Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59341 | −1.83381 | −0.916907 | − | 0.399100i | \(-0.869323\pi\) | ||||
−0.916907 | + | 0.399100i | \(0.869323\pi\) | |||||||
\(3\) | 1.69325 | 0.977600 | 0.488800 | − | 0.872396i | \(-0.337435\pi\) | ||||
0.488800 | + | 0.872396i | \(0.337435\pi\) | |||||||
\(4\) | 4.72575 | 2.36288 | ||||||||
\(5\) | −3.22826 | −1.44372 | −0.721861 | − | 0.692038i | \(-0.756713\pi\) | ||||
−0.721861 | + | 0.692038i | \(0.756713\pi\) | |||||||
\(6\) | −4.39129 | −1.79274 | ||||||||
\(7\) | −0.750732 | −0.283750 | −0.141875 | − | 0.989885i | \(-0.545313\pi\) | ||||
−0.141875 | + | 0.989885i | \(0.545313\pi\) | |||||||
\(8\) | −7.06898 | −2.49926 | ||||||||
\(9\) | −0.132895 | −0.0442983 | ||||||||
\(10\) | 8.37219 | 2.64752 | ||||||||
\(11\) | −1.90047 | −0.573012 | −0.286506 | − | 0.958078i | \(-0.592494\pi\) | ||||
−0.286506 | + | 0.958078i | \(0.592494\pi\) | |||||||
\(12\) | 8.00190 | 2.30995 | ||||||||
\(13\) | 3.93841 | 1.09232 | 0.546160 | − | 0.837681i | \(-0.316089\pi\) | ||||
0.546160 | + | 0.837681i | \(0.316089\pi\) | |||||||
\(14\) | 1.94695 | 0.520345 | ||||||||
\(15\) | −5.46626 | −1.41138 | ||||||||
\(16\) | 8.88124 | 2.22031 | ||||||||
\(17\) | −5.08204 | −1.23258 | −0.616288 | − | 0.787521i | \(-0.711364\pi\) | ||||
−0.616288 | + | 0.787521i | \(0.711364\pi\) | |||||||
\(18\) | 0.344651 | 0.0812349 | ||||||||
\(19\) | −5.14799 | −1.18103 | −0.590515 | − | 0.807027i | \(-0.701075\pi\) | ||||
−0.590515 | + | 0.807027i | \(0.701075\pi\) | |||||||
\(20\) | −15.2560 | −3.41134 | ||||||||
\(21\) | −1.27118 | −0.277394 | ||||||||
\(22\) | 4.92868 | 1.05080 | ||||||||
\(23\) | 0.476522 | 0.0993616 | 0.0496808 | − | 0.998765i | \(-0.484180\pi\) | ||||
0.0496808 | + | 0.998765i | \(0.484180\pi\) | |||||||
\(24\) | −11.9696 | −2.44328 | ||||||||
\(25\) | 5.42167 | 1.08433 | ||||||||
\(26\) | −10.2139 | −2.00311 | ||||||||
\(27\) | −5.30478 | −1.02091 | ||||||||
\(28\) | −3.54778 | −0.670467 | ||||||||
\(29\) | −8.68999 | −1.61369 | −0.806846 | − | 0.590762i | \(-0.798827\pi\) | ||||
−0.806846 | + | 0.590762i | \(0.798827\pi\) | |||||||
\(30\) | 14.1762 | 2.58821 | ||||||||
\(31\) | 2.91651 | 0.523821 | 0.261910 | − | 0.965092i | \(-0.415648\pi\) | ||||
0.261910 | + | 0.965092i | \(0.415648\pi\) | |||||||
\(32\) | −8.89469 | −1.57237 | ||||||||
\(33\) | −3.21797 | −0.560177 | ||||||||
\(34\) | 13.1798 | 2.26032 | ||||||||
\(35\) | 2.42356 | 0.409656 | ||||||||
\(36\) | −0.628029 | −0.104671 | ||||||||
\(37\) | −3.88758 | −0.639114 | −0.319557 | − | 0.947567i | \(-0.603534\pi\) | ||||
−0.319557 | + | 0.947567i | \(0.603534\pi\) | |||||||
\(38\) | 13.3508 | 2.16579 | ||||||||
\(39\) | 6.66873 | 1.06785 | ||||||||
\(40\) | 22.8205 | 3.60824 | ||||||||
\(41\) | 3.93068 | 0.613869 | 0.306935 | − | 0.951731i | \(-0.400697\pi\) | ||||
0.306935 | + | 0.951731i | \(0.400697\pi\) | |||||||
\(42\) | 3.29668 | 0.508689 | ||||||||
\(43\) | 11.6403 | 1.77513 | 0.887567 | − | 0.460679i | \(-0.152394\pi\) | ||||
0.887567 | + | 0.460679i | \(0.152394\pi\) | |||||||
\(44\) | −8.98114 | −1.35396 | ||||||||
\(45\) | 0.429020 | 0.0639545 | ||||||||
\(46\) | −1.23581 | −0.182211 | ||||||||
\(47\) | 6.60193 | 0.962990 | 0.481495 | − | 0.876449i | \(-0.340094\pi\) | ||||
0.481495 | + | 0.876449i | \(0.340094\pi\) | |||||||
\(48\) | 15.0382 | 2.17057 | ||||||||
\(49\) | −6.43640 | −0.919486 | ||||||||
\(50\) | −14.0606 | −1.98847 | ||||||||
\(51\) | −8.60518 | −1.20497 | ||||||||
\(52\) | 18.6120 | 2.58102 | ||||||||
\(53\) | −12.6826 | −1.74209 | −0.871043 | − | 0.491208i | \(-0.836556\pi\) | ||||
−0.871043 | + | 0.491208i | \(0.836556\pi\) | |||||||
\(54\) | 13.7575 | 1.87215 | ||||||||
\(55\) | 6.13520 | 0.827271 | ||||||||
\(56\) | 5.30691 | 0.709166 | ||||||||
\(57\) | −8.71685 | −1.15458 | ||||||||
\(58\) | 22.5367 | 2.95921 | ||||||||
\(59\) | 1.95762 | 0.254860 | 0.127430 | − | 0.991848i | \(-0.459327\pi\) | ||||
0.127430 | + | 0.991848i | \(0.459327\pi\) | |||||||
\(60\) | −25.8322 | −3.33492 | ||||||||
\(61\) | −7.61692 | −0.975247 | −0.487623 | − | 0.873054i | \(-0.662136\pi\) | ||||
−0.487623 | + | 0.873054i | \(0.662136\pi\) | |||||||
\(62\) | −7.56369 | −0.960590 | ||||||||
\(63\) | 0.0997685 | 0.0125697 | ||||||||
\(64\) | 5.30505 | 0.663132 | ||||||||
\(65\) | −12.7142 | −1.57701 | ||||||||
\(66\) | 8.34551 | 1.02726 | ||||||||
\(67\) | 6.12890 | 0.748764 | 0.374382 | − | 0.927275i | \(-0.377855\pi\) | ||||
0.374382 | + | 0.927275i | \(0.377855\pi\) | |||||||
\(68\) | −24.0165 | −2.91242 | ||||||||
\(69\) | 0.806872 | 0.0971359 | ||||||||
\(70\) | −6.28527 | −0.751234 | ||||||||
\(71\) | 13.0944 | 1.55401 | 0.777007 | − | 0.629492i | \(-0.216737\pi\) | ||||
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(72\) | 0.939432 | 0.110713 | ||||||||
\(73\) | 0.368318 | 0.0431084 | 0.0215542 | − | 0.999768i | \(-0.493139\pi\) | ||||
0.0215542 | + | 0.999768i | \(0.493139\pi\) | |||||||
\(74\) | 10.0821 | 1.17202 | ||||||||
\(75\) | 9.18025 | 1.06004 | ||||||||
\(76\) | −24.3281 | −2.79063 | ||||||||
\(77\) | 1.42674 | 0.162592 | ||||||||
\(78\) | −17.2947 | −1.95824 | ||||||||
\(79\) | −2.29585 | −0.258303 | −0.129151 | − | 0.991625i | \(-0.541225\pi\) | ||||
−0.129151 | + | 0.991625i | \(0.541225\pi\) | |||||||
\(80\) | −28.6710 | −3.20551 | ||||||||
\(81\) | −8.58365 | −0.953739 | ||||||||
\(82\) | −10.1938 | −1.12572 | ||||||||
\(83\) | 5.89811 | 0.647402 | 0.323701 | − | 0.946159i | \(-0.395073\pi\) | ||||
0.323701 | + | 0.946159i | \(0.395073\pi\) | |||||||
\(84\) | −6.00728 | −0.655448 | ||||||||
\(85\) | 16.4061 | 1.77950 | ||||||||
\(86\) | −30.1881 | −3.25527 | ||||||||
\(87\) | −14.7144 | −1.57754 | ||||||||
\(88\) | 13.4344 | 1.43211 | ||||||||
\(89\) | −9.35226 | −0.991338 | −0.495669 | − | 0.868512i | \(-0.665077\pi\) | ||||
−0.495669 | + | 0.868512i | \(0.665077\pi\) | |||||||
\(90\) | −1.11262 | −0.117281 | ||||||||
\(91\) | −2.95669 | −0.309946 | ||||||||
\(92\) | 2.25192 | 0.234779 | ||||||||
\(93\) | 4.93839 | 0.512087 | ||||||||
\(94\) | −17.1215 | −1.76595 | ||||||||
\(95\) | 16.6191 | 1.70508 | ||||||||
\(96\) | −15.0610 | −1.53715 | ||||||||
\(97\) | 0.838216 | 0.0851080 | 0.0425540 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425540 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(98\) | 16.6922 | 1.68617 | ||||||||
\(99\) | 0.252563 | 0.0253835 | ||||||||
\(100\) | 25.6215 | 2.56215 | ||||||||
\(101\) | −8.14134 | −0.810094 | −0.405047 | − | 0.914296i | \(-0.632745\pi\) | ||||
−0.405047 | + | 0.914296i | \(0.632745\pi\) | |||||||
\(102\) | 22.3167 | 2.20968 | ||||||||
\(103\) | −2.23795 | −0.220512 | −0.110256 | − | 0.993903i | \(-0.535167\pi\) | ||||
−0.110256 | + | 0.993903i | \(0.535167\pi\) | |||||||
\(104\) | −27.8406 | −2.72999 | ||||||||
\(105\) | 4.10370 | 0.400480 | ||||||||
\(106\) | 32.8911 | 3.19466 | ||||||||
\(107\) | −1.68194 | −0.162599 | −0.0812997 | − | 0.996690i | \(-0.525907\pi\) | ||||
−0.0812997 | + | 0.996690i | \(0.525907\pi\) | |||||||
\(108\) | −25.0691 | −2.41227 | ||||||||
\(109\) | 5.44772 | 0.521796 | 0.260898 | − | 0.965366i | \(-0.415981\pi\) | ||||
0.260898 | + | 0.965366i | \(0.415981\pi\) | |||||||
\(110\) | −15.9111 | −1.51706 | ||||||||
\(111\) | −6.58266 | −0.624798 | ||||||||
\(112\) | −6.66743 | −0.630013 | ||||||||
\(113\) | 3.89333 | 0.366253 | 0.183127 | − | 0.983089i | \(-0.441378\pi\) | ||||
0.183127 | + | 0.983089i | \(0.441378\pi\) | |||||||
\(114\) | 22.6063 | 2.11728 | ||||||||
\(115\) | −1.53834 | −0.143451 | ||||||||
\(116\) | −41.0668 | −3.81295 | ||||||||
\(117\) | −0.523395 | −0.0483879 | ||||||||
\(118\) | −5.07689 | −0.467366 | ||||||||
\(119\) | 3.81525 | 0.349743 | ||||||||
\(120\) | 38.6409 | 3.52742 | ||||||||
\(121\) | −7.38822 | −0.671657 | ||||||||
\(122\) | 19.7538 | 1.78842 | ||||||||
\(123\) | 6.65563 | 0.600118 | ||||||||
\(124\) | 13.7827 | 1.23772 | ||||||||
\(125\) | −1.36125 | −0.121754 | ||||||||
\(126\) | −0.258740 | −0.0230504 | ||||||||
\(127\) | −11.1026 | −0.985195 | −0.492597 | − | 0.870257i | \(-0.663952\pi\) | ||||
−0.492597 | + | 0.870257i | \(0.663952\pi\) | |||||||
\(128\) | 4.03122 | 0.356313 | ||||||||
\(129\) | 19.7100 | 1.73537 | ||||||||
\(130\) | 32.9732 | 2.89194 | ||||||||
\(131\) | 22.0662 | 1.92793 | 0.963967 | − | 0.266021i | \(-0.0857092\pi\) | ||||
0.963967 | + | 0.266021i | \(0.0857092\pi\) | |||||||
\(132\) | −15.2073 | −1.32363 | ||||||||
\(133\) | 3.86476 | 0.335117 | ||||||||
\(134\) | −15.8947 | −1.37309 | ||||||||
\(135\) | 17.1252 | 1.47390 | ||||||||
\(136\) | 35.9249 | 3.08053 | ||||||||
\(137\) | −3.02361 | −0.258324 | −0.129162 | − | 0.991623i | \(-0.541229\pi\) | ||||
−0.129162 | + | 0.991623i | \(0.541229\pi\) | |||||||
\(138\) | −2.09255 | −0.178129 | ||||||||
\(139\) | 13.0157 | 1.10397 | 0.551987 | − | 0.833853i | \(-0.313870\pi\) | ||||
0.551987 | + | 0.833853i | \(0.313870\pi\) | |||||||
\(140\) | 11.4531 | 0.967967 | ||||||||
\(141\) | 11.1787 | 0.941419 | ||||||||
\(142\) | −33.9590 | −2.84977 | ||||||||
\(143\) | −7.48483 | −0.625913 | ||||||||
\(144\) | −1.18027 | −0.0983560 | ||||||||
\(145\) | 28.0536 | 2.32972 | ||||||||
\(146\) | −0.955199 | −0.0790529 | ||||||||
\(147\) | −10.8985 | −0.898889 | ||||||||
\(148\) | −18.3718 | −1.51015 | ||||||||
\(149\) | 12.8203 | 1.05028 | 0.525141 | − | 0.851015i | \(-0.324013\pi\) | ||||
0.525141 | + | 0.851015i | \(0.324013\pi\) | |||||||
\(150\) | −23.8081 | −1.94392 | ||||||||
\(151\) | 8.05227 | 0.655284 | 0.327642 | − | 0.944802i | \(-0.393746\pi\) | ||||
0.327642 | + | 0.944802i | \(0.393746\pi\) | |||||||
\(152\) | 36.3911 | 2.95171 | ||||||||
\(153\) | 0.675377 | 0.0546010 | ||||||||
\(154\) | −3.70012 | −0.298164 | ||||||||
\(155\) | −9.41526 | −0.756252 | ||||||||
\(156\) | 31.5148 | 2.52320 | ||||||||
\(157\) | 11.1112 | 0.886767 | 0.443383 | − | 0.896332i | \(-0.353778\pi\) | ||||
0.443383 | + | 0.896332i | \(0.353778\pi\) | |||||||
\(158\) | 5.95406 | 0.473679 | ||||||||
\(159\) | −21.4748 | −1.70306 | ||||||||
\(160\) | 28.7144 | 2.27007 | ||||||||
\(161\) | −0.357740 | −0.0281939 | ||||||||
\(162\) | 22.2609 | 1.74898 | ||||||||
\(163\) | −17.6950 | −1.38598 | −0.692990 | − | 0.720947i | \(-0.743707\pi\) | ||||
−0.692990 | + | 0.720947i | \(0.743707\pi\) | |||||||
\(164\) | 18.5754 | 1.45050 | ||||||||
\(165\) | 10.3885 | 0.808740 | ||||||||
\(166\) | −15.2962 | −1.18722 | ||||||||
\(167\) | 13.1943 | 1.02101 | 0.510504 | − | 0.859876i | \(-0.329459\pi\) | ||||
0.510504 | + | 0.859876i | \(0.329459\pi\) | |||||||
\(168\) | 8.98595 | 0.693281 | ||||||||
\(169\) | 2.51111 | 0.193162 | ||||||||
\(170\) | −42.5478 | −3.26327 | ||||||||
\(171\) | 0.684142 | 0.0523177 | ||||||||
\(172\) | 55.0093 | 4.19442 | ||||||||
\(173\) | −13.3258 | −1.01315 | −0.506573 | − | 0.862197i | \(-0.669088\pi\) | ||||
−0.506573 | + | 0.862197i | \(0.669088\pi\) | |||||||
\(174\) | 38.1603 | 2.89292 | ||||||||
\(175\) | −4.07022 | −0.307680 | ||||||||
\(176\) | −16.8785 | −1.27227 | ||||||||
\(177\) | 3.31474 | 0.249151 | ||||||||
\(178\) | 24.2542 | 1.81793 | ||||||||
\(179\) | 2.92950 | 0.218961 | 0.109481 | − | 0.993989i | \(-0.465081\pi\) | ||||
0.109481 | + | 0.993989i | \(0.465081\pi\) | |||||||
\(180\) | 2.02744 | 0.151117 | ||||||||
\(181\) | 14.5296 | 1.07997 | 0.539987 | − | 0.841673i | \(-0.318429\pi\) | ||||
0.539987 | + | 0.841673i | \(0.318429\pi\) | |||||||
\(182\) | 7.66791 | 0.568383 | ||||||||
\(183\) | −12.8974 | −0.953401 | ||||||||
\(184\) | −3.36852 | −0.248331 | ||||||||
\(185\) | 12.5501 | 0.922704 | ||||||||
\(186\) | −12.8072 | −0.939073 | ||||||||
\(187\) | 9.65825 | 0.706281 | ||||||||
\(188\) | 31.1991 | 2.27543 | ||||||||
\(189\) | 3.98247 | 0.289682 | ||||||||
\(190\) | −43.1000 | −3.12680 | ||||||||
\(191\) | 10.7150 | 0.775307 | 0.387654 | − | 0.921805i | \(-0.373286\pi\) | ||||
0.387654 | + | 0.921805i | \(0.373286\pi\) | |||||||
\(192\) | 8.98279 | 0.648277 | ||||||||
\(193\) | 23.4016 | 1.68449 | 0.842243 | − | 0.539098i | \(-0.181235\pi\) | ||||
0.842243 | + | 0.539098i | \(0.181235\pi\) | |||||||
\(194\) | −2.17383 | −0.156072 | ||||||||
\(195\) | −21.5284 | −1.54168 | ||||||||
\(196\) | −30.4168 | −2.17263 | ||||||||
\(197\) | 6.48951 | 0.462358 | 0.231179 | − | 0.972911i | \(-0.425742\pi\) | ||||
0.231179 | + | 0.972911i | \(0.425742\pi\) | |||||||
\(198\) | −0.654997 | −0.0465486 | ||||||||
\(199\) | −11.3346 | −0.803486 | −0.401743 | − | 0.915753i | \(-0.631595\pi\) | ||||
−0.401743 | + | 0.915753i | \(0.631595\pi\) | |||||||
\(200\) | −38.3257 | −2.71003 | ||||||||
\(201\) | 10.3778 | 0.731992 | ||||||||
\(202\) | 21.1138 | 1.48556 | ||||||||
\(203\) | 6.52386 | 0.457885 | ||||||||
\(204\) | −40.6659 | −2.84719 | ||||||||
\(205\) | −12.6893 | −0.886256 | ||||||||
\(206\) | 5.80392 | 0.404378 | ||||||||
\(207\) | −0.0633273 | −0.00440155 | ||||||||
\(208\) | 34.9780 | 2.42529 | ||||||||
\(209\) | 9.78359 | 0.676745 | ||||||||
\(210\) | −10.6426 | −0.734406 | ||||||||
\(211\) | −1.76338 | −0.121396 | −0.0606981 | − | 0.998156i | \(-0.519333\pi\) | ||||
−0.0606981 | + | 0.998156i | \(0.519333\pi\) | |||||||
\(212\) | −59.9347 | −4.11633 | ||||||||
\(213\) | 22.1721 | 1.51920 | ||||||||
\(214\) | 4.36196 | 0.298177 | ||||||||
\(215\) | −37.5780 | −2.56280 | ||||||||
\(216\) | 37.4994 | 2.55151 | ||||||||
\(217\) | −2.18952 | −0.148634 | ||||||||
\(218\) | −14.1281 | −0.956878 | ||||||||
\(219\) | 0.623656 | 0.0421428 | ||||||||
\(220\) | 28.9935 | 1.95474 | ||||||||
\(221\) | −20.0152 | −1.34637 | ||||||||
\(222\) | 17.0715 | 1.14576 | ||||||||
\(223\) | −21.3538 | −1.42996 | −0.714979 | − | 0.699146i | \(-0.753564\pi\) | ||||
−0.714979 | + | 0.699146i | \(0.753564\pi\) | |||||||
\(224\) | 6.67753 | 0.446161 | ||||||||
\(225\) | −0.720512 | −0.0480342 | ||||||||
\(226\) | −10.0970 | −0.671641 | ||||||||
\(227\) | −24.7642 | −1.64366 | −0.821830 | − | 0.569733i | \(-0.807047\pi\) | ||||
−0.821830 | + | 0.569733i | \(0.807047\pi\) | |||||||
\(228\) | −41.1937 | −2.72812 | ||||||||
\(229\) | 11.6397 | 0.769174 | 0.384587 | − | 0.923089i | \(-0.374344\pi\) | ||||
0.384587 | + | 0.923089i | \(0.374344\pi\) | |||||||
\(230\) | 3.98953 | 0.263062 | ||||||||
\(231\) | 2.41583 | 0.158950 | ||||||||
\(232\) | 61.4294 | 4.03304 | ||||||||
\(233\) | −4.82430 | −0.316051 | −0.158025 | − | 0.987435i | \(-0.550513\pi\) | ||||
−0.158025 | + | 0.987435i | \(0.550513\pi\) | |||||||
\(234\) | 1.35738 | 0.0887345 | ||||||||
\(235\) | −21.3127 | −1.39029 | ||||||||
\(236\) | 9.25121 | 0.602202 | ||||||||
\(237\) | −3.88745 | −0.252517 | ||||||||
\(238\) | −9.89449 | −0.641365 | ||||||||
\(239\) | −0.764649 | −0.0494610 | −0.0247305 | − | 0.999694i | \(-0.507873\pi\) | ||||
−0.0247305 | + | 0.999694i | \(0.507873\pi\) | |||||||
\(240\) | −48.5472 | −3.13371 | ||||||||
\(241\) | −14.4360 | −0.929906 | −0.464953 | − | 0.885335i | \(-0.653929\pi\) | ||||
−0.464953 | + | 0.885335i | \(0.653929\pi\) | |||||||
\(242\) | 19.1607 | 1.23169 | ||||||||
\(243\) | 1.38005 | 0.0885305 | ||||||||
\(244\) | −35.9957 | −2.30439 | ||||||||
\(245\) | 20.7784 | 1.32748 | ||||||||
\(246\) | −17.2608 | −1.10051 | ||||||||
\(247\) | −20.2749 | −1.29006 | ||||||||
\(248\) | −20.6168 | −1.30917 | ||||||||
\(249\) | 9.98699 | 0.632900 | ||||||||
\(250\) | 3.53028 | 0.223274 | ||||||||
\(251\) | 29.2242 | 1.84461 | 0.922307 | − | 0.386459i | \(-0.126302\pi\) | ||||
0.922307 | + | 0.386459i | \(0.126302\pi\) | |||||||
\(252\) | 0.471481 | 0.0297005 | ||||||||
\(253\) | −0.905614 | −0.0569355 | ||||||||
\(254\) | 28.7935 | 1.80666 | ||||||||
\(255\) | 27.7798 | 1.73964 | ||||||||
\(256\) | −21.0647 | −1.31654 | ||||||||
\(257\) | −17.3034 | −1.07936 | −0.539679 | − | 0.841871i | \(-0.681454\pi\) | ||||
−0.539679 | + | 0.841871i | \(0.681454\pi\) | |||||||
\(258\) | −51.1161 | −3.18235 | ||||||||
\(259\) | 2.91853 | 0.181349 | ||||||||
\(260\) | −60.0843 | −3.72627 | ||||||||
\(261\) | 1.15486 | 0.0714838 | ||||||||
\(262\) | −57.2267 | −3.53547 | ||||||||
\(263\) | 12.4461 | 0.767461 | 0.383730 | − | 0.923445i | \(-0.374639\pi\) | ||||
0.383730 | + | 0.923445i | \(0.374639\pi\) | |||||||
\(264\) | 22.7478 | 1.40003 | ||||||||
\(265\) | 40.9426 | 2.51509 | ||||||||
\(266\) | −10.0229 | −0.614543 | ||||||||
\(267\) | −15.8357 | −0.969132 | ||||||||
\(268\) | 28.9637 | 1.76924 | ||||||||
\(269\) | −26.1504 | −1.59442 | −0.797210 | − | 0.603702i | \(-0.793692\pi\) | ||||
−0.797210 | + | 0.603702i | \(0.793692\pi\) | |||||||
\(270\) | −44.4127 | −2.70287 | ||||||||
\(271\) | 9.18322 | 0.557841 | 0.278920 | − | 0.960314i | \(-0.410023\pi\) | ||||
0.278920 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(272\) | −45.1348 | −2.73670 | ||||||||
\(273\) | −5.00643 | −0.303003 | ||||||||
\(274\) | 7.84144 | 0.473719 | ||||||||
\(275\) | −10.3037 | −0.621337 | ||||||||
\(276\) | 3.81308 | 0.229520 | ||||||||
\(277\) | −18.0381 | −1.08380 | −0.541901 | − | 0.840442i | \(-0.682295\pi\) | ||||
−0.541901 | + | 0.840442i | \(0.682295\pi\) | |||||||
\(278\) | −33.7549 | −2.02448 | ||||||||
\(279\) | −0.387590 | −0.0232044 | ||||||||
\(280\) | −17.1321 | −1.02384 | ||||||||
\(281\) | 15.2901 | 0.912128 | 0.456064 | − | 0.889947i | \(-0.349259\pi\) | ||||
0.456064 | + | 0.889947i | \(0.349259\pi\) | |||||||
\(282\) | −28.9910 | −1.72639 | ||||||||
\(283\) | 27.2624 | 1.62058 | 0.810291 | − | 0.586028i | \(-0.199309\pi\) | ||||
0.810291 | + | 0.586028i | \(0.199309\pi\) | |||||||
\(284\) | 61.8807 | 3.67194 | ||||||||
\(285\) | 28.1403 | 1.66689 | ||||||||
\(286\) | 19.4112 | 1.14781 | ||||||||
\(287\) | −2.95089 | −0.174185 | ||||||||
\(288\) | 1.18206 | 0.0696535 | ||||||||
\(289\) | 8.82712 | 0.519242 | ||||||||
\(290\) | −72.7543 | −4.27228 | ||||||||
\(291\) | 1.41931 | 0.0832015 | ||||||||
\(292\) | 1.74058 | 0.101860 | ||||||||
\(293\) | −12.3434 | −0.721109 | −0.360554 | − | 0.932738i | \(-0.617412\pi\) | ||||
−0.360554 | + | 0.932738i | \(0.617412\pi\) | |||||||
\(294\) | 28.2641 | 1.64840 | ||||||||
\(295\) | −6.31969 | −0.367947 | ||||||||
\(296\) | 27.4813 | 1.59732 | ||||||||
\(297\) | 10.0816 | 0.584992 | ||||||||
\(298\) | −33.2483 | −1.92602 | ||||||||
\(299\) | 1.87674 | 0.108535 | ||||||||
\(300\) | 43.3836 | 2.50475 | ||||||||
\(301\) | −8.73877 | −0.503694 | ||||||||
\(302\) | −20.8828 | −1.20167 | ||||||||
\(303\) | −13.7854 | −0.791948 | ||||||||
\(304\) | −45.7205 | −2.62225 | ||||||||
\(305\) | 24.5894 | 1.40799 | ||||||||
\(306\) | −1.75153 | −0.100128 | ||||||||
\(307\) | 11.0014 | 0.627881 | 0.313941 | − | 0.949443i | \(-0.398351\pi\) | ||||
0.313941 | + | 0.949443i | \(0.398351\pi\) | |||||||
\(308\) | 6.74243 | 0.384186 | ||||||||
\(309\) | −3.78942 | −0.215572 | ||||||||
\(310\) | 24.4176 | 1.38683 | ||||||||
\(311\) | 16.7087 | 0.947464 | 0.473732 | − | 0.880669i | \(-0.342907\pi\) | ||||
0.473732 | + | 0.880669i | \(0.342907\pi\) | |||||||
\(312\) | −47.1412 | −2.66884 | ||||||||
\(313\) | 16.9364 | 0.957303 | 0.478651 | − | 0.878005i | \(-0.341126\pi\) | ||||
0.478651 | + | 0.878005i | \(0.341126\pi\) | |||||||
\(314\) | −28.8157 | −1.62617 | ||||||||
\(315\) | −0.322079 | −0.0181471 | ||||||||
\(316\) | −10.8496 | −0.610338 | ||||||||
\(317\) | 11.3436 | 0.637118 | 0.318559 | − | 0.947903i | \(-0.396801\pi\) | ||||
0.318559 | + | 0.947903i | \(0.396801\pi\) | |||||||
\(318\) | 55.6929 | 3.12310 | ||||||||
\(319\) | 16.5150 | 0.924665 | ||||||||
\(320\) | −17.1261 | −0.957378 | ||||||||
\(321\) | −2.84795 | −0.158957 | ||||||||
\(322\) | 0.927765 | 0.0517023 | ||||||||
\(323\) | 26.1623 | 1.45571 | ||||||||
\(324\) | −40.5642 | −2.25357 | ||||||||
\(325\) | 21.3528 | 1.18444 | ||||||||
\(326\) | 45.8904 | 2.54163 | ||||||||
\(327\) | 9.22436 | 0.510108 | ||||||||
\(328\) | −27.7859 | −1.53422 | ||||||||
\(329\) | −4.95628 | −0.273249 | ||||||||
\(330\) | −26.9415 | −1.48308 | ||||||||
\(331\) | 31.8616 | 1.75127 | 0.875635 | − | 0.482974i | \(-0.160443\pi\) | ||||
0.875635 | + | 0.482974i | \(0.160443\pi\) | |||||||
\(332\) | 27.8730 | 1.52973 | ||||||||
\(333\) | 0.516640 | 0.0283117 | ||||||||
\(334\) | −34.2182 | −1.87234 | ||||||||
\(335\) | −19.7857 | −1.08101 | ||||||||
\(336\) | −11.2896 | −0.615901 | ||||||||
\(337\) | −13.7083 | −0.746741 | −0.373370 | − | 0.927682i | \(-0.621798\pi\) | ||||
−0.373370 | + | 0.927682i | \(0.621798\pi\) | |||||||
\(338\) | −6.51233 | −0.354224 | ||||||||
\(339\) | 6.59239 | 0.358049 | ||||||||
\(340\) | 77.5314 | 4.20473 | ||||||||
\(341\) | −5.54273 | −0.300156 | ||||||||
\(342\) | −1.77426 | −0.0959409 | ||||||||
\(343\) | 10.0871 | 0.544654 | ||||||||
\(344\) | −82.2853 | −4.43653 | ||||||||
\(345\) | −2.60479 | −0.140237 | ||||||||
\(346\) | 34.5593 | 1.85792 | ||||||||
\(347\) | 34.3853 | 1.84590 | 0.922949 | − | 0.384923i | \(-0.125772\pi\) | ||||
0.922949 | + | 0.384923i | \(0.125772\pi\) | |||||||
\(348\) | −69.5364 | −3.72754 | ||||||||
\(349\) | −19.1978 | −1.02763 | −0.513817 | − | 0.857900i | \(-0.671769\pi\) | ||||
−0.513817 | + | 0.857900i | \(0.671769\pi\) | |||||||
\(350\) | 10.5557 | 0.564228 | ||||||||
\(351\) | −20.8924 | −1.11516 | ||||||||
\(352\) | 16.9041 | 0.900989 | ||||||||
\(353\) | 23.1527 | 1.23230 | 0.616148 | − | 0.787631i | \(-0.288692\pi\) | ||||
0.616148 | + | 0.787631i | \(0.288692\pi\) | |||||||
\(354\) | −8.59646 | −0.456897 | ||||||||
\(355\) | −42.2720 | −2.24356 | ||||||||
\(356\) | −44.1965 | −2.34241 | ||||||||
\(357\) | 6.46018 | 0.341909 | ||||||||
\(358\) | −7.59739 | −0.401535 | ||||||||
\(359\) | −4.55174 | −0.240232 | −0.120116 | − | 0.992760i | \(-0.538327\pi\) | ||||
−0.120116 | + | 0.992760i | \(0.538327\pi\) | |||||||
\(360\) | −3.03273 | −0.159839 | ||||||||
\(361\) | 7.50181 | 0.394832 | ||||||||
\(362\) | −37.6811 | −1.98047 | ||||||||
\(363\) | −12.5101 | −0.656612 | ||||||||
\(364\) | −13.9726 | −0.732364 | ||||||||
\(365\) | −1.18903 | −0.0622366 | ||||||||
\(366\) | 33.4481 | 1.74836 | ||||||||
\(367\) | 9.77515 | 0.510259 | 0.255129 | − | 0.966907i | \(-0.417882\pi\) | ||||
0.255129 | + | 0.966907i | \(0.417882\pi\) | |||||||
\(368\) | 4.23210 | 0.220614 | ||||||||
\(369\) | −0.522368 | −0.0271934 | ||||||||
\(370\) | −32.5476 | −1.69207 | ||||||||
\(371\) | 9.52121 | 0.494317 | ||||||||
\(372\) | 23.3376 | 1.21000 | ||||||||
\(373\) | 10.6942 | 0.553724 | 0.276862 | − | 0.960910i | \(-0.410706\pi\) | ||||
0.276862 | + | 0.960910i | \(0.410706\pi\) | |||||||
\(374\) | −25.0478 | −1.29519 | ||||||||
\(375\) | −2.30494 | −0.119027 | ||||||||
\(376\) | −46.6689 | −2.40677 | ||||||||
\(377\) | −34.2248 | −1.76267 | ||||||||
\(378\) | −10.3282 | −0.531223 | ||||||||
\(379\) | −10.4880 | −0.538735 | −0.269367 | − | 0.963037i | \(-0.586815\pi\) | ||||
−0.269367 | + | 0.963037i | \(0.586815\pi\) | |||||||
\(380\) | 78.5376 | 4.02889 | ||||||||
\(381\) | −18.7995 | −0.963126 | ||||||||
\(382\) | −27.7882 | −1.42177 | ||||||||
\(383\) | −18.8764 | −0.964540 | −0.482270 | − | 0.876023i | \(-0.660188\pi\) | ||||
−0.482270 | + | 0.876023i | \(0.660188\pi\) | |||||||
\(384\) | 6.82587 | 0.348331 | ||||||||
\(385\) | −4.60590 | −0.234738 | ||||||||
\(386\) | −60.6899 | −3.08904 | ||||||||
\(387\) | −1.54694 | −0.0786354 | ||||||||
\(388\) | 3.96120 | 0.201100 | ||||||||
\(389\) | 37.3675 | 1.89461 | 0.947303 | − | 0.320340i | \(-0.103797\pi\) | ||||
0.947303 | + | 0.320340i | \(0.103797\pi\) | |||||||
\(390\) | 55.8319 | 2.82716 | ||||||||
\(391\) | −2.42170 | −0.122471 | ||||||||
\(392\) | 45.4988 | 2.29804 | ||||||||
\(393\) | 37.3637 | 1.88475 | ||||||||
\(394\) | −16.8299 | −0.847879 | ||||||||
\(395\) | 7.41159 | 0.372917 | ||||||||
\(396\) | 1.19355 | 0.0599781 | ||||||||
\(397\) | −0.903344 | −0.0453376 | −0.0226688 | − | 0.999743i | \(-0.507216\pi\) | ||||
−0.0226688 | + | 0.999743i | \(0.507216\pi\) | |||||||
\(398\) | 29.3951 | 1.47344 | ||||||||
\(399\) | 6.54402 | 0.327611 | ||||||||
\(400\) | 48.1511 | 2.40756 | ||||||||
\(401\) | −26.8156 | −1.33911 | −0.669555 | − | 0.742763i | \(-0.733515\pi\) | ||||
−0.669555 | + | 0.742763i | \(0.733515\pi\) | |||||||
\(402\) | −26.9138 | −1.34234 | ||||||||
\(403\) | 11.4864 | 0.572180 | ||||||||
\(404\) | −38.4740 | −1.91415 | ||||||||
\(405\) | 27.7103 | 1.37693 | ||||||||
\(406\) | −16.9190 | −0.839676 | ||||||||
\(407\) | 7.38822 | 0.366221 | ||||||||
\(408\) | 60.8299 | 3.01153 | ||||||||
\(409\) | −12.5241 | −0.619275 | −0.309637 | − | 0.950855i | \(-0.600208\pi\) | ||||
−0.309637 | + | 0.950855i | \(0.600208\pi\) | |||||||
\(410\) | 32.9084 | 1.62523 | ||||||||
\(411\) | −5.11973 | −0.252538 | ||||||||
\(412\) | −10.5760 | −0.521043 | ||||||||
\(413\) | −1.46964 | −0.0723165 | ||||||||
\(414\) | 0.164233 | 0.00807163 | ||||||||
\(415\) | −19.0406 | −0.934668 | ||||||||
\(416\) | −35.0310 | −1.71753 | ||||||||
\(417\) | 22.0388 | 1.07924 | ||||||||
\(418\) | −25.3728 | −1.24103 | ||||||||
\(419\) | 27.6385 | 1.35023 | 0.675114 | − | 0.737713i | \(-0.264094\pi\) | ||||
0.675114 | + | 0.737713i | \(0.264094\pi\) | |||||||
\(420\) | 19.3931 | 0.946285 | ||||||||
\(421\) | 23.0022 | 1.12106 | 0.560530 | − | 0.828134i | \(-0.310597\pi\) | ||||
0.560530 | + | 0.828134i | \(0.310597\pi\) | |||||||
\(422\) | 4.57316 | 0.222618 | ||||||||
\(423\) | −0.877363 | −0.0426589 | ||||||||
\(424\) | 89.6529 | 4.35393 | ||||||||
\(425\) | −27.5531 | −1.33652 | ||||||||
\(426\) | −57.5011 | −2.78594 | ||||||||
\(427\) | 5.71827 | 0.276726 | ||||||||
\(428\) | −7.94844 | −0.384202 | ||||||||
\(429\) | −12.6737 | −0.611892 | ||||||||
\(430\) | 97.4550 | 4.69970 | ||||||||
\(431\) | 11.5806 | 0.557816 | 0.278908 | − | 0.960318i | \(-0.410028\pi\) | ||||
0.278908 | + | 0.960318i | \(0.410028\pi\) | |||||||
\(432\) | −47.1130 | −2.26673 | ||||||||
\(433\) | −18.0607 | −0.867943 | −0.433972 | − | 0.900926i | \(-0.642888\pi\) | ||||
−0.433972 | + | 0.900926i | \(0.642888\pi\) | |||||||
\(434\) | 5.67831 | 0.272568 | ||||||||
\(435\) | 47.5018 | 2.27754 | ||||||||
\(436\) | 25.7446 | 1.23294 | ||||||||
\(437\) | −2.45313 | −0.117349 | ||||||||
\(438\) | −1.61739 | −0.0772821 | ||||||||
\(439\) | 27.9317 | 1.33311 | 0.666554 | − | 0.745457i | \(-0.267769\pi\) | ||||
0.666554 | + | 0.745457i | \(0.267769\pi\) | |||||||
\(440\) | −43.3697 | −2.06757 | ||||||||
\(441\) | 0.855365 | 0.0407317 | ||||||||
\(442\) | 51.9075 | 2.46899 | ||||||||
\(443\) | −32.5806 | −1.54795 | −0.773975 | − | 0.633216i | \(-0.781735\pi\) | ||||
−0.773975 | + | 0.633216i | \(0.781735\pi\) | |||||||
\(444\) | −31.1080 | −1.47632 | ||||||||
\(445\) | 30.1915 | 1.43122 | ||||||||
\(446\) | 55.3792 | 2.62228 | ||||||||
\(447\) | 21.7080 | 1.02676 | ||||||||
\(448\) | −3.98267 | −0.188164 | ||||||||
\(449\) | −14.7323 | −0.695261 | −0.347630 | − | 0.937632i | \(-0.613014\pi\) | ||||
−0.347630 | + | 0.937632i | \(0.613014\pi\) | |||||||
\(450\) | 1.86858 | 0.0880857 | ||||||||
\(451\) | −7.47013 | −0.351755 | ||||||||
\(452\) | 18.3989 | 0.865412 | ||||||||
\(453\) | 13.6345 | 0.640606 | ||||||||
\(454\) | 64.2237 | 3.01417 | ||||||||
\(455\) | 9.54498 | 0.447476 | ||||||||
\(456\) | 61.6193 | 2.88559 | ||||||||
\(457\) | −10.5137 | −0.491811 | −0.245906 | − | 0.969294i | \(-0.579085\pi\) | ||||
−0.245906 | + | 0.969294i | \(0.579085\pi\) | |||||||
\(458\) | −30.1865 | −1.41052 | ||||||||
\(459\) | 26.9591 | 1.25834 | ||||||||
\(460\) | −7.26980 | −0.338956 | ||||||||
\(461\) | −0.897127 | −0.0417834 | −0.0208917 | − | 0.999782i | \(-0.506651\pi\) | ||||
−0.0208917 | + | 0.999782i | \(0.506651\pi\) | |||||||
\(462\) | −6.26524 | −0.291485 | ||||||||
\(463\) | 32.7247 | 1.52085 | 0.760423 | − | 0.649428i | \(-0.224992\pi\) | ||||
0.760423 | + | 0.649428i | \(0.224992\pi\) | |||||||
\(464\) | −77.1779 | −3.58289 | ||||||||
\(465\) | −15.9424 | −0.739311 | ||||||||
\(466\) | 12.5114 | 0.579578 | ||||||||
\(467\) | −31.8393 | −1.47335 | −0.736675 | − | 0.676247i | \(-0.763605\pi\) | ||||
−0.736675 | + | 0.676247i | \(0.763605\pi\) | |||||||
\(468\) | −2.47344 | −0.114335 | ||||||||
\(469\) | −4.60116 | −0.212462 | ||||||||
\(470\) | 55.2726 | 2.54954 | ||||||||
\(471\) | 18.8140 | 0.866903 | ||||||||
\(472\) | −13.8384 | −0.636962 | ||||||||
\(473\) | −22.1221 | −1.01717 | ||||||||
\(474\) | 10.0817 | 0.463069 | ||||||||
\(475\) | −27.9107 | −1.28063 | ||||||||
\(476\) | 18.0299 | 0.826401 | ||||||||
\(477\) | 1.68545 | 0.0771714 | ||||||||
\(478\) | 1.98304 | 0.0907023 | ||||||||
\(479\) | 13.6228 | 0.622442 | 0.311221 | − | 0.950338i | \(-0.399262\pi\) | ||||
0.311221 | + | 0.950338i | \(0.399262\pi\) | |||||||
\(480\) | 48.6207 | 2.21922 | ||||||||
\(481\) | −15.3109 | −0.698117 | ||||||||
\(482\) | 37.4385 | 1.70528 | ||||||||
\(483\) | −0.605745 | −0.0275623 | ||||||||
\(484\) | −34.9149 | −1.58704 | ||||||||
\(485\) | −2.70598 | −0.122872 | ||||||||
\(486\) | −3.57904 | −0.162348 | ||||||||
\(487\) | −20.2084 | −0.915732 | −0.457866 | − | 0.889021i | \(-0.651386\pi\) | ||||
−0.457866 | + | 0.889021i | \(0.651386\pi\) | |||||||
\(488\) | 53.8439 | 2.43740 | ||||||||
\(489\) | −29.9621 | −1.35493 | ||||||||
\(490\) | −53.8868 | −2.43436 | ||||||||
\(491\) | −1.34490 | −0.0606947 | −0.0303473 | − | 0.999539i | \(-0.509661\pi\) | ||||
−0.0303473 | + | 0.999539i | \(0.509661\pi\) | |||||||
\(492\) | 31.4529 | 1.41801 | ||||||||
\(493\) | 44.1629 | 1.98900 | ||||||||
\(494\) | 52.5811 | 2.36574 | ||||||||
\(495\) | −0.815338 | −0.0366467 | ||||||||
\(496\) | 25.9022 | 1.16304 | ||||||||
\(497\) | −9.83035 | −0.440952 | ||||||||
\(498\) | −25.9003 | −1.16062 | ||||||||
\(499\) | 14.3490 | 0.642350 | 0.321175 | − | 0.947020i | \(-0.395922\pi\) | ||||
0.321175 | + | 0.947020i | \(0.395922\pi\) | |||||||
\(500\) | −6.43294 | −0.287690 | ||||||||
\(501\) | 22.3413 | 0.998137 | ||||||||
\(502\) | −75.7901 | −3.38268 | ||||||||
\(503\) | −3.24888 | −0.144860 | −0.0724301 | − | 0.997373i | \(-0.523075\pi\) | ||||
−0.0724301 | + | 0.997373i | \(0.523075\pi\) | |||||||
\(504\) | −0.705262 | −0.0314149 | ||||||||
\(505\) | 26.2824 | 1.16955 | ||||||||
\(506\) | 2.34862 | 0.104409 | ||||||||
\(507\) | 4.25194 | 0.188835 | ||||||||
\(508\) | −52.4681 | −2.32789 | ||||||||
\(509\) | 6.33035 | 0.280588 | 0.140294 | − | 0.990110i | \(-0.455195\pi\) | ||||
0.140294 | + | 0.990110i | \(0.455195\pi\) | |||||||
\(510\) | −72.0442 | −3.19017 | ||||||||
\(511\) | −0.276509 | −0.0122320 | ||||||||
\(512\) | 46.5668 | 2.05798 | ||||||||
\(513\) | 27.3090 | 1.20572 | ||||||||
\(514\) | 44.8748 | 1.97934 | ||||||||
\(515\) | 7.22469 | 0.318358 | ||||||||
\(516\) | 93.1447 | 4.10047 | ||||||||
\(517\) | −12.5468 | −0.551805 | ||||||||
\(518\) | −7.56894 | −0.332560 | ||||||||
\(519\) | −22.5640 | −0.990451 | ||||||||
\(520\) | 89.8767 | 3.94135 | ||||||||
\(521\) | −2.89812 | −0.126969 | −0.0634844 | − | 0.997983i | \(-0.520221\pi\) | ||||
−0.0634844 | + | 0.997983i | \(0.520221\pi\) | |||||||
\(522\) | −2.99501 | −0.131088 | ||||||||
\(523\) | −32.0569 | −1.40175 | −0.700875 | − | 0.713284i | \(-0.747207\pi\) | ||||
−0.700875 | + | 0.713284i | \(0.747207\pi\) | |||||||
\(524\) | 104.279 | 4.55547 | ||||||||
\(525\) | −6.89191 | −0.300788 | ||||||||
\(526\) | −32.2778 | −1.40738 | ||||||||
\(527\) | −14.8218 | −0.645649 | ||||||||
\(528\) | −28.5796 | −1.24377 | ||||||||
\(529\) | −22.7729 | −0.990127 | ||||||||
\(530\) | −106.181 | −4.61220 | ||||||||
\(531\) | −0.260157 | −0.0112899 | ||||||||
\(532\) | 18.2639 | 0.791841 | ||||||||
\(533\) | 15.4806 | 0.670541 | ||||||||
\(534\) | 41.0685 | 1.77721 | ||||||||
\(535\) | 5.42975 | 0.234748 | ||||||||
\(536\) | −43.3251 | −1.87136 | ||||||||
\(537\) | 4.96039 | 0.214057 | ||||||||
\(538\) | 67.8187 | 2.92387 | ||||||||
\(539\) | 12.2322 | 0.526877 | ||||||||
\(540\) | 80.9296 | 3.48265 | ||||||||
\(541\) | 45.6333 | 1.96193 | 0.980964 | − | 0.194190i | \(-0.0622079\pi\) | ||||
0.980964 | + | 0.194190i | \(0.0622079\pi\) | |||||||
\(542\) | −23.8158 | −1.02298 | ||||||||
\(543\) | 24.6022 | 1.05578 | ||||||||
\(544\) | 45.2031 | 1.93807 | ||||||||
\(545\) | −17.5866 | −0.753329 | ||||||||
\(546\) | 12.9837 | 0.555651 | ||||||||
\(547\) | 14.3464 | 0.613407 | 0.306704 | − | 0.951805i | \(-0.400774\pi\) | ||||
0.306704 | + | 0.951805i | \(0.400774\pi\) | |||||||
\(548\) | −14.2888 | −0.610388 | ||||||||
\(549\) | 1.01225 | 0.0432018 | ||||||||
\(550\) | 26.7217 | 1.13942 | ||||||||
\(551\) | 44.7360 | 1.90582 | ||||||||
\(552\) | −5.70376 | −0.242768 | ||||||||
\(553\) | 1.72357 | 0.0732934 | ||||||||
\(554\) | 46.7800 | 1.98749 | ||||||||
\(555\) | 21.2505 | 0.902035 | ||||||||
\(556\) | 61.5088 | 2.60855 | ||||||||
\(557\) | 4.44027 | 0.188140 | 0.0940702 | − | 0.995566i | \(-0.470012\pi\) | ||||
0.0940702 | + | 0.995566i | \(0.470012\pi\) | |||||||
\(558\) | 1.00518 | 0.0425525 | ||||||||
\(559\) | 45.8444 | 1.93901 | ||||||||
\(560\) | 21.5242 | 0.909564 | ||||||||
\(561\) | 16.3539 | 0.690460 | ||||||||
\(562\) | −39.6533 | −1.67267 | ||||||||
\(563\) | 37.2623 | 1.57042 | 0.785209 | − | 0.619231i | \(-0.212555\pi\) | ||||
0.785209 | + | 0.619231i | \(0.212555\pi\) | |||||||
\(564\) | 52.8279 | 2.22446 | ||||||||
\(565\) | −12.5687 | −0.528768 | ||||||||
\(566\) | −70.7025 | −2.97185 | ||||||||
\(567\) | 6.44403 | 0.270624 | ||||||||
\(568\) | −92.5638 | −3.88389 | ||||||||
\(569\) | 25.5184 | 1.06978 | 0.534892 | − | 0.844920i | \(-0.320352\pi\) | ||||
0.534892 | + | 0.844920i | \(0.320352\pi\) | |||||||
\(570\) | −72.9791 | −3.05676 | ||||||||
\(571\) | −13.8242 | −0.578526 | −0.289263 | − | 0.957250i | \(-0.593410\pi\) | ||||
−0.289263 | + | 0.957250i | \(0.593410\pi\) | |||||||
\(572\) | −35.3715 | −1.47895 | ||||||||
\(573\) | 18.1431 | 0.757940 | ||||||||
\(574\) | 7.65285 | 0.319424 | ||||||||
\(575\) | 2.58354 | 0.107741 | ||||||||
\(576\) | −0.705015 | −0.0293756 | ||||||||
\(577\) | 24.5403 | 1.02163 | 0.510813 | − | 0.859692i | \(-0.329344\pi\) | ||||
0.510813 | + | 0.859692i | \(0.329344\pi\) | |||||||
\(578\) | −22.8923 | −0.952194 | ||||||||
\(579\) | 39.6249 | 1.64675 | ||||||||
\(580\) | 132.574 | 5.50485 | ||||||||
\(581\) | −4.42790 | −0.183700 | ||||||||
\(582\) | −3.68085 | −0.152576 | ||||||||
\(583\) | 24.1028 | 0.998236 | ||||||||
\(584\) | −2.60364 | −0.107739 | ||||||||
\(585\) | 1.68966 | 0.0698587 | ||||||||
\(586\) | 32.0114 | 1.32238 | ||||||||
\(587\) | −10.6040 | −0.437675 | −0.218838 | − | 0.975761i | \(-0.570227\pi\) | ||||
−0.218838 | + | 0.975761i | \(0.570227\pi\) | |||||||
\(588\) | −51.5034 | −2.12396 | ||||||||
\(589\) | −15.0142 | −0.618648 | ||||||||
\(590\) | 16.3895 | 0.674746 | ||||||||
\(591\) | 10.9884 | 0.452001 | ||||||||
\(592\) | −34.5265 | −1.41903 | ||||||||
\(593\) | −19.6125 | −0.805388 | −0.402694 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402694 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(594\) | −26.1456 | −1.07277 | ||||||||
\(595\) | −12.3166 | −0.504932 | ||||||||
\(596\) | 60.5857 | 2.48169 | ||||||||
\(597\) | −19.1923 | −0.785488 | ||||||||
\(598\) | −4.86715 | −0.199033 | ||||||||
\(599\) | −22.1832 | −0.906379 | −0.453190 | − | 0.891414i | \(-0.649714\pi\) | ||||
−0.453190 | + | 0.891414i | \(0.649714\pi\) | |||||||
\(600\) | −64.8951 | −2.64933 | ||||||||
\(601\) | −16.5455 | −0.674905 | −0.337453 | − | 0.941343i | \(-0.609565\pi\) | ||||
−0.337453 | + | 0.941343i | \(0.609565\pi\) | |||||||
\(602\) | 22.6632 | 0.923682 | ||||||||
\(603\) | −0.814500 | −0.0331690 | ||||||||
\(604\) | 38.0530 | 1.54836 | ||||||||
\(605\) | 23.8511 | 0.969686 | ||||||||
\(606\) | 35.7510 | 1.45229 | ||||||||
\(607\) | 21.1646 | 0.859044 | 0.429522 | − | 0.903056i | \(-0.358682\pi\) | ||||
0.429522 | + | 0.903056i | \(0.358682\pi\) | |||||||
\(608\) | 45.7898 | 1.85702 | ||||||||
\(609\) | 11.0465 | 0.447628 | ||||||||
\(610\) | −63.7703 | −2.58198 | ||||||||
\(611\) | 26.0011 | 1.05189 | ||||||||
\(612\) | 3.19167 | 0.129015 | ||||||||
\(613\) | 43.8957 | 1.77293 | 0.886464 | − | 0.462797i | \(-0.153154\pi\) | ||||
0.886464 | + | 0.462797i | \(0.153154\pi\) | |||||||
\(614\) | −28.5310 | −1.15142 | ||||||||
\(615\) | −21.4861 | −0.866404 | ||||||||
\(616\) | −10.0856 | −0.406361 | ||||||||
\(617\) | −35.8634 | −1.44381 | −0.721904 | − | 0.691993i | \(-0.756733\pi\) | ||||
−0.721904 | + | 0.691993i | \(0.756733\pi\) | |||||||
\(618\) | 9.82750 | 0.395320 | ||||||||
\(619\) | −1.70051 | −0.0683494 | −0.0341747 | − | 0.999416i | \(-0.510880\pi\) | ||||
−0.0341747 | + | 0.999416i | \(0.510880\pi\) | |||||||
\(620\) | −44.4942 | −1.78693 | ||||||||
\(621\) | −2.52784 | −0.101439 | ||||||||
\(622\) | −43.3325 | −1.73747 | ||||||||
\(623\) | 7.02104 | 0.281292 | ||||||||
\(624\) | 59.2266 | 2.37096 | ||||||||
\(625\) | −22.7139 | −0.908554 | ||||||||
\(626\) | −43.9230 | −1.75552 | ||||||||
\(627\) | 16.5661 | 0.661586 | ||||||||
\(628\) | 52.5086 | 2.09532 | ||||||||
\(629\) | 19.7568 | 0.787757 | ||||||||
\(630\) | 0.835281 | 0.0332784 | ||||||||
\(631\) | 11.5062 | 0.458053 | 0.229026 | − | 0.973420i | \(-0.426446\pi\) | ||||
0.229026 | + | 0.973420i | \(0.426446\pi\) | |||||||
\(632\) | 16.2293 | 0.645567 | ||||||||
\(633\) | −2.98585 | −0.118677 | ||||||||
\(634\) | −29.4185 | −1.16836 | ||||||||
\(635\) | 35.8420 | 1.42235 | ||||||||
\(636\) | −101.485 | −4.02413 | ||||||||
\(637\) | −25.3492 | −1.00437 | ||||||||
\(638\) | −42.8302 | −1.69566 | ||||||||
\(639\) | −1.74017 | −0.0688402 | ||||||||
\(640\) | −13.0138 | −0.514417 | ||||||||
\(641\) | 25.4406 | 1.00484 | 0.502421 | − | 0.864623i | \(-0.332443\pi\) | ||||
0.502421 | + | 0.864623i | \(0.332443\pi\) | |||||||
\(642\) | 7.38590 | 0.291498 | ||||||||
\(643\) | 18.2160 | 0.718367 | 0.359183 | − | 0.933267i | \(-0.383055\pi\) | ||||
0.359183 | + | 0.933267i | \(0.383055\pi\) | |||||||
\(644\) | −1.69059 | −0.0666187 | ||||||||
\(645\) | −63.6291 | −2.50539 | ||||||||
\(646\) | −67.8494 | −2.66950 | ||||||||
\(647\) | 30.0129 | 1.17993 | 0.589964 | − | 0.807430i | \(-0.299142\pi\) | ||||
0.589964 | + | 0.807430i | \(0.299142\pi\) | |||||||
\(648\) | 60.6777 | 2.38365 | ||||||||
\(649\) | −3.72038 | −0.146038 | ||||||||
\(650\) | −55.3764 | −2.17204 | ||||||||
\(651\) | −3.70741 | −0.145305 | ||||||||
\(652\) | −83.6223 | −3.27490 | ||||||||
\(653\) | 0.146955 | 0.00575079 | 0.00287540 | − | 0.999996i | \(-0.499085\pi\) | ||||
0.00287540 | + | 0.999996i | \(0.499085\pi\) | |||||||
\(654\) | −23.9225 | −0.935444 | ||||||||
\(655\) | −71.2355 | −2.78340 | ||||||||
\(656\) | 34.9093 | 1.36298 | ||||||||
\(657\) | −0.0489477 | −0.00190963 | ||||||||
\(658\) | 12.8536 | 0.501087 | ||||||||
\(659\) | 20.0542 | 0.781199 | 0.390600 | − | 0.920561i | \(-0.372268\pi\) | ||||
0.390600 | + | 0.920561i | \(0.372268\pi\) | |||||||
\(660\) | 49.0933 | 1.91095 | ||||||||
\(661\) | 11.5108 | 0.447717 | 0.223858 | − | 0.974622i | \(-0.428135\pi\) | ||||
0.223858 | + | 0.974622i | \(0.428135\pi\) | |||||||
\(662\) | −82.6299 | −3.21150 | ||||||||
\(663\) | −33.8908 | −1.31621 | ||||||||
\(664\) | −41.6937 | −1.61803 | ||||||||
\(665\) | −12.4765 | −0.483816 | ||||||||
\(666\) | −1.33986 | −0.0519184 | ||||||||
\(667\) | −4.14097 | −0.160339 | ||||||||
\(668\) | 62.3531 | 2.41252 | ||||||||
\(669\) | −36.1574 | −1.39793 | ||||||||
\(670\) | 51.3123 | 1.98237 | ||||||||
\(671\) | 14.4757 | 0.558829 | ||||||||
\(672\) | 11.3067 | 0.436167 | ||||||||
\(673\) | −6.35746 | −0.245062 | −0.122531 | − | 0.992465i | \(-0.539101\pi\) | ||||
−0.122531 | + | 0.992465i | \(0.539101\pi\) | |||||||
\(674\) | 35.5513 | 1.36938 | ||||||||
\(675\) | −28.7608 | −1.10700 | ||||||||
\(676\) | 11.8669 | 0.456419 | ||||||||
\(677\) | 28.0154 | 1.07672 | 0.538360 | − | 0.842715i | \(-0.319044\pi\) | ||||
0.538360 | + | 0.842715i | \(0.319044\pi\) | |||||||
\(678\) | −17.0967 | −0.656596 | ||||||||
\(679\) | −0.629276 | −0.0241494 | ||||||||
\(680\) | −115.975 | −4.44743 | ||||||||
\(681\) | −41.9321 | −1.60684 | ||||||||
\(682\) | 14.3746 | 0.550430 | ||||||||
\(683\) | 51.6176 | 1.97509 | 0.987547 | − | 0.157325i | \(-0.0502869\pi\) | ||||
0.987547 | + | 0.157325i | \(0.0502869\pi\) | |||||||
\(684\) | 3.23309 | 0.123620 | ||||||||
\(685\) | 9.76099 | 0.372948 | ||||||||
\(686\) | −26.1600 | −0.998795 | ||||||||
\(687\) | 19.7090 | 0.751945 | ||||||||
\(688\) | 103.381 | 3.94135 | ||||||||
\(689\) | −49.9492 | −1.90291 | ||||||||
\(690\) | 6.75528 | 0.257169 | ||||||||
\(691\) | 9.58150 | 0.364497 | 0.182249 | − | 0.983252i | \(-0.441662\pi\) | ||||
0.182249 | + | 0.983252i | \(0.441662\pi\) | |||||||
\(692\) | −62.9747 | −2.39394 | ||||||||
\(693\) | −0.189607 | −0.00720257 | ||||||||
\(694\) | −89.1749 | −3.38503 | ||||||||
\(695\) | −42.0179 | −1.59383 | ||||||||
\(696\) | 104.016 | 3.94270 | ||||||||
\(697\) | −19.9759 | −0.756640 | ||||||||
\(698\) | 49.7877 | 1.88449 | ||||||||
\(699\) | −8.16876 | −0.308971 | ||||||||
\(700\) | −19.2349 | −0.727009 | ||||||||
\(701\) | 9.19586 | 0.347323 | 0.173661 | − | 0.984805i | \(-0.444440\pi\) | ||||
0.173661 | + | 0.984805i | \(0.444440\pi\) | |||||||
\(702\) | 54.1826 | 2.04499 | ||||||||
\(703\) | 20.0132 | 0.754813 | ||||||||
\(704\) | −10.0821 | −0.379983 | ||||||||
\(705\) | −36.0879 | −1.35915 | ||||||||
\(706\) | −60.0444 | −2.25980 | ||||||||
\(707\) | 6.11197 | 0.229864 | ||||||||
\(708\) | 15.6646 | 0.588713 | ||||||||
\(709\) | −37.4936 | −1.40810 | −0.704051 | − | 0.710149i | \(-0.748628\pi\) | ||||
−0.704051 | + | 0.710149i | \(0.748628\pi\) | |||||||
\(710\) | 109.628 | 4.11428 | ||||||||
\(711\) | 0.305106 | 0.0114424 | ||||||||
\(712\) | 66.1110 | 2.47761 | ||||||||
\(713\) | 1.38978 | 0.0520477 | ||||||||
\(714\) | −16.7539 | −0.626998 | ||||||||
\(715\) | 24.1630 | 0.903644 | ||||||||
\(716\) | 13.8441 | 0.517379 | ||||||||
\(717\) | −1.29474 | −0.0483531 | ||||||||
\(718\) | 11.8045 | 0.440540 | ||||||||
\(719\) | 5.12401 | 0.191093 | 0.0955466 | − | 0.995425i | \(-0.469540\pi\) | ||||
0.0955466 | + | 0.995425i | \(0.469540\pi\) | |||||||
\(720\) | 3.81023 | 0.141999 | ||||||||
\(721\) | 1.68010 | 0.0625703 | ||||||||
\(722\) | −19.4552 | −0.724049 | ||||||||
\(723\) | −24.4438 | −0.909077 | ||||||||
\(724\) | 68.6632 | 2.55185 | ||||||||
\(725\) | −47.1143 | −1.74978 | ||||||||
\(726\) | 32.4438 | 1.20410 | ||||||||
\(727\) | −2.64598 | −0.0981341 | −0.0490671 | − | 0.998795i | \(-0.515625\pi\) | ||||
−0.0490671 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(728\) | 20.9008 | 0.774636 | ||||||||
\(729\) | 28.0877 | 1.04029 | ||||||||
\(730\) | 3.08363 | 0.114130 | ||||||||
\(731\) | −59.1566 | −2.18799 | ||||||||
\(732\) | −60.9498 | −2.25277 | ||||||||
\(733\) | −30.7659 | −1.13637 | −0.568183 | − | 0.822902i | \(-0.692353\pi\) | ||||
−0.568183 | + | 0.822902i | \(0.692353\pi\) | |||||||
\(734\) | −25.3509 | −0.935720 | ||||||||
\(735\) | 35.1831 | 1.29775 | ||||||||
\(736\) | −4.23851 | −0.156234 | ||||||||
\(737\) | −11.6478 | −0.429051 | ||||||||
\(738\) | 1.35471 | 0.0498676 | ||||||||
\(739\) | 24.4851 | 0.900699 | 0.450350 | − | 0.892852i | \(-0.351299\pi\) | ||||
0.450350 | + | 0.892852i | \(0.351299\pi\) | |||||||
\(740\) | 59.3088 | 2.18023 | ||||||||
\(741\) | −34.3306 | −1.26117 | ||||||||
\(742\) | −24.6924 | −0.906485 | ||||||||
\(743\) | 8.46018 | 0.310374 | 0.155187 | − | 0.987885i | \(-0.450402\pi\) | ||||
0.155187 | + | 0.987885i | \(0.450402\pi\) | |||||||
\(744\) | −34.9094 | −1.27984 | ||||||||
\(745\) | −41.3873 | −1.51632 | ||||||||
\(746\) | −27.7344 | −1.01543 | ||||||||
\(747\) | −0.783829 | −0.0286788 | ||||||||
\(748\) | 45.6425 | 1.66886 | ||||||||
\(749\) | 1.26269 | 0.0461376 | ||||||||
\(750\) | 5.97765 | 0.218273 | ||||||||
\(751\) | −42.8284 | −1.56283 | −0.781415 | − | 0.624012i | \(-0.785502\pi\) | ||||
−0.781415 | + | 0.624012i | \(0.785502\pi\) | |||||||
\(752\) | 58.6333 | 2.13814 | ||||||||
\(753\) | 49.4839 | 1.80329 | ||||||||
\(754\) | 88.7588 | 3.23240 | ||||||||
\(755\) | −25.9948 | −0.946048 | ||||||||
\(756\) | 18.8202 | 0.684483 | ||||||||
\(757\) | −53.6680 | −1.95060 | −0.975298 | − | 0.220894i | \(-0.929103\pi\) | ||||
−0.975298 | + | 0.220894i | \(0.929103\pi\) | |||||||
\(758\) | 27.1998 | 0.987940 | ||||||||
\(759\) | −1.53343 | −0.0556601 | ||||||||
\(760\) | −117.480 | −4.26144 | ||||||||
\(761\) | 6.35272 | 0.230286 | 0.115143 | − | 0.993349i | \(-0.463267\pi\) | ||||
0.115143 | + | 0.993349i | \(0.463267\pi\) | |||||||
\(762\) | 48.7547 | 1.76620 | ||||||||
\(763\) | −4.08978 | −0.148060 | ||||||||
\(764\) | 50.6363 | 1.83196 | ||||||||
\(765\) | −2.18029 | −0.0788287 | ||||||||
\(766\) | 48.9542 | 1.76879 | ||||||||
\(767\) | 7.70990 | 0.278388 | ||||||||
\(768\) | −35.6678 | −1.28705 | ||||||||
\(769\) | −8.05600 | −0.290507 | −0.145253 | − | 0.989394i | \(-0.546400\pi\) | ||||
−0.145253 | + | 0.989394i | \(0.546400\pi\) | |||||||
\(770\) | 11.9450 | 0.430466 | ||||||||
\(771\) | −29.2991 | −1.05518 | ||||||||
\(772\) | 110.590 | 3.98023 | ||||||||
\(773\) | −13.5121 | −0.485997 | −0.242998 | − | 0.970027i | \(-0.578131\pi\) | ||||
−0.242998 | + | 0.970027i | \(0.578131\pi\) | |||||||
\(774\) | 4.01184 | 0.144203 | ||||||||
\(775\) | 15.8123 | 0.567996 | ||||||||
\(776\) | −5.92534 | −0.212707 | ||||||||
\(777\) | 4.94181 | 0.177287 | ||||||||
\(778\) | −96.9090 | −3.47436 | ||||||||
\(779\) | −20.2351 | −0.724998 | ||||||||
\(780\) | −101.738 | −3.64280 | ||||||||
\(781\) | −24.8854 | −0.890469 | ||||||||
\(782\) | 6.28046 | 0.224589 | ||||||||
\(783\) | 46.0985 | 1.64743 | ||||||||
\(784\) | −57.1632 | −2.04154 | ||||||||
\(785\) | −35.8697 | −1.28024 | ||||||||
\(786\) | −96.8992 | −3.45628 | ||||||||
\(787\) | 26.2460 | 0.935569 | 0.467784 | − | 0.883843i | \(-0.345052\pi\) | ||||
0.467784 | + | 0.883843i | \(0.345052\pi\) | |||||||
\(788\) | 30.6678 | 1.09250 | ||||||||
\(789\) | 21.0744 | 0.750270 | ||||||||
\(790\) | −19.2213 | −0.683862 | ||||||||
\(791\) | −2.92285 | −0.103924 | ||||||||
\(792\) | −1.78536 | −0.0634400 | ||||||||
\(793\) | −29.9986 | −1.06528 | ||||||||
\(794\) | 2.34274 | 0.0831407 | ||||||||
\(795\) | 69.3262 | 2.45875 | ||||||||
\(796\) | −53.5643 | −1.89854 | ||||||||
\(797\) | −35.9770 | −1.27437 | −0.637185 | − | 0.770711i | \(-0.719901\pi\) | ||||
−0.637185 | + | 0.770711i | \(0.719901\pi\) | |||||||
\(798\) | −16.9713 | −0.600778 | ||||||||
\(799\) | −33.5513 | −1.18696 | ||||||||
\(800\) | −48.2240 | −1.70498 | ||||||||
\(801\) | 1.24287 | 0.0439146 | ||||||||
\(802\) | 69.5438 | 2.45568 | ||||||||
\(803\) | −0.699977 | −0.0247017 | ||||||||
\(804\) | 49.0428 | 1.72961 | ||||||||
\(805\) | 1.15488 | 0.0407041 | ||||||||
\(806\) | −29.7890 | −1.04927 | ||||||||
\(807\) | −44.2793 | −1.55871 | ||||||||
\(808\) | 57.5510 | 2.02464 | ||||||||
\(809\) | 15.6571 | 0.550473 | 0.275236 | − | 0.961377i | \(-0.411244\pi\) | ||||
0.275236 | + | 0.961377i | \(0.411244\pi\) | |||||||
\(810\) | −71.8640 | −2.52504 | ||||||||
\(811\) | 5.90148 | 0.207229 | 0.103614 | − | 0.994618i | \(-0.466959\pi\) | ||||
0.103614 | + | 0.994618i | \(0.466959\pi\) | |||||||
\(812\) | 30.8301 | 1.08193 | ||||||||
\(813\) | 15.5495 | 0.545345 | ||||||||
\(814\) | −19.1607 | −0.671581 | ||||||||
\(815\) | 57.1241 | 2.00097 | ||||||||
\(816\) | −76.4246 | −2.67540 | ||||||||
\(817\) | −59.9243 | −2.09649 | ||||||||
\(818\) | 32.4800 | 1.13564 | ||||||||
\(819\) | 0.392930 | 0.0137301 | ||||||||
\(820\) | −59.9663 | −2.09411 | ||||||||
\(821\) | 31.0639 | 1.08414 | 0.542068 | − | 0.840335i | \(-0.317641\pi\) | ||||
0.542068 | + | 0.840335i | \(0.317641\pi\) | |||||||
\(822\) | 13.2775 | 0.463107 | ||||||||
\(823\) | 27.1781 | 0.947369 | 0.473685 | − | 0.880695i | \(-0.342924\pi\) | ||||
0.473685 | + | 0.880695i | \(0.342924\pi\) | |||||||
\(824\) | 15.8200 | 0.551117 | ||||||||
\(825\) | −17.4468 | −0.607419 | ||||||||
\(826\) | 3.81139 | 0.132615 | ||||||||
\(827\) | −53.9201 | −1.87499 | −0.937493 | − | 0.348004i | \(-0.886859\pi\) | ||||
−0.937493 | + | 0.348004i | \(0.886859\pi\) | |||||||
\(828\) | −0.299269 | −0.0104003 | ||||||||
\(829\) | 51.5068 | 1.78890 | 0.894452 | − | 0.447164i | \(-0.147566\pi\) | ||||
0.894452 | + | 0.447164i | \(0.147566\pi\) | |||||||
\(830\) | 49.3801 | 1.71401 | ||||||||
\(831\) | −30.5430 | −1.05953 | ||||||||
\(832\) | 20.8935 | 0.724352 | ||||||||
\(833\) | 32.7100 | 1.13334 | ||||||||
\(834\) | −57.1555 | −1.97913 | ||||||||
\(835\) | −42.5947 | −1.47405 | ||||||||
\(836\) | 46.2348 | 1.59907 | ||||||||
\(837\) | −15.4715 | −0.534772 | ||||||||
\(838\) | −71.6778 | −2.47607 | ||||||||
\(839\) | −23.2282 | −0.801926 | −0.400963 | − | 0.916094i | \(-0.631324\pi\) | ||||
−0.400963 | + | 0.916094i | \(0.631324\pi\) | |||||||
\(840\) | −29.0090 | −1.00090 | ||||||||
\(841\) | 46.5160 | 1.60400 | ||||||||
\(842\) | −59.6541 | −2.05582 | ||||||||
\(843\) | 25.8899 | 0.891697 | ||||||||
\(844\) | −8.33331 | −0.286844 | ||||||||
\(845\) | −8.10652 | −0.278873 | ||||||||
\(846\) | 2.27536 | 0.0782284 | ||||||||
\(847\) | 5.54658 | 0.190583 | ||||||||
\(848\) | −112.637 | −3.86797 | ||||||||
\(849\) | 46.1621 | 1.58428 | ||||||||
\(850\) | 71.4564 | 2.45094 | ||||||||
\(851\) | −1.85252 | −0.0635035 | ||||||||
\(852\) | 104.780 | 3.58969 | ||||||||
\(853\) | 10.3715 | 0.355114 | 0.177557 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177557 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(854\) | −14.8298 | −0.507465 | ||||||||
\(855\) | −2.20859 | −0.0755322 | ||||||||
\(856\) | 11.8896 | 0.406379 | ||||||||
\(857\) | 6.06354 | 0.207126 | 0.103563 | − | 0.994623i | \(-0.466976\pi\) | ||||
0.103563 | + | 0.994623i | \(0.466976\pi\) | |||||||
\(858\) | 32.8681 | 1.12210 | ||||||||
\(859\) | −41.1329 | −1.40344 | −0.701718 | − | 0.712455i | \(-0.747583\pi\) | ||||
−0.701718 | + | 0.712455i | \(0.747583\pi\) | |||||||
\(860\) | −177.584 | −6.05558 | ||||||||
\(861\) | −4.99660 | −0.170284 | ||||||||
\(862\) | −30.0331 | −1.02293 | ||||||||
\(863\) | 26.8911 | 0.915383 | 0.457691 | − | 0.889111i | \(-0.348676\pi\) | ||||
0.457691 | + | 0.889111i | \(0.348676\pi\) | |||||||
\(864\) | 47.1844 | 1.60525 | ||||||||
\(865\) | 43.0193 | 1.46270 | ||||||||
\(866\) | 46.8388 | 1.59165 | ||||||||
\(867\) | 14.9465 | 0.507611 | ||||||||
\(868\) | −10.3471 | −0.351204 | ||||||||
\(869\) | 4.36318 | 0.148011 | ||||||||
\(870\) | −123.191 | −4.17658 | ||||||||
\(871\) | 24.1381 | 0.817890 | ||||||||
\(872\) | −38.5098 | −1.30411 | ||||||||
\(873\) | −0.111395 | −0.00377014 | ||||||||
\(874\) | 6.36196 | 0.215197 | ||||||||
\(875\) | 1.02194 | 0.0345477 | ||||||||
\(876\) | 2.94725 | 0.0995782 | ||||||||
\(877\) | −16.9538 | −0.572488 | −0.286244 | − | 0.958157i | \(-0.592407\pi\) | ||||
−0.286244 | + | 0.958157i | \(0.592407\pi\) | |||||||
\(878\) | −72.4382 | −2.44467 | ||||||||
\(879\) | −20.9005 | −0.704956 | ||||||||
\(880\) | 54.4882 | 1.83680 | ||||||||
\(881\) | −38.7528 | −1.30561 | −0.652807 | − | 0.757524i | \(-0.726409\pi\) | ||||
−0.652807 | + | 0.757524i | \(0.726409\pi\) | |||||||
\(882\) | −2.21831 | −0.0746944 | ||||||||
\(883\) | −20.7850 | −0.699471 | −0.349736 | − | 0.936848i | \(-0.613729\pi\) | ||||
−0.349736 | + | 0.936848i | \(0.613729\pi\) | |||||||
\(884\) | −94.5868 | −3.18130 | ||||||||
\(885\) | −10.7008 | −0.359705 | ||||||||
\(886\) | 84.4947 | 2.83866 | ||||||||
\(887\) | −24.8321 | −0.833782 | −0.416891 | − | 0.908957i | \(-0.636880\pi\) | ||||
−0.416891 | + | 0.908957i | \(0.636880\pi\) | |||||||
\(888\) | 46.5327 | 1.56154 | ||||||||
\(889\) | 8.33506 | 0.279549 | ||||||||
\(890\) | −78.2989 | −2.62459 | ||||||||
\(891\) | 16.3130 | 0.546505 | ||||||||
\(892\) | −100.913 | −3.37882 | ||||||||
\(893\) | −33.9867 | −1.13732 | ||||||||
\(894\) | −56.2978 | −1.88288 | ||||||||
\(895\) | −9.45720 | −0.316119 | ||||||||
\(896\) | −3.02637 | −0.101104 | ||||||||
\(897\) | 3.17780 | 0.106103 | ||||||||
\(898\) | 38.2069 | 1.27498 | ||||||||
\(899\) | −25.3445 | −0.845285 | ||||||||
\(900\) | −3.40496 | −0.113499 | ||||||||
\(901\) | 64.4533 | 2.14725 | ||||||||
\(902\) | 19.3731 | 0.645053 | ||||||||
\(903\) | −14.7969 | −0.492411 | ||||||||
\(904\) | −27.5219 | −0.915364 | ||||||||
\(905\) | −46.9053 | −1.55918 | ||||||||
\(906\) | −35.3599 | −1.17475 | ||||||||
\(907\) | −24.4876 | −0.813099 | −0.406549 | − | 0.913629i | \(-0.633268\pi\) | ||||
−0.406549 | + | 0.913629i | \(0.633268\pi\) | |||||||
\(908\) | −117.030 | −3.88377 | ||||||||
\(909\) | 1.08194 | 0.0358858 | ||||||||
\(910\) | −24.7540 | −0.820587 | ||||||||
\(911\) | 19.4839 | 0.645530 | 0.322765 | − | 0.946479i | \(-0.395388\pi\) | ||||
0.322765 | + | 0.946479i | \(0.395388\pi\) | |||||||
\(912\) | −77.4164 | −2.56351 | ||||||||
\(913\) | −11.2092 | −0.370969 | ||||||||
\(914\) | 27.2664 | 0.901891 | ||||||||
\(915\) | 41.6361 | 1.37645 | ||||||||
\(916\) | 55.0065 | 1.81746 | ||||||||
\(917\) | −16.5658 | −0.547052 | ||||||||
\(918\) | −69.9159 | −2.30757 | ||||||||
\(919\) | −23.7854 | −0.784609 | −0.392305 | − | 0.919835i | \(-0.628322\pi\) | ||||
−0.392305 | + | 0.919835i | \(0.628322\pi\) | |||||||
\(920\) | 10.8745 | 0.358521 | ||||||||
\(921\) | 18.6281 | 0.613816 | ||||||||
\(922\) | 2.32661 | 0.0766229 | ||||||||
\(923\) | 51.5710 | 1.69748 | ||||||||
\(924\) | 11.4166 | 0.375580 | ||||||||
\(925\) | −21.0772 | −0.693013 | ||||||||
\(926\) | −84.8685 | −2.78895 | ||||||||
\(927\) | 0.297413 | 0.00976831 | ||||||||
\(928\) | 77.2948 | 2.53732 | ||||||||
\(929\) | −21.4773 | −0.704649 | −0.352324 | − | 0.935878i | \(-0.614609\pi\) | ||||
−0.352324 | + | 0.935878i | \(0.614609\pi\) | |||||||
\(930\) | 41.3451 | 1.35576 | ||||||||
\(931\) | 33.1345 | 1.08594 | ||||||||
\(932\) | −22.7985 | −0.746789 | ||||||||
\(933\) | 28.2921 | 0.926241 | ||||||||
\(934\) | 82.5723 | 2.70185 | ||||||||
\(935\) | −31.1793 | −1.01967 | ||||||||
\(936\) | 3.69987 | 0.120934 | ||||||||
\(937\) | −28.1170 | −0.918544 | −0.459272 | − | 0.888296i | \(-0.651890\pi\) | ||||
−0.459272 | + | 0.888296i | \(0.651890\pi\) | |||||||
\(938\) | 11.9327 | 0.389616 | ||||||||
\(939\) | 28.6776 | 0.935859 | ||||||||
\(940\) | −100.719 | −3.28508 | ||||||||
\(941\) | 20.7050 | 0.674962 | 0.337481 | − | 0.941332i | \(-0.390425\pi\) | ||||
0.337481 | + | 0.941332i | \(0.390425\pi\) | |||||||
\(942\) | −48.7923 | −1.58974 | ||||||||
\(943\) | 1.87305 | 0.0609950 | ||||||||
\(944\) | 17.3860 | 0.565868 | ||||||||
\(945\) | −12.8565 | −0.418221 | ||||||||
\(946\) | 57.3715 | 1.86531 | ||||||||
\(947\) | −31.1915 | −1.01359 | −0.506794 | − | 0.862067i | \(-0.669169\pi\) | ||||
−0.506794 | + | 0.862067i | \(0.669169\pi\) | |||||||
\(948\) | −18.3711 | −0.596666 | ||||||||
\(949\) | 1.45059 | 0.0470882 | ||||||||
\(950\) | 72.3838 | 2.34844 | ||||||||
\(951\) | 19.2075 | 0.622847 | ||||||||
\(952\) | −26.9699 | −0.874101 | ||||||||
\(953\) | −45.7916 | −1.48334 | −0.741668 | − | 0.670767i | \(-0.765965\pi\) | ||||
−0.741668 | + | 0.670767i | \(0.765965\pi\) | |||||||
\(954\) | −4.37106 | −0.141518 | ||||||||
\(955\) | −34.5907 | −1.11933 | ||||||||
\(956\) | −3.61354 | −0.116870 | ||||||||
\(957\) | 27.9642 | 0.903953 | ||||||||
\(958\) | −35.3295 | −1.14144 | ||||||||
\(959\) | 2.26992 | 0.0732995 | ||||||||
\(960\) | −28.9988 | −0.935932 | ||||||||
\(961\) | −22.4940 | −0.725612 | ||||||||
\(962\) | 39.7074 | 1.28022 | ||||||||
\(963\) | 0.223522 | 0.00720288 | ||||||||
\(964\) | −68.2211 | −2.19725 | ||||||||
\(965\) | −75.5466 | −2.43193 | ||||||||
\(966\) | 1.57094 | 0.0505442 | ||||||||
\(967\) | 5.94135 | 0.191061 | 0.0955304 | − | 0.995427i | \(-0.469545\pi\) | ||||
0.0955304 | + | 0.995427i | \(0.469545\pi\) | |||||||
\(968\) | 52.2272 | 1.67865 | ||||||||
\(969\) | 44.2994 | 1.42310 | ||||||||
\(970\) | 7.01771 | 0.225325 | ||||||||
\(971\) | −15.4255 | −0.495027 | −0.247513 | − | 0.968884i | \(-0.579613\pi\) | ||||
−0.247513 | + | 0.968884i | \(0.579613\pi\) | |||||||
\(972\) | 6.52179 | 0.209187 | ||||||||
\(973\) | −9.77127 | −0.313253 | ||||||||
\(974\) | 52.4087 | 1.67928 | ||||||||
\(975\) | 36.1556 | 1.15791 | ||||||||
\(976\) | −67.6477 | −2.16535 | ||||||||
\(977\) | −12.2469 | −0.391812 | −0.195906 | − | 0.980623i | \(-0.562765\pi\) | ||||
−0.195906 | + | 0.980623i | \(0.562765\pi\) | |||||||
\(978\) | 77.7040 | 2.48470 | ||||||||
\(979\) | 17.7737 | 0.568049 | ||||||||
\(980\) | 98.1935 | 3.13668 | ||||||||
\(981\) | −0.723974 | −0.0231147 | ||||||||
\(982\) | 3.48788 | 0.111303 | ||||||||
\(983\) | −29.3212 | −0.935202 | −0.467601 | − | 0.883940i | \(-0.654882\pi\) | ||||
−0.467601 | + | 0.883940i | \(0.654882\pi\) | |||||||
\(984\) | −47.0486 | −1.49985 | ||||||||
\(985\) | −20.9498 | −0.667517 | ||||||||
\(986\) | −114.532 | −3.64745 | ||||||||
\(987\) | −8.39224 | −0.267128 | ||||||||
\(988\) | −95.8143 | −3.04826 | ||||||||
\(989\) | 5.54687 | 0.176380 | ||||||||
\(990\) | 2.11450 | 0.0672033 | ||||||||
\(991\) | 16.4889 | 0.523788 | 0.261894 | − | 0.965097i | \(-0.415653\pi\) | ||||
0.261894 | + | 0.965097i | \(0.415653\pi\) | |||||||
\(992\) | −25.9414 | −0.823642 | ||||||||
\(993\) | 53.9497 | 1.71204 | ||||||||
\(994\) | 25.4941 | 0.808624 | ||||||||
\(995\) | 36.5909 | 1.16001 | ||||||||
\(996\) | 47.1961 | 1.49546 | ||||||||
\(997\) | −38.7685 | −1.22781 | −0.613905 | − | 0.789380i | \(-0.710402\pi\) | ||||
−0.613905 | + | 0.789380i | \(0.710402\pi\) | |||||||
\(998\) | −37.2128 | −1.17795 | ||||||||
\(999\) | 20.6228 | 0.652476 |
(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 | 4019.2.a.b.1.11 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.11 | ✓ | 186 | 1.1 | even | 1 | trivial |