Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.62538 | −0.938415 | −0.469208 | − | 0.883088i | \(-0.655460\pi\) | ||||
−0.469208 | + | 0.883088i | \(0.655460\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.42157 | 1.67120 | 0.835599 | − | 0.549340i | \(-0.185121\pi\) | ||||
0.835599 | + | 0.549340i | \(0.185121\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.358130 | −0.119377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.81850 | −0.548297 | −0.274149 | − | 0.961687i | \(-0.588396\pi\) | ||||
−0.274149 | + | 0.961687i | \(0.588396\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.06376 | −0.295033 | −0.147517 | − | 0.989060i | \(-0.547128\pi\) | ||||
−0.147517 | + | 0.989060i | \(0.547128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.62538 | 0.419672 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.23283 | −0.299004 | −0.149502 | − | 0.988761i | \(-0.547767\pi\) | ||||
−0.149502 | + | 0.988761i | \(0.547767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.12363 | 0.946024 | 0.473012 | − | 0.881056i | \(-0.343167\pi\) | ||||
0.473012 | + | 0.881056i | \(0.343167\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.18675 | −1.56828 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.61525 | −0.962345 | −0.481173 | − | 0.876626i | \(-0.659789\pi\) | ||||
−0.481173 | + | 0.876626i | \(0.659789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.45825 | 1.05044 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.847315 | 0.157342 | 0.0786712 | − | 0.996901i | \(-0.474932\pi\) | ||||
0.0786712 | + | 0.996901i | \(0.474932\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.697606 | −0.125294 | −0.0626469 | − | 0.998036i | \(-0.519954\pi\) | ||||
−0.0626469 | + | 0.998036i | \(0.519954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.95575 | 0.514531 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.42157 | −0.747382 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.45352 | 0.567755 | 0.283877 | − | 0.958861i | \(-0.408379\pi\) | ||||
0.283877 | + | 0.958861i | \(0.408379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.72901 | 0.276864 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.20797 | −0.501001 | −0.250500 | − | 0.968116i | \(-0.580595\pi\) | ||||
−0.250500 | + | 0.968116i | \(0.580595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5027 | −1.60164 | −0.800820 | − | 0.598905i | \(-0.795603\pi\) | ||||
−0.800820 | + | 0.598905i | \(0.795603\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.358130 | 0.0533869 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.77104 | 0.695928 | 0.347964 | − | 0.937508i | \(-0.386873\pi\) | ||||
0.347964 | + | 0.937508i | \(0.386873\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.5503 | 1.79290 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00381 | 0.280590 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.05860 | 0.420131 | 0.210066 | − | 0.977687i | \(-0.432632\pi\) | ||||
0.210066 | + | 0.977687i | \(0.432632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.81850 | 0.245206 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.70247 | −0.887764 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5261 | −1.37038 | −0.685191 | − | 0.728364i | \(-0.740281\pi\) | ||||
−0.685191 | + | 0.728364i | \(0.740281\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.43455 | 1.20797 | 0.603985 | − | 0.796996i | \(-0.293579\pi\) | ||||
0.603985 | + | 0.796996i | \(0.293579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.58350 | −0.199502 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.06376 | 0.131943 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.76942 | 0.582677 | 0.291339 | − | 0.956620i | \(-0.405899\pi\) | ||||
0.291339 | + | 0.956620i | \(0.405899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.50154 | 0.903080 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.533751 | 0.0633446 | 0.0316723 | − | 0.999498i | \(-0.489917\pi\) | ||||
0.0316723 | + | 0.999498i | \(0.489917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.64125 | −0.894341 | −0.447171 | − | 0.894449i | \(-0.647568\pi\) | ||||
−0.447171 | + | 0.894449i | \(0.647568\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.62538 | −0.187683 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.04062 | −0.916313 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.62077 | −1.08242 | −0.541210 | − | 0.840887i | \(-0.682034\pi\) | ||||
−0.541210 | + | 0.840887i | \(0.682034\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.79735 | −0.866372 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.01040 | −0.659727 | −0.329864 | − | 0.944029i | \(-0.607003\pi\) | ||||
−0.329864 | + | 0.944029i | \(0.607003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.23283 | 0.133719 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.37721 | −0.147653 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.21176 | −0.658445 | −0.329222 | − | 0.944252i | \(-0.606787\pi\) | ||||
−0.329222 | + | 0.944252i | \(0.606787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.70348 | −0.493059 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.13388 | 0.117578 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.12363 | −0.423075 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6850 | 1.28797 | 0.643984 | − | 0.765039i | \(-0.277280\pi\) | ||||
0.643984 | + | 0.765039i | \(0.277280\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.651259 | 0.0654540 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.56613 | −0.951865 | −0.475933 | − | 0.879482i | \(-0.657889\pi\) | ||||
−0.475933 | + | 0.879482i | \(0.657889\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.56470 | −0.942438 | −0.471219 | − | 0.882016i | \(-0.656186\pi\) | ||||
−0.471219 | + | 0.882016i | \(0.656186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.18675 | 0.701355 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.77911 | 0.655361 | 0.327681 | − | 0.944789i | \(-0.393733\pi\) | ||||
0.327681 | + | 0.944789i | \(0.393733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.53790 | 0.530435 | 0.265217 | − | 0.964189i | \(-0.414556\pi\) | ||||
0.265217 | + | 0.964189i | \(0.414556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.61329 | −0.532790 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.2741 | −1.53094 | −0.765471 | − | 0.643470i | \(-0.777494\pi\) | ||||
−0.765471 | + | 0.643470i | \(0.777494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.61525 | 0.430374 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.380964 | 0.0352201 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.45103 | −0.499695 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.69307 | −0.699370 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.21418 | 0.470147 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.53521 | −0.136228 | −0.0681140 | − | 0.997678i | \(-0.521698\pi\) | ||||
−0.0681140 | + | 0.997678i | \(0.521698\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.0708 | 1.50300 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.1128 | 1.49515 | 0.747576 | − | 0.664176i | \(-0.231218\pi\) | ||||
0.747576 | + | 0.664176i | \(0.231218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.2329 | 1.58099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.45825 | −0.469771 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.8091 | 1.77784 | 0.888920 | − | 0.458062i | \(-0.151456\pi\) | ||||
0.888920 | + | 0.458062i | \(0.151456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.51691 | 0.128662 | 0.0643312 | − | 0.997929i | \(-0.479509\pi\) | ||||
0.0643312 | + | 0.997929i | \(0.479509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.75477 | −0.653069 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.93444 | 0.161766 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.847315 | −0.0703657 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.3991 | −1.68249 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.4601 | 1.84000 | 0.920000 | − | 0.391919i | \(-0.128189\pi\) | ||||
0.920000 | + | 0.391919i | \(0.128189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.6913 | 1.60245 | 0.801227 | − | 0.598360i | \(-0.204181\pi\) | ||||
0.801227 | + | 0.598360i | \(0.204181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.441512 | 0.0356942 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.697606 | 0.0560331 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.04837 | 0.163478 | 0.0817388 | − | 0.996654i | \(-0.473953\pi\) | ||||
0.0817388 | + | 0.996654i | \(0.473953\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.97140 | −0.394258 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.4067 | −1.60827 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.99410 | −0.312842 | −0.156421 | − | 0.987690i | \(-0.549996\pi\) | ||||
−0.156421 | + | 0.987690i | \(0.549996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.95575 | −0.230105 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3495 | −1.18778 | −0.593889 | − | 0.804547i | \(-0.702408\pi\) | ||||
−0.593889 | + | 0.804547i | \(0.702408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8684 | −0.912955 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.47680 | −0.112933 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.3080 | −1.84810 | −0.924051 | − | 0.382270i | \(-0.875143\pi\) | ||||
−0.924051 | + | 0.382270i | \(0.875143\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.42157 | 0.334240 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.1089 | 1.28599 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.21931 | 0.390110 | 0.195055 | − | 0.980792i | \(-0.437512\pi\) | ||||
0.195055 | + | 0.980792i | \(0.437512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.44881 | 0.553666 | 0.276833 | − | 0.960918i | \(-0.410715\pi\) | ||||
0.276833 | + | 0.960918i | \(0.410715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.3347 | −1.13358 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.45352 | −0.253908 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24189 | 0.163943 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.1340 | 1.75549 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4691 | −0.757515 | −0.378757 | − | 0.925496i | \(-0.623649\pi\) | ||||
−0.378757 | + | 0.925496i | \(0.623649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.75123 | 0.198038 | 0.0990189 | − | 0.995086i | \(-0.468430\pi\) | ||||
0.0990189 | + | 0.995086i | \(0.468430\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.72901 | −0.123817 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.62752 | 0.115956 | 0.0579781 | − | 0.998318i | \(-0.481535\pi\) | ||||
0.0579781 | + | 0.998318i | \(0.481535\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7008 | −1.25477 | −0.627387 | − | 0.778707i | \(-0.715876\pi\) | ||||
−0.627387 | + | 0.778707i | \(0.715876\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.75213 | −0.546793 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.74647 | 0.262950 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.20797 | 0.224054 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.65286 | 0.114882 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.49880 | −0.518703 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.62214 | 0.593573 | 0.296786 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296786 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.867550 | −0.0594435 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.5027 | 0.716276 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.08452 | −0.209391 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.4200 | 0.839263 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.31143 | 0.0882162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0986 | 0.810185 | 0.405092 | − | 0.914276i | \(-0.367239\pi\) | ||||
0.405092 | + | 0.914276i | \(0.367239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.358130 | −0.0238754 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.8451 | −1.78177 | −0.890887 | − | 0.454226i | \(-0.849916\pi\) | ||||
−0.890887 | + | 0.454226i | \(0.849916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.38780 | −0.488200 | −0.244100 | − | 0.969750i | \(-0.578492\pi\) | ||||
−0.244100 | + | 0.969750i | \(0.578492\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.0691 | 0.859882 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.1908 | −1.38825 | −0.694127 | − | 0.719853i | \(-0.744209\pi\) | ||||
−0.694127 | + | 0.719853i | \(0.744209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.77104 | −0.311228 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.6374 | 1.01576 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.29768 | 0.342678 | 0.171339 | − | 0.985212i | \(-0.445191\pi\) | ||||
0.171339 | + | 0.985212i | \(0.445191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.28096 | 0.340177 | 0.170088 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170088 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.70106 | −0.237423 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.5503 | −0.801810 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.38654 | −0.279109 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.76920 | 0.619098 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.21532 | 0.329188 | 0.164594 | − | 0.986361i | \(-0.447369\pi\) | ||||
0.164594 | + | 0.986361i | \(0.447369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.39281 | 0.527651 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00381 | −0.125484 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.33349 | −0.519829 | −0.259914 | − | 0.965632i | \(-0.583694\pi\) | ||||
−0.259914 | + | 0.965632i | \(0.583694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.2700 | 0.948831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.303449 | −0.0187830 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9773 | 0.985203 | 0.492601 | − | 0.870255i | \(-0.336046\pi\) | ||||
0.492601 | + | 0.870255i | \(0.336046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.05860 | −0.187888 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0965 | 0.617895 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.74626 | 0.228413 | 0.114207 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114207 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8456 | −0.841060 | −0.420530 | − | 0.907279i | \(-0.638156\pi\) | ||||
−0.420530 | + | 0.907279i | \(0.638156\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.64496 | 0.462694 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.81850 | −0.109659 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.46676 | 0.0881289 | 0.0440645 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440645 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.249834 | 0.0149572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.0767 | −1.73457 | −0.867284 | − | 0.497813i | \(-0.834136\pi\) | ||||
−0.867284 | + | 0.497813i | \(0.834136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6843 | 1.52678 | 0.763388 | − | 0.645941i | \(-0.223535\pi\) | ||||
0.763388 | + | 0.645941i | \(0.223535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.70247 | 0.397020 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.1843 | −0.837272 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4801 | −0.910597 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.6180 | −1.20865 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.96190 | 0.348298 | 0.174149 | − | 0.984719i | \(-0.444283\pi\) | ||||
0.174149 | + | 0.984719i | \(0.444283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5261 | 0.612853 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.92581 | −0.575954 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.90950 | 0.283924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.4383 | −2.67666 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.5486 | 0.893245 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.43455 | −0.540220 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.14528 | −0.293656 | −0.146828 | − | 0.989162i | \(-0.546906\pi\) | ||||
−0.146828 | + | 0.989162i | \(0.546906\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5463 | 0.884399 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.26295 | 0.0716154 | 0.0358077 | − | 0.999359i | \(-0.488600\pi\) | ||||
0.0358077 | + | 0.999359i | \(0.488600\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8392 | 0.782239 | 0.391120 | − | 0.920340i | \(-0.372088\pi\) | ||||
0.391120 | + | 0.920340i | \(0.372088\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.58350 | 0.0892201 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.93169 | 0.276991 | 0.138496 | − | 0.990363i | \(-0.455773\pi\) | ||||
0.138496 | + | 0.990363i | \(0.455773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.54084 | −0.0862704 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0186 | −0.615001 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.08371 | −0.282865 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.06376 | −0.0590067 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.00121 | −0.497768 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.0955 | 1.16303 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4049 | −0.571908 | −0.285954 | − | 0.958243i | \(-0.592310\pi\) | ||||
−0.285954 | + | 0.958243i | \(0.592310\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.23681 | −0.0677768 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.76942 | −0.260581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.0621 | −1.36522 | −0.682610 | − | 0.730783i | \(-0.739155\pi\) | ||||
−0.682610 | + | 0.730783i | \(0.739155\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.4517 | 1.43666 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.26859 | 0.0686983 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.5411 | 1.32510 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.50154 | −0.403870 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.8943 | 0.745887 | 0.372943 | − | 0.927854i | \(-0.378349\pi\) | ||||
0.372943 | + | 0.927854i | \(0.378349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8128 | −0.632327 | −0.316163 | − | 0.948705i | \(-0.602395\pi\) | ||||
−0.316163 | + | 0.948705i | \(0.602395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.80625 | −0.309915 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.2525 | −0.971485 | −0.485743 | − | 0.874102i | \(-0.661451\pi\) | ||||
−0.485743 | + | 0.874102i | \(0.661451\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.533751 | −0.0283286 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.86001 | 0.468921 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.0793 | −1.48197 | −0.740986 | − | 0.671521i | \(-0.765641\pi\) | ||||
−0.740986 | + | 0.671521i | \(0.765641\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.99572 | −0.105038 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.5042 | 0.656299 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.64125 | 0.399961 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.686369 | 0.0358282 | 0.0179141 | − | 0.999840i | \(-0.494297\pi\) | ||||
0.0179141 | + | 0.999840i | \(0.494297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.14887 | 0.0598079 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5238 | 0.702123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.58581 | −0.289222 | −0.144611 | − | 0.989489i | \(-0.546193\pi\) | ||||
−0.144611 | + | 0.989489i | \(0.546193\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.62538 | 0.0839344 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.901338 | −0.0464213 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.47553 | −0.486726 | −0.243363 | − | 0.969935i | \(-0.578251\pi\) | ||||
−0.243363 | + | 0.969935i | \(0.578251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.49531 | 0.127838 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.02327 | 0.154482 | 0.0772409 | − | 0.997012i | \(-0.475389\pi\) | ||||
0.0772409 | + | 0.997012i | \(0.475389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.04062 | 0.409788 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.76132 | 0.191199 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.8063 | −1.00422 | −0.502109 | − | 0.864804i | \(-0.667442\pi\) | ||||
−0.502109 | + | 0.864804i | \(0.667442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.68979 | 0.287745 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.8148 | −1.40307 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.62077 | 0.484073 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.0475 | −1.15672 | −0.578362 | − | 0.815781i | \(-0.696308\pi\) | ||||
−0.578362 | + | 0.815781i | \(0.696308\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −29.6355 | −1.48363 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.742084 | 0.0369658 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.79735 | 0.387454 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.28021 | −0.311299 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.1460 | −1.44118 | −0.720588 | − | 0.693363i | \(-0.756128\pi\) | ||||
−0.720588 | + | 0.693363i | \(0.756128\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.8227 | −1.66835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −46.5419 | −2.29018 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.01040 | 0.295039 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.46556 | −0.120739 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.2572 | −0.501096 | −0.250548 | − | 0.968104i | \(-0.580611\pi\) | ||||
−0.250548 | + | 0.968104i | \(0.580611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.67406 | −0.0815889 | −0.0407945 | − | 0.999168i | \(-0.512989\pi\) | ||||
−0.0407945 | + | 0.999168i | \(0.512989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.70865 | −0.0830776 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.23283 | −0.0598008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.7155 | 2.01876 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.14421 | −0.151804 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7069 | −1.19009 | −0.595045 | − | 0.803692i | \(-0.702866\pi\) | ||||
−0.595045 | + | 0.803692i | \(0.702866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4314 | 1.51049 | 0.755247 | − | 0.655440i | \(-0.227517\pi\) | ||||
0.755247 | + | 0.655440i | \(0.227517\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.37721 | 0.0660322 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.0315 | −0.910402 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9372 | −0.712914 | −0.356457 | − | 0.934312i | \(-0.616015\pi\) | ||||
−0.356457 | + | 0.934312i | \(0.616015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.49465 | −0.214031 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.673491 | 0.0319985 | 0.0159993 | − | 0.999872i | \(-0.494907\pi\) | ||||
0.0159993 | + | 0.999872i | \(0.494907\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.21176 | 0.294466 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.5062 | −1.72668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.62968 | −0.407260 | −0.203630 | − | 0.979048i | \(-0.565274\pi\) | ||||
−0.203630 | + | 0.979048i | \(0.565274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.83368 | 0.274697 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.0059 | −1.50377 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.70348 | 0.220503 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.5412 | −1.42866 | −0.714329 | − | 0.699810i | \(-0.753268\pi\) | ||||
−0.714329 | + | 0.699810i | \(0.753268\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.72907 | −0.314086 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.8363 | −0.970444 | −0.485222 | − | 0.874391i | \(-0.661261\pi\) | ||||
−0.485222 | + | 0.874391i | \(0.661261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9447 | 0.555118 | 0.277559 | − | 0.960709i | \(-0.410475\pi\) | ||||
0.277559 | + | 0.960709i | \(0.410475\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.13388 | −0.0525823 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9025 | −0.967253 | −0.483627 | − | 0.875274i | \(-0.660681\pi\) | ||||
−0.483627 | + | 0.875274i | \(0.660681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0883 | 0.973769 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.32938 | −0.153410 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.0991 | 0.878175 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.12363 | 0.189205 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.09538 | −0.0501539 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.5391 | 1.30398 | 0.651992 | − | 0.758226i | \(-0.273934\pi\) | ||||
0.651992 | + | 0.758226i | \(0.273934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.67371 | −0.167507 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 33.1686 | 1.50922 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.6850 | −0.575997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1344 | 1.13895 | 0.569473 | − | 0.822010i | \(-0.307147\pi\) | ||||
0.569473 | + | 0.822010i | \(0.307147\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.49194 | 0.293576 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.2133 | −1.95019 | −0.975093 | − | 0.221794i | \(-0.928809\pi\) | ||||
−0.975093 | + | 0.221794i | \(0.928809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.04459 | −0.0470460 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.651259 | −0.0292719 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.36002 | 0.105861 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.2184 | 1.35276 | 0.676381 | − | 0.736552i | \(-0.263547\pi\) | ||||
0.676381 | + | 0.736552i | \(0.263547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.9488 | 1.11463 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.5662 | −1.09535 | −0.547676 | − | 0.836690i | \(-0.684488\pi\) | ||||
−0.547676 | + | 0.836690i | \(0.684488\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.56613 | 0.425687 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.2907 | 0.856731 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.2824 | −0.633057 | −0.316529 | − | 0.948583i | \(-0.602517\pi\) | ||||
−0.316529 | + | 0.948583i | \(0.602517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.7864 | −1.49462 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.5078 | 0.993742 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.56470 | 0.421471 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.67612 | −0.381575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.5098 | 1.73429 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8306 | −1.26309 | −0.631545 | − | 0.775339i | \(-0.717579\pi\) | ||||
−0.631545 | + | 0.775339i | \(0.717579\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7614 | 1.12647 | 0.563234 | − | 0.826297i | \(-0.309557\pi\) | ||||
0.563234 | + | 0.826297i | \(0.309557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.18675 | −0.313656 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.860027 | 0.0374634 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.69950 | −0.0738912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.76972 | 0.163592 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.41250 | 0.147812 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.77911 | −0.293086 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.48338 | −0.366085 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.8227 | −0.983044 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.2832 | −1.25898 | −0.629492 | − | 0.777007i | \(-0.716737\pi\) | ||||
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.1072 | −0.519568 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.53790 | −0.237218 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.2524 | −0.823175 | −0.411587 | − | 0.911370i | \(-0.635025\pi\) | ||||
−0.411587 | + | 0.911370i | \(0.635025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.37880 | −0.144204 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.49401 | 0.148850 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −42.5389 | −1.80894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.61329 | 0.238271 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8252 | 0.628162 | 0.314081 | − | 0.949396i | \(-0.398304\pi\) | ||||
0.314081 | + | 0.949396i | \(0.398304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1723 | 0.472537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.64393 | −0.153847 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.0922 | −0.551770 | −0.275885 | − | 0.961191i | \(-0.588971\pi\) | ||||
−0.275885 | + | 0.961191i | \(0.588971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.2741 | 0.684658 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −34.4766 | −1.44788 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.4256 | 0.898207 | 0.449104 | − | 0.893480i | \(-0.351743\pi\) | ||||
0.449104 | + | 0.893480i | \(0.351743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6522 | 0.613175 | 0.306587 | − | 0.951843i | \(-0.400813\pi\) | ||||
0.306587 | + | 0.951843i | \(0.400813\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.0162 | 0.710863 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.61525 | −0.192469 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.21697 | −0.217185 | −0.108593 | − | 0.994086i | \(-0.534634\pi\) | ||||
−0.108593 | + | 0.994086i | \(0.534634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.47180 | −0.185842 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.5754 | −1.10253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.56206 | −0.230357 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.380964 | −0.0157509 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.5655 | 1.50922 | 0.754611 | − | 0.656173i | \(-0.227826\pi\) | ||||
0.754611 | + | 0.656173i | \(0.227826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.87667 | −0.118531 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.64535 | −0.108815 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.1765 | −1.36239 | −0.681197 | − | 0.732100i | \(-0.738540\pi\) | ||||
−0.681197 | + | 0.732100i | \(0.738540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.45103 | 0.223470 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.7705 | 1.17750 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.54284 | −0.389910 | −0.194955 | − | 0.980812i | \(-0.562456\pi\) | ||||
−0.194955 | + | 0.980812i | \(0.562456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.3137 | −1.48127 | −0.740634 | − | 0.671909i | \(-0.765475\pi\) | ||||
−0.740634 | + | 0.671909i | \(0.765475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.70807 | −0.0695581 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.69307 | 0.312768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7975 | −0.925321 | −0.462660 | − | 0.886536i | \(-0.653105\pi\) | ||||
−0.462660 | + | 0.886536i | \(0.653105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.08944 | −0.246757 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.07523 | −0.205322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7378 | −0.595254 | −0.297627 | − | 0.954682i | \(-0.596195\pi\) | ||||
−0.297627 | + | 0.954682i | \(0.596195\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.21418 | −0.210256 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0465 | 0.404456 | 0.202228 | − | 0.979338i | \(-0.435182\pi\) | ||||
0.202228 | + | 0.979338i | \(0.435182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.3237 | −1.66094 | −0.830469 | − | 0.557065i | \(-0.811928\pi\) | ||||
−0.830469 | + | 0.557065i | \(0.811928\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.1912 | −1.01089 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.4657 | −1.10039 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.1884 | 0.486759 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.25759 | −0.169761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4599 | 1.29221 | 0.646105 | − | 0.763249i | \(-0.276397\pi\) | ||||
0.646105 | + | 0.763249i | \(0.276397\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0143 | −0.557018 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.53521 | 0.0609230 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.3505 | −0.528966 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.191152 | −0.00756187 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.29789 | −0.130259 | −0.0651293 | − | 0.997877i | \(-0.520746\pi\) | ||||
−0.0651293 | + | 0.997877i | \(0.520746\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.89098 | −0.271754 | −0.135877 | − | 0.990726i | \(-0.543385\pi\) | ||||
−0.135877 | + | 0.990726i | \(0.543385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.0708 | −0.672164 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.35604 | −0.328510 | −0.164255 | − | 0.986418i | \(-0.552522\pi\) | ||||
−0.164255 | + | 0.986418i | \(0.552522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.1417 | 0.751376 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.01352 | 0.196495 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.1612 | 1.33683 | 0.668416 | − | 0.743788i | \(-0.266973\pi\) | ||||
0.668416 | + | 0.743788i | \(0.266973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1128 | −0.668652 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.73656 | 0.106764 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.9226 | 0.776074 | 0.388037 | − | 0.921644i | \(-0.373153\pi\) | ||||
0.388037 | + | 0.921644i | \(0.373153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.8320 | 1.62708 | 0.813539 | − | 0.581511i | \(-0.197538\pi\) | ||||
0.813539 | + | 0.581511i | \(0.197538\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.13157 | −0.0827834 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.2329 | −0.707042 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.91057 | −0.151418 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.6649 | −0.760290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.1567 | −0.662327 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.82606 | −0.224578 | −0.112289 | − | 0.993676i | \(-0.535818\pi\) | ||||
−0.112289 | + | 0.993676i | \(0.535818\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.45825 | 0.210088 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8212 | −0.531193 | −0.265596 | − | 0.964084i | \(-0.585569\pi\) | ||||
−0.265596 | + | 0.964084i | \(0.585569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 56.0877 | 2.15245 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.6336 | 1.67204 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.57951 | −0.213494 | −0.106747 | − | 0.994286i | \(-0.534043\pi\) | ||||
−0.106747 | + | 0.994286i | \(0.534043\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.8091 | −0.795075 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.0080 | 0.458134 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.25361 | −0.123953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.4727 | −1.53965 | −0.769826 | − | 0.638254i | \(-0.779657\pi\) | ||||
−0.769826 | + | 0.638254i | \(0.779657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.87959 | 0.109387 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.51691 | −0.0575396 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.95487 | 0.149801 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.4431 | 1.30276 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7507 | −0.745975 | −0.372987 | − | 0.927836i | \(-0.621666\pi\) | ||||
−0.372987 | + | 0.927836i | \(0.621666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.2410 | 0.537110 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.75477 | 0.292061 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −42.2973 | −1.59076 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.3283 | −0.951222 | −0.475611 | − | 0.879656i | \(-0.657773\pi\) | ||||
−0.475611 | + | 0.879656i | \(0.657773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.44549 | 0.129216 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.21963 | 0.120576 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.93444 | −0.0723440 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.61075 | −0.321574 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.17722 | −0.267665 | −0.133833 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133833 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.2910 | −1.57500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.58359 | −0.319227 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.847315 | 0.0314685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7846 | 1.03047 | 0.515237 | − | 0.857048i | \(-0.327704\pi\) | ||||
0.515237 | + | 0.857048i | \(0.327704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.4077 | 1.08917 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.9479 | 0.478897 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5720 | −0.870653 | −0.435327 | − | 0.900273i | \(-0.643367\pi\) | ||||
−0.435327 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.3991 | 0.752431 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.67317 | −0.319480 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.1819 | −1.77240 | −0.886200 | − | 0.463303i | \(-0.846664\pi\) | ||||
−0.886200 | + | 0.463303i | \(0.846664\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.12980 | 0.261920 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9637 | 0.915830 | 0.457915 | − | 0.888996i | \(-0.348596\pi\) | ||||
0.457915 | + | 0.888996i | \(0.348596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.4601 | −0.822873 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.15251 | 0.0787561 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.9743 | 1.09524 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.31934 | −0.121125 | −0.0605623 | − | 0.998164i | \(-0.519289\pi\) | ||||
−0.0605623 | + | 0.998164i | \(0.519289\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.47690 | −0.308915 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.6913 | −0.716640 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4811 | 1.07151 | 0.535754 | − | 0.844374i | \(-0.320028\pi\) | ||||
0.535754 | + | 0.844374i | \(0.320028\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.6415 | −0.495156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.4559 | −0.632777 | −0.316388 | − | 0.948630i | \(-0.602470\pi\) | ||||
−0.316388 | + | 0.948630i | \(0.602470\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.4863 | 0.886462 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.441512 | −0.0159629 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1972 | 0.404308 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.1727 | 0.655325 | 0.327662 | − | 0.944795i | \(-0.393739\pi\) | ||||
0.327662 | + | 0.944795i | \(0.393739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.5451 | 0.487815 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.8354 | 1.21697 | 0.608487 | − | 0.793564i | \(-0.291777\pi\) | ||||
0.608487 | + | 0.793564i | \(0.291777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.697606 | −0.0250588 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.8196 | −0.890397 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.2285 | −0.473959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.970624 | −0.0347317 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.62485 | 0.165279 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.04837 | −0.0731094 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.92229 | 0.353692 | 0.176846 | − | 0.984239i | \(-0.443411\pi\) | ||||
0.176846 | + | 0.984239i | \(0.443411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.9692 | −0.924529 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −71.9573 | −2.55851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0361 | −0.356391 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.97140 | 0.176317 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.2666 | −1.00126 | −0.500628 | − | 0.865663i | \(-0.666897\pi\) | ||||
−0.500628 | + | 0.865663i | \(0.666897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.88186 | −0.208085 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.22462 | 0.0786030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.8956 | 0.490365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.4067 | 0.719240 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.08910 | −0.214346 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.7494 | −1.39752 | −0.698758 | − | 0.715358i | \(-0.746264\pi\) | ||||
−0.698758 | + | 0.715358i | \(0.746264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.60060 | 0.196664 | 0.0983319 | − | 0.995154i | \(-0.468649\pi\) | ||||
0.0983319 | + | 0.995154i | \(0.468649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.5044 | 0.789264 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.99410 | 0.139907 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.3090 | −1.51519 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.68446 | 0.0588598 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.6542 | −1.03494 | −0.517469 | − | 0.855702i | \(-0.673126\pi\) | ||||
−0.517469 | + | 0.855702i | \(0.673126\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4945 | −0.435531 | −0.217765 | − | 0.976001i | \(-0.569877\pi\) | ||||
−0.217765 | + | 0.976001i | \(0.569877\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.95575 | 0.102906 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.2840 | −1.15740 | −0.578700 | − | 0.815541i | \(-0.696440\pi\) | ||||
−0.578700 | + | 0.815541i | \(0.696440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.0337 | −1.14731 | −0.573654 | − | 0.819098i | \(-0.694474\pi\) | ||||
−0.573654 | + | 0.819098i | \(0.694474\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.38404 | −0.0827015 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.4723 | −0.536085 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.3495 | 0.531191 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.80771 | −0.131614 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.3786 | −0.807120 | −0.403560 | − | 0.914953i | \(-0.632227\pi\) | ||||
−0.403560 | + | 0.914953i | \(0.632227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2821 | −0.975243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.2607 | 1.62775 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.8684 | 0.408286 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.0155 | −1.16879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.7469 | −1.43275 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.9388 | −0.546376 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.9431 | 1.12795 | 0.563975 | − | 0.825792i | \(-0.309271\pi\) | ||||
0.563975 | + | 0.825792i | \(0.309271\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.47680 | 0.0505053 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.72706 | 0.263951 | 0.131976 | − | 0.991253i | \(-0.457868\pi\) | ||||
0.131976 | + | 0.991253i | \(0.457868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8310 | −0.744863 | −0.372431 | − | 0.928060i | \(-0.621476\pi\) | ||||
−0.372431 | + | 0.928060i | \(0.621476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.0549 | 0.785709 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.3905 | −0.830263 | −0.415131 | − | 0.909761i | \(-0.636264\pi\) | ||||
−0.415131 | + | 0.909761i | \(0.636264\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.3080 | 0.826496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.1612 | 0.854518 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.4953 | 0.593489 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.07350 | −0.171909 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.54289 | −0.153753 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.42157 | −0.149476 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.89927 | −0.199204 | −0.0996021 | − | 0.995027i | \(-0.531757\pi\) | ||||
−0.0996021 | + | 0.995027i | \(0.531757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.69038 | −0.326848 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.9087 | 0.569668 | 0.284834 | − | 0.958577i | \(-0.408061\pi\) | ||||
0.284834 | + | 0.958577i | \(0.408061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9248 | 0.906091 | 0.453046 | − | 0.891487i | \(-0.350337\pi\) | ||||
0.453046 | + | 0.891487i | \(0.350337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.1089 | −0.575111 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.5378 | 1.19324 | 0.596621 | − | 0.802523i | \(-0.296510\pi\) | ||||
0.596621 | + | 0.802523i | \(0.296510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.78805 | −0.227664 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.1795 | 0.475030 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.6740 | 0.658365 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.21931 | −0.174462 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.97982 | −0.266439 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.591092 | −0.0197140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.77072 | −0.125621 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 75.4800 | 2.51182 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.44881 | −0.247607 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.02937 | 0.0341796 | 0.0170898 | − | 0.999854i | \(-0.494560\pi\) | ||||
0.0170898 | + | 0.999854i | \(0.494560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.42592 | 0.113631 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.9038 | 0.493785 | 0.246893 | − | 0.969043i | \(-0.420591\pi\) | ||||
0.246893 | + | 0.969043i | \(0.420591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9299 | 0.361727 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.3347 | 0.506951 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 75.6655 | 2.49869 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.36916 | −0.276073 | −0.138037 | − | 0.990427i | \(-0.544079\pi\) | ||||
−0.138037 | + | 0.990427i | \(0.544079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.36305 | 0.275572 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.567782 | −0.0186888 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.45352 | 0.113551 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.42541 | 0.112505 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.9155 | −1.44082 | −0.720410 | − | 0.693548i | \(-0.756046\pi\) | ||||
−0.720410 | + | 0.693548i | \(0.756046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.7528 | 1.69613 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.05278 | −0.0672049 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.24189 | −0.0733176 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.5033 | 1.38852 | 0.694261 | − | 0.719724i | \(-0.255731\pi\) | ||||
0.694261 | + | 0.719724i | \(0.255731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4940 | −0.734065 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.9326 | −0.649783 | −0.324891 | − | 0.945751i | \(-0.605328\pi\) | ||||
−0.324891 | + | 0.945751i | \(0.605328\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.8056 | 0.482136 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.1340 | −0.785081 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.7373 | −1.29129 | −0.645644 | − | 0.763639i | \(-0.723411\pi\) | ||||
−0.645644 | + | 0.763639i | \(0.723411\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.12844 | 0.263860 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.01589 | −0.259933 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.10032 | 0.197609 | 0.0988044 | − | 0.995107i | \(-0.468498\pi\) | ||||
0.0988044 | + | 0.995107i | \(0.468498\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4691 | 0.338771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.50445 | 0.0809575 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 92.0089 | 2.97112 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5133 | −0.984301 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.42781 | −0.0782349 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.75123 | −0.0885652 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.4093 | −0.688478 | −0.344239 | − | 0.938882i | \(-0.611863\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.26298 | 0.265445 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.5770 | 0.628256 | 0.314128 | − | 0.949381i | \(-0.398288\pi\) | ||||
0.314128 | + | 0.949381i | \(0.398288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.70712 | 0.215020 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.72901 | 0.0553728 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0987 | 0.675009 | 0.337504 | − | 0.941324i | \(-0.390417\pi\) | ||||
0.337504 | + | 0.941324i | \(0.390417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.2961 | 0.361024 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.98329 | −0.0633216 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5009 | 0.717667 | 0.358834 | − | 0.933402i | \(-0.383175\pi\) | ||||
0.358834 | + | 0.933402i | \(0.383175\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.62752 | −0.0518572 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.2883 | −1.09141 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.4724 | 1.54133 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6980 | 0.816322 | 0.408161 | − | 0.912910i | \(-0.366170\pi\) | ||||
0.408161 | + | 0.912910i | \(0.366170\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.9120 | 0.536687 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.7008 | 0.561152 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.6604 | 1.60443 | 0.802216 | − | 0.597034i | \(-0.203654\pi\) | ||||
0.802216 | + | 0.597034i | \(0.203654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.8502 | 0.596393 |
(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 | 8020.2.a.c.1.6 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.6 | ✓ | 28 | 1.1 | even | 1 | trivial |