11706 | 0.507995 | ||||||||
\(146\) | −0.189903 | −0.0157165 | ||||||||
\(147\) | 18.8794 | 1.55714 | ||||||||
\(148\) | 1.83077 | 0.150489 | ||||||||
\(149\) | 14.3445 | 1.17515 | 0.587574 | − | 0.809170i | \(-0.300083\pi\) | ||||
0.587574 | + | 0.809170i | \(0.300083\pi\) | |||||||
\(150\) | 6.00922 | 0.490651 | ||||||||
\(151\) | −19.9450 | −1.62310 | −0.811551 | − | 0.584281i | \(-0.801376\pi\) | ||||
−0.811551 | + | 0.584281i | \(0.801376\pi\) | |||||||
\(152\) | 4.26835 | 0.346209 | ||||||||
\(153\) | 7.86768 | 0.636065 | ||||||||
\(154\) | −1.05510 | −0.0850223 | ||||||||
\(155\) | 4.85265 | 0.389775 | ||||||||
\(156\) | −15.5034 | −1.24126 | ||||||||
\(157\) | 6.65329 | 0.530990 | 0.265495 | − | 0.964112i | \(-0.414465\pi\) | ||||
0.265495 | + | 0.964112i | \(0.414465\pi\) | |||||||
\(158\) | −12.0283 | −0.956923 | ||||||||
\(159\) | −36.0035 | −2.85526 | ||||||||
\(160\) | 1.68662 | 0.133339 | ||||||||
\(161\) | 3.21069 | 0.253038 | ||||||||
\(162\) | −0.535012 | −0.0420345 | ||||||||
\(163\) | 17.4424 | 1.36619 | 0.683097 | − | 0.730328i | \(-0.260633\pi\) | ||||
0.683097 | + | 0.730328i | \(0.260633\pi\) | |||||||
\(164\) | 6.78226 | 0.529606 | ||||||||
\(165\) | −10.3785 | −0.807967 | ||||||||
\(166\) | 5.45551 | 0.423430 | ||||||||
\(167\) | −4.36510 | −0.337781 | −0.168891 | − | 0.985635i | \(-0.554018\pi\) | ||||
−0.168891 | + | 0.985635i | \(0.554018\pi\) | |||||||
\(168\) | 1.33286 | 0.102832 | ||||||||
\(169\) | 17.9201 | 1.37847 | ||||||||
\(170\) | 2.77995 | 0.213213 | ||||||||
\(171\) | 20.3745 | 1.55807 | ||||||||
\(172\) | 1.02674 | 0.0782882 | ||||||||
\(173\) | −2.68710 | −0.204297 | −0.102148 | − | 0.994769i | \(-0.532572\pi\) | ||||
−0.102148 | + | 0.994769i | \(0.532572\pi\) | |||||||
\(174\) | −10.1119 | −0.766579 | ||||||||
\(175\) | 1.03037 | 0.0778884 | ||||||||
\(176\) | 2.20706 | 0.166364 | ||||||||
\(177\) | −17.9239 | −1.34724 | ||||||||
\(178\) | −12.7133 | −0.952902 | ||||||||
\(179\) | 6.98478 | 0.522067 | 0.261033 | − | 0.965330i | \(-0.415937\pi\) | ||||
0.261033 | + | 0.965330i | \(0.415937\pi\) | |||||||
\(180\) | 8.05085 | 0.600075 | ||||||||
\(181\) | 8.12867 | 0.604199 | 0.302100 | − | 0.953276i | \(-0.402313\pi\) | ||||
0.302100 | + | 0.953276i | \(0.402313\pi\) | |||||||
\(182\) | −2.65827 | −0.197044 | ||||||||
\(183\) | −12.0876 | −0.893542 | ||||||||
\(184\) | −6.71615 | −0.495121 | ||||||||
\(185\) | 3.08781 | 0.227020 | ||||||||
\(186\) | −8.02173 | −0.588182 | ||||||||
\(187\) | 3.63778 | 0.266021 | ||||||||
\(188\) | 10.3458 | 0.754543 | ||||||||
\(189\) | 2.36365 | 0.171930 | ||||||||
\(190\) | 7.19907 | 0.522275 | ||||||||
\(191\) | −6.84039 | −0.494954 | −0.247477 | − | 0.968894i | \(-0.579601\pi\) | ||||
−0.247477 | + | 0.968894i | \(0.579601\pi\) | |||||||
\(192\) | −2.78808 | −0.201212 | ||||||||
\(193\) | 20.5250 | 1.47742 | 0.738710 | − | 0.674023i | \(-0.235435\pi\) | ||||
0.738710 | + | 0.674023i | \(0.235435\pi\) | |||||||
\(194\) | −5.00870 | −0.359603 | ||||||||
\(195\) | −26.1482 | −1.87251 | ||||||||
\(196\) | −6.77146 | −0.483676 | ||||||||
\(197\) | 23.6099 | 1.68214 | 0.841068 | − | 0.540929i | \(-0.181927\pi\) | ||||
0.841068 | + | 0.540929i | \(0.181927\pi\) | |||||||
\(198\) | 10.5351 | 0.748700 | ||||||||
\(199\) | −17.2752 | −1.22461 | −0.612304 | − | 0.790623i | \(-0.709757\pi\) | ||||
−0.612304 | + | 0.790623i | \(0.709757\pi\) | |||||||
\(200\) | −2.15533 | −0.152405 | ||||||||
\(201\) | 27.0106 | 1.90518 | ||||||||
\(202\) | −6.47702 | −0.455722 | ||||||||
\(203\) | −1.73382 | −0.121691 | ||||||||
\(204\) | −4.59543 | −0.321744 | ||||||||
\(205\) | 11.4391 | 0.798939 | ||||||||
\(206\) | −3.67441 | −0.256009 | ||||||||
\(207\) | −32.0587 | −2.22823 | ||||||||
\(208\) | 5.56059 | 0.385557 | ||||||||
\(209\) | 9.42053 | 0.651632 | ||||||||
\(210\) | 2.24801 | 0.155128 | ||||||||
\(211\) | 4.04319 | 0.278344 | 0.139172 | − | 0.990268i | \(-0.455556\pi\) | ||||
0.139172 | + | 0.990268i | \(0.455556\pi\) | |||||||
\(212\) | 12.9134 | 0.886894 | ||||||||
\(213\) | −12.1572 | −0.832996 | ||||||||
\(214\) | −16.3658 | −1.11874 | ||||||||
\(215\) | 1.73172 | 0.118102 | ||||||||
\(216\) | −4.94431 | −0.336418 | ||||||||
\(217\) | −1.37544 | −0.0933709 | ||||||||
\(218\) | −0.447873 | −0.0303338 | ||||||||
\(219\) | 0.529464 | 0.0357779 | ||||||||
\(220\) | 3.72247 | 0.250969 | ||||||||
\(221\) | 9.16520 | 0.616518 | ||||||||
\(222\) | −5.10433 | −0.342581 | ||||||||
\(223\) | 4.68255 | 0.313567 | 0.156783 | − | 0.987633i | \(-0.449888\pi\) | ||||
0.156783 | + | 0.987633i | \(0.449888\pi\) | |||||||
\(224\) | −0.478055 | −0.0319414 | ||||||||
\(225\) | −10.2882 | −0.685880 | ||||||||
\(226\) | 2.96760 | 0.197402 | ||||||||
\(227\) | 21.4011 | 1.42044 | 0.710221 | − | 0.703978i | \(-0.248595\pi\) | ||||
0.710221 | + | 0.703978i | \(0.248595\pi\) | |||||||
\(228\) | −11.9005 | −0.788130 | ||||||||
\(229\) | 12.6702 | 0.837267 | 0.418634 | − | 0.908155i | \(-0.362509\pi\) | ||||
0.418634 | + | 0.908155i | \(0.362509\pi\) | |||||||
\(230\) | −11.3276 | −0.746917 | ||||||||
\(231\) | 2.94170 | 0.193550 | ||||||||
\(232\) | 3.62683 | 0.238113 | ||||||||
\(233\) | 2.85283 | 0.186895 | 0.0934476 | − | 0.995624i | \(-0.470211\pi\) | ||||
0.0934476 | + | 0.995624i | \(0.470211\pi\) | |||||||
\(234\) | 26.5428 | 1.73516 | ||||||||
\(235\) | 17.4493 | 1.13827 | ||||||||
\(236\) | 6.42878 | 0.418478 | ||||||||
\(237\) | 33.5359 | 2.17839 | ||||||||
\(238\) | −0.787952 | −0.0510753 | ||||||||
\(239\) | −13.6057 | −0.880079 | −0.440040 | − | 0.897978i | \(-0.645036\pi\) | ||||
−0.440040 | + | 0.897978i | \(0.645036\pi\) | |||||||
\(240\) | −4.70241 | −0.303540 | ||||||||
\(241\) | 16.2213 | 1.04491 | 0.522454 | − | 0.852668i | \(-0.325017\pi\) | ||||
0.522454 | + | 0.852668i | \(0.325017\pi\) | |||||||
\(242\) | −6.12887 | −0.393979 | ||||||||
\(243\) | 16.3246 | 1.04722 | ||||||||
\(244\) | 4.33547 | 0.277550 | ||||||||
\(245\) | −11.4209 | −0.729652 | ||||||||
\(246\) | −18.9095 | −1.20562 | ||||||||
\(247\) | 23.7346 | 1.51019 | ||||||||
\(248\) | 2.87716 | 0.182700 | ||||||||
\(249\) | −15.2104 | −0.963919 | ||||||||
\(250\) | −12.0683 | −0.763265 | ||||||||
\(251\) | 4.08474 | 0.257826 | 0.128913 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128913 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(252\) | −2.28194 | −0.143749 | ||||||||
\(253\) | −14.8230 | −0.931912 | ||||||||
\(254\) | −5.87319 | −0.368517 | ||||||||
\(255\) | −7.75072 | −0.485369 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.7789 | −0.672372 | −0.336186 | − | 0.941796i | \(-0.609137\pi\) | ||||
−0.336186 | + | 0.941796i | \(0.609137\pi\) | |||||||
\(258\) | −2.86263 | −0.178220 | ||||||||
\(259\) | −0.875211 | −0.0543829 | ||||||||
\(260\) | 9.37857 | 0.581635 | ||||||||
\(261\) | 17.3122 | 1.07160 | ||||||||
\(262\) | −16.5788 | −1.02424 | ||||||||
\(263\) | −23.3509 | −1.43988 | −0.719940 | − | 0.694036i | \(-0.755831\pi\) | ||||
−0.719940 | + | 0.694036i | \(0.755831\pi\) | |||||||
\(264\) | −6.15347 | −0.378720 | ||||||||
\(265\) | 21.7799 | 1.33793 | ||||||||
\(266\) | −2.04051 | −0.125112 | ||||||||
\(267\) | 35.4457 | 2.16924 | ||||||||
\(268\) | −9.68788 | −0.591781 | ||||||||
\(269\) | 4.24828 | 0.259022 | 0.129511 | − | 0.991578i | \(-0.458659\pi\) | ||||
0.129511 | + | 0.991578i | \(0.458659\pi\) | |||||||
\(270\) | −8.33915 | −0.507504 | ||||||||
\(271\) | 8.46851 | 0.514426 | 0.257213 | − | 0.966355i | \(-0.417196\pi\) | ||||
0.257213 | + | 0.966355i | \(0.417196\pi\) | |||||||
\(272\) | 1.64824 | 0.0999394 | ||||||||
\(273\) | 7.41146 | 0.448562 | ||||||||
\(274\) | 6.99325 | 0.422478 | ||||||||
\(275\) | −4.75695 | −0.286855 | ||||||||
\(276\) | 18.7251 | 1.12712 | ||||||||
\(277\) | 22.8520 | 1.37304 | 0.686521 | − | 0.727110i | \(-0.259137\pi\) | ||||
0.686521 | + | 0.727110i | \(0.259137\pi\) | |||||||
\(278\) | 0.329142 | 0.0197406 | ||||||||
\(279\) | 13.7337 | 0.822218 | ||||||||
\(280\) | −0.806296 | −0.0481854 | ||||||||
\(281\) | 2.97082 | 0.177224 | 0.0886122 | − | 0.996066i | \(-0.471757\pi\) | ||||
0.0886122 | + | 0.996066i | \(0.471757\pi\) | |||||||
\(282\) | −28.8448 | −1.71768 | ||||||||
\(283\) | 24.7400 | 1.47064 | 0.735319 | − | 0.677721i | \(-0.237032\pi\) | ||||
0.735319 | + | 0.677721i | \(0.237032\pi\) | |||||||
\(284\) | 4.36042 | 0.258743 | ||||||||
\(285\) | −20.0716 | −1.18894 | ||||||||
\(286\) | 12.2726 | 0.725693 | ||||||||
\(287\) | −3.24230 | −0.191387 | ||||||||
\(288\) | 4.77338 | 0.281274 | ||||||||
\(289\) | −14.2833 | −0.840194 | ||||||||
\(290\) | 6.11706 | 0.359206 | ||||||||
\(291\) | 13.9646 | 0.818621 | ||||||||
\(292\) | −0.189903 | −0.0111132 | ||||||||
\(293\) | 5.69462 | 0.332683 | 0.166342 | − | 0.986068i | \(-0.446805\pi\) | ||||
0.166342 | + | 0.986068i | \(0.446805\pi\) | |||||||
\(294\) | 18.8794 | 1.10107 | ||||||||
\(295\) | 10.8429 | 0.631296 | ||||||||
\(296\) | 1.83077 | 0.106411 | ||||||||
\(297\) | −10.9124 | −0.633202 | ||||||||
\(298\) | 14.3445 | 0.830956 | ||||||||
\(299\) | −37.3457 | −2.15976 | ||||||||
\(300\) | 6.00922 | 0.346943 | ||||||||
\(301\) | −0.490839 | −0.0282915 | ||||||||
\(302\) | −19.9450 | −1.14771 | ||||||||
\(303\) | 18.0584 | 1.03743 | ||||||||
\(304\) | 4.26835 | 0.244807 | ||||||||
\(305\) | 7.31226 | 0.418699 | ||||||||
\(306\) | 7.86768 | 0.449766 | ||||||||
\(307\) | −1.44560 | −0.0825050 | −0.0412525 | − | 0.999149i | \(-0.513135\pi\) | ||||
−0.0412525 | + | 0.999149i | \(0.513135\pi\) | |||||||
\(308\) | −1.05510 | −0.0601199 | ||||||||
\(309\) | 10.2446 | 0.582792 | ||||||||
\(310\) | 4.85265 | 0.275612 | ||||||||
\(311\) | −25.2656 | −1.43268 | −0.716342 | − | 0.697750i | \(-0.754185\pi\) | ||||
−0.716342 | + | 0.697750i | \(0.754185\pi\) | |||||||
\(312\) | −15.5034 | −0.877704 | ||||||||
\(313\) | 25.7334 | 1.45454 | 0.727268 | − | 0.686353i | \(-0.240790\pi\) | ||||
0.727268 | + | 0.686353i | \(0.240790\pi\) | |||||||
\(314\) | 6.65329 | 0.375467 | ||||||||
\(315\) | −3.84875 | −0.216853 | ||||||||
\(316\) | −12.0283 | −0.676647 | ||||||||
\(317\) | −2.01159 | −0.112982 | −0.0564911 | − | 0.998403i | \(-0.517991\pi\) | ||||
−0.0564911 | + | 0.998403i | \(0.517991\pi\) | |||||||
\(318\) | −36.0035 | −2.01897 | ||||||||
\(319\) | 8.00464 | 0.448174 | ||||||||
\(320\) | 1.68662 | 0.0942847 | ||||||||
\(321\) | 45.6292 | 2.54677 | ||||||||
\(322\) | 3.21069 | 0.178925 | ||||||||
\(323\) | 7.03528 | 0.391454 | ||||||||
\(324\) | −0.535012 | −0.0297229 | ||||||||
\(325\) | −11.9849 | −0.664802 | ||||||||
\(326\) | 17.4424 | 0.966044 | ||||||||
\(327\) | 1.24870 | 0.0690535 | ||||||||
\(328\) | 6.78226 | 0.374488 | ||||||||
\(329\) | −4.94585 | −0.272674 | ||||||||
\(330\) | −10.3785 | −0.571319 | ||||||||
\(331\) | −17.5611 | −0.965248 | −0.482624 | − | 0.875828i | \(-0.660316\pi\) | ||||
−0.482624 | + | 0.875828i | \(0.660316\pi\) | |||||||
\(332\) | 5.45551 | 0.299410 | ||||||||
\(333\) | 8.73896 | 0.478892 | ||||||||
\(334\) | −4.36510 | −0.238848 | ||||||||
\(335\) | −16.3397 | −0.892735 | ||||||||
\(336\) | 1.33286 | 0.0727132 | ||||||||
\(337\) | −6.66556 | −0.363096 | −0.181548 | − | 0.983382i | \(-0.558111\pi\) | ||||
−0.181548 | + | 0.983382i | \(0.558111\pi\) | |||||||
\(338\) | 17.9201 | 0.974728 | ||||||||
\(339\) | −8.27389 | −0.449376 | ||||||||
\(340\) | 2.77995 | 0.150764 | ||||||||
\(341\) | 6.35007 | 0.343875 | ||||||||
\(342\) | 20.3745 | 1.10172 | ||||||||
\(343\) | 6.58352 | 0.355477 | ||||||||
\(344\) | 1.02674 | 0.0553581 | ||||||||
\(345\) | 31.5821 | 1.70032 | ||||||||
\(346\) | −2.68710 | −0.144460 | ||||||||
\(347\) | 17.9000 | 0.960922 | 0.480461 | − | 0.877016i | \(-0.340469\pi\) | ||||
0.480461 | + | 0.877016i | \(0.340469\pi\) | |||||||
\(348\) | −10.1119 | −0.542054 | ||||||||
\(349\) | −10.0449 | −0.537694 | −0.268847 | − | 0.963183i | \(-0.586643\pi\) | ||||
−0.268847 | + | 0.963183i | \(0.586643\pi\) | |||||||
\(350\) | 1.03037 | 0.0550754 | ||||||||
\(351\) | −27.4933 | −1.46748 | ||||||||
\(352\) | 2.20706 | 0.117637 | ||||||||
\(353\) | −4.49994 | −0.239508 | −0.119754 | − | 0.992804i | \(-0.538211\pi\) | ||||
−0.119754 | + | 0.992804i | \(0.538211\pi\) | |||||||
\(354\) | −17.9239 | −0.952646 | ||||||||
\(355\) | 7.35434 | 0.390328 | ||||||||
\(356\) | −12.7133 | −0.673803 | ||||||||
\(357\) | 2.19687 | 0.116271 | ||||||||
\(358\) | 6.98478 | 0.369157 | ||||||||
\(359\) | 7.05175 | 0.372177 | 0.186089 | − | 0.982533i | \(-0.440419\pi\) | ||||
0.186089 | + | 0.982533i | \(0.440419\pi\) | |||||||
\(360\) | 8.05085 | 0.424317 | ||||||||
\(361\) | −0.781163 | −0.0411138 | ||||||||
\(362\) | 8.12867 | 0.427233 | ||||||||
\(363\) | 17.0878 | 0.896875 | ||||||||
\(364\) | −2.65827 | −0.139331 | ||||||||
\(365\) | −0.320293 | −0.0167649 | ||||||||
\(366\) | −12.0876 | −0.631830 | ||||||||
\(367\) | 23.1937 | 1.21070 | 0.605352 | − | 0.795958i | \(-0.293033\pi\) | ||||
0.605352 | + | 0.795958i | \(0.293033\pi\) | |||||||
\(368\) | −6.71615 | −0.350103 | ||||||||
\(369\) | 32.3743 | 1.68534 | ||||||||
\(370\) | 3.08781 | 0.160528 | ||||||||
\(371\) | −6.17330 | −0.320502 | ||||||||
\(372\) | −8.02173 | −0.415907 | ||||||||
\(373\) | −30.7680 | −1.59311 | −0.796553 | − | 0.604568i | \(-0.793346\pi\) | ||||
−0.796553 | + | 0.604568i | \(0.793346\pi\) | |||||||
\(374\) | 3.63778 | 0.188105 | ||||||||
\(375\) | 33.6473 | 1.73754 | ||||||||
\(376\) | 10.3458 | 0.533542 | ||||||||
\(377\) | 20.1673 | 1.03867 | ||||||||
\(378\) | 2.36365 | 0.121573 | ||||||||
\(379\) | 1.67234 | 0.0859022 | 0.0429511 | − | 0.999077i | \(-0.486324\pi\) | ||||
0.0429511 | + | 0.999077i | \(0.486324\pi\) | |||||||
\(380\) | 7.19907 | 0.369304 | ||||||||
\(381\) | 16.3749 | 0.838912 | ||||||||
\(382\) | −6.84039 | −0.349985 | ||||||||
\(383\) | −3.82222 | −0.195306 | −0.0976531 | − | 0.995221i | \(-0.531134\pi\) | ||||
−0.0976531 | + | 0.995221i | \(0.531134\pi\) | |||||||
\(384\) | −2.78808 | −0.142278 | ||||||||
\(385\) | −1.77955 | −0.0906941 | ||||||||
\(386\) | 20.5250 | 1.04469 | ||||||||
\(387\) | 4.90102 | 0.249133 | ||||||||
\(388\) | −5.00870 | −0.254278 | ||||||||
\(389\) | 3.29055 | 0.166838 | 0.0834188 | − | 0.996515i | \(-0.473416\pi\) | ||||
0.0834188 | + | 0.996515i | \(0.473416\pi\) | |||||||
\(390\) | −26.1482 | −1.32407 | ||||||||
\(391\) | −11.0698 | −0.559826 | ||||||||
\(392\) | −6.77146 | −0.342011 | ||||||||
\(393\) | 46.2230 | 2.33164 | ||||||||
\(394\) | 23.6099 | 1.18945 | ||||||||
\(395\) | −20.2872 | −1.02076 | ||||||||
\(396\) | 10.5351 | 0.529411 | ||||||||
\(397\) | −22.9518 | −1.15192 | −0.575958 | − | 0.817479i | \(-0.695371\pi\) | ||||
−0.575958 | + | 0.817479i | \(0.695371\pi\) | |||||||
\(398\) | −17.2752 | −0.865928 | ||||||||
\(399\) | 5.68910 | 0.284811 | ||||||||
\(400\) | −2.15533 | −0.107766 | ||||||||
\(401\) | −30.7638 | −1.53627 | −0.768136 | − | 0.640287i | \(-0.778815\pi\) | ||||
−0.768136 | + | 0.640287i | \(0.778815\pi\) | |||||||
\(402\) | 27.0106 | 1.34716 | ||||||||
\(403\) | 15.9987 | 0.796951 | ||||||||
\(404\) | −6.47702 | −0.322244 | ||||||||
\(405\) | −0.902360 | −0.0448386 | ||||||||
\(406\) | −1.73382 | −0.0860483 | ||||||||
\(407\) | 4.04063 | 0.200287 | ||||||||
\(408\) | −4.59543 | −0.227508 | ||||||||
\(409\) | 28.3717 | 1.40289 | 0.701446 | − | 0.712723i | \(-0.252538\pi\) | ||||
0.701446 | + | 0.712723i | \(0.252538\pi\) | |||||||
\(410\) | 11.4391 | 0.564935 | ||||||||
\(411\) | −19.4977 | −0.961751 | ||||||||
\(412\) | −3.67441 | −0.181025 | ||||||||
\(413\) | −3.07331 | −0.151228 | ||||||||
\(414\) | −32.0587 | −1.57560 | ||||||||
\(415\) | 9.20134 | 0.451676 | ||||||||
\(416\) | 5.56059 | 0.272630 | ||||||||
\(417\) | −0.917674 | −0.0449387 | ||||||||
\(418\) | 9.42053 | 0.460773 | ||||||||
\(419\) | −14.8052 | −0.723279 | −0.361640 | − | 0.932318i | \(-0.617783\pi\) | ||||
−0.361640 | + | 0.932318i | \(0.617783\pi\) | |||||||
\(420\) | 2.24801 | 0.109692 | ||||||||
\(421\) | 34.4115 | 1.67711 | 0.838556 | − | 0.544816i | \(-0.183400\pi\) | ||||
0.838556 | + | 0.544816i | \(0.183400\pi\) | |||||||
\(422\) | 4.04319 | 0.196819 | ||||||||
\(423\) | 49.3842 | 2.40114 | ||||||||
\(424\) | 12.9134 | 0.627128 | ||||||||
\(425\) | −3.55251 | −0.172322 | ||||||||
\(426\) | −12.1572 | −0.589017 | ||||||||
\(427\) | −2.07259 | −0.100300 | ||||||||
\(428\) | −16.3658 | −0.791071 | ||||||||
\(429\) | −34.2169 | −1.65201 | ||||||||
\(430\) | 1.73172 | 0.0835107 | ||||||||
\(431\) | −2.03361 | −0.0979555 | −0.0489778 | − | 0.998800i | \(-0.515596\pi\) | ||||
−0.0489778 | + | 0.998800i | \(0.515596\pi\) | |||||||
\(432\) | −4.94431 | −0.237883 | ||||||||
\(433\) | −19.3295 | −0.928914 | −0.464457 | − | 0.885596i | \(-0.653751\pi\) | ||||
−0.464457 | + | 0.885596i | \(0.653751\pi\) | |||||||
\(434\) | −1.37544 | −0.0660232 | ||||||||
\(435\) | −17.0548 | −0.817717 | ||||||||
\(436\) | −0.447873 | −0.0214492 | ||||||||
\(437\) | −28.6669 | −1.37132 | ||||||||
\(438\) | 0.529464 | 0.0252988 | ||||||||
\(439\) | −15.0399 | −0.717817 | −0.358909 | − | 0.933373i | \(-0.616851\pi\) | ||||
−0.358909 | + | 0.933373i | \(0.616851\pi\) | |||||||
\(440\) | 3.72247 | 0.177462 | ||||||||
\(441\) | −32.3227 | −1.53918 | ||||||||
\(442\) | 9.16520 | 0.435944 | ||||||||
\(443\) | 8.06470 | 0.383166 | 0.191583 | − | 0.981476i | \(-0.438638\pi\) | ||||
0.191583 | + | 0.981476i | \(0.438638\pi\) | |||||||
\(444\) | −5.10433 | −0.242241 | ||||||||
\(445\) | −21.4424 | −1.01647 | ||||||||
\(446\) | 4.68255 | 0.221725 | ||||||||
\(447\) | −39.9936 | −1.89163 | ||||||||
\(448\) | −0.478055 | −0.0225860 | ||||||||
\(449\) | −30.5246 | −1.44055 | −0.720274 | − | 0.693690i | \(-0.755984\pi\) | ||||
−0.720274 | + | 0.693690i | \(0.755984\pi\) | |||||||
\(450\) | −10.2882 | −0.484990 | ||||||||
\(451\) | 14.9689 | 0.704857 | ||||||||
\(452\) | 2.96760 | 0.139584 | ||||||||
\(453\) | 55.6082 | 2.61270 | ||||||||
\(454\) | 21.4011 | 1.00440 | ||||||||
\(455\) | −4.48348 | −0.210189 | ||||||||
\(456\) | −11.9005 | −0.557292 | ||||||||
\(457\) | 35.7756 | 1.67351 | 0.836755 | − | 0.547577i | \(-0.184450\pi\) | ||||
0.836755 | + | 0.547577i | \(0.184450\pi\) | |||||||
\(458\) | 12.6702 | 0.592037 | ||||||||
\(459\) | −8.14942 | −0.380382 | ||||||||
\(460\) | −11.3276 | −0.528150 | ||||||||
\(461\) | 33.8197 | 1.57514 | 0.787571 | − | 0.616225i | \(-0.211339\pi\) | ||||
0.787571 | + | 0.616225i | \(0.211339\pi\) | |||||||
\(462\) | 2.94170 | 0.136860 | ||||||||
\(463\) | −26.5118 | −1.23211 | −0.616054 | − | 0.787704i | \(-0.711270\pi\) | ||||
−0.616054 | + | 0.787704i | \(0.711270\pi\) | |||||||
\(464\) | 3.62683 | 0.168371 | ||||||||
\(465\) | −13.5296 | −0.627419 | ||||||||
\(466\) | 2.85283 | 0.132155 | ||||||||
\(467\) | 23.1866 | 1.07295 | 0.536473 | − | 0.843918i | \(-0.319756\pi\) | ||||
0.536473 | + | 0.843918i | \(0.319756\pi\) | |||||||
\(468\) | 26.5428 | 1.22694 | ||||||||
\(469\) | 4.63134 | 0.213856 | ||||||||
\(470\) | 17.4493 | 0.804878 | ||||||||
\(471\) | −18.5499 | −0.854734 | ||||||||
\(472\) | 6.42878 | 0.295908 | ||||||||
\(473\) | 2.26608 | 0.104195 | ||||||||
\(474\) | 33.5359 | 1.54036 | ||||||||
\(475\) | −9.19970 | −0.422111 | ||||||||
\(476\) | −0.787952 | −0.0361157 | ||||||||
\(477\) | 61.6403 | 2.82232 | ||||||||
\(478\) | −13.6057 | −0.622310 | ||||||||
\(479\) | −24.2960 | −1.11011 | −0.555056 | − | 0.831813i | \(-0.687303\pi\) | ||||
−0.555056 | + | 0.831813i | \(0.687303\pi\) | |||||||
\(480\) | −4.70241 | −0.214635 | ||||||||
\(481\) | 10.1802 | 0.464176 | ||||||||
\(482\) | 16.2213 | 0.738861 | ||||||||
\(483\) | −8.95165 | −0.407314 | ||||||||
\(484\) | −6.12887 | −0.278585 | ||||||||
\(485\) | −8.44774 | −0.383592 | ||||||||
\(486\) | 16.3246 | 0.740498 | ||||||||
\(487\) | 16.6398 | 0.754021 | 0.377011 | − | 0.926209i | \(-0.376952\pi\) | ||||
0.377011 | + | 0.926209i | \(0.376952\pi\) | |||||||
\(488\) | 4.33547 | 0.196257 | ||||||||
\(489\) | −48.6307 | −2.19916 | ||||||||
\(490\) | −11.4209 | −0.515942 | ||||||||
\(491\) | 6.51985 | 0.294237 | 0.147118 | − | 0.989119i | \(-0.453000\pi\) | ||||
0.147118 | + | 0.989119i | \(0.453000\pi\) | |||||||
\(492\) | −18.9095 | −0.852505 | ||||||||
\(493\) | 5.97789 | 0.269231 | ||||||||
\(494\) | 23.7346 | 1.06787 | ||||||||
\(495\) | 17.7687 | 0.798645 | ||||||||
\(496\) | 2.87716 | 0.129188 | ||||||||
\(497\) | −2.08452 | −0.0935035 | ||||||||
\(498\) | −15.2104 | −0.681593 | ||||||||
\(499\) | 9.47873 | 0.424326 | 0.212163 | − | 0.977234i | \(-0.431949\pi\) | ||||
0.212163 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(500\) | −12.0683 | −0.539710 | ||||||||
\(501\) | 12.1702 | 0.543726 | ||||||||
\(502\) | 4.08474 | 0.182311 | ||||||||
\(503\) | 8.74160 | 0.389769 | 0.194884 | − | 0.980826i | \(-0.437567\pi\) | ||||
0.194884 | + | 0.980826i | \(0.437567\pi\) | |||||||
\(504\) | −2.28194 | −0.101646 | ||||||||
\(505\) | −10.9242 | −0.486122 | ||||||||
\(506\) | −14.8230 | −0.658961 | ||||||||
\(507\) | −49.9628 | −2.21892 | ||||||||
\(508\) | −5.87319 | −0.260581 | ||||||||
\(509\) | 28.0557 | 1.24355 | 0.621774 | − | 0.783197i | \(-0.286412\pi\) | ||||
0.621774 | + | 0.783197i | \(0.286412\pi\) | |||||||
\(510\) | −7.75072 | −0.343208 | ||||||||
\(511\) | 0.0907842 | 0.00401606 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −21.1041 | −0.931767 | ||||||||
\(514\) | −10.7789 | −0.475439 | ||||||||
\(515\) | −6.19732 | −0.273087 | ||||||||
\(516\) | −2.86263 | −0.126020 | ||||||||
\(517\) | 22.8338 | 1.00423 | ||||||||
\(518\) | −0.875211 | −0.0384545 | ||||||||
\(519\) | 7.49186 | 0.328856 | ||||||||
\(520\) | 9.37857 | 0.411278 | ||||||||
\(521\) | −0.755597 | −0.0331033 | −0.0165516 | − | 0.999863i | \(-0.505269\pi\) | ||||
−0.0165516 | + | 0.999863i | \(0.505269\pi\) | |||||||
\(522\) | 17.3122 | 0.757735 | ||||||||
\(523\) | 14.9165 | 0.652252 | 0.326126 | − | 0.945326i | \(-0.394257\pi\) | ||||
0.326126 | + | 0.945326i | \(0.394257\pi\) | |||||||
\(524\) | −16.5788 | −0.724248 | ||||||||
\(525\) | −2.87274 | −0.125377 | ||||||||
\(526\) | −23.3509 | −1.01815 | ||||||||
\(527\) | 4.74225 | 0.206576 | ||||||||
\(528\) | −6.15347 | −0.267795 | ||||||||
\(529\) | 22.1066 | 0.961157 | ||||||||
\(530\) | 21.7799 | 0.946058 | ||||||||
\(531\) | 30.6870 | 1.33170 | ||||||||
\(532\) | −2.04051 | −0.0884673 | ||||||||
\(533\) | 37.7134 | 1.63355 | ||||||||
\(534\) | 35.4457 | 1.53388 | ||||||||
\(535\) | −27.6028 | −1.19337 | ||||||||
\(536\) | −9.68788 | −0.418453 | ||||||||
\(537\) | −19.4741 | −0.840369 | ||||||||
\(538\) | 4.24828 | 0.183156 | ||||||||
\(539\) | −14.9451 | −0.643729 | ||||||||
\(540\) | −8.33915 | −0.358860 | ||||||||
\(541\) | 17.2044 | 0.739676 | 0.369838 | − | 0.929096i | \(-0.379413\pi\) | ||||
0.369838 | + | 0.929096i | \(0.379413\pi\) | |||||||
\(542\) | 8.46851 | 0.363754 | ||||||||
\(543\) | −22.6634 | −0.972578 | ||||||||
\(544\) | 1.64824 | 0.0706678 | ||||||||
\(545\) | −0.755389 | −0.0323573 | ||||||||
\(546\) | 7.41146 | 0.317181 | ||||||||
\(547\) | −11.2801 | −0.482302 | −0.241151 | − | 0.970488i | \(-0.577525\pi\) | ||||
−0.241151 | + | 0.970488i | \(0.577525\pi\) | |||||||
\(548\) | 6.99325 | 0.298737 | ||||||||
\(549\) | 20.6948 | 0.883233 | ||||||||
\(550\) | −4.75695 | −0.202837 | ||||||||
\(551\) | 15.4806 | 0.659495 | ||||||||
\(552\) | 18.7251 | 0.796995 | ||||||||
\(553\) | 5.75021 | 0.244524 | ||||||||
\(554\) | 22.8520 | 0.970887 | ||||||||
\(555\) | −8.60905 | −0.365434 | ||||||||
\(556\) | 0.329142 | 0.0139587 | ||||||||
\(557\) | −12.1698 | −0.515650 | −0.257825 | − | 0.966192i | \(-0.583006\pi\) | ||||
−0.257825 | + | 0.966192i | \(0.583006\pi\) | |||||||
\(558\) | 13.7337 | 0.581396 | ||||||||
\(559\) | 5.70928 | 0.241477 | ||||||||
\(560\) | −0.806296 | −0.0340722 | ||||||||
\(561\) | −10.1424 | −0.428213 | ||||||||
\(562\) | 2.97082 | 0.125317 | ||||||||
\(563\) | 27.9875 | 1.17953 | 0.589766 | − | 0.807574i | \(-0.299220\pi\) | ||||
0.589766 | + | 0.807574i | \(0.299220\pi\) | |||||||
\(564\) | −28.8448 | −1.21459 | ||||||||
\(565\) | 5.00519 | 0.210570 | ||||||||
\(566\) | 24.7400 | 1.03990 | ||||||||
\(567\) | 0.255766 | 0.0107411 | ||||||||
\(568\) | 4.36042 | 0.182959 | ||||||||
\(569\) | 27.9075 | 1.16994 | 0.584971 | − | 0.811054i | \(-0.301106\pi\) | ||||
0.584971 | + | 0.811054i | \(0.301106\pi\) | |||||||
\(570\) | −20.0716 | −0.840705 | ||||||||
\(571\) | 20.8409 | 0.872165 | 0.436083 | − | 0.899907i | \(-0.356366\pi\) | ||||
0.436083 | + | 0.899907i | \(0.356366\pi\) | |||||||
\(572\) | 12.2726 | 0.513142 | ||||||||
\(573\) | 19.0715 | 0.796725 | ||||||||
\(574\) | −3.24230 | −0.135331 | ||||||||
\(575\) | 14.4755 | 0.603670 | ||||||||
\(576\) | 4.77338 | 0.198891 | ||||||||
\(577\) | −26.5218 | −1.10412 | −0.552059 | − | 0.833805i | \(-0.686158\pi\) | ||||
−0.552059 | + | 0.833805i | \(0.686158\pi\) | |||||||
\(578\) | −14.2833 | −0.594107 | ||||||||
\(579\) | −57.2252 | −2.37820 | ||||||||
\(580\) | 6.11706 | 0.253997 | ||||||||
\(581\) | −2.60804 | −0.108200 | ||||||||
\(582\) | 13.9646 | 0.578853 | ||||||||
\(583\) | 28.5006 | 1.18038 | ||||||||
\(584\) | −0.189903 | −0.00785824 | ||||||||
\(585\) | 44.7675 | 1.85091 | ||||||||
\(586\) | 5.69462 | 0.235243 | ||||||||
\(587\) | −12.7019 | −0.524262 | −0.262131 | − | 0.965032i | \(-0.584425\pi\) | ||||
−0.262131 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(588\) | 18.8794 | 0.778572 | ||||||||
\(589\) | 12.2807 | 0.506018 | ||||||||
\(590\) | 10.8429 | 0.446394 | ||||||||
\(591\) | −65.8262 | −2.70773 | ||||||||
\(592\) | 1.83077 | 0.0752443 | ||||||||
\(593\) | 0.655127 | 0.0269028 | 0.0134514 | − | 0.999910i | \(-0.495718\pi\) | ||||
0.0134514 | + | 0.999910i | \(0.495718\pi\) | |||||||
\(594\) | −10.9124 | −0.447741 | ||||||||
\(595\) | −1.32897 | −0.0544825 | ||||||||
\(596\) | 14.3445 | 0.587574 | ||||||||
\(597\) | 48.1646 | 1.97125 | ||||||||
\(598\) | −37.3457 | −1.52718 | ||||||||
\(599\) | 42.1444 | 1.72197 | 0.860987 | − | 0.508627i | \(-0.169847\pi\) | ||||
0.860987 | + | 0.508627i | \(0.169847\pi\) | |||||||
\(600\) | 6.00922 | 0.245325 | ||||||||
\(601\) | −41.2275 | −1.68170 | −0.840852 | − | 0.541265i | \(-0.817946\pi\) | ||||
−0.840852 | + | 0.541265i | \(0.817946\pi\) | |||||||
\(602\) | −0.490839 | −0.0200051 | ||||||||
\(603\) | −46.2439 | −1.88320 | ||||||||
\(604\) | −19.9450 | −0.811551 | ||||||||
\(605\) | −10.3370 | −0.420261 | ||||||||
\(606\) | 18.0584 | 0.733574 | ||||||||
\(607\) | −10.1623 | −0.412475 | −0.206238 | − | 0.978502i | \(-0.566122\pi\) | ||||
−0.206238 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(608\) | 4.26835 | 0.173105 | ||||||||
\(609\) | 4.83404 | 0.195885 | ||||||||
\(610\) | 7.31226 | 0.296065 | ||||||||
\(611\) | 57.5286 | 2.32736 | ||||||||
\(612\) | 7.86768 | 0.318032 | ||||||||
\(613\) | −19.9943 | −0.807560 | −0.403780 | − | 0.914856i | \(-0.632304\pi\) | ||||
−0.403780 | + | 0.914856i | \(0.632304\pi\) | |||||||
\(614\) | −1.44560 | −0.0583398 | ||||||||
\(615\) | −31.8930 | −1.28605 | ||||||||
\(616\) | −1.05510 | −0.0425112 | ||||||||
\(617\) | 30.5781 | 1.23103 | 0.615515 | − | 0.788125i | \(-0.288948\pi\) | ||||
0.615515 | + | 0.788125i | \(0.288948\pi\) | |||||||
\(618\) | 10.2446 | 0.412096 | ||||||||
\(619\) | 11.2306 | 0.451394 | 0.225697 | − | 0.974198i | \(-0.427534\pi\) | ||||
0.225697 | + | 0.974198i | \(0.427534\pi\) | |||||||
\(620\) | 4.85265 | 0.194887 | ||||||||
\(621\) | 33.2067 | 1.33254 | ||||||||
\(622\) | −25.2656 | −1.01306 | ||||||||
\(623\) | 6.07766 | 0.243496 | ||||||||
\(624\) | −15.5034 | −0.620631 | ||||||||
\(625\) | −9.57792 | −0.383117 | ||||||||
\(626\) | 25.7334 | 1.02851 | ||||||||
\(627\) | −26.2652 | −1.04893 | ||||||||
\(628\) | 6.65329 | 0.265495 | ||||||||
\(629\) | 3.01756 | 0.120318 | ||||||||
\(630\) | −3.84875 | −0.153338 | ||||||||
\(631\) | 24.6022 | 0.979399 | 0.489700 | − | 0.871891i | \(-0.337106\pi\) | ||||
0.489700 | + | 0.871891i | \(0.337106\pi\) | |||||||
\(632\) | −12.0283 | −0.478461 | ||||||||
\(633\) | −11.2727 | −0.448050 | ||||||||
\(634\) | −2.01159 | −0.0798905 | ||||||||
\(635\) | −9.90581 | −0.393100 | ||||||||
\(636\) | −36.0035 | −1.42763 | ||||||||
\(637\) | −37.6533 | −1.49188 | ||||||||
\(638\) | 8.00464 | 0.316907 | ||||||||
\(639\) | 20.8139 | 0.823385 | ||||||||
\(640\) | 1.68662 | 0.0666693 | ||||||||
\(641\) | 21.8401 | 0.862632 | 0.431316 | − | 0.902201i | \(-0.358049\pi\) | ||||
0.431316 | + | 0.902201i | \(0.358049\pi\) | |||||||
\(642\) | 45.6292 | 1.80084 | ||||||||
\(643\) | 13.4891 | 0.531960 | 0.265980 | − | 0.963979i | \(-0.414305\pi\) | ||||
0.265980 | + | 0.963979i | \(0.414305\pi\) | |||||||
\(644\) | 3.21069 | 0.126519 | ||||||||
\(645\) | −4.82816 | −0.190108 | ||||||||
\(646\) | 7.03528 | 0.276800 | ||||||||
\(647\) | 22.7573 | 0.894683 | 0.447342 | − | 0.894363i | \(-0.352371\pi\) | ||||
0.447342 | + | 0.894363i | \(0.352371\pi\) | |||||||
\(648\) | −0.535012 | −0.0210173 | ||||||||
\(649\) | 14.1887 | 0.556956 | ||||||||
\(650\) | −11.9849 | −0.470086 | ||||||||
\(651\) | 3.83483 | 0.150299 | ||||||||
\(652\) | 17.4424 | 0.683097 | ||||||||
\(653\) | −12.0355 | −0.470985 | −0.235493 | − | 0.971876i | \(-0.575670\pi\) | ||||
−0.235493 | + | 0.971876i | \(0.575670\pi\) | |||||||
\(654\) | 1.24870 | 0.0488282 | ||||||||
\(655\) | −27.9620 | −1.09257 | ||||||||
\(656\) | 6.78226 | 0.264803 | ||||||||
\(657\) | −0.906478 | −0.0353651 | ||||||||
\(658\) | −4.94585 | −0.192809 | ||||||||
\(659\) | 36.4807 | 1.42109 | 0.710543 | − | 0.703654i | \(-0.248449\pi\) | ||||
0.710543 | + | 0.703654i | \(0.248449\pi\) | |||||||
\(660\) | −10.3785 | −0.403984 | ||||||||
\(661\) | 26.0746 | 1.01419 | 0.507093 | − | 0.861891i | \(-0.330720\pi\) | ||||
0.507093 | + | 0.861891i | \(0.330720\pi\) | |||||||
\(662\) | −17.5611 | −0.682533 | ||||||||
\(663\) | −25.5533 | −0.992408 | ||||||||
\(664\) | 5.45551 | 0.211715 | ||||||||
\(665\) | −3.44155 | −0.133458 | ||||||||
\(666\) | 8.73896 | 0.338628 | ||||||||
\(667\) | −24.3583 | −0.943157 | ||||||||
\(668\) | −4.36510 | −0.168891 | ||||||||
\(669\) | −13.0553 | −0.504747 | ||||||||
\(670\) | −16.3397 | −0.631259 | ||||||||
\(671\) | 9.56865 | 0.369394 | ||||||||
\(672\) | 1.33286 | 0.0514160 | ||||||||
\(673\) | −25.9618 | −1.00076 | −0.500378 | − | 0.865807i | \(-0.666806\pi\) | ||||
−0.500378 | + | 0.865807i | \(0.666806\pi\) | |||||||
\(674\) | −6.66556 | −0.256748 | ||||||||
\(675\) | 10.6566 | 0.410173 | ||||||||
\(676\) | 17.9201 | 0.689237 | ||||||||
\(677\) | −43.6384 | −1.67716 | −0.838580 | − | 0.544779i | \(-0.816614\pi\) | ||||
−0.838580 | + | 0.544779i | \(0.816614\pi\) | |||||||
\(678\) | −8.27389 | −0.317757 | ||||||||
\(679\) | 2.39443 | 0.0918900 | ||||||||
\(680\) | 2.77995 | 0.106606 | ||||||||
\(681\) | −59.6680 | −2.28648 | ||||||||
\(682\) | 6.35007 | 0.243157 | ||||||||
\(683\) | −2.25353 | −0.0862290 | −0.0431145 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431145 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(684\) | 20.3745 | 0.779037 | ||||||||
\(685\) | 11.7949 | 0.450661 | ||||||||
\(686\) | 6.58352 | 0.251360 | ||||||||
\(687\) | −35.3254 | −1.34775 | ||||||||
\(688\) | 1.02674 | 0.0391441 | ||||||||
\(689\) | 71.8059 | 2.73559 | ||||||||
\(690\) | 31.5821 | 1.20231 | ||||||||
\(691\) | −45.8134 | −1.74282 | −0.871412 | − | 0.490552i | \(-0.836795\pi\) | ||||
−0.871412 | + | 0.490552i | \(0.836795\pi\) | |||||||
\(692\) | −2.68710 | −0.102148 | ||||||||
\(693\) | −5.03638 | −0.191316 | ||||||||
\(694\) | 17.9000 | 0.679475 | ||||||||
\(695\) | 0.555136 | 0.0210575 | ||||||||
\(696\) | −10.1119 | −0.383290 | ||||||||
\(697\) | 11.1788 | 0.423428 | ||||||||
\(698\) | −10.0449 | −0.380207 | ||||||||
\(699\) | −7.95391 | −0.300845 | ||||||||
\(700\) | 1.03037 | 0.0389442 | ||||||||
\(701\) | 9.67099 | 0.365268 | 0.182634 | − | 0.983181i | \(-0.441538\pi\) | ||||
0.182634 | + | 0.983181i | \(0.441538\pi\) | |||||||
\(702\) | −27.4933 | −1.03767 | ||||||||
\(703\) | 7.81438 | 0.294725 | ||||||||
\(704\) | 2.20706 | 0.0831819 | ||||||||
\(705\) | −48.6501 | −1.83227 | ||||||||
\(706\) | −4.49994 | −0.169358 | ||||||||
\(707\) | 3.09637 | 0.116451 | ||||||||
\(708\) | −17.9239 | −0.673622 | ||||||||
\(709\) | −29.5138 | −1.10841 | −0.554207 | − | 0.832379i | \(-0.686978\pi\) | ||||
−0.554207 | + | 0.832379i | \(0.686978\pi\) | |||||||
\(710\) | 7.35434 | 0.276004 | ||||||||
\(711\) | −57.4157 | −2.15326 | ||||||||
\(712\) | −12.7133 | −0.476451 | ||||||||
\(713\) | −19.3234 | −0.723667 | ||||||||
\(714\) | 2.19687 | 0.0822158 | ||||||||
\(715\) | 20.6991 | 0.774103 | ||||||||
\(716\) | 6.98478 | 0.261033 | ||||||||
\(717\) | 37.9337 | 1.41666 | ||||||||
\(718\) | 7.05175 | 0.263169 | ||||||||
\(719\) | −7.43147 | −0.277147 | −0.138574 | − | 0.990352i | \(-0.544252\pi\) | ||||
−0.138574 | + | 0.990352i | \(0.544252\pi\) | |||||||
\(720\) | 8.05085 | 0.300037 | ||||||||
\(721\) | 1.75657 | 0.0654182 | ||||||||
\(722\) | −0.781163 | −0.0290719 | ||||||||
\(723\) | −45.2263 | −1.68198 | ||||||||
\(724\) | 8.12867 | 0.302100 | ||||||||
\(725\) | −7.81701 | −0.290316 | ||||||||
\(726\) | 17.0878 | 0.634186 | ||||||||
\(727\) | −3.38859 | −0.125676 | −0.0628379 | − | 0.998024i | \(-0.520015\pi\) | ||||
−0.0628379 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(728\) | −2.65827 | −0.0985220 | ||||||||
\(729\) | −43.9092 | −1.62627 | ||||||||
\(730\) | −0.320293 | −0.0118546 | ||||||||
\(731\) | 1.69232 | 0.0625926 | ||||||||
\(732\) | −12.0876 | −0.446771 | ||||||||
\(733\) | 40.9806 | 1.51365 | 0.756827 | − | 0.653615i | \(-0.226748\pi\) | ||||
0.756827 | + | 0.653615i | \(0.226748\pi\) | |||||||
\(734\) | 23.1937 | 0.856096 | ||||||||
\(735\) | 31.8422 | 1.17452 | ||||||||
\(736\) | −6.71615 | −0.247560 | ||||||||
\(737\) | −21.3818 | −0.787608 | ||||||||
\(738\) | 32.3743 | 1.19171 | ||||||||
\(739\) | −1.27282 | −0.0468215 | −0.0234107 | − | 0.999726i | \(-0.507453\pi\) | ||||
−0.0234107 | + | 0.999726i | \(0.507453\pi\) | |||||||
\(740\) | 3.08781 | 0.113510 | ||||||||
\(741\) | −66.1738 | −2.43095 | ||||||||
\(742\) | −6.17330 | −0.226629 | ||||||||
\(743\) | −6.06834 | −0.222626 | −0.111313 | − | 0.993785i | \(-0.535506\pi\) | ||||
−0.111313 | + | 0.993785i | \(0.535506\pi\) | |||||||
\(744\) | −8.02173 | −0.294091 | ||||||||
\(745\) | 24.1937 | 0.886388 | ||||||||
\(746\) | −30.7680 | −1.12650 | ||||||||
\(747\) | 26.0412 | 0.952797 | ||||||||
\(748\) | 3.63778 | 0.133010 | ||||||||
\(749\) | 7.82377 | 0.285874 | ||||||||
\(750\) | 33.6473 | 1.22863 | ||||||||
\(751\) | −37.1670 | −1.35624 | −0.678121 | − | 0.734950i | \(-0.737206\pi\) | ||||
−0.678121 | + | 0.734950i | \(0.737206\pi\) | |||||||
\(752\) | 10.3458 | 0.377271 | ||||||||
\(753\) | −11.3886 | −0.415022 | ||||||||
\(754\) | 20.1673 | 0.734450 | ||||||||
\(755\) | −33.6396 | −1.22427 | ||||||||
\(756\) | 2.36365 | 0.0859652 | ||||||||
\(757\) | 23.1285 | 0.840619 | 0.420310 | − | 0.907381i | \(-0.361921\pi\) | ||||
0.420310 | + | 0.907381i | \(0.361921\pi\) | |||||||
\(758\) | 1.67234 | 0.0607421 | ||||||||
\(759\) | 41.3276 | 1.50010 | ||||||||
\(760\) | 7.19907 | 0.261138 | ||||||||
\(761\) | −33.8114 | −1.22566 | −0.612830 | − | 0.790214i | \(-0.709969\pi\) | ||||
−0.612830 | + | 0.790214i | \(0.709969\pi\) | |||||||
\(762\) | 16.3749 | 0.593200 | ||||||||
\(763\) | 0.214108 | 0.00775123 | ||||||||
\(764\) | −6.84039 | −0.247477 | ||||||||
\(765\) | 13.2698 | 0.479769 | ||||||||
\(766\) | −3.82222 | −0.138102 | ||||||||
\(767\) | 35.7478 | 1.29078 | ||||||||
\(768\) | −2.78808 | −0.100606 | ||||||||
\(769\) | 44.6314 | 1.60945 | 0.804724 | − | 0.593648i | \(-0.202313\pi\) | ||||
0.804724 | + | 0.593648i | \(0.202313\pi\) | |||||||
\(770\) | −1.77955 | −0.0641304 | ||||||||
\(771\) | 30.0525 | 1.08232 | ||||||||
\(772\) | 20.5250 | 0.738710 | ||||||||
\(773\) | −37.9486 | −1.36492 | −0.682458 | − | 0.730925i | \(-0.739089\pi\) | ||||
−0.682458 | + | 0.730925i | \(0.739089\pi\) | |||||||
\(774\) | 4.90102 | 0.176163 | ||||||||
\(775\) | −6.20121 | −0.222754 | ||||||||
\(776\) | −5.00870 | −0.179802 | ||||||||
\(777\) | 2.44015 | 0.0875401 | ||||||||
\(778\) | 3.29055 | 0.117972 | ||||||||
\(779\) | 28.9491 | 1.03721 | ||||||||
\(780\) | −26.1482 | −0.936255 | ||||||||
\(781\) | 9.62372 | 0.344364 | ||||||||
\(782\) | −11.0698 | −0.395857 | ||||||||
\(783\) | −17.9322 | −0.640843 | ||||||||
\(784\) | −6.77146 | −0.241838 | ||||||||
\(785\) | 11.2215 | 0.400514 | ||||||||
\(786\) | 46.2230 | 1.64872 | ||||||||
\(787\) | 3.75804 | 0.133960 | 0.0669799 | − | 0.997754i | \(-0.478664\pi\) | ||||
0.0669799 | + | 0.997754i | \(0.478664\pi\) | |||||||
\(788\) | 23.6099 | 0.841068 | ||||||||
\(789\) | 65.1042 | 2.31777 | ||||||||
\(790\) | −20.2872 | −0.721785 | ||||||||
\(791\) | −1.41868 | −0.0504423 | ||||||||
\(792\) | 10.5351 | 0.374350 | ||||||||
\(793\) | 24.1077 | 0.856091 | ||||||||
\(794\) | −22.9518 | −0.814527 | ||||||||
\(795\) | −60.7240 | −2.15366 | ||||||||
\(796\) | −17.2752 | −0.612304 | ||||||||
\(797\) | 10.0792 | 0.357023 | 0.178512 | − | 0.983938i | \(-0.442872\pi\) | ||||
0.178512 | + | 0.983938i | \(0.442872\pi\) | |||||||
\(798\) | 5.68910 | 0.201392 | ||||||||
\(799\) | 17.0523 | 0.603268 | ||||||||
\(800\) | −2.15533 | −0.0762024 | ||||||||
\(801\) | −60.6854 | −2.14421 | ||||||||
\(802\) | −30.7638 | −1.08631 | ||||||||
\(803\) | −0.419128 | −0.0147907 | ||||||||
\(804\) | 27.0106 | 0.952589 | ||||||||
\(805\) | 5.41520 | 0.190861 | ||||||||
\(806\) | 15.9987 | 0.563529 | ||||||||
\(807\) | −11.8445 | −0.416947 | ||||||||
\(808\) | −6.47702 | −0.227861 | ||||||||
\(809\) | −45.9563 | −1.61574 | −0.807869 | − | 0.589362i | \(-0.799379\pi\) | ||||
−0.807869 | + | 0.589362i | \(0.799379\pi\) | |||||||
\(810\) | −0.902360 | −0.0317057 | ||||||||
\(811\) | −23.7415 | −0.833677 | −0.416838 | − | 0.908981i | \(-0.636862\pi\) | ||||
−0.416838 | + | 0.908981i | \(0.636862\pi\) | |||||||
\(812\) | −1.73382 | −0.0608453 | ||||||||
\(813\) | −23.6109 | −0.828070 | ||||||||
\(814\) | 4.04063 | 0.141624 | ||||||||
\(815\) | 29.4186 | 1.03049 | ||||||||
\(816\) | −4.59543 | −0.160872 | ||||||||
\(817\) | 4.38249 | 0.153324 | ||||||||
\(818\) | 28.3717 | 0.991994 | ||||||||
\(819\) | −12.6889 | −0.443387 | ||||||||
\(820\) | 11.4391 | 0.399469 | ||||||||
\(821\) | 4.39466 | 0.153375 | 0.0766873 | − | 0.997055i | \(-0.475566\pi\) | ||||
0.0766873 | + | 0.997055i | \(0.475566\pi\) | |||||||
\(822\) | −19.4977 | −0.680061 | ||||||||
\(823\) | 4.72146 | 0.164580 | 0.0822898 | − | 0.996608i | \(-0.473777\pi\) | ||||
0.0822898 | + | 0.996608i | \(0.473777\pi\) | |||||||
\(824\) | −3.67441 | −0.128004 | ||||||||
\(825\) | 13.2627 | 0.461749 | ||||||||
\(826\) | −3.07331 | −0.106934 | ||||||||
\(827\) | −45.0152 | −1.56533 | −0.782666 | − | 0.622442i | \(-0.786141\pi\) | ||||
−0.782666 | + | 0.622442i | \(0.786141\pi\) | |||||||
\(828\) | −32.0587 | −1.11412 | ||||||||
\(829\) | −10.8984 | −0.378516 | −0.189258 | − | 0.981927i | \(-0.560608\pi\) | ||||
−0.189258 | + | 0.981927i | \(0.560608\pi\) | |||||||
\(830\) | 9.20134 | 0.319383 | ||||||||
\(831\) | −63.7130 | −2.21018 | ||||||||
\(832\) | 5.56059 | 0.192779 | ||||||||
\(833\) | −11.1610 | −0.386706 | ||||||||
\(834\) | −0.917674 | −0.0317765 | ||||||||
\(835\) | −7.36224 | −0.254781 | ||||||||
\(836\) | 9.42053 | 0.325816 | ||||||||
\(837\) | −14.2255 | −0.491707 | ||||||||
\(838\) | −14.8052 | −0.511435 | ||||||||
\(839\) | −4.15441 | −0.143426 | −0.0717130 | − | 0.997425i | \(-0.522847\pi\) | ||||
−0.0717130 | + | 0.997425i | \(0.522847\pi\) | |||||||
\(840\) | 2.24801 | 0.0775639 | ||||||||
\(841\) | −15.8461 | −0.546418 | ||||||||
\(842\) | 34.4115 | 1.18590 | ||||||||
\(843\) | −8.28288 | −0.285278 | ||||||||
\(844\) | 4.04319 | 0.139172 | ||||||||
\(845\) | 30.2244 | 1.03975 | ||||||||
\(846\) | 49.3842 | 1.69787 | ||||||||
\(847\) | 2.92994 | 0.100674 | ||||||||
\(848\) | 12.9134 | 0.443447 | ||||||||
\(849\) | −68.9770 | −2.36728 | ||||||||
\(850\) | −3.55251 | −0.121850 | ||||||||
\(851\) | −12.2957 | −0.421492 | ||||||||
\(852\) | −12.1572 | −0.416498 | ||||||||
\(853\) | −38.8860 | −1.33143 | −0.665716 | − | 0.746205i | \(-0.731874\pi\) | ||||
−0.665716 | + | 0.746205i | \(0.731874\pi\) | |||||||
\(854\) | −2.07259 | −0.0709227 | ||||||||
\(855\) | 34.3639 | 1.17522 | ||||||||
\(856\) | −16.3658 | −0.559372 | ||||||||
\(857\) | 24.8510 | 0.848894 | 0.424447 | − | 0.905453i | \(-0.360469\pi\) | ||||
0.424447 | + | 0.905453i | \(0.360469\pi\) | |||||||
\(858\) | −34.2169 | −1.16815 | ||||||||
\(859\) | 27.4246 | 0.935714 | 0.467857 | − | 0.883804i | \(-0.345026\pi\) | ||||
0.467857 | + | 0.883804i | \(0.345026\pi\) | |||||||
\(860\) | 1.73172 | 0.0590510 | ||||||||
\(861\) | 9.03977 | 0.308075 | ||||||||
\(862\) | −2.03361 | −0.0692650 | ||||||||
\(863\) | 21.3701 | 0.727448 | 0.363724 | − | 0.931507i | \(-0.381505\pi\) | ||||
0.363724 | + | 0.931507i | \(0.381505\pi\) | |||||||
\(864\) | −4.94431 | −0.168209 | ||||||||
\(865\) | −4.53211 | −0.154096 | ||||||||
\(866\) | −19.3295 | −0.656842 | ||||||||
\(867\) | 39.8229 | 1.35246 | ||||||||
\(868\) | −1.37544 | −0.0466855 | ||||||||
\(869\) | −26.5473 | −0.900555 | ||||||||
\(870\) | −17.0548 | −0.578214 | ||||||||
\(871\) | −53.8703 | −1.82533 | ||||||||
\(872\) | −0.447873 | −0.0151669 | ||||||||
\(873\) | −23.9084 | −0.809176 | ||||||||
\(874\) | −28.6669 | −0.969672 | ||||||||
\(875\) | 5.76931 | 0.195038 | ||||||||
\(876\) | 0.529464 | 0.0178889 | ||||||||
\(877\) | 28.4297 | 0.960002 | 0.480001 | − | 0.877268i | \(-0.340636\pi\) | ||||
0.480001 | + | 0.877268i | \(0.340636\pi\) | |||||||
\(878\) | −15.0399 | −0.507574 | ||||||||
\(879\) | −15.8770 | −0.535519 | ||||||||
\(880\) | 3.72247 | 0.125484 | ||||||||
\(881\) | −13.5102 | −0.455172 | −0.227586 | − | 0.973758i | \(-0.573083\pi\) | ||||
−0.227586 | + | 0.973758i | \(0.573083\pi\) | |||||||
\(882\) | −32.3227 | −1.08836 | ||||||||
\(883\) | −23.4769 | −0.790061 | −0.395030 | − | 0.918668i | \(-0.629266\pi\) | ||||
−0.395030 | + | 0.918668i | \(0.629266\pi\) | |||||||
\(884\) | 9.16520 | 0.308259 | ||||||||
\(885\) | −30.2308 | −1.01620 | ||||||||
\(886\) | 8.06470 | 0.270939 | ||||||||
\(887\) | −15.2173 | −0.510947 | −0.255474 | − | 0.966816i | \(-0.582231\pi\) | ||||
−0.255474 | + | 0.966816i | \(0.582231\pi\) | |||||||
\(888\) | −5.10433 | −0.171290 | ||||||||
\(889\) | 2.80771 | 0.0941676 | ||||||||
\(890\) | −21.4424 | −0.718752 | ||||||||
\(891\) | −1.18081 | −0.0395585 | ||||||||
\(892\) | 4.68255 | 0.156783 | ||||||||
\(893\) | 44.1594 | 1.47774 | ||||||||
\(894\) | −39.9936 | −1.33759 | ||||||||
\(895\) | 11.7806 | 0.393783 | ||||||||
\(896\) | −0.478055 | −0.0159707 | ||||||||
\(897\) | 104.123 | 3.47656 | ||||||||
\(898\) | −30.5246 | −1.01862 | ||||||||
\(899\) | 10.4349 | 0.348025 | ||||||||
\(900\) | −10.2882 | −0.342940 | ||||||||
\(901\) | 21.2844 | 0.709085 | ||||||||
\(902\) | 14.9689 | 0.498409 | ||||||||
\(903\) | 1.36850 | 0.0455407 | ||||||||
\(904\) | 2.96760 | 0.0987008 | ||||||||
\(905\) | 13.7099 | 0.455734 | ||||||||
\(906\) | 55.6082 | 1.84746 | ||||||||
\(907\) | −50.0011 | −1.66026 | −0.830130 | − | 0.557569i | \(-0.811734\pi\) | ||||
−0.830130 | + | 0.557569i | \(0.811734\pi\) | |||||||
\(908\) | 21.4011 | 0.710221 | ||||||||
\(909\) | −30.9173 | −1.02546 | ||||||||
\(910\) | −4.48348 | −0.148626 | ||||||||
\(911\) | −44.2728 | −1.46682 | −0.733412 | − | 0.679784i | \(-0.762074\pi\) | ||||
−0.733412 | + | 0.679784i | \(0.762074\pi\) | |||||||
\(912\) | −11.9005 | −0.394065 | ||||||||
\(913\) | 12.0407 | 0.398488 | ||||||||
\(914\) | 35.7756 | 1.18335 | ||||||||
\(915\) | −20.3872 | −0.673979 | ||||||||
\(916\) | 12.6702 | 0.418634 | ||||||||
\(917\) | 7.92558 | 0.261726 | ||||||||
\(918\) | −8.14942 | −0.268971 | ||||||||
\(919\) | 29.2871 | 0.966092 | 0.483046 | − | 0.875595i | \(-0.339530\pi\) | ||||
0.483046 | + | 0.875595i | \(0.339530\pi\) | |||||||
\(920\) | −11.3276 | −0.373458 | ||||||||
\(921\) | 4.03046 | 0.132808 | ||||||||
\(922\) | 33.8197 | 1.11379 | ||||||||
\(923\) | 24.2465 | 0.798082 | ||||||||
\(924\) | 2.94170 | 0.0967748 | ||||||||
\(925\) | −3.94592 | −0.129741 | ||||||||
\(926\) | −26.5118 | −0.871233 | ||||||||
\(927\) | −17.5394 | −0.576068 | ||||||||
\(928\) | 3.62683 | 0.119056 | ||||||||
\(929\) | −24.3930 | −0.800310 | −0.400155 | − | 0.916448i | \(-0.631044\pi\) | ||||
−0.400155 | + | 0.916448i | \(0.631044\pi\) | |||||||
\(930\) | −13.5296 | −0.443652 | ||||||||
\(931\) | −28.9030 | −0.947257 | ||||||||
\(932\) | 2.85283 | 0.0934476 | ||||||||
\(933\) | 70.4426 | 2.30619 | ||||||||
\(934\) | 23.1866 | 0.758687 | ||||||||
\(935\) | 6.13553 | 0.200653 | ||||||||
\(936\) | 26.5428 | 0.867578 | ||||||||
\(937\) | −7.48744 | −0.244604 | −0.122302 | − | 0.992493i | \(-0.539028\pi\) | ||||
−0.122302 | + | 0.992493i | \(0.539028\pi\) | |||||||
\(938\) | 4.63134 | 0.151219 | ||||||||
\(939\) | −71.7466 | −2.34136 | ||||||||
\(940\) | 17.4493 | 0.569134 | ||||||||
\(941\) | −46.2791 | −1.50866 | −0.754328 | − | 0.656498i | \(-0.772037\pi\) | ||||
−0.754328 | + | 0.656498i | \(0.772037\pi\) | |||||||
\(942\) | −18.5499 | −0.604388 | ||||||||
\(943\) | −45.5507 | −1.48333 | ||||||||
\(944\) | 6.42878 | 0.209239 | ||||||||
\(945\) | 3.98657 | 0.129683 | ||||||||
\(946\) | 2.26608 | 0.0736766 | ||||||||
\(947\) | 19.5323 | 0.634713 | 0.317357 | − | 0.948306i | \(-0.397205\pi\) | ||||
0.317357 | + | 0.948306i | \(0.397205\pi\) | |||||||
\(948\) | 33.5359 | 1.08920 | ||||||||
\(949\) | −1.05597 | −0.0342783 | ||||||||
\(950\) | −9.19970 | −0.298478 | ||||||||
\(951\) | 5.60847 | 0.181867 | ||||||||
\(952\) | −0.787952 | −0.0255377 | ||||||||
\(953\) | 0.246261 | 0.00797717 | 0.00398859 | − | 0.999992i | \(-0.498730\pi\) | ||||
0.00398859 | + | 0.999992i | \(0.498730\pi\) | |||||||
\(954\) | 61.6403 | 1.99568 | ||||||||
\(955\) | −11.5371 | −0.373332 | ||||||||
\(956\) | −13.6057 | −0.440040 | ||||||||
\(957\) | −22.3176 | −0.721424 | ||||||||
\(958\) | −24.2960 | −0.784968 | ||||||||
\(959\) | −3.34316 | −0.107956 | ||||||||
\(960\) | −4.70241 | −0.151770 | ||||||||
\(961\) | −22.7220 | −0.732967 | ||||||||
\(962\) | 10.1802 | 0.328222 | ||||||||
\(963\) | −78.1202 | −2.51739 | ||||||||
\(964\) | 16.2213 | 0.522454 | ||||||||
\(965\) | 34.6178 | 1.11438 | ||||||||
\(966\) | −8.95165 | −0.288015 | ||||||||
\(967\) | 9.27650 | 0.298312 | 0.149156 | − | 0.988814i | \(-0.452344\pi\) | ||||
0.149156 | + | 0.988814i | \(0.452344\pi\) | |||||||
\(968\) | −6.12887 | −0.196989 | ||||||||
\(969\) | −19.6149 | −0.630122 | ||||||||
\(970\) | −8.44774 | −0.271241 | ||||||||
\(971\) | −33.1115 | −1.06260 | −0.531299 | − | 0.847185i | \(-0.678296\pi\) | ||||
−0.531299 | + | 0.847185i | \(0.678296\pi\) | |||||||
\(972\) | 16.3246 | 0.523611 | ||||||||
\(973\) | −0.157348 | −0.00504435 | ||||||||
\(974\) | 16.6398 | 0.533173 | ||||||||
\(975\) | 33.4148 | 1.07013 | ||||||||
\(976\) | 4.33547 | 0.138775 | ||||||||
\(977\) | 35.0471 | 1.12126 | 0.560629 | − | 0.828067i | \(-0.310560\pi\) | ||||
0.560629 | + | 0.828067i | \(0.310560\pi\) | |||||||
\(978\) | −48.6307 | −1.55504 | ||||||||
\(979\) | −28.0591 | −0.896772 | ||||||||
\(980\) | −11.4209 | −0.364826 | ||||||||
\(981\) | −2.13786 | −0.0682567 | ||||||||
\(982\) | 6.51985 | 0.208057 | ||||||||
\(983\) | −26.8722 | −0.857091 | −0.428546 | − | 0.903520i | \(-0.640974\pi\) | ||||
−0.428546 | + | 0.903520i | \(0.640974\pi\) | |||||||
\(984\) | −18.9095 | −0.602812 | ||||||||
\(985\) | 39.8208 | 1.26880 | ||||||||
\(986\) | 5.97789 | 0.190375 | ||||||||
\(987\) | 13.7894 | 0.438922 | ||||||||
\(988\) | 23.7346 | 0.755097 | ||||||||
\(989\) | −6.89573 | −0.219272 | ||||||||
\(990\) | 17.7687 | 0.564728 | ||||||||
\(991\) | 49.6279 | 1.57648 | 0.788241 | − | 0.615367i | \(-0.210992\pi\) | ||||
0.788241 | + | 0.615367i | \(0.210992\pi\) | |||||||
\(992\) | 2.87716 | 0.0913498 | ||||||||
\(993\) | 48.9618 | 1.55376 | ||||||||
\(994\) | −2.08452 | −0.0661170 | ||||||||
\(995\) | −29.1366 | −0.923694 | ||||||||
\(996\) | −15.2104 | −0.481959 | ||||||||
\(997\) | −5.68832 | −0.180151 | −0.0900755 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900755 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(998\) | 9.47873 | 0.300044 | ||||||||
\(999\) | −9.05190 | −0.286390 |
(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 | 8042.2.a.d.1.11 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.d.1.11 | ✓ | 101 | 1.1 | even | 1 | trivial |