Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | 2.45195 | 1.41563 | 0.707816 | − | 0.706397i | \(-0.249681\pi\) | ||||
0.707816 | + | 0.706397i | \(0.249681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.279836 | 0.125146 | 0.0625732 | − | 0.998040i | \(-0.480069\pi\) | ||||
0.0625732 | + | 0.998040i | \(0.480069\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64586 | 1.37801 | 0.689003 | − | 0.724758i | \(-0.258048\pi\) | ||||
0.689003 | + | 0.724758i | \(0.258048\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.01204 | 1.00401 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.16835 | 1.25680 | 0.628402 | − | 0.777889i | \(-0.283709\pi\) | ||||
0.628402 | + | 0.777889i | \(0.283709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.225891 | −0.0626509 | −0.0313254 | − | 0.999509i | \(-0.509973\pi\) | ||||
−0.0313254 | + | 0.999509i | \(0.509973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.686143 | 0.177161 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.76597 | 0.428310 | 0.214155 | − | 0.976800i | \(-0.431300\pi\) | ||||
0.214155 | + | 0.976800i | \(0.431300\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09795 | −0.481303 | −0.240651 | − | 0.970612i | \(-0.577361\pi\) | ||||
−0.240651 | + | 0.970612i | \(0.577361\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.93946 | 1.95075 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.12140 | −0.442343 | −0.221172 | − | 0.975235i | \(-0.570988\pi\) | ||||
−0.221172 | + | 0.975235i | \(0.570988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92169 | −0.984338 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.0295247 | 0.00568202 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.16954 | 0.217178 | 0.108589 | − | 0.994087i | \(-0.465367\pi\) | ||||
0.108589 | + | 0.994087i | \(0.465367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.55159 | 1.35631 | 0.678153 | − | 0.734921i | \(-0.262781\pi\) | ||||
0.678153 | + | 0.734921i | \(0.262781\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.2206 | 1.77917 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.02024 | 0.172453 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.81161 | −0.462226 | −0.231113 | − | 0.972927i | \(-0.574237\pi\) | ||||
−0.231113 | + | 0.972927i | \(0.574237\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.553872 | −0.0886906 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.812621 | 0.126910 | 0.0634550 | − | 0.997985i | \(-0.479788\pi\) | ||||
0.0634550 | + | 0.997985i | \(0.479788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.36747 | 1.12353 | 0.561765 | − | 0.827297i | \(-0.310123\pi\) | ||||
0.561765 | + | 0.827297i | \(0.310123\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.842877 | 0.125649 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.04461 | 0.589967 | 0.294984 | − | 0.955502i | \(-0.404686\pi\) | ||||
0.294984 | + | 0.955502i | \(0.404686\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.29232 | 0.898903 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.33006 | 0.606330 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.886240 | 0.121734 | 0.0608672 | − | 0.998146i | \(-0.480613\pi\) | ||||
0.0608672 | + | 0.998146i | \(0.480613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16645 | 0.157285 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.14406 | −0.681348 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.749409 | 0.0975647 | 0.0487824 | − | 0.998809i | \(-0.484466\pi\) | ||||
0.0487824 | + | 0.998809i | \(0.484466\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.77767 | −0.995829 | −0.497914 | − | 0.867226i | \(-0.665901\pi\) | ||||
−0.497914 | + | 0.867226i | \(0.665901\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.9815 | 1.38354 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0632124 | −0.00784053 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.9861 | 1.83084 | 0.915420 | − | 0.402500i | \(-0.131859\pi\) | ||||
0.915420 | + | 0.402500i | \(0.131859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.20157 | −0.626195 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.01214 | −0.713510 | −0.356755 | − | 0.934198i | \(-0.616117\pi\) | ||||
−0.356755 | + | 0.934198i | \(0.616117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.3943 | −1.80177 | −0.900885 | − | 0.434059i | \(-0.857081\pi\) | ||||
−0.900885 | + | 0.434059i | \(0.857081\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0677 | −1.39346 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.1972 | 1.73189 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4183 | 1.73469 | 0.867346 | − | 0.497705i | \(-0.165824\pi\) | ||||
0.867346 | + | 0.497705i | \(0.165824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.96373 | −0.995970 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.28502 | −0.360578 | −0.180289 | − | 0.983614i | \(-0.557703\pi\) | ||||
−0.180289 | + | 0.983614i | \(0.557703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.494181 | 0.0536015 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.86765 | 0.307445 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.17270 | −0.336306 | −0.168153 | − | 0.985761i | \(-0.553780\pi\) | ||||
−0.168153 | + | 0.985761i | \(0.553780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.823567 | −0.0863333 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.5161 | 1.92003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.587082 | −0.0602333 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.57560 | −0.972255 | −0.486128 | − | 0.873888i | \(-0.661591\pi\) | ||||
−0.486128 | + | 0.873888i | \(0.661591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.5552 | 1.26185 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1773 | −1.31119 | −0.655594 | − | 0.755113i | \(-0.727582\pi\) | ||||
−0.655594 | + | 0.755113i | \(0.727582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0313 | −1.48108 | −0.740541 | − | 0.672012i | \(-0.765431\pi\) | ||||
−0.740541 | + | 0.672012i | \(0.765431\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.50158 | 0.244129 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.74626 | −0.942206 | −0.471103 | − | 0.882078i | \(-0.656144\pi\) | ||||
−0.471103 | + | 0.882078i | \(0.656144\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.14740 | −0.684597 | −0.342299 | − | 0.939591i | \(-0.611205\pi\) | ||||
−0.342299 | + | 0.939591i | \(0.611205\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.89392 | −0.654342 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.8344 | 1.39550 | 0.697751 | − | 0.716340i | \(-0.254184\pi\) | ||||
0.697751 | + | 0.716340i | \(0.254184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.593645 | −0.0553577 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.680393 | −0.0629023 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.43848 | 0.590214 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.37513 | 0.579557 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.99250 | 0.179658 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.77645 | −0.248333 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.44701 | 0.838287 | 0.419143 | − | 0.907920i | \(-0.362330\pi\) | ||||
0.419143 | + | 0.907920i | \(0.362330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.0646 | 1.59050 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.27582 | −0.810433 | −0.405216 | − | 0.914221i | \(-0.632804\pi\) | ||||
−0.405216 | + | 0.914221i | \(0.632804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.64884 | −0.663239 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.00826206 | 0.000711085 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6122 | −1.16297 | −0.581485 | − | 0.813557i | \(-0.697528\pi\) | ||||
−0.581485 | + | 0.813557i | \(0.697528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5093 | −0.976205 | −0.488102 | − | 0.872786i | \(-0.662311\pi\) | ||||
−0.488102 | + | 0.872786i | \(0.662311\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.91717 | 0.835177 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.941592 | −0.0787399 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.327280 | 0.0271791 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.4284 | 1.27252 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2726 | 1.16925 | 0.584627 | − | 0.811302i | \(-0.301241\pi\) | ||||
0.584627 | + | 0.811302i | \(0.301241\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5122 | 1.09960 | 0.549802 | − | 0.835295i | \(-0.314703\pi\) | ||||
0.549802 | + | 0.835295i | \(0.314703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.31917 | 0.430029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.11321 | 0.169737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.1266 | 1.52647 | 0.763233 | − | 0.646123i | \(-0.223611\pi\) | ||||
0.763233 | + | 0.646123i | \(0.223611\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.17301 | 0.172331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.73435 | −0.609552 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7533 | −0.842262 | −0.421131 | − | 0.907000i | \(-0.638367\pi\) | ||||
−0.421131 | + | 0.907000i | \(0.638367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.86008 | 0.222657 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.46576 | 0.190807 | 0.0954033 | − | 0.995439i | \(-0.469586\pi\) | ||||
0.0954033 | + | 0.995439i | \(0.469586\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9490 | −0.996075 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.31911 | −0.483235 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.4963 | −1.71036 | −0.855179 | − | 0.518333i | \(-0.826553\pi\) | ||||
−0.855179 | + | 0.518333i | \(0.826553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.9438 | −1.35643 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.83751 | 0.138116 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7480 | 1.02757 | 0.513787 | − | 0.857918i | \(-0.328242\pi\) | ||||
0.513787 | + | 0.857918i | \(0.328242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4413 | 1.29640 | 0.648202 | − | 0.761469i | \(-0.275521\pi\) | ||||
0.648202 | + | 0.761469i | \(0.275521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.0704 | −1.40973 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.786790 | −0.0578460 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.36117 | 0.538302 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.107643 | 0.00782987 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.4928 | 1.77224 | 0.886118 | − | 0.463459i | \(-0.153392\pi\) | ||||
0.886118 | + | 0.463459i | \(0.153392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7880 | 0.992484 | 0.496242 | − | 0.868184i | \(-0.334713\pi\) | ||||
0.496242 | + | 0.868184i | \(0.334713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.154993 | −0.0110993 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.93368 | −0.137769 | −0.0688846 | − | 0.997625i | \(-0.521944\pi\) | ||||
−0.0688846 | + | 0.997625i | \(0.521944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.3959 | −0.949613 | −0.474807 | − | 0.880090i | \(-0.657482\pi\) | ||||
−0.474807 | + | 0.880090i | \(0.657482\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.7450 | 2.59180 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.26399 | 0.299273 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.227401 | 0.0158823 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.38975 | −0.444119 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.74499 | −0.604903 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2044 | 0.771342 | 0.385671 | − | 0.922636i | \(-0.373970\pi\) | ||||
0.385671 | + | 0.922636i | \(0.373970\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.7415 | −1.01007 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.06168 | 0.140606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.5321 | 1.86900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −37.7461 | −2.55064 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.398916 | −0.0268340 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7475 | −1.59025 | −0.795124 | − | 0.606447i | \(-0.792594\pi\) | ||||
−0.795124 | + | 0.606447i | \(0.792594\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.8243 | −0.988289 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.0382 | 1.46273 | 0.731364 | − | 0.681987i | \(-0.238884\pi\) | ||||
0.731364 | + | 0.681987i | \(0.238884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5814 | 0.699238 | 0.349619 | − | 0.936892i | \(-0.386311\pi\) | ||||
0.349619 | + | 0.936892i | \(0.386311\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 37.2628 | 2.45171 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.44152 | 0.0944370 | 0.0472185 | − | 0.998885i | \(-0.484964\pi\) | ||||
0.0472185 | + | 0.998885i | \(0.484964\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.13183 | 0.0738323 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.8048 | 2.45569 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.72999 | 0.305957 | 0.152979 | − | 0.988229i | \(-0.451113\pi\) | ||||
0.152979 | + | 0.988229i | \(0.451113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.11002 | −0.457997 | −0.228998 | − | 0.973427i | \(-0.573545\pi\) | ||||
−0.228998 | + | 0.973427i | \(0.573545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0672 | −1.41561 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.76082 | 0.112495 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.473908 | 0.0301540 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.05470 | −0.510446 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0189 | −0.632387 | −0.316193 | − | 0.948695i | \(-0.602405\pi\) | ||||
−0.316193 | + | 0.948695i | \(0.602405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.84275 | −0.555939 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.21171 | 0.0758800 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.56785 | −0.0977998 | −0.0488999 | − | 0.998804i | \(-0.515572\pi\) | ||||
−0.0488999 | + | 0.998804i | \(0.515572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.2508 | −0.636951 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.52271 | 0.218050 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.115444 | −0.00711857 | −0.00355929 | − | 0.999994i | \(-0.501133\pi\) | ||||
−0.00355929 | + | 0.999994i | \(0.501133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.248002 | 0.0152346 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.77930 | −0.476085 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.6495 | 0.649311 | 0.324656 | − | 0.945832i | \(-0.394752\pi\) | ||||
0.324656 | + | 0.945832i | \(0.394752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.22698 | −0.256771 | −0.128385 | − | 0.991724i | \(-0.540979\pi\) | ||||
−0.128385 | + | 0.991724i | \(0.540979\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.01934 | −0.122216 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.5153 | −1.23712 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.26245 | −0.135938 | −0.0679688 | − | 0.997687i | \(-0.521652\pi\) | ||||
−0.0679688 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.7457 | 1.36175 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.5615 | 1.28625 | 0.643125 | − | 0.765761i | \(-0.277638\pi\) | ||||
0.643125 | + | 0.765761i | \(0.277638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8384 | 0.763164 | 0.381582 | − | 0.924335i | \(-0.375379\pi\) | ||||
0.381582 | + | 0.924335i | \(0.375379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.43949 | −0.0852682 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.96271 | 0.174883 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8814 | −0.816550 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.4789 | −1.37636 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8753 | 1.16112 | 0.580562 | − | 0.814216i | \(-0.302833\pi\) | ||||
0.580562 | + | 0.814216i | \(0.302833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.209712 | 0.0122099 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.123069 | 0.00714119 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.479206 | 0.0277132 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8608 | 1.54823 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.3100 | −1.85616 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.17647 | −0.124624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5054 | −0.599575 | −0.299787 | − | 0.954006i | \(-0.596916\pi\) | ||||
−0.299787 | + | 0.954006i | \(0.596916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.8560 | −2.09667 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5735 | 0.599566 | 0.299783 | − | 0.954007i | \(-0.403086\pi\) | ||||
0.299783 | + | 0.954007i | \(0.403086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.370212 | −0.0209256 | −0.0104628 | − | 0.999945i | \(-0.503330\pi\) | ||||
−0.0104628 | + | 0.999945i | \(0.503330\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.07302 | 0.173145 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9384 | 0.614362 | 0.307181 | − | 0.951651i | \(-0.400614\pi\) | ||||
0.307181 | + | 0.951651i | \(0.400614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.87505 | 0.272951 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.8973 | −1.33382 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.70491 | −0.206147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.11177 | 0.0616696 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.5250 | −0.969137 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.7461 | 0.812979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4728 | 0.850460 | 0.425230 | − | 0.905085i | \(-0.360193\pi\) | ||||
0.425230 | + | 0.905085i | \(0.360193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.46869 | −0.464081 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.19364 | 0.229123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.67136 | −0.363412 | −0.181706 | − | 0.983353i | \(-0.558162\pi\) | ||||
−0.181706 | + | 0.983353i | \(0.558162\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.3731 | 1.97552 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.4776 | 1.70461 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.58010 | −0.139312 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.45559 | −0.0783661 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.5236 | −0.994400 | −0.497200 | − | 0.867636i | \(-0.665638\pi\) | ||||
−0.497200 | + | 0.867636i | \(0.665638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7643 | −0.683256 | −0.341628 | − | 0.939835i | \(-0.610978\pi\) | ||||
−0.341628 | + | 0.939835i | \(0.610978\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.00666935 | −0.000355984 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.2783 | −0.919633 | −0.459816 | − | 0.888014i | \(-0.652085\pi\) | ||||
−0.459816 | + | 0.888014i | \(0.652085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.68241 | −0.0892932 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.7868 | 0.835526 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.2555 | 1.01627 | 0.508133 | − | 0.861279i | \(-0.330336\pi\) | ||||
0.508133 | + | 0.861279i | \(0.330336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5986 | −0.768348 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.6315 | 0.820440 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.30788 | −0.225485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5451 | −0.707047 | −0.353524 | − | 0.935426i | \(-0.615017\pi\) | ||||
−0.353524 | + | 0.935426i | \(0.615017\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.44765 | 0.127419 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.23111 | 0.167751 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9860 | 0.620614 | 0.310307 | − | 0.950636i | \(-0.399568\pi\) | ||||
0.310307 | + | 0.950636i | \(0.399568\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.80770 | −0.351548 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.264189 | −0.0136064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3111 | −1.14604 | −0.573021 | − | 0.819540i | \(-0.694229\pi\) | ||||
−0.573021 | + | 0.819540i | \(0.694229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.1636 | 1.18671 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.9953 | 0.612929 | 0.306464 | − | 0.951882i | \(-0.400854\pi\) | ||||
0.306464 | + | 0.951882i | \(0.400854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.25273 | 0.216739 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.1911 | 1.12804 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1536 | 1.32604 | 0.663019 | − | 0.748602i | \(-0.269275\pi\) | ||||
0.663019 | + | 0.748602i | \(0.269275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.74633 | −0.189460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.7438 | −1.14727 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.31459 | 0.217091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.895828 | 0.0449603 | 0.0224802 | − | 0.999747i | \(-0.492844\pi\) | ||||
0.0224802 | + | 0.999747i | \(0.492844\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.7545 | −0.938902 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1250 | −0.755307 | −0.377654 | − | 0.925947i | \(-0.623269\pi\) | ||||
−0.377654 | + | 0.925947i | \(0.623269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.70583 | −0.0849737 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.50837 | −0.124642 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7198 | −0.580928 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.6119 | −1.46421 | −0.732107 | − | 0.681190i | \(-0.761463\pi\) | ||||
−0.732107 | + | 0.681190i | \(0.761463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.3764 | −1.64634 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.73224 | 0.134445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.919267 | −0.0451250 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.2201 | −1.38195 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.05052 | −0.295587 | −0.147794 | − | 0.989018i | \(-0.547217\pi\) | ||||
−0.147794 | + | 0.989018i | \(0.547217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.0551 | −1.17237 | −0.586186 | − | 0.810176i | \(-0.699371\pi\) | ||||
−0.586186 | + | 0.810176i | \(0.699371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.1825 | 0.592335 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.69155 | −0.421602 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.3563 | −1.37226 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.30873 | −0.111467 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.4569 | −1.12988 | −0.564940 | − | 0.825132i | \(-0.691101\pi\) | ||||
−0.564940 | + | 0.825132i | \(0.691101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3380 | −0.881266 | −0.440633 | − | 0.897687i | \(-0.645246\pi\) | ||||
−0.440633 | + | 0.897687i | \(0.645246\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.802472 | 0.0384756 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.45060 | 0.212901 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7869 | 1.03983 | 0.519917 | − | 0.854217i | \(-0.325963\pi\) | ||||
0.519917 | + | 0.854217i | \(0.325963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.9527 | 0.902511 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.8636 | −1.65642 | −0.828210 | − | 0.560418i | \(-0.810641\pi\) | ||||
−0.828210 | + | 0.560418i | \(0.810641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.887836 | −0.0420875 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.9956 | 1.65523 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.5288 | 1.62951 | 0.814757 | − | 0.579802i | \(-0.196870\pi\) | ||||
0.814757 | + | 0.579802i | \(0.196870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.38729 | 0.159501 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.1311 | 1.55664 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.230464 | −0.0108043 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.0723 | −1.26639 | −0.633195 | − | 0.773993i | \(-0.718257\pi\) | ||||
−0.633195 | + | 0.773993i | \(0.718257\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0521396 | 0.00243367 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.06196 | −0.422058 | −0.211029 | − | 0.977480i | \(-0.567681\pi\) | ||||
−0.211029 | + | 0.977480i | \(0.567681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.9997 | −0.929466 | −0.464733 | − | 0.885451i | \(-0.653850\pi\) | ||||
−0.464733 | + | 0.885451i | \(0.653850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.18147 | 0.240285 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.34435 | 0.432405 | 0.216202 | − | 0.976349i | \(-0.430633\pi\) | ||||
0.216202 | + | 0.976349i | \(0.430633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.6372 | 2.52291 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.8973 | 2.16092 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.7102 | 1.41206 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3255 | 0.473765 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.66939 | 0.122223 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.81702 | 0.0830215 | 0.0415108 | − | 0.999138i | \(-0.486783\pi\) | ||||
0.0415108 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.635118 | 0.0289589 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.9642 | −0.862901 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.67960 | −0.121674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0300 | −0.817019 | −0.408510 | − | 0.912754i | \(-0.633951\pi\) | ||||
−0.408510 | + | 0.912754i | \(0.633951\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.3665 | −1.19233 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.2552 | −1.54591 | −0.772957 | − | 0.634458i | \(-0.781223\pi\) | ||||
−0.772957 | + | 0.634458i | \(0.781223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.06537 | 0.0930197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.51341 | 0.157916 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.9195 | −0.983222 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.11779 | −0.408168 | −0.204084 | − | 0.978953i | \(-0.565422\pi\) | ||||
−0.204084 | + | 0.978953i | \(0.565422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.04592 | 0.270112 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.68748 | −0.164091 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.7502 | −1.41008 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6683 | −0.472862 | −0.236431 | − | 0.971648i | \(-0.575978\pi\) | ||||
−0.236431 | + | 0.971648i | \(0.575978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.1256 | −2.48285 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0619413 | −0.00273477 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.20631 | −0.185352 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.8594 | 0.741473 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −55.1596 | −2.42124 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.57053 | −0.419293 | −0.209646 | − | 0.977777i | \(-0.567231\pi\) | ||||
−0.209646 | + | 0.977777i | \(0.567231\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.3693 | −0.890689 | −0.445344 | − | 0.895359i | \(-0.646919\pi\) | ||||
−0.445344 | + | 0.895359i | \(0.646919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −43.9973 | −1.92020 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.3359 | 0.580919 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.4996 | −0.804333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.25725 | 0.0979563 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.183564 | −0.00795103 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.72735 | −0.117914 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.7094 | 1.45467 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.2286 | 1.12975 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.8467 | −1.36920 | −0.684599 | − | 0.728920i | \(-0.740023\pi\) | ||||
−0.684599 | + | 0.728920i | \(0.740023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 42.7652 | 1.83523 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00010 | −0.0856749 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.4629 | −1.17423 | −0.587114 | − | 0.809505i | \(-0.699736\pi\) | ||||
−0.587114 | + | 0.809505i | \(0.699736\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.4267 | −0.999826 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.45364 | −0.104529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.2130 | 2.39042 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.92917 | −0.0818886 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.3783 | 1.49903 | 0.749514 | − | 0.661989i | \(-0.230287\pi\) | ||||
0.749514 | + | 0.661989i | \(0.230287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.66425 | −0.0703901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0492 | 0.762038 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.1900 | −1.06163 | −0.530816 | − | 0.847487i | \(-0.678115\pi\) | ||||
−0.530816 | + | 0.847487i | \(0.678115\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.15120 | 0.174642 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −32.6805 | −1.37245 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.1636 | 0.551846 | 0.275923 | − | 0.961180i | \(-0.411017\pi\) | ||||
0.275923 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.95587 | 0.416640 | 0.208320 | − | 0.978061i | \(-0.433200\pi\) | ||||
0.208320 | + | 0.978061i | \(0.433200\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.0550 | 2.50884 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.4409 | 0.435415 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1666 | 0.881176 | 0.440588 | − | 0.897710i | \(-0.354770\pi\) | ||||
0.440588 | + | 0.897710i | \(0.354770\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.8075 | 1.40499 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.9767 | −0.496879 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.69416 | 0.152996 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.190398 | −0.00787200 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3303 | 0.550202 | 0.275101 | − | 0.961415i | \(-0.411289\pi\) | ||||
0.275101 | + | 0.961415i | \(0.411289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.8429 | −0.652794 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.74129 | −0.195030 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.44323 | 0.387787 | 0.193893 | − | 0.981023i | \(-0.437888\pi\) | ||||
0.193893 | + | 0.981023i | \(0.437888\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.80172 | 0.0738632 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.8461 | −1.34430 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0118 | 0.981097 | 0.490549 | − | 0.871414i | \(-0.336796\pi\) | ||||
0.490549 | + | 0.871414i | \(0.336796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.0203 | 1.83641 | 0.918207 | − | 0.396100i | \(-0.129637\pi\) | ||||
0.918207 | + | 0.396100i | \(0.129637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.1387 | 1.83819 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.78399 | 0.0725295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.44273 | 0.302091 | 0.151046 | − | 0.988527i | \(-0.451736\pi\) | ||||
0.151046 | + | 0.988527i | \(0.451736\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.4551 | 0.423661 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.913641 | −0.0369620 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.4172 | −1.14776 | −0.573879 | − | 0.818940i | \(-0.694562\pi\) | ||||
−0.573879 | + | 0.818940i | \(0.694562\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.557574 | 0.0224836 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.2593 | 1.05716 | 0.528579 | − | 0.848884i | \(-0.322725\pi\) | ||||
0.528579 | + | 0.848884i | \(0.322725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0880 | 0.727019 | 0.363509 | − | 0.931590i | \(-0.381578\pi\) | ||||
0.363509 | + | 0.931590i | \(0.381578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0626337 | −0.00251340 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.5672 | −0.463432 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8315 | 0.953260 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.4422 | −0.856321 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.96522 | −0.197976 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4988 | −1.05490 | −0.527451 | − | 0.849586i | \(-0.676852\pi\) | ||||
−0.527451 | + | 0.849586i | \(0.676852\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.4726 | 1.09194 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.64361 | 0.104909 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.42138 | −0.0563171 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.1088 | −0.716374 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.9823 | 1.46071 | 0.730357 | − | 0.683066i | \(-0.239354\pi\) | ||||
0.730357 | + | 0.683066i | \(0.239354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.21713 | −0.324052 | −0.162026 | − | 0.986787i | \(-0.551803\pi\) | ||||
−0.162026 | + | 0.986787i | \(0.551803\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.05514 | 0.199046 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.1321 | 1.45982 | 0.729908 | − | 0.683546i | \(-0.239563\pi\) | ||||
0.729908 | + | 0.683546i | \(0.239563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.12380 | 0.122620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 67.5071 | 2.64581 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.4087 | 0.407325 | 0.203662 | − | 0.979041i | \(-0.434716\pi\) | ||||
0.203662 | + | 0.979041i | \(0.434716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.59571 | −0.101423 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −46.3683 | −1.80900 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.11547 | −0.160316 | −0.0801579 | − | 0.996782i | \(-0.525542\pi\) | ||||
−0.0801579 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.06571 | −0.235929 | −0.117964 | − | 0.993018i | \(-0.537637\pi\) | ||||
−0.117964 | + | 0.993018i | \(0.537637\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.978121 | −0.0379871 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.14042 | −0.0830019 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.48107 | −0.0960673 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −58.2275 | −2.25121 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.4200 | −1.25156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4558 | 1.09689 | 0.548445 | − | 0.836187i | \(-0.315220\pi\) | ||||
0.548445 | + | 0.836187i | \(0.315220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.145311 | −0.00559304 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.44305 | −0.286060 | −0.143030 | − | 0.989718i | \(-0.545684\pi\) | ||||
−0.143030 | + | 0.989718i | \(0.545684\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.9113 | −1.33977 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54.0365 | 2.07068 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.0920853 | −0.00352354 | −0.00176177 | − | 0.999998i | \(-0.500561\pi\) | ||||
−0.00176177 | + | 0.999998i | \(0.500561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.80919 | −0.145542 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.9450 | 0.989863 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.200194 | −0.00762677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4439 | −0.967932 | −0.483966 | − | 0.875087i | \(-0.660804\pi\) | ||||
−0.483966 | + | 0.875087i | \(0.660804\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45.7747 | 1.73884 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.22071 | −0.122169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.43506 | 0.0543569 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.53452 | 0.133688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.52065 | −0.208512 | −0.104256 | − | 0.994550i | \(-0.533246\pi\) | ||||
−0.104256 | + | 0.994550i | \(0.533246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.89862 | 0.222471 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.77518 | 0.104519 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −48.0426 | −1.80683 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.5373 | 0.959074 | 0.479537 | − | 0.877522i | \(-0.340805\pi\) | ||||
0.479537 | + | 0.877522i | \(0.340805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.4405 | 1.74166 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0200 | −0.599952 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.263491 | −0.00985401 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.5977 | 0.433123 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.5238 | −1.06376 | −0.531880 | − | 0.846820i | \(-0.678514\pi\) | ||||
−0.531880 | + | 0.846820i | \(0.678514\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.8022 | −2.04094 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.4334 | −0.648355 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.75612 | −0.213777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.4473 | −0.684171 | −0.342086 | − | 0.939669i | \(-0.611133\pi\) | ||||
−0.342086 | + | 0.939669i | \(0.611133\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.2163 | −1.00801 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0107 | 0.481219 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.9309 | 0.440677 | 0.220338 | − | 0.975424i | \(-0.429284\pi\) | ||||
0.220338 | + | 0.975424i | \(0.429284\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.31743 | 0.159251 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 62.4672 | 2.30101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6370 | −0.538431 | −0.269215 | − | 0.963080i | \(-0.586764\pi\) | ||||
−0.269215 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.16200 | 0.0426870 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.3801 | −0.784360 | −0.392180 | − | 0.919889i | \(-0.628279\pi\) | ||||
−0.392180 | + | 0.919889i | \(0.628279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.99398 | 0.146328 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.89462 | −0.362025 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.5335 | −1.29837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.67550 | −0.134121 | −0.0670605 | − | 0.997749i | \(-0.521362\pi\) | ||||
−0.0670605 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.5658 | −0.895227 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.78119 | 0.137612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.4950 | 1.18105 | 0.590525 | − | 0.807019i | \(-0.298921\pi\) | ||||
0.590525 | + | 0.807019i | \(0.298921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.6819 | −0.787005 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0784 | −1.09034 | −0.545170 | − | 0.838326i | \(-0.683535\pi\) | ||||
−0.545170 | + | 0.838326i | \(0.683535\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.0585 | −0.943380 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.48849 | 0.0538166 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.169285 | −0.00611251 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.8504 | −1.50917 | −0.754583 | − | 0.656205i | \(-0.772161\pi\) | ||||
−0.754583 | + | 0.656205i | \(0.772161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.84429 | −0.138449 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.1452 | 1.47989 | 0.739945 | − | 0.672668i | \(-0.234852\pi\) | ||||
0.739945 | + | 0.672668i | \(0.234852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.1666 | −1.33506 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.1343 | −0.901688 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.70484 | −0.0610822 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.0607 | −0.896743 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0345303 | 0.00123401 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.35230 | 0.191032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.9028 | 0.994627 | 0.497313 | − | 0.867571i | \(-0.334320\pi\) | ||||
0.497313 | + | 0.867571i | \(0.334320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.283062 | −0.0100773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.0842 | 1.92301 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.75691 | 0.0623895 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.608087 | 0.0215666 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.48784 | −0.123545 | −0.0617727 | − | 0.998090i | \(-0.519675\pi\) | ||||
−0.0617727 | + | 0.998090i | \(0.519675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.14266 | 0.252689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.55631 | −0.337656 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −64.1689 | −2.26447 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.16435 | −0.0762832 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.1120 | 0.919186 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.9333 | −0.806291 | −0.403146 | − | 0.915136i | \(-0.632083\pi\) | ||||
−0.403146 | + | 0.915136i | \(0.632083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1255 | −0.531128 | −0.265564 | − | 0.964093i | \(-0.585558\pi\) | ||||
−0.265564 | + | 0.964093i | \(0.585558\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.3643 | −0.363493 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.00916 | −0.105406 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.4566 | −0.540758 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.48062 | −0.0866798 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.73331 | 0.200094 | 0.100047 | − | 0.994983i | \(-0.468101\pi\) | ||||
0.100047 | + | 0.994983i | \(0.468101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.64174 | −0.231516 | −0.115758 | − | 0.993277i | \(-0.536930\pi\) | ||||
−0.115758 | + | 0.993277i | \(0.536930\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −50.3025 | −1.75131 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9616 | −1.00709 | −0.503547 | − | 0.863968i | \(-0.667972\pi\) | ||||
−0.503547 | + | 0.863968i | \(0.667972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.9043 | 0.795498 | 0.397749 | − | 0.917494i | \(-0.369791\pi\) | ||||
0.397749 | + | 0.917494i | \(0.369791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.54741 | −0.192438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.1120 | 0.385009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.690009 | 0.0238788 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.222958 | 0.00770656 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.7724 | −0.717144 | −0.358572 | − | 0.933502i | \(-0.616736\pi\) | ||||
−0.358572 | + | 0.933502i | \(0.616736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6322 | −0.952834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 52.8676 | 1.82086 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.62359 | −0.124655 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.2429 | 0.798634 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.4791 | 1.08036 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.96456 | 0.204463 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.17843 | −0.211546 | −0.105773 | − | 0.994390i | \(-0.533732\pi\) | ||||
−0.105773 | + | 0.994390i | \(0.533732\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.76831 | −0.0604751 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.2746 | −1.03416 | −0.517080 | − | 0.855937i | \(-0.672981\pi\) | ||||
−0.517080 | + | 0.855937i | \(0.672981\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.8620 | 0.541206 | 0.270603 | − | 0.962691i | \(-0.412777\pi\) | ||||
0.270603 | + | 0.962691i | \(0.412777\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.26440 | 0.247570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0206 | 0.885753 | 0.442877 | − | 0.896583i | \(-0.353958\pi\) | ||||
0.442877 | + | 0.896583i | \(0.353958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.29526 | −0.214045 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.0363 | −1.15593 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.2688 | 2.18017 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.38522 | −0.114704 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.8421 | −0.976158 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1225 | −0.342204 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.1487 | −0.950515 | −0.475257 | − | 0.879847i | \(-0.657645\pi\) | ||||
−0.475257 | + | 0.879847i | \(0.657645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.7331 | 1.64373 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2636 | 0.952226 | 0.476113 | − | 0.879384i | \(-0.342045\pi\) | ||||
0.476113 | + | 0.879384i | \(0.342045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.1411 | 1.21625 | 0.608123 | − | 0.793843i | \(-0.291923\pi\) | ||||
0.608123 | + | 0.793843i | \(0.291923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.514201 | 0.0172847 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 58.0021 | 1.94752 | 0.973760 | − | 0.227579i | \(-0.0730810\pi\) | ||||
0.973760 | + | 0.227579i | \(0.0730810\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.4425 | 1.15517 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.3640 | −1.25174 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.48540 | −0.283953 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.84718 | 0.128597 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.17499 | 0.0392317 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.83189 | 0.294560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56507 | 0.0521401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65.8612 | 2.19173 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.88071 | 0.162240 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.593648 | −0.0197117 | −0.00985587 | − | 0.999951i | \(-0.503137\pi\) | ||||
−0.00985587 | + | 0.999951i | \(0.503137\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39.6905 | −1.31645 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.4928 | 1.63977 | 0.819885 | − | 0.572529i | \(-0.194037\pi\) | ||||
0.819885 | + | 0.572529i | \(0.194037\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.6931 | −0.453176 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.33659 | −0.176422 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.8184 | −1.11678 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.9431 | 0.954746 | 0.477373 | − | 0.878701i | \(-0.341589\pi\) | ||||
0.477373 | + | 0.878701i | \(0.341589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.7587 | −0.848777 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.35809 | 0.0447020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.8379 | 0.454987 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.2750 | −1.48703 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.16662 | −0.0710845 | −0.0355423 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355423 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.2010 | −0.432645 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.9255 | 0.848764 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.05992 | 0.0673666 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.0007 | 1.56811 | 0.784057 | − | 0.620689i | \(-0.213147\pi\) | ||||
0.784057 | + | 0.620689i | \(0.213147\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.907741 | −0.0296230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.4555 | −1.15581 | −0.577907 | − | 0.816102i | \(-0.696131\pi\) | ||||
−0.577907 | + | 0.816102i | \(0.696131\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.72390 | −0.0561378 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0301224 | 0.000979880 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.4416 | 0.859236 | 0.429618 | − | 0.903011i | \(-0.358648\pi\) | ||||
0.429618 | + | 0.903011i | \(0.358648\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.47744 | 0.112882 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.8204 | 0.869711 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.7670 | −1.80647 | −0.903236 | − | 0.429144i | \(-0.858815\pi\) | ||||
−0.903236 | + | 0.429144i | \(0.858815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.85397 | 0.221789 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.9534 | 0.386398 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.6283 | −1.60258 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.0265 | 0.839564 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.3561 | −0.945988 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.85839 | 0.124206 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.42604 | −0.238805 | −0.119403 | − | 0.992846i | \(-0.538098\pi\) | ||||
−0.119403 | + | 0.992846i | \(0.538098\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.08425 | −0.291828 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.333254 | 0.0106946 | 0.00534731 | − | 0.999986i | \(-0.498298\pi\) | ||||
0.00534731 | + | 0.999986i | \(0.498298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.9613 | −1.34522 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.72599 | 0.0873015 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.3521 | −1.45094 | −0.725470 | − | 0.688253i | \(-0.758378\pi\) | ||||
−0.725470 | + | 0.688253i | \(0.758378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.2249 | −0.422671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.5283 | −0.687345 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.6324 | 0.689965 | 0.344983 | − | 0.938609i | \(-0.387885\pi\) | ||||
0.344983 | + | 0.938609i | \(0.387885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.541114 | −0.0172413 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 36.1567 | 1.15088 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.6294 | −0.496985 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5815 | −1.32088 | −0.660441 | − | 0.750878i | \(-0.729630\pi\) | ||||
−0.660441 | + | 0.750878i | \(0.729630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.9384 | 1.20394 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.74867 | −0.118841 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3236 | 0.706995 | 0.353498 | − | 0.935435i | \(-0.384992\pi\) | ||||
0.353498 | + | 0.935435i | \(0.384992\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0830119 | −0.00262638 |
(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 | 4024.2.a.f.1.28 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.y.1.6 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.28 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.y.1.6 | 33 | 4.3 | odd | 2 |