Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 19x^{7} + 51x^{6} + 116x^{5} - 247x^{4} - 249x^{3} + 288x^{2} + 189x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(3.39317\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | 3.39317 | 1.95905 | 0.979524 | − | 0.201327i | \(-0.0645254\pi\) | ||||
0.979524 | + | 0.201327i | \(0.0645254\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.99177 | −1.78517 | −0.892587 | − | 0.450876i | \(-0.851112\pi\) | ||||
−0.892587 | + | 0.450876i | \(0.851112\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.51361 | 2.83787 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.5448 | −3.49724 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.471119 | −0.114263 | −0.0571316 | − | 0.998367i | \(-0.518195\pi\) | ||||
−0.0571316 | + | 0.998367i | \(0.518195\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.42544 | 1.70351 | 0.851757 | − | 0.523937i | \(-0.175537\pi\) | ||||
0.851757 | + | 0.523937i | \(0.175537\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.39317 | 0.740451 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.13086 | −0.652830 | −0.326415 | − | 0.945227i | \(-0.605841\pi\) | ||||
−0.326415 | + | 0.945227i | \(0.605841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.9342 | 2.18684 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.7086 | 3.60048 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.836190 | 0.155277 | 0.0776383 | − | 0.996982i | \(-0.475262\pi\) | ||||
0.0776383 | + | 0.996982i | \(0.475262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.21252 | 1.47501 | 0.737506 | − | 0.675341i | \(-0.236003\pi\) | ||||
0.737506 | + | 0.675341i | \(0.236003\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.39317 | 0.590675 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.99177 | −0.674732 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4440 | −1.71699 | −0.858495 | − | 0.512823i | \(-0.828600\pi\) | ||||
−0.858495 | + | 0.512823i | \(0.828600\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.39317 | −0.543342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.29525 | −0.670805 | −0.335402 | − | 0.942075i | \(-0.608872\pi\) | ||||
−0.335402 | + | 0.942075i | \(0.608872\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.12434 | −0.781455 | −0.390727 | − | 0.920506i | \(-0.627776\pi\) | ||||
−0.390727 | + | 0.920506i | \(0.627776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −33.9844 | −5.06609 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.87553 | −1.14876 | −0.574382 | − | 0.818587i | \(-0.694758\pi\) | ||||
−0.574382 | + | 0.818587i | \(0.694758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.59859 | −0.223847 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7025 | 1.47010 | 0.735050 | − | 0.678013i | \(-0.237159\pi\) | ||||
0.735050 | + | 0.678013i | \(0.237159\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.99177 | −0.538250 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 25.1958 | 3.33727 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.786985 | 0.102457 | 0.0512284 | − | 0.998687i | \(-0.483686\pi\) | ||||
0.0512284 | + | 0.998687i | \(0.483686\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4916 | 1.59939 | 0.799696 | − | 0.600406i | \(-0.204994\pi\) | ||||
0.799696 | + | 0.600406i | \(0.204994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.51361 | 1.07261 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.99177 | 0.495118 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.30389 | 0.770143 | 0.385072 | − | 0.922887i | \(-0.374177\pi\) | ||||
0.385072 | + | 0.922887i | \(0.374177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.6235 | −1.27892 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.21357 | 0.500059 | 0.250030 | − | 0.968238i | \(-0.419560\pi\) | ||||
0.250030 | + | 0.968238i | \(0.419560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.43518 | −0.285016 | −0.142508 | − | 0.989794i | \(-0.545517\pi\) | ||||
−0.142508 | + | 0.989794i | \(0.545517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 37.1017 | 4.28413 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.624254 | 0.0702341 | 0.0351171 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351171 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37.9407 | 4.21563 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.43620 | −0.377172 | −0.188586 | − | 0.982057i | \(-0.560390\pi\) | ||||
−0.188586 | + | 0.982057i | \(0.560390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88060 | 0.203980 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.83734 | 0.304194 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.92101 | 0.627626 | 0.313813 | − | 0.949485i | \(-0.398394\pi\) | ||||
0.313813 | + | 0.949485i | \(0.398394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.8665 | 2.88962 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −29.6407 | −3.04107 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.95552 | −0.300087 | −0.150044 | − | 0.988679i | \(-0.547941\pi\) | ||||
−0.150044 | + | 0.988679i | \(0.547941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.51361 | 0.855650 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.75909 | −0.175036 | −0.0875178 | − | 0.996163i | \(-0.527893\pi\) | ||||
−0.0875178 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.47902 | 0.933995 | 0.466998 | − | 0.884259i | \(-0.345336\pi\) | ||||
0.466998 | + | 0.884259i | \(0.345336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.5448 | −1.32183 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8890 | 1.34270 | 0.671352 | − | 0.741139i | \(-0.265714\pi\) | ||||
0.671352 | + | 0.741139i | \(0.265714\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.6380 | 1.30628 | 0.653142 | − | 0.757236i | \(-0.273451\pi\) | ||||
0.653142 | + | 0.757236i | \(0.273451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −35.4384 | −3.36366 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.13526 | 0.483085 | 0.241542 | − | 0.970390i | \(-0.422347\pi\) | ||||
0.241542 | + | 0.970390i | \(0.422347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.4977 | 1.16541 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.51361 | −0.787083 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.471119 | −0.0431874 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.5745 | −1.31414 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −23.6880 | −2.11872 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4155 | 1.45664 | 0.728322 | − | 0.685235i | \(-0.240300\pi\) | ||||
0.728322 | + | 0.685235i | \(0.240300\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.3878 | −1.53091 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.7001 | 1.89594 | 0.947972 | − | 0.318354i | \(-0.103130\pi\) | ||||
0.947972 | + | 0.318354i | \(0.103130\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.42544 | 0.643868 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −74.6805 | −6.42747 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4333 | −1.23312 | −0.616559 | − | 0.787308i | \(-0.711474\pi\) | ||||
−0.616559 | + | 0.787308i | \(0.711474\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.55665 | −0.556128 | −0.278064 | − | 0.960563i | \(-0.589693\pi\) | ||||
−0.278064 | + | 0.960563i | \(0.589693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −26.7230 | −2.25048 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.33788 | −0.277196 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.39317 | 0.279864 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.9584 | −1.06159 | −0.530795 | − | 0.847500i | \(-0.678107\pi\) | ||||
−0.530795 | + | 0.847500i | \(0.678107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4112 | 1.66104 | 0.830519 | − | 0.556990i | \(-0.188044\pi\) | ||||
0.830519 | + | 0.556990i | \(0.188044\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.01092 | −0.324264 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −32.7825 | −2.63315 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3074 | −0.822621 | −0.411310 | − | 0.911495i | \(-0.634929\pi\) | ||||
−0.411310 | + | 0.911495i | \(0.634929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 36.3154 | 2.88000 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.13086 | −0.246746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.63744 | 0.441559 | 0.220779 | − | 0.975324i | \(-0.429140\pi\) | ||||
0.220779 | + | 0.975324i | \(0.429140\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.5448 | −1.05446 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.07699 | −0.470251 | −0.235126 | − | 0.971965i | \(-0.575550\pi\) | ||||
−0.235126 | + | 0.971965i | \(0.575550\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 63.2173 | 4.83435 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8355 | −1.05189 | −0.525946 | − | 0.850518i | \(-0.676289\pi\) | ||||
−0.525946 | + | 0.850518i | \(0.676289\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9342 | 0.826549 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.67038 | 0.200718 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.61263 | 0.494251 | 0.247126 | − | 0.968983i | \(-0.420514\pi\) | ||||
0.247126 | + | 0.968983i | \(0.420514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.57204 | −0.191178 | −0.0955889 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955889 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 42.3863 | 3.13328 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 41.6902 | 3.06512 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.471119 | −0.0344516 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.7086 | 1.36085 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8567 | 1.00263 | 0.501317 | − | 0.865264i | \(-0.332849\pi\) | ||||
0.501317 | + | 0.865264i | \(0.332849\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.8940 | −1.79191 | −0.895956 | − | 0.444143i | \(-0.853508\pi\) | ||||
−0.895956 | + | 0.444143i | \(0.853508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.5448 | 0.969960 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.5198 | −1.96071 | −0.980354 | − | 0.197247i | \(-0.936800\pi\) | ||||
−0.980354 | + | 0.197247i | \(0.936800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7468 | 1.47070 | 0.735352 | − | 0.677686i | \(-0.237017\pi\) | ||||
0.735352 | + | 0.677686i | \(0.237017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3902 | 1.50875 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.836190 | 0.0586890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.1456 | 1.19750 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.6549 | −1.85265 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.42544 | 0.513629 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.7075 | −1.08135 | −0.540675 | − | 0.841231i | \(-0.681831\pi\) | ||||
−0.540675 | + | 0.841231i | \(0.681831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.2974 | 0.979640 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.4552 | 1.39503 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.21252 | 0.557502 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.26297 | −0.558360 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.471119 | 0.0316909 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1372 | −0.812764 | −0.406382 | − | 0.913703i | \(-0.633210\pi\) | ||||
−0.406382 | + | 0.913703i | \(0.633210\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 93.0896 | 6.20598 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.8476 | 0.985468 | 0.492734 | − | 0.870180i | \(-0.335998\pi\) | ||||
0.492734 | + | 0.870180i | \(0.335998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4440 | 1.08665 | 0.543325 | − | 0.839522i | \(-0.317165\pi\) | ||||
0.543325 | + | 0.839522i | \(0.317165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.39317 | 0.223254 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.39260 | −0.156745 | −0.0783724 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783724 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.4373 | 2.05074 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.11820 | 0.137592 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.98212 | −0.128213 | −0.0641063 | − | 0.997943i | \(-0.520420\pi\) | ||||
−0.0641063 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8311 | −1.40627 | −0.703133 | − | 0.711058i | \(-0.748216\pi\) | ||||
−0.703133 | + | 0.711058i | \(0.748216\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 72.6135 | 4.65816 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.99177 | −0.255025 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.42544 | −0.472470 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6596 | −0.738897 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.45012 | −0.217770 | −0.108885 | − | 0.994054i | \(-0.534728\pi\) | ||||
−0.108885 | + | 0.994054i | \(0.534728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.13086 | −0.196836 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.38119 | 0.399606 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.74867 | 0.109079 | 0.0545394 | − | 0.998512i | \(-0.482631\pi\) | ||||
0.0545394 | + | 0.998512i | \(0.482631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.4440 | −0.648961 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.11899 | 0.440655 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.1187 | −0.685609 | −0.342804 | − | 0.939407i | \(-0.611377\pi\) | ||||
−0.342804 | + | 0.939407i | \(0.611377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.7219 | −2.62438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.0910 | 1.22955 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.9283 | −1.76379 | −0.881895 | − | 0.471446i | \(-0.843732\pi\) | ||||
−0.881895 | + | 0.471446i | \(0.843732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6428 | −1.07172 | −0.535862 | − | 0.844306i | \(-0.680013\pi\) | ||||
−0.535862 | + | 0.844306i | \(0.680013\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.39317 | −0.205364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.9342 | 0.659358 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8448 | −1.55286 | −0.776432 | − | 0.630202i | \(-0.782972\pi\) | ||||
−0.776432 | + | 0.630202i | \(0.782972\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 69.9182 | 4.18589 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8889 | −0.947852 | −0.473926 | − | 0.880565i | \(-0.657164\pi\) | ||||
−0.473926 | + | 0.880565i | \(0.657164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.3295 | −0.732914 | −0.366457 | − | 0.930435i | \(-0.619429\pi\) | ||||
−0.366457 | + | 0.930435i | \(0.619429\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −100.576 | −5.95760 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.29525 | −0.253540 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7780 | −0.986944 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0286 | −0.587885 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.3645 | 1.59865 | 0.799325 | − | 0.600899i | \(-0.205191\pi\) | ||||
0.799325 | + | 0.600899i | \(0.205191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.14146 | −0.182903 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.7086 | 1.08558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.13086 | 0.181062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.12434 | −0.295362 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.96888 | −0.342903 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −49.8637 | −2.85519 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.83950 | −0.219132 | −0.109566 | − | 0.993980i | \(-0.534946\pi\) | ||||
−0.109566 | + | 0.993980i | \(0.534946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.1639 | 1.82974 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.89739 | −0.334411 | −0.167205 | − | 0.985922i | \(-0.553474\pi\) | ||||
−0.167205 | + | 0.985922i | \(0.553474\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9689 | 0.902618 | 0.451309 | − | 0.892368i | \(-0.350957\pi\) | ||||
0.451309 | + | 0.892368i | \(0.350957\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −33.9844 | −1.91480 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.0484 | −1.85618 | −0.928091 | − | 0.372353i | \(-0.878551\pi\) | ||||
−0.928091 | + | 0.372353i | \(0.878551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.836190 | 0.0468176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 47.1279 | 2.63042 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.49827 | −0.194649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.9342 | −0.606521 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 46.2761 | 2.55907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.87553 | −0.434192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.3928 | −1.12089 | −0.560445 | − | 0.828191i | \(-0.689370\pi\) | ||||
−0.560445 | + | 0.828191i | \(0.689370\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −88.9164 | −4.87259 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.1637 | −1.37484 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0614 | −0.602554 | −0.301277 | − | 0.953537i | \(-0.597413\pi\) | ||||
−0.301277 | + | 0.953537i | \(0.597413\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.4248 | 0.946386 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.21252 | 0.444733 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 42.4067 | 2.28310 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.4766 | −1.52871 | −0.764353 | − | 0.644798i | \(-0.776942\pi\) | ||||
−0.764353 | + | 0.644798i | \(0.776942\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.6756 | 1.69556 | 0.847778 | − | 0.530351i | \(-0.177940\pi\) | ||||
0.847778 | + | 0.530351i | \(0.177940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.7086 | −0.998592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.01966 | 0.0542710 | 0.0271355 | − | 0.999632i | \(-0.491361\pi\) | ||||
0.0271355 | + | 0.999632i | \(0.491361\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.8196 | −0.892692 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.59859 | −0.0846062 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6690 | 0.879754 | 0.439877 | − | 0.898058i | \(-0.355022\pi\) | ||||
0.439877 | + | 0.898058i | \(0.355022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.1372 | 1.90196 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.39317 | 0.178095 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.72066 | 0.508802 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5501 | −1.12491 | −0.562453 | − | 0.826829i | \(-0.690142\pi\) | ||||
−0.562453 | + | 0.826829i | \(0.690142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.5681 | −1.90366 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.7025 | 0.555646 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.5768 | −1.68677 | −0.843383 | − | 0.537313i | \(-0.819439\pi\) | ||||
−0.843383 | + | 0.537313i | \(0.819439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −80.3775 | −4.15067 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.836190 | −0.0430660 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5571 | 1.21005 | 0.605023 | − | 0.796208i | \(-0.293164\pi\) | ||||
0.605023 | + | 0.796208i | \(0.293164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 55.7008 | 2.85364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.5312 | 1.04909 | 0.524547 | − | 0.851382i | \(-0.324235\pi\) | ||||
0.524547 | + | 0.851382i | \(0.324235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.99177 | −0.203439 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −43.6266 | −2.21767 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.72332 | 0.138078 | 0.0690390 | − | 0.997614i | \(-0.478007\pi\) | ||||
0.0690390 | + | 0.997614i | \(0.478007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.47501 | 0.0745944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 73.6320 | 3.71425 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.49188 | −0.125380 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5807 | −0.731785 | −0.365892 | − | 0.930657i | \(-0.619236\pi\) | ||||
−0.365892 | + | 0.930657i | \(0.619236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.1958 | 1.26137 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.7872 | −1.28775 | −0.643877 | − | 0.765129i | \(-0.722675\pi\) | ||||
−0.643877 | + | 0.765129i | \(0.722675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.21252 | −0.409095 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −151.451 | −7.52564 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4440 | −0.517692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.719307 | −0.0355675 | −0.0177837 | − | 0.999842i | \(-0.505661\pi\) | ||||
−0.0177837 | + | 0.999842i | \(0.505661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −48.9746 | −2.41574 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.786985 | 0.0387250 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.7165 | 0.673317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.2478 | −1.08948 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0098 | 0.537864 | 0.268932 | − | 0.963159i | \(-0.413329\pi\) | ||||
0.268932 | + | 0.963159i | \(0.413329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.0020 | 1.36473 | 0.682367 | − | 0.731009i | \(-0.260950\pi\) | ||||
0.682367 | + | 0.731009i | \(0.260950\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −67.0492 | −3.26004 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.15132 | −0.249876 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4916 | 0.604513 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.39317 | −0.163824 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7009 | −0.611780 | −0.305890 | − | 0.952067i | \(-0.598954\pi\) | ||||
−0.305890 | + | 0.952067i | \(0.598954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.7026 | −0.610450 | −0.305225 | − | 0.952280i | \(-0.598732\pi\) | ||||
−0.305225 | + | 0.952280i | \(0.598732\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.3260 | −0.543039 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.2480 | −1.11210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.5765 | −1.60252 | −0.801259 | − | 0.598317i | \(-0.795836\pi\) | ||||
−0.801259 | + | 0.598317i | \(0.795836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.51361 | 0.405410 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8436 | −0.515194 | −0.257597 | − | 0.966252i | \(-0.582931\pi\) | ||||
−0.257597 | + | 0.966252i | \(0.582931\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.6353 | −1.12042 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −43.9699 | −2.07971 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.65806 | 0.361406 | 0.180703 | − | 0.983538i | \(-0.442163\pi\) | ||||
0.180703 | + | 0.983538i | \(0.442163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.29525 | −0.202255 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 69.2586 | 3.25405 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.99177 | 0.187137 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.8999 | −1.39866 | −0.699328 | − | 0.714801i | \(-0.746517\pi\) | ||||
−0.699328 | + | 0.714801i | \(0.746517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.81399 | −0.411402 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.0757 | −0.748719 | −0.374360 | − | 0.927284i | \(-0.622137\pi\) | ||||
−0.374360 | + | 0.927284i | \(0.622137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.374768 | −0.0174170 | −0.00870848 | − | 0.999962i | \(-0.502772\pi\) | ||||
−0.00870848 | + | 0.999962i | \(0.502772\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −111.237 | −5.15847 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.50639 | 0.347355 | 0.173677 | − | 0.984803i | \(-0.444435\pi\) | ||||
0.173677 | + | 0.984803i | \(0.444435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.30389 | 0.291087 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.9748 | −1.61155 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.12434 | −0.235618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 81.1914 | 3.72532 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 91.1168 | 4.17195 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.57393 | −0.208988 | −0.104494 | − | 0.994526i | \(-0.533322\pi\) | ||||
−0.104494 | + | 0.994526i | \(0.533322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.4440 | 0.476207 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.6235 | −0.483388 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.7977 | 0.535707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8977 | 1.21885 | 0.609425 | − | 0.792843i | \(-0.291400\pi\) | ||||
0.609425 | + | 0.792843i | \(0.291400\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.1288 | 0.865035 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.808321 | 0.0364790 | 0.0182395 | − | 0.999834i | \(-0.494194\pi\) | ||||
0.0182395 | + | 0.999834i | \(0.494194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.393945 | −0.0177424 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −33.9844 | −1.52748 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.21357 | 0.189005 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.93777 | −0.355344 | −0.177672 | − | 0.984090i | \(-0.556857\pi\) | ||||
−0.177672 | + | 0.984090i | \(0.556857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.6203 | −0.921245 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.88207 | −0.396032 | −0.198016 | − | 0.980199i | \(-0.563450\pi\) | ||||
−0.198016 | + | 0.980199i | \(0.563450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.02186 | 0.312469 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.39317 | 0.150696 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.6020 | 0.868843 | 0.434421 | − | 0.900710i | \(-0.356953\pi\) | ||||
0.434421 | + | 0.900710i | \(0.356953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.43518 | −0.107726 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 138.920 | 6.13346 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.8380 | −1.66734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.87553 | −0.346365 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.9462 | −2.06071 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.67605 | 0.0734292 | 0.0367146 | − | 0.999326i | \(-0.488311\pi\) | ||||
0.0367146 | + | 0.999326i | \(0.488311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9196 | 0.652386 | 0.326193 | − | 0.945303i | \(-0.394234\pi\) | ||||
0.326193 | + | 0.945303i | \(0.394234\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 37.1017 | 1.61925 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.86907 | −0.168539 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.1977 | −0.573813 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.70009 | 0.290759 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.29525 | 0.186048 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.4418 | −2.39696 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.4378 | 0.968262 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.34604 | 0.315831 | 0.157915 | − | 0.987453i | \(-0.449523\pi\) | ||||
0.157915 | + | 0.987453i | \(0.449523\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.72736 | −0.374527 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −54.4397 | −2.33194 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.3767 | −1.25606 | −0.628029 | − | 0.778190i | \(-0.716138\pi\) | ||||
−0.628029 | + | 0.778190i | \(0.716138\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 106.349 | 4.53886 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.20908 | 0.264516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.624254 | 0.0265460 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 141.462 | 6.00472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.41854 | −0.0601056 | −0.0300528 | − | 0.999548i | \(-0.509568\pi\) | ||||
−0.0300528 | + | 0.999548i | \(0.509568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12434 | 0.216737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.59859 | −0.0674924 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.98712 | −0.252327 | −0.126163 | − | 0.992009i | \(-0.540266\pi\) | ||||
−0.126163 | + | 0.992009i | \(0.540266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.4988 | −0.862390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.9407 | 1.59336 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.60728 | −0.235069 | −0.117535 | − | 0.993069i | \(-0.537499\pi\) | ||||
−0.117535 | + | 0.993069i | \(0.537499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.6024 | 1.57361 | 0.786805 | − | 0.617201i | \(-0.211733\pi\) | ||||
0.786805 | + | 0.617201i | \(0.211733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47.0180 | 1.96421 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.2335 | −1.42764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.1990 | −0.882527 | −0.441263 | − | 0.897378i | \(-0.645470\pi\) | ||||
−0.441263 | + | 0.897378i | \(0.645470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −84.4697 | −3.51044 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.43620 | −0.142557 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.7025 | 0.443252 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33.9844 | 1.40508 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.1120 | 0.953935 | 0.476967 | − | 0.878921i | \(-0.341736\pi\) | ||||
0.476967 | + | 0.878921i | \(0.341736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.9816 | 2.51270 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −93.3795 | −3.84112 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.6448 | −1.50482 | −0.752412 | − | 0.658693i | \(-0.771110\pi\) | ||||
−0.752412 | + | 0.658693i | \(0.771110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.88060 | 0.0770970 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 70.3975 | 2.88118 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.7963 | 1.01315 | 0.506575 | − | 0.862196i | \(-0.330911\pi\) | ||||
0.506575 | + | 0.862196i | \(0.330911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.57196 | 0.186494 | 0.0932471 | − | 0.995643i | \(-0.470275\pi\) | ||||
0.0932471 | + | 0.995643i | \(0.470275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 53.6689 | 2.18557 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.99177 | −0.162288 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.24592 | 0.294103 | 0.147051 | − | 0.989129i | \(-0.453022\pi\) | ||||
0.147051 | + | 0.989129i | \(0.453022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.83734 | 0.114975 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.87553 | 0.318610 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.24990 | 0.373600 | 0.186800 | − | 0.982398i | \(-0.440188\pi\) | ||||
0.186800 | + | 0.982398i | \(0.440188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 58.1781 | 2.34597 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.5364 | −1.35013 | −0.675063 | − | 0.737760i | \(-0.735884\pi\) | ||||
−0.675063 | + | 0.737760i | \(0.735884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.6828 | −0.469573 | −0.234787 | − | 0.972047i | \(-0.575439\pi\) | ||||
−0.234787 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −58.5741 | −2.35050 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.92101 | 0.237220 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 39.8860 | 1.59544 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.1958 | 1.00622 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.92038 | 0.196189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.5606 | −1.41565 | −0.707823 | − | 0.706389i | \(-0.750323\pi\) | ||||
−0.707823 | + | 0.706389i | \(0.750323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.2983 | −2.11842 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −65.5271 | −2.60036 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.8727 | 1.41910 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.5085 | −1.20501 | −0.602506 | − | 0.798114i | \(-0.705831\pi\) | ||||
−0.602506 | + | 0.798114i | \(0.705831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.9522 | 1.89105 | 0.945525 | − | 0.325549i | \(-0.105549\pi\) | ||||
0.945525 | + | 0.325549i | \(0.105549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 69.4079 | 2.73294 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.7878 | 1.32834 | 0.664168 | − | 0.747583i | \(-0.268786\pi\) | ||||
0.664168 | + | 0.747583i | \(0.268786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.786985 | 0.0308919 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.8665 | 1.09217 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.683141 | −0.0267334 | −0.0133667 | − | 0.999911i | \(-0.504255\pi\) | ||||
−0.0133667 | + | 0.999911i | \(0.504255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −86.6217 | −3.38459 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.7321 | −0.808837 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.3796 | −0.599103 | −0.299552 | − | 0.954080i | \(-0.596837\pi\) | ||||
−0.299552 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.2849 | 0.555617 | 0.277809 | − | 0.960636i | \(-0.410392\pi\) | ||||
0.277809 | + | 0.960636i | \(0.410392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.59859 | 0.0620840 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29.6407 | −1.14942 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.61799 | −0.101369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.1834 | −1.59224 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.4916 | 0.482235 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2419 | −0.780269 | −0.390135 | − | 0.920758i | \(-0.627572\pi\) | ||||
−0.390135 | + | 0.920758i | \(0.627572\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 204.564 | 7.87367 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.15471 | −0.351844 | −0.175922 | − | 0.984404i | \(-0.556291\pi\) | ||||
−0.175922 | + | 0.984404i | \(0.556291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.95552 | −0.113422 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.3804 | 1.93058 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.3870 | 0.550504 | 0.275252 | − | 0.961372i | \(-0.411239\pi\) | ||||
0.275252 | + | 0.961372i | \(0.411239\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57.6143 | 2.20133 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 55.7973 | 2.12880 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.7025 | −0.407732 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.92175 | 0.301358 | 0.150679 | − | 0.988583i | \(-0.451854\pi\) | ||||
0.150679 | + | 0.988583i | \(0.451854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.51361 | 0.323405 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.1726 | 0.992785 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.02357 | 0.0766483 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.11852 | −0.307071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3253 | −0.692136 | −0.346068 | − | 0.938209i | \(-0.612483\pi\) | ||||
−0.346068 | + | 0.938209i | \(0.612483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −77.5516 | −2.92491 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 106.672 | 4.01750 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.75909 | −0.0661572 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.6975 | 1.37820 | 0.689102 | − | 0.724664i | \(-0.258005\pi\) | ||||
0.689102 | + | 0.724664i | \(0.258005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.31466 | 0.199315 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.7123 | −0.962931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.99177 | 0.149284 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.72566 | −0.251174 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.7262 | 1.74259 | 0.871296 | − | 0.490757i | \(-0.163280\pi\) | ||||
0.871296 | + | 0.490757i | \(0.163280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.47902 | 0.353017 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −74.0767 | −2.75494 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.14308 | 0.339565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.79457 | −0.103645 | −0.0518225 | − | 0.998656i | \(-0.516503\pi\) | ||||
−0.0518225 | + | 0.998656i | \(0.516503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 132.568 | 4.90992 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.41418 | 0.0892915 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.797036 | −0.0294392 | −0.0147196 | − | 0.999892i | \(-0.504686\pi\) | ||||
−0.0147196 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.5448 | −0.499606 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.30389 | 0.232207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.15617 | 0.300030 | 0.150015 | − | 0.988684i | \(-0.452068\pi\) | ||||
0.150015 | + | 0.988684i | \(0.452068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.1958 | −0.925591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.7867 | −1.16614 | −0.583071 | − | 0.812421i | \(-0.698149\pi\) | ||||
−0.583071 | + | 0.812421i | \(0.698149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.7268 | 1.89512 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.2544 | −1.07036 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.8890 | 0.507494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.84752 | −0.322851 | −0.161425 | − | 0.986885i | \(-0.551609\pi\) | ||||
−0.161425 | + | 0.986885i | \(0.551609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.7068 | −0.426621 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −81.4767 | −2.96524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8038 | 0.647091 | 0.323545 | − | 0.946213i | \(-0.395125\pi\) | ||||
0.323545 | + | 0.946213i | \(0.395125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.6235 | −0.385610 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9426 | 0.686669 | 0.343335 | − | 0.939213i | \(-0.388444\pi\) | ||||
0.343335 | + | 0.939213i | \(0.388444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.6380 | 0.493729 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.0107 | 0.578867 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.786985 | −0.0284164 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.83217 | −0.354557 | −0.177279 | − | 0.984161i | \(-0.556729\pi\) | ||||
−0.177279 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.93352 | 0.213691 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.1236 | −0.759762 | −0.379881 | − | 0.925035i | \(-0.624035\pi\) | ||||
−0.379881 | + | 0.925035i | \(0.624035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 89.7974 | 3.22562 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.4384 | −1.27135 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.8941 | −1.14273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.21357 | 0.150774 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.6440 | 0.559069 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.1448 | 1.46852 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.0638 | 1.49941 | 0.749707 | − | 0.661770i | \(-0.230195\pi\) | ||||
0.749707 | + | 0.661770i | \(0.230195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.7277 | −1.34314 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.13526 | 0.182589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4916 | −0.443591 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −144.963 | −5.14129 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5229 | 0.620695 | 0.310347 | − | 0.950623i | \(-0.399555\pi\) | ||||
0.310347 | + | 0.950623i | \(0.399555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.71031 | 0.131261 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.4092 | 1.78112 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.43518 | −0.0859355 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.4977 | 0.440485 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −98.1587 | −3.45535 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.8780 | −1.19109 | −0.595543 | − | 0.803323i | \(-0.703063\pi\) | ||||
−0.595543 | + | 0.803323i | \(0.703063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.516687 | 0.0181433 | 0.00907167 | − | 0.999959i | \(-0.497112\pi\) | ||||
0.00907167 | + | 0.999959i | \(0.497112\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −59.8650 | −2.09956 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.5034 | −0.788259 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.0505 | −1.33122 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.51361 | −0.297490 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0218 | −0.419565 | −0.209782 | − | 0.977748i | \(-0.567276\pi\) | ||||
−0.209782 | + | 0.977748i | \(0.567276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.6058 | −0.927419 | −0.463709 | − | 0.885987i | \(-0.653482\pi\) | ||||
−0.463709 | + | 0.885987i | \(0.653482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 37.1017 | 1.29171 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.84556 | 0.0989498 | 0.0494749 | − | 0.998775i | \(-0.484245\pi\) | ||||
0.0494749 | + | 0.998775i | \(0.484245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3942 | 1.05563 | 0.527816 | − | 0.849358i | \(-0.323011\pi\) | ||||
0.527816 | + | 0.849358i | \(0.323011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −87.6958 | −3.04213 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.471119 | −0.0163233 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.2579 | 0.839480 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 153.645 | 5.31074 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.1903 | −0.627998 | −0.313999 | − | 0.949423i | \(-0.601669\pi\) | ||||
−0.313999 | + | 0.949423i | \(0.601669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3008 | −0.975889 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −53.9138 | −1.85689 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.99177 | −0.137321 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.8362 | −1.43581 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.6988 | 1.12090 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.4823 | 1.83120 | 0.915600 | − | 0.402090i | \(-0.131716\pi\) | ||||
0.915600 | + | 0.402090i | \(0.131716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −252.349 | −8.63015 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.7600 | 0.572509 | 0.286255 | − | 0.958154i | \(-0.407590\pi\) | ||||
0.286255 | + | 0.958154i | \(0.407590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.3561 | 0.899259 | 0.449630 | − | 0.893215i | \(-0.351556\pi\) | ||||
0.449630 | + | 0.893215i | \(0.351556\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.5745 | −0.496698 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5357 | 0.562882 | 0.281441 | − | 0.959579i | \(-0.409188\pi\) | ||||
0.281441 | + | 0.959579i | \(0.409188\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.2281 | 1.87781 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −56.9308 | −1.93347 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.624254 | 0.0211764 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.30389 | −0.213599 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.1621 | −0.851608 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.6880 | −0.800801 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.97842 | 0.0668066 | 0.0334033 | − | 0.999442i | \(-0.489365\pi\) | ||||
0.0334033 | + | 0.999442i | \(0.489365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 92.8523 | 3.13183 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.9104 | 1.74891 | 0.874453 | − | 0.485110i | \(-0.161220\pi\) | ||||
0.874453 | + | 0.485110i | \(0.161220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.0452 | 0.506311 | 0.253155 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253155 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.6595 | −0.358316 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5478 | −0.488468 | −0.244234 | − | 0.969716i | \(-0.578537\pi\) | ||||
−0.244234 | + | 0.969716i | \(0.578537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.4155 | 0.550560 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.9407 | 1.27106 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −58.4793 | −1.95694 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.3961 | −0.882324 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.6235 | 0.354710 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.86722 | 0.229035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.04215 | −0.167978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.3878 | −0.578629 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.2670 | 0.341286 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.1688 | −0.802513 | −0.401256 | − | 0.915966i | \(-0.631426\pi\) | ||||
−0.401256 | + | 0.915966i | \(0.631426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.9762 | −0.496728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.11985 | −0.0702337 | −0.0351168 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351168 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.43620 | −0.113722 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −169.196 | −5.59345 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.7001 | 0.716599 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.2016 | 0.699376 | 0.349688 | − | 0.936866i | \(-0.386288\pi\) | ||||
0.349688 | + | 0.936866i | \(0.386288\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.0281 | −0.429290 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.21357 | −0.138691 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −114.197 | −3.75479 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 80.7006 | 2.65056 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.3529 | 0.438095 | 0.219047 | − | 0.975714i | \(-0.429705\pi\) | ||||
0.219047 | + | 0.975714i | \(0.429705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.42544 | 0.243359 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.0109 | −0.655126 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.88060 | 0.0615021 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.4451 | −1.41929 | −0.709645 | − | 0.704559i | \(-0.751145\pi\) | ||||
−0.709645 | + | 0.704559i | \(0.751145\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.1854 | 1.76827 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.1935 | −0.756088 | −0.378044 | − | 0.925788i | \(-0.623403\pi\) | ||||
−0.378044 | + | 0.925788i | \(0.623403\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.4478 | 0.437921 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −74.6805 | −2.42936 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.55784 | −0.278092 | −0.139046 | − | 0.990286i | \(-0.544404\pi\) | ||||
−0.139046 | + | 0.990286i | \(0.544404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.43518 | 0.0790491 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −112.139 | −3.63635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.1413 | −0.425687 | −0.212844 | − | 0.977086i | \(-0.568273\pi\) | ||||
−0.212844 | + | 0.977086i | \(0.568273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55.3126 | −1.78987 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.83734 | 0.0917180 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.4333 | −0.466075 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.4454 | 1.17566 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 118.246 | 3.81042 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 99.3712 | 3.19887 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.7140 | −1.05201 | −0.526005 | − | 0.850481i | \(-0.676311\pi\) | ||||
−0.526005 | + | 0.850481i | \(0.676311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.8702 | −0.381326 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.3279 | 1.16582 | 0.582908 | − | 0.812538i | \(-0.301915\pi\) | ||||
0.582908 | + | 0.812538i | \(0.301915\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.55665 | −0.210197 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37.1017 | −1.18820 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.4953 | 0.815668 | 0.407834 | − | 0.913056i | \(-0.366284\pi\) | ||||
0.407834 | + | 0.913056i | \(0.366284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.92101 | 0.189236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 116.109 | 3.70706 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.2147 | 0.899908 | 0.449954 | − | 0.893052i | \(-0.351440\pi\) | ||||
0.449954 | + | 0.893052i | \(0.351440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 109.853 | 3.50020 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.7230 | −0.850603 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0436 | 0.510157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.36613 | −0.170461 | −0.0852303 | − | 0.996361i | \(-0.527163\pi\) | ||||
−0.0852303 | + | 0.996361i | \(0.527163\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −69.1963 | −2.19588 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −82.8165 | −2.62546 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8886 | 0.408186 | 0.204093 | − | 0.978952i | \(-0.434576\pi\) | ||||
0.204093 | + | 0.978952i | \(0.434576\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −195.393 | −6.18198 |
(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 | 4004.2.a.h.1.9 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.h.1.9 | ✓ | 9 | 1.1 | even | 1 | trivial |