Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69069 | 1.90261 | 0.951303 | − | 0.308256i | \(-0.0997454\pi\) | ||||
0.951303 | + | 0.308256i | \(0.0997454\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.23983 | 2.61991 | ||||||||
\(5\) | −3.39075 | −1.51639 | −0.758195 | − | 0.652028i | \(-0.773918\pi\) | ||||
−0.758195 | + | 0.652028i | \(0.773918\pi\) | |||||||
\(6\) | −2.69069 | −1.09847 | ||||||||
\(7\) | 3.55923 | 1.34526 | 0.672631 | − | 0.739978i | \(-0.265164\pi\) | ||||
0.672631 | + | 0.739978i | \(0.265164\pi\) | |||||||
\(8\) | 8.71737 | 3.08206 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.12347 | −2.88509 | ||||||||
\(11\) | 3.97019 | 1.19706 | 0.598529 | − | 0.801101i | \(-0.295752\pi\) | ||||
0.598529 | + | 0.801101i | \(0.295752\pi\) | |||||||
\(12\) | −5.23983 | −1.51261 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 9.57679 | 2.55950 | ||||||||
\(15\) | 3.39075 | 0.875488 | ||||||||
\(16\) | 12.9761 | 3.24403 | ||||||||
\(17\) | −5.69126 | −1.38033 | −0.690166 | − | 0.723651i | \(-0.742463\pi\) | ||||
−0.690166 | + | 0.723651i | \(0.742463\pi\) | |||||||
\(18\) | 2.69069 | 0.634202 | ||||||||
\(19\) | −3.19194 | −0.732282 | −0.366141 | − | 0.930559i | \(-0.619321\pi\) | ||||
−0.366141 | + | 0.930559i | \(0.619321\pi\) | |||||||
\(20\) | −17.7669 | −3.97281 | ||||||||
\(21\) | −3.55923 | −0.776687 | ||||||||
\(22\) | 10.6826 | 2.27753 | ||||||||
\(23\) | 4.70654 | 0.981382 | 0.490691 | − | 0.871334i | \(-0.336744\pi\) | ||||
0.490691 | + | 0.871334i | \(0.336744\pi\) | |||||||
\(24\) | −8.71737 | −1.77943 | ||||||||
\(25\) | 6.49719 | 1.29944 | ||||||||
\(26\) | 2.69069 | 0.527688 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 18.6497 | 3.52447 | ||||||||
\(29\) | 6.05116 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(30\) | 9.12347 | 1.66571 | ||||||||
\(31\) | 6.73805 | 1.21019 | 0.605095 | − | 0.796153i | \(-0.293135\pi\) | ||||
0.605095 | + | 0.796153i | \(0.293135\pi\) | |||||||
\(32\) | 17.4800 | 3.09006 | ||||||||
\(33\) | −3.97019 | −0.691122 | ||||||||
\(34\) | −15.3134 | −2.62623 | ||||||||
\(35\) | −12.0685 | −2.03994 | ||||||||
\(36\) | 5.23983 | 0.873304 | ||||||||
\(37\) | −7.13584 | −1.17313 | −0.586563 | − | 0.809904i | \(-0.699519\pi\) | ||||
−0.586563 | + | 0.809904i | \(0.699519\pi\) | |||||||
\(38\) | −8.58854 | −1.39324 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −29.5584 | −4.67360 | ||||||||
\(41\) | 1.26699 | 0.197871 | 0.0989355 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989355 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(42\) | −9.57679 | −1.47773 | ||||||||
\(43\) | −3.71867 | −0.567091 | −0.283546 | − | 0.958959i | \(-0.591511\pi\) | ||||
−0.283546 | + | 0.958959i | \(0.591511\pi\) | |||||||
\(44\) | 20.8031 | 3.13619 | ||||||||
\(45\) | −3.39075 | −0.505463 | ||||||||
\(46\) | 12.6639 | 1.86718 | ||||||||
\(47\) | −2.79607 | −0.407849 | −0.203924 | − | 0.978987i | \(-0.565370\pi\) | ||||
−0.203924 | + | 0.978987i | \(0.565370\pi\) | |||||||
\(48\) | −12.9761 | −1.87294 | ||||||||
\(49\) | 5.66810 | 0.809729 | ||||||||
\(50\) | 17.4819 | 2.47232 | ||||||||
\(51\) | 5.69126 | 0.796936 | ||||||||
\(52\) | 5.23983 | 0.726633 | ||||||||
\(53\) | 14.3686 | 1.97368 | 0.986840 | − | 0.161702i | \(-0.0516983\pi\) | ||||
0.986840 | + | 0.161702i | \(0.0516983\pi\) | |||||||
\(54\) | −2.69069 | −0.366157 | ||||||||
\(55\) | −13.4619 | −1.81521 | ||||||||
\(56\) | 31.0271 | 4.14617 | ||||||||
\(57\) | 3.19194 | 0.422783 | ||||||||
\(58\) | 16.2818 | 2.13791 | ||||||||
\(59\) | 10.9643 | 1.42743 | 0.713715 | − | 0.700437i | \(-0.247011\pi\) | ||||
0.713715 | + | 0.700437i | \(0.247011\pi\) | |||||||
\(60\) | 17.7669 | 2.29370 | ||||||||
\(61\) | −9.35699 | −1.19804 | −0.599020 | − | 0.800734i | \(-0.704443\pi\) | ||||
−0.599020 | + | 0.800734i | \(0.704443\pi\) | |||||||
\(62\) | 18.1300 | 2.30252 | ||||||||
\(63\) | 3.55923 | 0.448421 | ||||||||
\(64\) | 21.0811 | 2.63513 | ||||||||
\(65\) | −3.39075 | −0.420571 | ||||||||
\(66\) | −10.6826 | −1.31493 | ||||||||
\(67\) | −8.20608 | −1.00253 | −0.501266 | − | 0.865293i | \(-0.667132\pi\) | ||||
−0.501266 | + | 0.865293i | \(0.667132\pi\) | |||||||
\(68\) | −29.8212 | −3.61635 | ||||||||
\(69\) | −4.70654 | −0.566601 | ||||||||
\(70\) | −32.4725 | −3.88120 | ||||||||
\(71\) | −5.77396 | −0.685243 | −0.342622 | − | 0.939473i | \(-0.611315\pi\) | ||||
−0.342622 | + | 0.939473i | \(0.611315\pi\) | |||||||
\(72\) | 8.71737 | 1.02735 | ||||||||
\(73\) | −4.07053 | −0.476420 | −0.238210 | − | 0.971214i | \(-0.576561\pi\) | ||||
−0.238210 | + | 0.971214i | \(0.576561\pi\) | |||||||
\(74\) | −19.2004 | −2.23200 | ||||||||
\(75\) | −6.49719 | −0.750230 | ||||||||
\(76\) | −16.7252 | −1.91851 | ||||||||
\(77\) | 14.1308 | 1.61036 | ||||||||
\(78\) | −2.69069 | −0.304661 | ||||||||
\(79\) | 9.95930 | 1.12051 | 0.560254 | − | 0.828321i | \(-0.310703\pi\) | ||||
0.560254 | + | 0.828321i | \(0.310703\pi\) | |||||||
\(80\) | −43.9988 | −4.91921 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.40909 | 0.376471 | ||||||||
\(83\) | 15.1402 | 1.66185 | 0.830925 | − | 0.556385i | \(-0.187812\pi\) | ||||
0.830925 | + | 0.556385i | \(0.187812\pi\) | |||||||
\(84\) | −18.6497 | −2.03485 | ||||||||
\(85\) | 19.2976 | 2.09312 | ||||||||
\(86\) | −10.0058 | −1.07895 | ||||||||
\(87\) | −6.05116 | −0.648752 | ||||||||
\(88\) | 34.6096 | 3.68940 | ||||||||
\(89\) | 14.6677 | 1.55477 | 0.777384 | − | 0.629026i | \(-0.216546\pi\) | ||||
0.777384 | + | 0.629026i | \(0.216546\pi\) | |||||||
\(90\) | −9.12347 | −0.961698 | ||||||||
\(91\) | 3.55923 | 0.373108 | ||||||||
\(92\) | 24.6615 | 2.57114 | ||||||||
\(93\) | −6.73805 | −0.698704 | ||||||||
\(94\) | −7.52336 | −0.775975 | ||||||||
\(95\) | 10.8231 | 1.11042 | ||||||||
\(96\) | −17.4800 | −1.78404 | ||||||||
\(97\) | 6.18570 | 0.628063 | 0.314032 | − | 0.949413i | \(-0.398320\pi\) | ||||
0.314032 | + | 0.949413i | \(0.398320\pi\) | |||||||
\(98\) | 15.2511 | 1.54060 | ||||||||
\(99\) | 3.97019 | 0.399019 | ||||||||
\(100\) | 34.0441 | 3.40441 | ||||||||
\(101\) | −8.78051 | −0.873693 | −0.436847 | − | 0.899536i | \(-0.643905\pi\) | ||||
−0.436847 | + | 0.899536i | \(0.643905\pi\) | |||||||
\(102\) | 15.3134 | 1.51625 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 8.71737 | 0.854809 | ||||||||
\(105\) | 12.0685 | 1.17776 | ||||||||
\(106\) | 38.6615 | 3.75514 | ||||||||
\(107\) | −3.81774 | −0.369074 | −0.184537 | − | 0.982826i | \(-0.559079\pi\) | ||||
−0.184537 | + | 0.982826i | \(0.559079\pi\) | |||||||
\(108\) | −5.23983 | −0.504202 | ||||||||
\(109\) | −7.48563 | −0.716994 | −0.358497 | − | 0.933531i | \(-0.616711\pi\) | ||||
−0.358497 | + | 0.933531i | \(0.616711\pi\) | |||||||
\(110\) | −36.2219 | −3.45362 | ||||||||
\(111\) | 7.13584 | 0.677304 | ||||||||
\(112\) | 46.1850 | 4.36407 | ||||||||
\(113\) | 8.98479 | 0.845218 | 0.422609 | − | 0.906312i | \(-0.361114\pi\) | ||||
0.422609 | + | 0.906312i | \(0.361114\pi\) | |||||||
\(114\) | 8.58854 | 0.804390 | ||||||||
\(115\) | −15.9587 | −1.48816 | ||||||||
\(116\) | 31.7070 | 2.94392 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 29.5015 | 2.71584 | ||||||||
\(119\) | −20.2565 | −1.85691 | ||||||||
\(120\) | 29.5584 | 2.69830 | ||||||||
\(121\) | 4.76242 | 0.432947 | ||||||||
\(122\) | −25.1768 | −2.27940 | ||||||||
\(123\) | −1.26699 | −0.114241 | ||||||||
\(124\) | 35.3062 | 3.17059 | ||||||||
\(125\) | −5.07658 | −0.454063 | ||||||||
\(126\) | 9.57679 | 0.853168 | ||||||||
\(127\) | −0.0565956 | −0.00502204 | −0.00251102 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00251102 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(128\) | 21.7626 | 1.92356 | ||||||||
\(129\) | 3.71867 | 0.327410 | ||||||||
\(130\) | −9.12347 | −0.800181 | ||||||||
\(131\) | 14.0234 | 1.22523 | 0.612616 | − | 0.790381i | \(-0.290117\pi\) | ||||
0.612616 | + | 0.790381i | \(0.290117\pi\) | |||||||
\(132\) | −20.8031 | −1.81068 | ||||||||
\(133\) | −11.3608 | −0.985111 | ||||||||
\(134\) | −22.0800 | −1.90742 | ||||||||
\(135\) | 3.39075 | 0.291829 | ||||||||
\(136\) | −49.6128 | −4.25426 | ||||||||
\(137\) | −0.460919 | −0.0393790 | −0.0196895 | − | 0.999806i | \(-0.506268\pi\) | ||||
−0.0196895 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(138\) | −12.6639 | −1.07802 | ||||||||
\(139\) | −1.08724 | −0.0922185 | −0.0461092 | − | 0.998936i | \(-0.514682\pi\) | ||||
−0.0461092 | + | 0.998936i | \(0.514682\pi\) | |||||||
\(140\) | −63.2366 | −5.34447 | ||||||||
\(141\) | 2.79607 | 0.235471 | ||||||||
\(142\) | −15.5360 | −1.30375 | ||||||||
\(143\) | 3.97019 | 0.332004 | ||||||||
\(144\) | 12.9761 | 1.08134 | ||||||||
\(145\) | −20.5180 | −1.70392 | ||||||||
\(146\) | −10.9525 | −0.906439 | ||||||||
\(147\) | −5.66810 | −0.467497 | ||||||||
\(148\) | −37.3906 | −3.07349 | ||||||||
\(149\) | −12.0840 | −0.989960 | −0.494980 | − | 0.868904i | \(-0.664825\pi\) | ||||
−0.494980 | + | 0.868904i | \(0.664825\pi\) | |||||||
\(150\) | −17.4819 | −1.42739 | ||||||||
\(151\) | −2.12941 | −0.173289 | −0.0866446 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866446 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(152\) | −27.8254 | −2.25693 | ||||||||
\(153\) | −5.69126 | −0.460111 | ||||||||
\(154\) | 38.0217 | 3.06387 | ||||||||
\(155\) | −22.8471 | −1.83512 | ||||||||
\(156\) | −5.23983 | −0.419522 | ||||||||
\(157\) | 11.1255 | 0.887912 | 0.443956 | − | 0.896048i | \(-0.353575\pi\) | ||||
0.443956 | + | 0.896048i | \(0.353575\pi\) | |||||||
\(158\) | 26.7974 | 2.13189 | ||||||||
\(159\) | −14.3686 | −1.13950 | ||||||||
\(160\) | −59.2703 | −4.68573 | ||||||||
\(161\) | 16.7517 | 1.32022 | ||||||||
\(162\) | 2.69069 | 0.211401 | ||||||||
\(163\) | 0.480373 | 0.0376257 | 0.0188128 | − | 0.999823i | \(-0.494011\pi\) | ||||
0.0188128 | + | 0.999823i | \(0.494011\pi\) | |||||||
\(164\) | 6.63882 | 0.518405 | ||||||||
\(165\) | 13.4619 | 1.04801 | ||||||||
\(166\) | 40.7375 | 3.16185 | ||||||||
\(167\) | 1.79007 | 0.138520 | 0.0692598 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692598 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(168\) | −31.0271 | −2.39379 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 51.9240 | 3.98239 | ||||||||
\(171\) | −3.19194 | −0.244094 | ||||||||
\(172\) | −19.4852 | −1.48573 | ||||||||
\(173\) | −3.45807 | −0.262912 | −0.131456 | − | 0.991322i | \(-0.541965\pi\) | ||||
−0.131456 | + | 0.991322i | \(0.541965\pi\) | |||||||
\(174\) | −16.2818 | −1.23432 | ||||||||
\(175\) | 23.1250 | 1.74808 | ||||||||
\(176\) | 51.5177 | 3.88329 | ||||||||
\(177\) | −10.9643 | −0.824127 | ||||||||
\(178\) | 39.4662 | 2.95811 | ||||||||
\(179\) | −22.9901 | −1.71836 | −0.859181 | − | 0.511672i | \(-0.829026\pi\) | ||||
−0.859181 | + | 0.511672i | \(0.829026\pi\) | |||||||
\(180\) | −17.7669 | −1.32427 | ||||||||
\(181\) | −2.48918 | −0.185019 | −0.0925096 | − | 0.995712i | \(-0.529489\pi\) | ||||
−0.0925096 | + | 0.995712i | \(0.529489\pi\) | |||||||
\(182\) | 9.57679 | 0.709879 | ||||||||
\(183\) | 9.35699 | 0.691689 | ||||||||
\(184\) | 41.0287 | 3.02468 | ||||||||
\(185\) | 24.1959 | 1.77891 | ||||||||
\(186\) | −18.1300 | −1.32936 | ||||||||
\(187\) | −22.5954 | −1.65234 | ||||||||
\(188\) | −14.6509 | −1.06853 | ||||||||
\(189\) | −3.55923 | −0.258896 | ||||||||
\(190\) | 29.1216 | 2.11270 | ||||||||
\(191\) | −5.22992 | −0.378423 | −0.189212 | − | 0.981936i | \(-0.560593\pi\) | ||||
−0.189212 | + | 0.981936i | \(0.560593\pi\) | |||||||
\(192\) | −21.0811 | −1.52139 | ||||||||
\(193\) | −18.7320 | −1.34836 | −0.674178 | − | 0.738569i | \(-0.735502\pi\) | ||||
−0.674178 | + | 0.738569i | \(0.735502\pi\) | |||||||
\(194\) | 16.6438 | 1.19496 | ||||||||
\(195\) | 3.39075 | 0.242817 | ||||||||
\(196\) | 29.6999 | 2.12142 | ||||||||
\(197\) | 3.47184 | 0.247358 | 0.123679 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123679 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(198\) | 10.6826 | 0.759177 | ||||||||
\(199\) | −27.6483 | −1.95994 | −0.979968 | − | 0.199156i | \(-0.936180\pi\) | ||||
−0.979968 | + | 0.199156i | \(0.936180\pi\) | |||||||
\(200\) | 56.6384 | 4.00494 | ||||||||
\(201\) | 8.20608 | 0.578812 | ||||||||
\(202\) | −23.6256 | −1.66229 | ||||||||
\(203\) | 21.5374 | 1.51163 | ||||||||
\(204\) | 29.8212 | 2.08790 | ||||||||
\(205\) | −4.29606 | −0.300050 | ||||||||
\(206\) | −2.69069 | −0.187469 | ||||||||
\(207\) | 4.70654 | 0.327127 | ||||||||
\(208\) | 12.9761 | 0.899732 | ||||||||
\(209\) | −12.6726 | −0.876584 | ||||||||
\(210\) | 32.4725 | 2.24081 | ||||||||
\(211\) | −15.6447 | −1.07703 | −0.538513 | − | 0.842617i | \(-0.681014\pi\) | ||||
−0.538513 | + | 0.842617i | \(0.681014\pi\) | |||||||
\(212\) | 75.2890 | 5.17087 | ||||||||
\(213\) | 5.77396 | 0.395625 | ||||||||
\(214\) | −10.2724 | −0.702204 | ||||||||
\(215\) | 12.6091 | 0.859931 | ||||||||
\(216\) | −8.71737 | −0.593142 | ||||||||
\(217\) | 23.9823 | 1.62802 | ||||||||
\(218\) | −20.1415 | −1.36416 | ||||||||
\(219\) | 4.07053 | 0.275061 | ||||||||
\(220\) | −70.5381 | −4.75568 | ||||||||
\(221\) | −5.69126 | −0.382835 | ||||||||
\(222\) | 19.2004 | 1.28864 | ||||||||
\(223\) | 5.29312 | 0.354454 | 0.177227 | − | 0.984170i | \(-0.443287\pi\) | ||||
0.177227 | + | 0.984170i | \(0.443287\pi\) | |||||||
\(224\) | 62.2153 | 4.15693 | ||||||||
\(225\) | 6.49719 | 0.433146 | ||||||||
\(226\) | 24.1753 | 1.60812 | ||||||||
\(227\) | −1.22433 | −0.0812614 | −0.0406307 | − | 0.999174i | \(-0.512937\pi\) | ||||
−0.0406307 | + | 0.999174i | \(0.512937\pi\) | |||||||
\(228\) | 16.7252 | 1.10765 | ||||||||
\(229\) | 4.67193 | 0.308730 | 0.154365 | − | 0.988014i | \(-0.450667\pi\) | ||||
0.154365 | + | 0.988014i | \(0.450667\pi\) | |||||||
\(230\) | −42.9400 | −2.83138 | ||||||||
\(231\) | −14.1308 | −0.929739 | ||||||||
\(232\) | 52.7502 | 3.46322 | ||||||||
\(233\) | 17.6410 | 1.15570 | 0.577851 | − | 0.816142i | \(-0.303892\pi\) | ||||
0.577851 | + | 0.816142i | \(0.303892\pi\) | |||||||
\(234\) | 2.69069 | 0.175896 | ||||||||
\(235\) | 9.48077 | 0.618457 | ||||||||
\(236\) | 57.4510 | 3.73974 | ||||||||
\(237\) | −9.95930 | −0.646926 | ||||||||
\(238\) | −54.5040 | −3.53297 | ||||||||
\(239\) | −9.35839 | −0.605344 | −0.302672 | − | 0.953095i | \(-0.597879\pi\) | ||||
−0.302672 | + | 0.953095i | \(0.597879\pi\) | |||||||
\(240\) | 43.9988 | 2.84011 | ||||||||
\(241\) | −6.45712 | −0.415940 | −0.207970 | − | 0.978135i | \(-0.566686\pi\) | ||||
−0.207970 | + | 0.978135i | \(0.566686\pi\) | |||||||
\(242\) | 12.8142 | 0.823728 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −49.0290 | −3.13876 | ||||||||
\(245\) | −19.2191 | −1.22786 | ||||||||
\(246\) | −3.40909 | −0.217356 | ||||||||
\(247\) | −3.19194 | −0.203098 | ||||||||
\(248\) | 58.7381 | 3.72987 | ||||||||
\(249\) | −15.1402 | −0.959469 | ||||||||
\(250\) | −13.6595 | −0.863904 | ||||||||
\(251\) | −30.1157 | −1.90088 | −0.950442 | − | 0.310903i | \(-0.899368\pi\) | ||||
−0.950442 | + | 0.310903i | \(0.899368\pi\) | |||||||
\(252\) | 18.6497 | 1.17482 | ||||||||
\(253\) | 18.6859 | 1.17477 | ||||||||
\(254\) | −0.152281 | −0.00955498 | ||||||||
\(255\) | −19.2976 | −1.20846 | ||||||||
\(256\) | 16.3945 | 1.02465 | ||||||||
\(257\) | 30.2724 | 1.88834 | 0.944169 | − | 0.329461i | \(-0.106867\pi\) | ||||
0.944169 | + | 0.329461i | \(0.106867\pi\) | |||||||
\(258\) | 10.0058 | 0.622933 | ||||||||
\(259\) | −25.3981 | −1.57816 | ||||||||
\(260\) | −17.7669 | −1.10186 | ||||||||
\(261\) | 6.05116 | 0.374557 | ||||||||
\(262\) | 37.7327 | 2.33113 | ||||||||
\(263\) | −20.4793 | −1.26281 | −0.631404 | − | 0.775454i | \(-0.717521\pi\) | ||||
−0.631404 | + | 0.775454i | \(0.717521\pi\) | |||||||
\(264\) | −34.6096 | −2.13008 | ||||||||
\(265\) | −48.7203 | −2.99287 | ||||||||
\(266\) | −30.5686 | −1.87428 | ||||||||
\(267\) | −14.6677 | −0.897646 | ||||||||
\(268\) | −42.9984 | −2.62655 | ||||||||
\(269\) | −1.59398 | −0.0971869 | −0.0485935 | − | 0.998819i | \(-0.515474\pi\) | ||||
−0.0485935 | + | 0.998819i | \(0.515474\pi\) | |||||||
\(270\) | 9.12347 | 0.555236 | ||||||||
\(271\) | 3.86498 | 0.234781 | 0.117390 | − | 0.993086i | \(-0.462547\pi\) | ||||
0.117390 | + | 0.993086i | \(0.462547\pi\) | |||||||
\(272\) | −73.8504 | −4.47784 | ||||||||
\(273\) | −3.55923 | −0.215414 | ||||||||
\(274\) | −1.24019 | −0.0749227 | ||||||||
\(275\) | 25.7951 | 1.55550 | ||||||||
\(276\) | −24.6615 | −1.48445 | ||||||||
\(277\) | 1.88019 | 0.112970 | 0.0564849 | − | 0.998403i | \(-0.482011\pi\) | ||||
0.0564849 | + | 0.998403i | \(0.482011\pi\) | |||||||
\(278\) | −2.92543 | −0.175455 | ||||||||
\(279\) | 6.73805 | 0.403397 | ||||||||
\(280\) | −105.205 | −6.28721 | ||||||||
\(281\) | 20.1209 | 1.20031 | 0.600156 | − | 0.799883i | \(-0.295105\pi\) | ||||
0.600156 | + | 0.799883i | \(0.295105\pi\) | |||||||
\(282\) | 7.52336 | 0.448010 | ||||||||
\(283\) | −31.4850 | −1.87159 | −0.935796 | − | 0.352543i | \(-0.885317\pi\) | ||||
−0.935796 | + | 0.352543i | \(0.885317\pi\) | |||||||
\(284\) | −30.2546 | −1.79528 | ||||||||
\(285\) | −10.8231 | −0.641104 | ||||||||
\(286\) | 10.6826 | 0.631673 | ||||||||
\(287\) | 4.50952 | 0.266188 | ||||||||
\(288\) | 17.4800 | 1.03002 | ||||||||
\(289\) | 15.3904 | 0.905319 | ||||||||
\(290\) | −55.2075 | −3.24190 | ||||||||
\(291\) | −6.18570 | −0.362612 | ||||||||
\(292\) | −21.3289 | −1.24818 | ||||||||
\(293\) | 24.8054 | 1.44915 | 0.724573 | − | 0.689198i | \(-0.242037\pi\) | ||||
0.724573 | + | 0.689198i | \(0.242037\pi\) | |||||||
\(294\) | −15.2511 | −0.889463 | ||||||||
\(295\) | −37.1772 | −2.16454 | ||||||||
\(296\) | −62.2058 | −3.61564 | ||||||||
\(297\) | −3.97019 | −0.230374 | ||||||||
\(298\) | −32.5143 | −1.88350 | ||||||||
\(299\) | 4.70654 | 0.272186 | ||||||||
\(300\) | −34.0441 | −1.96554 | ||||||||
\(301\) | −13.2356 | −0.762886 | ||||||||
\(302\) | −5.72960 | −0.329701 | ||||||||
\(303\) | 8.78051 | 0.504427 | ||||||||
\(304\) | −41.4190 | −2.37554 | ||||||||
\(305\) | 31.7272 | 1.81670 | ||||||||
\(306\) | −15.3134 | −0.875410 | ||||||||
\(307\) | 11.8603 | 0.676905 | 0.338453 | − | 0.940983i | \(-0.390097\pi\) | ||||
0.338453 | + | 0.940983i | \(0.390097\pi\) | |||||||
\(308\) | 74.0430 | 4.21899 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −61.4744 | −3.49151 | ||||||||
\(311\) | −5.91420 | −0.335364 | −0.167682 | − | 0.985841i | \(-0.553628\pi\) | ||||
−0.167682 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(312\) | −8.71737 | −0.493524 | ||||||||
\(313\) | −26.7960 | −1.51460 | −0.757301 | − | 0.653066i | \(-0.773482\pi\) | ||||
−0.757301 | + | 0.653066i | \(0.773482\pi\) | |||||||
\(314\) | 29.9353 | 1.68935 | ||||||||
\(315\) | −12.0685 | −0.679980 | ||||||||
\(316\) | 52.1850 | 2.93563 | ||||||||
\(317\) | 0.676898 | 0.0380184 | 0.0190092 | − | 0.999819i | \(-0.493949\pi\) | ||||
0.0190092 | + | 0.999819i | \(0.493949\pi\) | |||||||
\(318\) | −38.6615 | −2.16803 | ||||||||
\(319\) | 24.0243 | 1.34510 | ||||||||
\(320\) | −71.4806 | −3.99589 | ||||||||
\(321\) | 3.81774 | 0.213085 | ||||||||
\(322\) | 45.0736 | 2.51185 | ||||||||
\(323\) | 18.1662 | 1.01079 | ||||||||
\(324\) | 5.23983 | 0.291101 | ||||||||
\(325\) | 6.49719 | 0.360399 | ||||||||
\(326\) | 1.29253 | 0.0715869 | ||||||||
\(327\) | 7.48563 | 0.413957 | ||||||||
\(328\) | 11.0448 | 0.609850 | ||||||||
\(329\) | −9.95185 | −0.548663 | ||||||||
\(330\) | 36.2219 | 1.99395 | ||||||||
\(331\) | −36.1015 | −1.98432 | −0.992159 | − | 0.124984i | \(-0.960112\pi\) | ||||
−0.992159 | + | 0.124984i | \(0.960112\pi\) | |||||||
\(332\) | 79.3318 | 4.35390 | ||||||||
\(333\) | −7.13584 | −0.391042 | ||||||||
\(334\) | 4.81652 | 0.263548 | ||||||||
\(335\) | 27.8248 | 1.52023 | ||||||||
\(336\) | −46.1850 | −2.51960 | ||||||||
\(337\) | 17.8760 | 0.973765 | 0.486883 | − | 0.873467i | \(-0.338134\pi\) | ||||
0.486883 | + | 0.873467i | \(0.338134\pi\) | |||||||
\(338\) | 2.69069 | 0.146354 | ||||||||
\(339\) | −8.98479 | −0.487987 | ||||||||
\(340\) | 101.116 | 5.48380 | ||||||||
\(341\) | 26.7514 | 1.44867 | ||||||||
\(342\) | −8.58854 | −0.464415 | ||||||||
\(343\) | −4.74053 | −0.255965 | ||||||||
\(344\) | −32.4170 | −1.74781 | ||||||||
\(345\) | 15.9587 | 0.859188 | ||||||||
\(346\) | −9.30459 | −0.500218 | ||||||||
\(347\) | −13.2962 | −0.713776 | −0.356888 | − | 0.934147i | \(-0.616162\pi\) | ||||
−0.356888 | + | 0.934147i | \(0.616162\pi\) | |||||||
\(348\) | −31.7070 | −1.69967 | ||||||||
\(349\) | −14.7753 | −0.790905 | −0.395453 | − | 0.918486i | \(-0.629412\pi\) | ||||
−0.395453 | + | 0.918486i | \(0.629412\pi\) | |||||||
\(350\) | 62.2222 | 3.32591 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 69.3989 | 3.69898 | ||||||||
\(353\) | −24.9011 | −1.32535 | −0.662675 | − | 0.748907i | \(-0.730579\pi\) | ||||
−0.662675 | + | 0.748907i | \(0.730579\pi\) | |||||||
\(354\) | −29.5015 | −1.56799 | ||||||||
\(355\) | 19.5781 | 1.03910 | ||||||||
\(356\) | 76.8560 | 4.07336 | ||||||||
\(357\) | 20.2565 | 1.07209 | ||||||||
\(358\) | −61.8593 | −3.26937 | ||||||||
\(359\) | −15.6686 | −0.826958 | −0.413479 | − | 0.910514i | \(-0.635686\pi\) | ||||
−0.413479 | + | 0.910514i | \(0.635686\pi\) | |||||||
\(360\) | −29.5584 | −1.55787 | ||||||||
\(361\) | −8.81150 | −0.463763 | ||||||||
\(362\) | −6.69761 | −0.352019 | ||||||||
\(363\) | −4.76242 | −0.249962 | ||||||||
\(364\) | 18.6497 | 0.977512 | ||||||||
\(365\) | 13.8022 | 0.722438 | ||||||||
\(366\) | 25.1768 | 1.31601 | ||||||||
\(367\) | 24.8164 | 1.29540 | 0.647702 | − | 0.761893i | \(-0.275730\pi\) | ||||
0.647702 | + | 0.761893i | \(0.275730\pi\) | |||||||
\(368\) | 61.0727 | 3.18363 | ||||||||
\(369\) | 1.26699 | 0.0659570 | ||||||||
\(370\) | 65.1036 | 3.38457 | ||||||||
\(371\) | 51.1411 | 2.65511 | ||||||||
\(372\) | −35.3062 | −1.83054 | ||||||||
\(373\) | 6.40834 | 0.331812 | 0.165906 | − | 0.986142i | \(-0.446945\pi\) | ||||
0.165906 | + | 0.986142i | \(0.446945\pi\) | |||||||
\(374\) | −60.7972 | −3.14375 | ||||||||
\(375\) | 5.07658 | 0.262154 | ||||||||
\(376\) | −24.3744 | −1.25701 | ||||||||
\(377\) | 6.05116 | 0.311650 | ||||||||
\(378\) | −9.57679 | −0.492577 | ||||||||
\(379\) | 22.9273 | 1.17769 | 0.588847 | − | 0.808244i | \(-0.299582\pi\) | ||||
0.588847 | + | 0.808244i | \(0.299582\pi\) | |||||||
\(380\) | 56.7110 | 2.90922 | ||||||||
\(381\) | 0.0565956 | 0.00289948 | ||||||||
\(382\) | −14.0721 | −0.719991 | ||||||||
\(383\) | −25.1672 | −1.28598 | −0.642992 | − | 0.765873i | \(-0.722307\pi\) | ||||
−0.642992 | + | 0.765873i | \(0.722307\pi\) | |||||||
\(384\) | −21.7626 | −1.11057 | ||||||||
\(385\) | −47.9141 | −2.44193 | ||||||||
\(386\) | −50.4019 | −2.56539 | ||||||||
\(387\) | −3.71867 | −0.189030 | ||||||||
\(388\) | 32.4120 | 1.64547 | ||||||||
\(389\) | −35.7493 | −1.81256 | −0.906281 | − | 0.422675i | \(-0.861091\pi\) | ||||
−0.906281 | + | 0.422675i | \(0.861091\pi\) | |||||||
\(390\) | 9.12347 | 0.461985 | ||||||||
\(391\) | −26.7862 | −1.35463 | ||||||||
\(392\) | 49.4110 | 2.49563 | ||||||||
\(393\) | −14.0234 | −0.707388 | ||||||||
\(394\) | 9.34165 | 0.470626 | ||||||||
\(395\) | −33.7695 | −1.69913 | ||||||||
\(396\) | 20.8031 | 1.04540 | ||||||||
\(397\) | −25.1766 | −1.26358 | −0.631788 | − | 0.775142i | \(-0.717679\pi\) | ||||
−0.631788 | + | 0.775142i | \(0.717679\pi\) | |||||||
\(398\) | −74.3931 | −3.72899 | ||||||||
\(399\) | 11.3608 | 0.568754 | ||||||||
\(400\) | 84.3083 | 4.21541 | ||||||||
\(401\) | 1.50056 | 0.0749342 | 0.0374671 | − | 0.999298i | \(-0.488071\pi\) | ||||
0.0374671 | + | 0.999298i | \(0.488071\pi\) | |||||||
\(402\) | 22.0800 | 1.10125 | ||||||||
\(403\) | 6.73805 | 0.335646 | ||||||||
\(404\) | −46.0083 | −2.28900 | ||||||||
\(405\) | −3.39075 | −0.168488 | ||||||||
\(406\) | 57.9506 | 2.87604 | ||||||||
\(407\) | −28.3307 | −1.40430 | ||||||||
\(408\) | 49.6128 | 2.45620 | ||||||||
\(409\) | 11.9081 | 0.588817 | 0.294409 | − | 0.955680i | \(-0.404877\pi\) | ||||
0.294409 | + | 0.955680i | \(0.404877\pi\) | |||||||
\(410\) | −11.5594 | −0.570876 | ||||||||
\(411\) | 0.460919 | 0.0227355 | ||||||||
\(412\) | −5.23983 | −0.258148 | ||||||||
\(413\) | 39.0244 | 1.92027 | ||||||||
\(414\) | 12.6639 | 0.622395 | ||||||||
\(415\) | −51.3365 | −2.52001 | ||||||||
\(416\) | 17.4800 | 0.857027 | ||||||||
\(417\) | 1.08724 | 0.0532424 | ||||||||
\(418\) | −34.0981 | −1.66779 | ||||||||
\(419\) | 26.3736 | 1.28844 | 0.644219 | − | 0.764841i | \(-0.277183\pi\) | ||||
0.644219 | + | 0.764841i | \(0.277183\pi\) | |||||||
\(420\) | 63.2366 | 3.08563 | ||||||||
\(421\) | −28.8430 | −1.40572 | −0.702861 | − | 0.711328i | \(-0.748094\pi\) | ||||
−0.702861 | + | 0.711328i | \(0.748094\pi\) | |||||||
\(422\) | −42.0951 | −2.04916 | ||||||||
\(423\) | −2.79607 | −0.135950 | ||||||||
\(424\) | 125.256 | 6.08299 | ||||||||
\(425\) | −36.9772 | −1.79366 | ||||||||
\(426\) | 15.5360 | 0.752719 | ||||||||
\(427\) | −33.3037 | −1.61168 | ||||||||
\(428\) | −20.0043 | −0.966943 | ||||||||
\(429\) | −3.97019 | −0.191683 | ||||||||
\(430\) | 33.9271 | 1.63611 | ||||||||
\(431\) | −32.0033 | −1.54154 | −0.770771 | − | 0.637112i | \(-0.780129\pi\) | ||||
−0.770771 | + | 0.637112i | \(0.780129\pi\) | |||||||
\(432\) | −12.9761 | −0.624314 | ||||||||
\(433\) | 39.4532 | 1.89600 | 0.947999 | − | 0.318272i | \(-0.103103\pi\) | ||||
0.947999 | + | 0.318272i | \(0.103103\pi\) | |||||||
\(434\) | 64.5289 | 3.09749 | ||||||||
\(435\) | 20.5180 | 0.983761 | ||||||||
\(436\) | −39.2234 | −1.87846 | ||||||||
\(437\) | −15.0230 | −0.718648 | ||||||||
\(438\) | 10.9525 | 0.523333 | ||||||||
\(439\) | 2.96596 | 0.141558 | 0.0707788 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707788 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(440\) | −117.353 | −5.59457 | ||||||||
\(441\) | 5.66810 | 0.269910 | ||||||||
\(442\) | −15.3134 | −0.728385 | ||||||||
\(443\) | 19.6265 | 0.932485 | 0.466242 | − | 0.884657i | \(-0.345607\pi\) | ||||
0.466242 | + | 0.884657i | \(0.345607\pi\) | |||||||
\(444\) | 37.3906 | 1.77448 | ||||||||
\(445\) | −49.7344 | −2.35764 | ||||||||
\(446\) | 14.2422 | 0.674386 | ||||||||
\(447\) | 12.0840 | 0.571554 | ||||||||
\(448\) | 75.0323 | 3.54494 | ||||||||
\(449\) | −21.9477 | −1.03577 | −0.517887 | − | 0.855449i | \(-0.673281\pi\) | ||||
−0.517887 | + | 0.855449i | \(0.673281\pi\) | |||||||
\(450\) | 17.4819 | 0.824106 | ||||||||
\(451\) | 5.03020 | 0.236863 | ||||||||
\(452\) | 47.0787 | 2.21440 | ||||||||
\(453\) | 2.12941 | 0.100049 | ||||||||
\(454\) | −3.29428 | −0.154608 | ||||||||
\(455\) | −12.0685 | −0.565778 | ||||||||
\(456\) | 27.8254 | 1.30304 | ||||||||
\(457\) | 8.34457 | 0.390342 | 0.195171 | − | 0.980769i | \(-0.437474\pi\) | ||||
0.195171 | + | 0.980769i | \(0.437474\pi\) | |||||||
\(458\) | 12.5707 | 0.587392 | ||||||||
\(459\) | 5.69126 | 0.265645 | ||||||||
\(460\) | −83.6209 | −3.89884 | ||||||||
\(461\) | 4.64128 | 0.216166 | 0.108083 | − | 0.994142i | \(-0.465529\pi\) | ||||
0.108083 | + | 0.994142i | \(0.465529\pi\) | |||||||
\(462\) | −38.0217 | −1.76893 | ||||||||
\(463\) | −31.7309 | −1.47466 | −0.737329 | − | 0.675534i | \(-0.763913\pi\) | ||||
−0.737329 | + | 0.675534i | \(0.763913\pi\) | |||||||
\(464\) | 78.5205 | 3.64522 | ||||||||
\(465\) | 22.8471 | 1.05951 | ||||||||
\(466\) | 47.4666 | 2.19885 | ||||||||
\(467\) | −39.6191 | −1.83335 | −0.916677 | − | 0.399628i | \(-0.869139\pi\) | ||||
−0.916677 | + | 0.399628i | \(0.869139\pi\) | |||||||
\(468\) | 5.23983 | 0.242211 | ||||||||
\(469\) | −29.2073 | −1.34867 | ||||||||
\(470\) | 25.5098 | 1.17668 | ||||||||
\(471\) | −11.1255 | −0.512636 | ||||||||
\(472\) | 95.5798 | 4.39942 | ||||||||
\(473\) | −14.7638 | −0.678841 | ||||||||
\(474\) | −26.7974 | −1.23085 | ||||||||
\(475\) | −20.7386 | −0.951554 | ||||||||
\(476\) | −106.140 | −4.86494 | ||||||||
\(477\) | 14.3686 | 0.657893 | ||||||||
\(478\) | −25.1805 | −1.15173 | ||||||||
\(479\) | 3.23975 | 0.148028 | 0.0740141 | − | 0.997257i | \(-0.476419\pi\) | ||||
0.0740141 | + | 0.997257i | \(0.476419\pi\) | |||||||
\(480\) | 59.2703 | 2.70531 | ||||||||
\(481\) | −7.13584 | −0.325366 | ||||||||
\(482\) | −17.3741 | −0.791370 | ||||||||
\(483\) | −16.7517 | −0.762227 | ||||||||
\(484\) | 24.9542 | 1.13428 | ||||||||
\(485\) | −20.9742 | −0.952388 | ||||||||
\(486\) | −2.69069 | −0.122052 | ||||||||
\(487\) | 26.9052 | 1.21919 | 0.609596 | − | 0.792712i | \(-0.291332\pi\) | ||||
0.609596 | + | 0.792712i | \(0.291332\pi\) | |||||||
\(488\) | −81.5684 | −3.69243 | ||||||||
\(489\) | −0.480373 | −0.0217232 | ||||||||
\(490\) | −51.7127 | −2.33614 | ||||||||
\(491\) | −24.2946 | −1.09640 | −0.548201 | − | 0.836347i | \(-0.684687\pi\) | ||||
−0.548201 | + | 0.836347i | \(0.684687\pi\) | |||||||
\(492\) | −6.63882 | −0.299301 | ||||||||
\(493\) | −34.4387 | −1.55104 | ||||||||
\(494\) | −8.58854 | −0.386416 | ||||||||
\(495\) | −13.4619 | −0.605069 | ||||||||
\(496\) | 87.4338 | 3.92589 | ||||||||
\(497\) | −20.5508 | −0.921831 | ||||||||
\(498\) | −40.7375 | −1.82549 | ||||||||
\(499\) | −32.8172 | −1.46910 | −0.734551 | − | 0.678554i | \(-0.762607\pi\) | ||||
−0.734551 | + | 0.678554i | \(0.762607\pi\) | |||||||
\(500\) | −26.6004 | −1.18961 | ||||||||
\(501\) | −1.79007 | −0.0799743 | ||||||||
\(502\) | −81.0320 | −3.61663 | ||||||||
\(503\) | 4.80346 | 0.214176 | 0.107088 | − | 0.994250i | \(-0.465847\pi\) | ||||
0.107088 | + | 0.994250i | \(0.465847\pi\) | |||||||
\(504\) | 31.0271 | 1.38206 | ||||||||
\(505\) | 29.7725 | 1.32486 | ||||||||
\(506\) | 50.2780 | 2.23513 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −0.296551 | −0.0131573 | ||||||||
\(509\) | 12.3488 | 0.547350 | 0.273675 | − | 0.961822i | \(-0.411761\pi\) | ||||
0.273675 | + | 0.961822i | \(0.411761\pi\) | |||||||
\(510\) | −51.9240 | −2.29923 | ||||||||
\(511\) | −14.4879 | −0.640909 | ||||||||
\(512\) | 0.587183 | 0.0259501 | ||||||||
\(513\) | 3.19194 | 0.140928 | ||||||||
\(514\) | 81.4536 | 3.59277 | ||||||||
\(515\) | 3.39075 | 0.149414 | ||||||||
\(516\) | 19.4852 | 0.857786 | ||||||||
\(517\) | −11.1009 | −0.488218 | ||||||||
\(518\) | −68.3384 | −3.00262 | ||||||||
\(519\) | 3.45807 | 0.151792 | ||||||||
\(520\) | −29.5584 | −1.29622 | ||||||||
\(521\) | 38.7317 | 1.69687 | 0.848434 | − | 0.529302i | \(-0.177546\pi\) | ||||
0.848434 | + | 0.529302i | \(0.177546\pi\) | |||||||
\(522\) | 16.2818 | 0.712635 | ||||||||
\(523\) | −12.4507 | −0.544431 | −0.272216 | − | 0.962236i | \(-0.587756\pi\) | ||||
−0.272216 | + | 0.962236i | \(0.587756\pi\) | |||||||
\(524\) | 73.4802 | 3.21000 | ||||||||
\(525\) | −23.1250 | −1.00926 | ||||||||
\(526\) | −55.1035 | −2.40263 | ||||||||
\(527\) | −38.3480 | −1.67046 | ||||||||
\(528\) | −51.5177 | −2.24202 | ||||||||
\(529\) | −0.848443 | −0.0368888 | ||||||||
\(530\) | −131.091 | −5.69425 | ||||||||
\(531\) | 10.9643 | 0.475810 | ||||||||
\(532\) | −59.5289 | −2.58090 | ||||||||
\(533\) | 1.26699 | 0.0548796 | ||||||||
\(534\) | −39.4662 | −1.70787 | ||||||||
\(535\) | 12.9450 | 0.559661 | ||||||||
\(536\) | −71.5354 | −3.08986 | ||||||||
\(537\) | 22.9901 | 0.992097 | ||||||||
\(538\) | −4.28892 | −0.184909 | ||||||||
\(539\) | 22.5034 | 0.969292 | ||||||||
\(540\) | 17.7669 | 0.764567 | ||||||||
\(541\) | 28.1218 | 1.20905 | 0.604526 | − | 0.796585i | \(-0.293363\pi\) | ||||
0.604526 | + | 0.796585i | \(0.293363\pi\) | |||||||
\(542\) | 10.3995 | 0.446696 | ||||||||
\(543\) | 2.48918 | 0.106821 | ||||||||
\(544\) | −99.4832 | −4.26531 | ||||||||
\(545\) | 25.3819 | 1.08724 | ||||||||
\(546\) | −9.57679 | −0.409849 | ||||||||
\(547\) | 39.7301 | 1.69874 | 0.849369 | − | 0.527799i | \(-0.176983\pi\) | ||||
0.849369 | + | 0.527799i | \(0.176983\pi\) | |||||||
\(548\) | −2.41513 | −0.103169 | ||||||||
\(549\) | −9.35699 | −0.399347 | ||||||||
\(550\) | 69.4066 | 2.95951 | ||||||||
\(551\) | −19.3149 | −0.822844 | ||||||||
\(552\) | −41.0287 | −1.74630 | ||||||||
\(553\) | 35.4474 | 1.50738 | ||||||||
\(554\) | 5.05902 | 0.214937 | ||||||||
\(555\) | −24.1959 | −1.02706 | ||||||||
\(556\) | −5.69695 | −0.241604 | ||||||||
\(557\) | −34.1735 | −1.44798 | −0.723989 | − | 0.689811i | \(-0.757693\pi\) | ||||
−0.723989 | + | 0.689811i | \(0.757693\pi\) | |||||||
\(558\) | 18.1300 | 0.767505 | ||||||||
\(559\) | −3.71867 | −0.157283 | ||||||||
\(560\) | −156.602 | −6.61763 | ||||||||
\(561\) | 22.5954 | 0.953978 | ||||||||
\(562\) | 54.1391 | 2.28372 | ||||||||
\(563\) | −40.7054 | −1.71553 | −0.857764 | − | 0.514044i | \(-0.828147\pi\) | ||||
−0.857764 | + | 0.514044i | \(0.828147\pi\) | |||||||
\(564\) | 14.6509 | 0.616915 | ||||||||
\(565\) | −30.4652 | −1.28168 | ||||||||
\(566\) | −84.7166 | −3.56090 | ||||||||
\(567\) | 3.55923 | 0.149474 | ||||||||
\(568\) | −50.3338 | −2.11196 | ||||||||
\(569\) | −2.06896 | −0.0867353 | −0.0433677 | − | 0.999059i | \(-0.513809\pi\) | ||||
−0.0433677 | + | 0.999059i | \(0.513809\pi\) | |||||||
\(570\) | −29.1216 | −1.21977 | ||||||||
\(571\) | 22.3349 | 0.934685 | 0.467343 | − | 0.884076i | \(-0.345211\pi\) | ||||
0.467343 | + | 0.884076i | \(0.345211\pi\) | |||||||
\(572\) | 20.8031 | 0.869822 | ||||||||
\(573\) | 5.22992 | 0.218483 | ||||||||
\(574\) | 12.1337 | 0.506452 | ||||||||
\(575\) | 30.5793 | 1.27524 | ||||||||
\(576\) | 21.0811 | 0.878377 | ||||||||
\(577\) | 16.6712 | 0.694029 | 0.347015 | − | 0.937860i | \(-0.387195\pi\) | ||||
0.347015 | + | 0.937860i | \(0.387195\pi\) | |||||||
\(578\) | 41.4109 | 1.72247 | ||||||||
\(579\) | 18.7320 | 0.778473 | ||||||||
\(580\) | −107.511 | −4.46413 | ||||||||
\(581\) | 53.8873 | 2.23562 | ||||||||
\(582\) | −16.6438 | −0.689909 | ||||||||
\(583\) | 57.0461 | 2.36261 | ||||||||
\(584\) | −35.4843 | −1.46835 | ||||||||
\(585\) | −3.39075 | −0.140190 | ||||||||
\(586\) | 66.7436 | 2.75715 | ||||||||
\(587\) | −36.3447 | −1.50011 | −0.750054 | − | 0.661377i | \(-0.769972\pi\) | ||||
−0.750054 | + | 0.661377i | \(0.769972\pi\) | |||||||
\(588\) | −29.6999 | −1.22480 | ||||||||
\(589\) | −21.5075 | −0.886200 | ||||||||
\(590\) | −100.032 | −4.11827 | ||||||||
\(591\) | −3.47184 | −0.142812 | ||||||||
\(592\) | −92.5955 | −3.80565 | ||||||||
\(593\) | −14.5823 | −0.598822 | −0.299411 | − | 0.954124i | \(-0.596790\pi\) | ||||
−0.299411 | + | 0.954124i | \(0.596790\pi\) | |||||||
\(594\) | −10.6826 | −0.438311 | ||||||||
\(595\) | 68.6847 | 2.81580 | ||||||||
\(596\) | −63.3181 | −2.59361 | ||||||||
\(597\) | 27.6483 | 1.13157 | ||||||||
\(598\) | 12.6639 | 0.517864 | ||||||||
\(599\) | 45.3540 | 1.85311 | 0.926557 | − | 0.376155i | \(-0.122754\pi\) | ||||
0.926557 | + | 0.376155i | \(0.122754\pi\) | |||||||
\(600\) | −56.6384 | −2.31225 | ||||||||
\(601\) | 20.1306 | 0.821143 | 0.410572 | − | 0.911828i | \(-0.365329\pi\) | ||||
0.410572 | + | 0.911828i | \(0.365329\pi\) | |||||||
\(602\) | −35.6129 | −1.45147 | ||||||||
\(603\) | −8.20608 | −0.334177 | ||||||||
\(604\) | −11.1578 | −0.454003 | ||||||||
\(605\) | −16.1482 | −0.656517 | ||||||||
\(606\) | 23.6256 | 0.959726 | ||||||||
\(607\) | 35.9338 | 1.45851 | 0.729253 | − | 0.684244i | \(-0.239868\pi\) | ||||
0.729253 | + | 0.684244i | \(0.239868\pi\) | |||||||
\(608\) | −55.7951 | −2.26279 | ||||||||
\(609\) | −21.5374 | −0.872741 | ||||||||
\(610\) | 85.3682 | 3.45646 | ||||||||
\(611\) | −2.79607 | −0.113117 | ||||||||
\(612\) | −29.8212 | −1.20545 | ||||||||
\(613\) | −13.3918 | −0.540890 | −0.270445 | − | 0.962735i | \(-0.587171\pi\) | ||||
−0.270445 | + | 0.962735i | \(0.587171\pi\) | |||||||
\(614\) | 31.9125 | 1.28788 | ||||||||
\(615\) | 4.29606 | 0.173234 | ||||||||
\(616\) | 123.184 | 4.96321 | ||||||||
\(617\) | −17.0134 | −0.684934 | −0.342467 | − | 0.939530i | \(-0.611263\pi\) | ||||
−0.342467 | + | 0.939530i | \(0.611263\pi\) | |||||||
\(618\) | 2.69069 | 0.108236 | ||||||||
\(619\) | −47.2728 | −1.90006 | −0.950028 | − | 0.312165i | \(-0.898946\pi\) | ||||
−0.950028 | + | 0.312165i | \(0.898946\pi\) | |||||||
\(620\) | −119.715 | −4.80785 | ||||||||
\(621\) | −4.70654 | −0.188867 | ||||||||
\(622\) | −15.9133 | −0.638065 | ||||||||
\(623\) | 52.2055 | 2.09157 | ||||||||
\(624\) | −12.9761 | −0.519460 | ||||||||
\(625\) | −15.2725 | −0.610900 | ||||||||
\(626\) | −72.0999 | −2.88169 | ||||||||
\(627\) | 12.6726 | 0.506096 | ||||||||
\(628\) | 58.2957 | 2.32625 | ||||||||
\(629\) | 40.6119 | 1.61930 | ||||||||
\(630\) | −32.4725 | −1.29373 | ||||||||
\(631\) | −3.17379 | −0.126347 | −0.0631733 | − | 0.998003i | \(-0.520122\pi\) | ||||
−0.0631733 | + | 0.998003i | \(0.520122\pi\) | |||||||
\(632\) | 86.8189 | 3.45347 | ||||||||
\(633\) | 15.6447 | 0.621822 | ||||||||
\(634\) | 1.82132 | 0.0723340 | ||||||||
\(635\) | 0.191901 | 0.00761538 | ||||||||
\(636\) | −75.2890 | −2.98540 | ||||||||
\(637\) | 5.66810 | 0.224578 | ||||||||
\(638\) | 64.6419 | 2.55920 | ||||||||
\(639\) | −5.77396 | −0.228414 | ||||||||
\(640\) | −73.7917 | −2.91687 | ||||||||
\(641\) | −41.2087 | −1.62765 | −0.813824 | − | 0.581112i | \(-0.802618\pi\) | ||||
−0.813824 | + | 0.581112i | \(0.802618\pi\) | |||||||
\(642\) | 10.2724 | 0.405417 | ||||||||
\(643\) | 44.1860 | 1.74252 | 0.871262 | − | 0.490818i | \(-0.163302\pi\) | ||||
0.871262 | + | 0.490818i | \(0.163302\pi\) | |||||||
\(644\) | 87.7758 | 3.45885 | ||||||||
\(645\) | −12.6091 | −0.496481 | ||||||||
\(646\) | 48.8796 | 1.92314 | ||||||||
\(647\) | 30.2881 | 1.19075 | 0.595374 | − | 0.803449i | \(-0.297004\pi\) | ||||
0.595374 | + | 0.803449i | \(0.297004\pi\) | |||||||
\(648\) | 8.71737 | 0.342451 | ||||||||
\(649\) | 43.5303 | 1.70872 | ||||||||
\(650\) | 17.4819 | 0.685698 | ||||||||
\(651\) | −23.9823 | −0.939939 | ||||||||
\(652\) | 2.51707 | 0.0985760 | ||||||||
\(653\) | −18.6600 | −0.730223 | −0.365112 | − | 0.930964i | \(-0.618969\pi\) | ||||
−0.365112 | + | 0.930964i | \(0.618969\pi\) | |||||||
\(654\) | 20.1415 | 0.787597 | ||||||||
\(655\) | −47.5499 | −1.85793 | ||||||||
\(656\) | 16.4407 | 0.641900 | ||||||||
\(657\) | −4.07053 | −0.158807 | ||||||||
\(658\) | −26.7774 | −1.04389 | ||||||||
\(659\) | 27.0943 | 1.05545 | 0.527723 | − | 0.849417i | \(-0.323046\pi\) | ||||
0.527723 | + | 0.849417i | \(0.323046\pi\) | |||||||
\(660\) | 70.5381 | 2.74569 | ||||||||
\(661\) | −43.8094 | −1.70399 | −0.851994 | − | 0.523552i | \(-0.824607\pi\) | ||||
−0.851994 | + | 0.523552i | \(0.824607\pi\) | |||||||
\(662\) | −97.1380 | −3.77538 | ||||||||
\(663\) | 5.69126 | 0.221030 | ||||||||
\(664\) | 131.982 | 5.12191 | ||||||||
\(665\) | 38.5218 | 1.49381 | ||||||||
\(666\) | −19.2004 | −0.743999 | ||||||||
\(667\) | 28.4800 | 1.10275 | ||||||||
\(668\) | 9.37964 | 0.362909 | ||||||||
\(669\) | −5.29312 | −0.204644 | ||||||||
\(670\) | 74.8679 | 2.89240 | ||||||||
\(671\) | −37.1490 | −1.43412 | ||||||||
\(672\) | −62.2153 | −2.40001 | ||||||||
\(673\) | 18.1591 | 0.699981 | 0.349991 | − | 0.936753i | \(-0.386185\pi\) | ||||
0.349991 | + | 0.936753i | \(0.386185\pi\) | |||||||
\(674\) | 48.0987 | 1.85269 | ||||||||
\(675\) | −6.49719 | −0.250077 | ||||||||
\(676\) | 5.23983 | 0.201532 | ||||||||
\(677\) | −26.3658 | −1.01332 | −0.506659 | − | 0.862146i | \(-0.669120\pi\) | ||||
−0.506659 | + | 0.862146i | \(0.669120\pi\) | |||||||
\(678\) | −24.1753 | −0.928447 | ||||||||
\(679\) | 22.0163 | 0.844909 | ||||||||
\(680\) | 168.225 | 6.45112 | ||||||||
\(681\) | 1.22433 | 0.0469163 | ||||||||
\(682\) | 71.9797 | 2.75624 | ||||||||
\(683\) | 51.7241 | 1.97917 | 0.989584 | − | 0.143959i | \(-0.0459834\pi\) | ||||
0.989584 | + | 0.143959i | \(0.0459834\pi\) | |||||||
\(684\) | −16.7252 | −0.639505 | ||||||||
\(685\) | 1.56286 | 0.0597138 | ||||||||
\(686\) | −12.7553 | −0.487000 | ||||||||
\(687\) | −4.67193 | −0.178245 | ||||||||
\(688\) | −48.2538 | −1.83966 | ||||||||
\(689\) | 14.3686 | 0.547400 | ||||||||
\(690\) | 42.9400 | 1.63470 | ||||||||
\(691\) | 2.96484 | 0.112788 | 0.0563938 | − | 0.998409i | \(-0.482040\pi\) | ||||
0.0563938 | + | 0.998409i | \(0.482040\pi\) | |||||||
\(692\) | −18.1197 | −0.688806 | ||||||||
\(693\) | 14.1308 | 0.536785 | ||||||||
\(694\) | −35.7759 | −1.35803 | ||||||||
\(695\) | 3.68656 | 0.139839 | ||||||||
\(696\) | −52.7502 | −1.99949 | ||||||||
\(697\) | −7.21078 | −0.273128 | ||||||||
\(698\) | −39.7559 | −1.50478 | ||||||||
\(699\) | −17.6410 | −0.667245 | ||||||||
\(700\) | 121.171 | 4.57982 | ||||||||
\(701\) | −14.6820 | −0.554533 | −0.277266 | − | 0.960793i | \(-0.589428\pi\) | ||||
−0.277266 | + | 0.960793i | \(0.589428\pi\) | |||||||
\(702\) | −2.69069 | −0.101554 | ||||||||
\(703\) | 22.7772 | 0.859058 | ||||||||
\(704\) | 83.6958 | 3.15441 | ||||||||
\(705\) | −9.48077 | −0.357066 | ||||||||
\(706\) | −67.0011 | −2.52162 | ||||||||
\(707\) | −31.2518 | −1.17535 | ||||||||
\(708\) | −57.4510 | −2.15914 | ||||||||
\(709\) | 7.49469 | 0.281469 | 0.140735 | − | 0.990047i | \(-0.455054\pi\) | ||||
0.140735 | + | 0.990047i | \(0.455054\pi\) | |||||||
\(710\) | 52.6785 | 1.97699 | ||||||||
\(711\) | 9.95930 | 0.373503 | ||||||||
\(712\) | 127.863 | 4.79189 | ||||||||
\(713\) | 31.7129 | 1.18766 | ||||||||
\(714\) | 54.5040 | 2.03976 | ||||||||
\(715\) | −13.4619 | −0.503447 | ||||||||
\(716\) | −120.464 | −4.50196 | ||||||||
\(717\) | 9.35839 | 0.349495 | ||||||||
\(718\) | −42.1594 | −1.57338 | ||||||||
\(719\) | 15.1168 | 0.563760 | 0.281880 | − | 0.959450i | \(-0.409042\pi\) | ||||
0.281880 | + | 0.959450i | \(0.409042\pi\) | |||||||
\(720\) | −43.9988 | −1.63974 | ||||||||
\(721\) | −3.55923 | −0.132553 | ||||||||
\(722\) | −23.7090 | −0.882359 | ||||||||
\(723\) | 6.45712 | 0.240143 | ||||||||
\(724\) | −13.0429 | −0.484734 | ||||||||
\(725\) | 39.3155 | 1.46014 | ||||||||
\(726\) | −12.8142 | −0.475580 | ||||||||
\(727\) | −5.12143 | −0.189943 | −0.0949717 | − | 0.995480i | \(-0.530276\pi\) | ||||
−0.0949717 | + | 0.995480i | \(0.530276\pi\) | |||||||
\(728\) | 31.0271 | 1.14994 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 37.1374 | 1.37452 | ||||||||
\(731\) | 21.1639 | 0.782775 | ||||||||
\(732\) | 49.0290 | 1.81216 | ||||||||
\(733\) | −30.0695 | −1.11064 | −0.555321 | − | 0.831636i | \(-0.687405\pi\) | ||||
−0.555321 | + | 0.831636i | \(0.687405\pi\) | |||||||
\(734\) | 66.7733 | 2.46465 | ||||||||
\(735\) | 19.2191 | 0.708908 | ||||||||
\(736\) | 82.2704 | 3.03253 | ||||||||
\(737\) | −32.5797 | −1.20009 | ||||||||
\(738\) | 3.40909 | 0.125490 | ||||||||
\(739\) | 35.8412 | 1.31844 | 0.659220 | − | 0.751950i | \(-0.270886\pi\) | ||||
0.659220 | + | 0.751950i | \(0.270886\pi\) | |||||||
\(740\) | 126.782 | 4.66060 | ||||||||
\(741\) | 3.19194 | 0.117259 | ||||||||
\(742\) | 137.605 | 5.05164 | ||||||||
\(743\) | 0.491872 | 0.0180450 | 0.00902252 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902252 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(744\) | −58.7381 | −2.15344 | ||||||||
\(745\) | 40.9738 | 1.50116 | ||||||||
\(746\) | 17.2429 | 0.631307 | ||||||||
\(747\) | 15.1402 | 0.553950 | ||||||||
\(748\) | −118.396 | −4.32898 | ||||||||
\(749\) | −13.5882 | −0.496502 | ||||||||
\(750\) | 13.6595 | 0.498775 | ||||||||
\(751\) | −2.47358 | −0.0902624 | −0.0451312 | − | 0.998981i | \(-0.514371\pi\) | ||||
−0.0451312 | + | 0.998981i | \(0.514371\pi\) | |||||||
\(752\) | −36.2821 | −1.32307 | ||||||||
\(753\) | 30.1157 | 1.09748 | ||||||||
\(754\) | 16.2818 | 0.592948 | ||||||||
\(755\) | 7.22031 | 0.262774 | ||||||||
\(756\) | −18.6497 | −0.678284 | ||||||||
\(757\) | 3.37719 | 0.122746 | 0.0613731 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613731 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(758\) | 61.6902 | 2.24069 | ||||||||
\(759\) | −18.6859 | −0.678254 | ||||||||
\(760\) | 94.3488 | 3.42239 | ||||||||
\(761\) | 37.6906 | 1.36628 | 0.683142 | − | 0.730286i | \(-0.260613\pi\) | ||||
0.683142 | + | 0.730286i | \(0.260613\pi\) | |||||||
\(762\) | 0.152281 | 0.00551657 | ||||||||
\(763\) | −26.6431 | −0.964544 | ||||||||
\(764\) | −27.4038 | −0.991436 | ||||||||
\(765\) | 19.2976 | 0.697707 | ||||||||
\(766\) | −67.7172 | −2.44672 | ||||||||
\(767\) | 10.9643 | 0.395898 | ||||||||
\(768\) | −16.3945 | −0.591584 | ||||||||
\(769\) | 5.57218 | 0.200938 | 0.100469 | − | 0.994940i | \(-0.467966\pi\) | ||||
0.100469 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(770\) | −128.922 | −4.64603 | ||||||||
\(771\) | −30.2724 | −1.09023 | ||||||||
\(772\) | −98.1522 | −3.53257 | ||||||||
\(773\) | 7.56955 | 0.272258 | 0.136129 | − | 0.990691i | \(-0.456534\pi\) | ||||
0.136129 | + | 0.990691i | \(0.456534\pi\) | |||||||
\(774\) | −10.0058 | −0.359650 | ||||||||
\(775\) | 43.7784 | 1.57257 | ||||||||
\(776\) | 53.9231 | 1.93573 | ||||||||
\(777\) | 25.3981 | 0.911151 | ||||||||
\(778\) | −96.1904 | −3.44859 | ||||||||
\(779\) | −4.04417 | −0.144897 | ||||||||
\(780\) | 17.7669 | 0.636158 | ||||||||
\(781\) | −22.9237 | −0.820276 | ||||||||
\(782\) | −72.0733 | −2.57734 | ||||||||
\(783\) | −6.05116 | −0.216251 | ||||||||
\(784\) | 73.5500 | 2.62678 | ||||||||
\(785\) | −37.7238 | −1.34642 | ||||||||
\(786\) | −37.7327 | −1.34588 | ||||||||
\(787\) | −27.3002 | −0.973147 | −0.486574 | − | 0.873640i | \(-0.661753\pi\) | ||||
−0.486574 | + | 0.873640i | \(0.661753\pi\) | |||||||
\(788\) | 18.1918 | 0.648057 | ||||||||
\(789\) | 20.4793 | 0.729083 | ||||||||
\(790\) | −90.8633 | −3.23277 | ||||||||
\(791\) | 31.9789 | 1.13704 | ||||||||
\(792\) | 34.6096 | 1.22980 | ||||||||
\(793\) | −9.35699 | −0.332277 | ||||||||
\(794\) | −67.7424 | −2.40409 | ||||||||
\(795\) | 48.7203 | 1.72793 | ||||||||
\(796\) | −144.872 | −5.13486 | ||||||||
\(797\) | 50.4628 | 1.78748 | 0.893741 | − | 0.448583i | \(-0.148071\pi\) | ||||
0.893741 | + | 0.448583i | \(0.148071\pi\) | |||||||
\(798\) | 30.5686 | 1.08211 | ||||||||
\(799\) | 15.9131 | 0.562967 | ||||||||
\(800\) | 113.571 | 4.01533 | ||||||||
\(801\) | 14.6677 | 0.518256 | ||||||||
\(802\) | 4.03754 | 0.142570 | ||||||||
\(803\) | −16.1608 | −0.570302 | ||||||||
\(804\) | 42.9984 | 1.51644 | ||||||||
\(805\) | −56.8007 | −2.00196 | ||||||||
\(806\) | 18.1300 | 0.638603 | ||||||||
\(807\) | 1.59398 | 0.0561109 | ||||||||
\(808\) | −76.5430 | −2.69277 | ||||||||
\(809\) | −18.4900 | −0.650075 | −0.325037 | − | 0.945701i | \(-0.605377\pi\) | ||||
−0.325037 | + | 0.945701i | \(0.605377\pi\) | |||||||
\(810\) | −9.12347 | −0.320566 | ||||||||
\(811\) | −2.17608 | −0.0764124 | −0.0382062 | − | 0.999270i | \(-0.512164\pi\) | ||||
−0.0382062 | + | 0.999270i | \(0.512164\pi\) | |||||||
\(812\) | 112.852 | 3.96035 | ||||||||
\(813\) | −3.86498 | −0.135551 | ||||||||
\(814\) | −76.2291 | −2.67183 | ||||||||
\(815\) | −1.62882 | −0.0570552 | ||||||||
\(816\) | 73.8504 | 2.58528 | ||||||||
\(817\) | 11.8698 | 0.415271 | ||||||||
\(818\) | 32.0410 | 1.12029 | ||||||||
\(819\) | 3.55923 | 0.124369 | ||||||||
\(820\) | −22.5106 | −0.786104 | ||||||||
\(821\) | −6.56440 | −0.229099 | −0.114550 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114550 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(822\) | 1.24019 | 0.0432566 | ||||||||
\(823\) | 40.2319 | 1.40239 | 0.701197 | − | 0.712967i | \(-0.252649\pi\) | ||||
0.701197 | + | 0.712967i | \(0.252649\pi\) | |||||||
\(824\) | −8.71737 | −0.303684 | ||||||||
\(825\) | −25.7951 | −0.898069 | ||||||||
\(826\) | 105.003 | 3.65351 | ||||||||
\(827\) | 38.9788 | 1.35542 | 0.677712 | − | 0.735327i | \(-0.262971\pi\) | ||||
0.677712 | + | 0.735327i | \(0.262971\pi\) | |||||||
\(828\) | 24.6615 | 0.857045 | ||||||||
\(829\) | −35.8071 | −1.24363 | −0.621816 | − | 0.783164i | \(-0.713605\pi\) | ||||
−0.621816 | + | 0.783164i | \(0.713605\pi\) | |||||||
\(830\) | −138.131 | −4.79459 | ||||||||
\(831\) | −1.88019 | −0.0652232 | ||||||||
\(832\) | 21.0811 | 0.730854 | ||||||||
\(833\) | −32.2586 | −1.11770 | ||||||||
\(834\) | 2.92543 | 0.101299 | ||||||||
\(835\) | −6.06967 | −0.210050 | ||||||||
\(836\) | −66.4023 | −2.29657 | ||||||||
\(837\) | −6.73805 | −0.232901 | ||||||||
\(838\) | 70.9634 | 2.45139 | ||||||||
\(839\) | 3.01513 | 0.104094 | 0.0520470 | − | 0.998645i | \(-0.483425\pi\) | ||||
0.0520470 | + | 0.998645i | \(0.483425\pi\) | |||||||
\(840\) | 105.205 | 3.62992 | ||||||||
\(841\) | 7.61651 | 0.262638 | ||||||||
\(842\) | −77.6076 | −2.67453 | ||||||||
\(843\) | −20.1209 | −0.693001 | ||||||||
\(844\) | −81.9756 | −2.82172 | ||||||||
\(845\) | −3.39075 | −0.116645 | ||||||||
\(846\) | −7.52336 | −0.258658 | ||||||||
\(847\) | 16.9505 | 0.582427 | ||||||||
\(848\) | 186.449 | 6.40267 | ||||||||
\(849\) | 31.4850 | 1.08056 | ||||||||
\(850\) | −99.4942 | −3.41262 | ||||||||
\(851\) | −33.5852 | −1.15128 | ||||||||
\(852\) | 30.2546 | 1.03650 | ||||||||
\(853\) | 40.4998 | 1.38669 | 0.693343 | − | 0.720608i | \(-0.256137\pi\) | ||||
0.693343 | + | 0.720608i | \(0.256137\pi\) | |||||||
\(854\) | −89.6099 | −3.06639 | ||||||||
\(855\) | 10.8231 | 0.370141 | ||||||||
\(856\) | −33.2806 | −1.13751 | ||||||||
\(857\) | 39.2621 | 1.34117 | 0.670583 | − | 0.741834i | \(-0.266044\pi\) | ||||
0.670583 | + | 0.741834i | \(0.266044\pi\) | |||||||
\(858\) | −10.6826 | −0.364697 | ||||||||
\(859\) | 10.4351 | 0.356041 | 0.178020 | − | 0.984027i | \(-0.443031\pi\) | ||||
0.178020 | + | 0.984027i | \(0.443031\pi\) | |||||||
\(860\) | 66.0693 | 2.25294 | ||||||||
\(861\) | −4.50952 | −0.153684 | ||||||||
\(862\) | −86.1109 | −2.93295 | ||||||||
\(863\) | −18.3631 | −0.625087 | −0.312543 | − | 0.949904i | \(-0.601181\pi\) | ||||
−0.312543 | + | 0.949904i | \(0.601181\pi\) | |||||||
\(864\) | −17.4800 | −0.594682 | ||||||||
\(865\) | 11.7254 | 0.398677 | ||||||||
\(866\) | 106.156 | 3.60734 | ||||||||
\(867\) | −15.3904 | −0.522686 | ||||||||
\(868\) | 125.663 | 4.26528 | ||||||||
\(869\) | 39.5403 | 1.34131 | ||||||||
\(870\) | 55.2075 | 1.87171 | ||||||||
\(871\) | −8.20608 | −0.278052 | ||||||||
\(872\) | −65.2551 | −2.20982 | ||||||||
\(873\) | 6.18570 | 0.209354 | ||||||||
\(874\) | −40.4223 | −1.36731 | ||||||||
\(875\) | −18.0687 | −0.610834 | ||||||||
\(876\) | 21.3289 | 0.720636 | ||||||||
\(877\) | −8.53828 | −0.288317 | −0.144159 | − | 0.989555i | \(-0.546048\pi\) | ||||
−0.144159 | + | 0.989555i | \(0.546048\pi\) | |||||||
\(878\) | 7.98048 | 0.269328 | ||||||||
\(879\) | −24.8054 | −0.836665 | ||||||||
\(880\) | −174.684 | −5.88858 | ||||||||
\(881\) | 6.88497 | 0.231961 | 0.115980 | − | 0.993252i | \(-0.462999\pi\) | ||||
0.115980 | + | 0.993252i | \(0.462999\pi\) | |||||||
\(882\) | 15.2511 | 0.513532 | ||||||||
\(883\) | 12.1994 | 0.410542 | 0.205271 | − | 0.978705i | \(-0.434192\pi\) | ||||
0.205271 | + | 0.978705i | \(0.434192\pi\) | |||||||
\(884\) | −29.8212 | −1.00300 | ||||||||
\(885\) | 37.1772 | 1.24970 | ||||||||
\(886\) | 52.8090 | 1.77415 | ||||||||
\(887\) | −8.27124 | −0.277721 | −0.138861 | − | 0.990312i | \(-0.544344\pi\) | ||||
−0.138861 | + | 0.990312i | \(0.544344\pi\) | |||||||
\(888\) | 62.2058 | 2.08749 | ||||||||
\(889\) | −0.201437 | −0.00675596 | ||||||||
\(890\) | −133.820 | −4.48565 | ||||||||
\(891\) | 3.97019 | 0.133006 | ||||||||
\(892\) | 27.7350 | 0.928638 | ||||||||
\(893\) | 8.92489 | 0.298660 | ||||||||
\(894\) | 32.5143 | 1.08744 | ||||||||
\(895\) | 77.9537 | 2.60571 | ||||||||
\(896\) | 77.4582 | 2.58770 | ||||||||
\(897\) | −4.70654 | −0.157147 | ||||||||
\(898\) | −59.0544 | −1.97067 | ||||||||
\(899\) | 40.7730 | 1.35986 | ||||||||
\(900\) | 34.0441 | 1.13480 | ||||||||
\(901\) | −81.7754 | −2.72433 | ||||||||
\(902\) | 13.5347 | 0.450657 | ||||||||
\(903\) | 13.2356 | 0.440452 | ||||||||
\(904\) | 78.3238 | 2.60501 | ||||||||
\(905\) | 8.44018 | 0.280561 | ||||||||
\(906\) | 5.72960 | 0.190353 | ||||||||
\(907\) | 54.4054 | 1.80650 | 0.903251 | − | 0.429114i | \(-0.141174\pi\) | ||||
0.903251 | + | 0.429114i | \(0.141174\pi\) | |||||||
\(908\) | −6.41525 | −0.212898 | ||||||||
\(909\) | −8.78051 | −0.291231 | ||||||||
\(910\) | −32.4725 | −1.07645 | ||||||||
\(911\) | 1.33568 | 0.0442529 | 0.0221264 | − | 0.999755i | \(-0.492956\pi\) | ||||
0.0221264 | + | 0.999755i | \(0.492956\pi\) | |||||||
\(912\) | 41.4190 | 1.37152 | ||||||||
\(913\) | 60.1094 | 1.98933 | ||||||||
\(914\) | 22.4527 | 0.742668 | ||||||||
\(915\) | −31.7272 | −1.04887 | ||||||||
\(916\) | 24.4801 | 0.808846 | ||||||||
\(917\) | 49.9125 | 1.64826 | ||||||||
\(918\) | 15.3134 | 0.505418 | ||||||||
\(919\) | 46.1937 | 1.52379 | 0.761895 | − | 0.647701i | \(-0.224269\pi\) | ||||
0.761895 | + | 0.647701i | \(0.224269\pi\) | |||||||
\(920\) | −139.118 | −4.58659 | ||||||||
\(921\) | −11.8603 | −0.390811 | ||||||||
\(922\) | 12.4882 | 0.411278 | ||||||||
\(923\) | −5.77396 | −0.190052 | ||||||||
\(924\) | −74.0430 | −2.43584 | ||||||||
\(925\) | −46.3629 | −1.52440 | ||||||||
\(926\) | −85.3780 | −2.80570 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 105.774 | 3.47221 | ||||||||
\(929\) | 22.6032 | 0.741587 | 0.370793 | − | 0.928715i | \(-0.379086\pi\) | ||||
0.370793 | + | 0.928715i | \(0.379086\pi\) | |||||||
\(930\) | 61.4744 | 2.01582 | ||||||||
\(931\) | −18.0923 | −0.592950 | ||||||||
\(932\) | 92.4359 | 3.02784 | ||||||||
\(933\) | 5.91420 | 0.193622 | ||||||||
\(934\) | −106.603 | −3.48815 | ||||||||
\(935\) | 76.6153 | 2.50559 | ||||||||
\(936\) | 8.71737 | 0.284936 | ||||||||
\(937\) | −25.3624 | −0.828554 | −0.414277 | − | 0.910151i | \(-0.635965\pi\) | ||||
−0.414277 | + | 0.910151i | \(0.635965\pi\) | |||||||
\(938\) | −78.5878 | −2.56598 | ||||||||
\(939\) | 26.7960 | 0.874456 | ||||||||
\(940\) | 49.6776 | 1.62030 | ||||||||
\(941\) | −20.7246 | −0.675604 | −0.337802 | − | 0.941217i | \(-0.609683\pi\) | ||||
−0.337802 | + | 0.941217i | \(0.609683\pi\) | |||||||
\(942\) | −29.9353 | −0.975346 | ||||||||
\(943\) | 5.96316 | 0.194187 | ||||||||
\(944\) | 142.274 | 4.63062 | ||||||||
\(945\) | 12.0685 | 0.392587 | ||||||||
\(946\) | −39.7249 | −1.29157 | ||||||||
\(947\) | 8.01337 | 0.260399 | 0.130200 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130200 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(948\) | −52.1850 | −1.69489 | ||||||||
\(949\) | −4.07053 | −0.132135 | ||||||||
\(950\) | −55.8013 | −1.81043 | ||||||||
\(951\) | −0.676898 | −0.0219499 | ||||||||
\(952\) | −176.583 | −5.72310 | ||||||||
\(953\) | −50.2186 | −1.62674 | −0.813371 | − | 0.581746i | \(-0.802370\pi\) | ||||
−0.813371 | + | 0.581746i | \(0.802370\pi\) | |||||||
\(954\) | 38.6615 | 1.25171 | ||||||||
\(955\) | 17.7333 | 0.573837 | ||||||||
\(956\) | −49.0363 | −1.58595 | ||||||||
\(957\) | −24.0243 | −0.776594 | ||||||||
\(958\) | 8.71718 | 0.281639 | ||||||||
\(959\) | −1.64052 | −0.0529750 | ||||||||
\(960\) | 71.4806 | 2.30703 | ||||||||
\(961\) | 14.4014 | 0.464560 | ||||||||
\(962\) | −19.2004 | −0.619044 | ||||||||
\(963\) | −3.81774 | −0.123025 | ||||||||
\(964\) | −33.8342 | −1.08973 | ||||||||
\(965\) | 63.5154 | 2.04463 | ||||||||
\(966\) | −45.0736 | −1.45022 | ||||||||
\(967\) | 19.1682 | 0.616409 | 0.308205 | − | 0.951320i | \(-0.400272\pi\) | ||||
0.308205 | + | 0.951320i | \(0.400272\pi\) | |||||||
\(968\) | 41.5158 | 1.33437 | ||||||||
\(969\) | −18.1662 | −0.583581 | ||||||||
\(970\) | −56.4351 | −1.81202 | ||||||||
\(971\) | −8.71813 | −0.279778 | −0.139889 | − | 0.990167i | \(-0.544675\pi\) | ||||
−0.139889 | + | 0.990167i | \(0.544675\pi\) | |||||||
\(972\) | −5.23983 | −0.168067 | ||||||||
\(973\) | −3.86973 | −0.124058 | ||||||||
\(974\) | 72.3937 | 2.31964 | ||||||||
\(975\) | −6.49719 | −0.208076 | ||||||||
\(976\) | −121.417 | −3.88648 | ||||||||
\(977\) | −33.2068 | −1.06238 | −0.531190 | − | 0.847253i | \(-0.678255\pi\) | ||||
−0.531190 | + | 0.847253i | \(0.678255\pi\) | |||||||
\(978\) | −1.29253 | −0.0413307 | ||||||||
\(979\) | 58.2334 | 1.86115 | ||||||||
\(980\) | −100.705 | −3.21690 | ||||||||
\(981\) | −7.48563 | −0.238998 | ||||||||
\(982\) | −65.3694 | −2.08602 | ||||||||
\(983\) | 31.5305 | 1.00567 | 0.502834 | − | 0.864383i | \(-0.332291\pi\) | ||||
0.502834 | + | 0.864383i | \(0.332291\pi\) | |||||||
\(984\) | −11.0448 | −0.352097 | ||||||||
\(985\) | −11.7721 | −0.375092 | ||||||||
\(986\) | −92.6639 | −2.95102 | ||||||||
\(987\) | 9.95185 | 0.316771 | ||||||||
\(988\) | −16.7252 | −0.532100 | ||||||||
\(989\) | −17.5021 | −0.556533 | ||||||||
\(990\) | −36.2219 | −1.15121 | ||||||||
\(991\) | 14.2588 | 0.452945 | 0.226472 | − | 0.974018i | \(-0.427281\pi\) | ||||
0.226472 | + | 0.974018i | \(0.427281\pi\) | |||||||
\(992\) | 117.781 | 3.73956 | ||||||||
\(993\) | 36.1015 | 1.14565 | ||||||||
\(994\) | −55.2960 | −1.75388 | ||||||||
\(995\) | 93.7485 | 2.97203 | ||||||||
\(996\) | −79.3318 | −2.51373 | ||||||||
\(997\) | 25.8738 | 0.819432 | 0.409716 | − | 0.912213i | \(-0.365628\pi\) | ||||
0.409716 | + | 0.912213i | \(0.365628\pi\) | |||||||
\(998\) | −88.3011 | −2.79512 | ||||||||
\(999\) | 7.13584 | 0.225768 |
(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 | 4017.2.a.j.1.24 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.24 | ✓ | 25 | 1.1 | even | 1 | trivial |