Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 26x^{7} + 93x^{6} - 113x^{5} - 230x^{4} + 197x^{3} + 201x^{2} - 115x + 8 \) |
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 | 1.3 | ||
Root | \(-1.64280\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.64280 | −0.948473 | −0.474236 | − | 0.880398i | \(-0.657276\pi\) | ||||
−0.474236 | + | 0.880398i | \(0.657276\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.39966 | 1.07316 | 0.536579 | − | 0.843850i | \(-0.319716\pi\) | ||||
0.536579 | + | 0.843850i | \(0.319716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.301198 | −0.100399 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.94216 | −1.01786 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.56268 | −1.34915 | −0.674574 | − | 0.738207i | \(-0.735673\pi\) | ||||
−0.674574 | + | 0.738207i | \(0.735673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.34299 | 0.308104 | 0.154052 | − | 0.988063i | \(-0.450768\pi\) | ||||
0.154052 | + | 0.988063i | \(0.450768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.64280 | 0.358489 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.38656 | 0.497631 | 0.248816 | − | 0.968551i | \(-0.419959\pi\) | ||||
0.248816 | + | 0.968551i | \(0.419959\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.758347 | 0.151669 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.42322 | 1.04370 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.520193 | −0.0965975 | −0.0482987 | − | 0.998833i | \(-0.515380\pi\) | ||||
−0.0482987 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.43959 | 1.51579 | 0.757897 | − | 0.652374i | \(-0.226227\pi\) | ||||
0.757897 | + | 0.652374i | \(0.226227\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.64280 | 0.285975 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.39966 | −0.405616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.34732 | −0.879094 | −0.439547 | − | 0.898219i | \(-0.644861\pi\) | ||||
−0.439547 | + | 0.898219i | \(0.644861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.64280 | 0.263059 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.51389 | 0.236429 | 0.118215 | − | 0.992988i | \(-0.462283\pi\) | ||||
0.118215 | + | 0.992988i | \(0.462283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.44676 | 1.28812 | 0.644060 | − | 0.764975i | \(-0.277249\pi\) | ||||
0.644060 | + | 0.764975i | \(0.277249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.722772 | −0.107745 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.408568 | −0.0595957 | −0.0297978 | − | 0.999556i | \(-0.509486\pi\) | ||||
−0.0297978 | + | 0.999556i | \(0.509486\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.13839 | 1.27963 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.0707 | 1.93275 | 0.966377 | − | 0.257128i | \(-0.0827761\pi\) | ||||
0.966377 | + | 0.257128i | \(0.0827761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.39966 | −0.323569 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.20628 | −0.292228 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2923 | −1.86070 | −0.930350 | − | 0.366673i | \(-0.880497\pi\) | ||||
−0.930350 | + | 0.366673i | \(0.880497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50404 | 0.704720 | 0.352360 | − | 0.935864i | \(-0.385379\pi\) | ||||
0.352360 | + | 0.935864i | \(0.385379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.301198 | 0.0379474 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.39966 | −0.297641 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.69135 | −0.695309 | −0.347654 | − | 0.937623i | \(-0.613022\pi\) | ||||
−0.347654 | + | 0.937623i | \(0.613022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.92064 | −0.471990 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2452 | 1.45324 | 0.726619 | − | 0.687040i | \(-0.241090\pi\) | ||||
0.726619 | + | 0.687040i | \(0.241090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4010 | 1.68550 | 0.842752 | − | 0.538302i | \(-0.180934\pi\) | ||||
0.842752 | + | 0.538302i | \(0.180934\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.24581 | −0.143854 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.5736 | −1.86467 | −0.932336 | − | 0.361593i | \(-0.882233\pi\) | ||||
−0.932336 | + | 0.361593i | \(0.882233\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.00568 | −0.889520 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.85861 | −0.643066 | −0.321533 | − | 0.946898i | \(-0.604198\pi\) | ||||
−0.321533 | + | 0.946898i | \(0.604198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.3485 | −1.44785 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.854575 | 0.0916200 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7968 | −1.67445 | −0.837226 | − | 0.546857i | \(-0.815824\pi\) | ||||
−0.837226 | + | 0.546857i | \(0.815824\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.8646 | −1.43769 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.22273 | 0.330645 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.66235 | −0.676459 | −0.338230 | − | 0.941064i | \(-0.609828\pi\) | ||||
−0.338230 | + | 0.941064i | \(0.609828\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.301198 | 0.0302716 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4762 | −1.24143 | −0.620713 | − | 0.784038i | \(-0.713157\pi\) | ||||
−0.620713 | + | 0.784038i | \(0.713157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.85198 | 0.576613 | 0.288306 | − | 0.957538i | \(-0.406908\pi\) | ||||
0.288306 | + | 0.957538i | \(0.406908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.94216 | 0.384716 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.437393 | −0.0422843 | −0.0211422 | − | 0.999776i | \(-0.506730\pi\) | ||||
−0.0211422 | + | 0.999776i | \(0.506730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.86084 | −0.944498 | −0.472249 | − | 0.881465i | \(-0.656558\pi\) | ||||
−0.472249 | + | 0.881465i | \(0.656558\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.78460 | 0.833797 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3863 | −1.07113 | −0.535565 | − | 0.844494i | \(-0.679901\pi\) | ||||
−0.535565 | + | 0.844494i | \(0.679901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.72691 | 0.534037 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.301198 | 0.0278458 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.56268 | 0.509930 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.48702 | −0.224247 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1785 | −0.910393 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7019 | 1.57079 | 0.785396 | − | 0.618993i | \(-0.212459\pi\) | ||||
0.785396 | + | 0.618993i | \(0.212459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.8764 | −1.22175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0693 | 1.22924 | 0.614622 | − | 0.788822i | \(-0.289309\pi\) | ||||
0.614622 | + | 0.788822i | \(0.289309\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.34299 | −0.116452 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.0139 | 1.12005 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.7925 | −0.922068 | −0.461034 | − | 0.887382i | \(-0.652521\pi\) | ||||
−0.461034 | + | 0.887382i | \(0.652521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.23174 | 0.358932 | 0.179466 | − | 0.983764i | \(-0.442563\pi\) | ||||
0.179466 | + | 0.983764i | \(0.442563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.671196 | 0.0565249 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.24828 | −0.103664 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.64280 | −0.135496 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0923 | −1.31833 | −0.659165 | − | 0.751998i | \(-0.729090\pi\) | ||||
−0.659165 | + | 0.751998i | \(0.729090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.49449 | 0.365756 | 0.182878 | − | 0.983136i | \(-0.441459\pi\) | ||||
0.182878 | + | 0.983136i | \(0.441459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.67547 | 0.135454 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.2521 | 1.62669 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.4728 | −1.55410 | −0.777050 | − | 0.629439i | \(-0.783285\pi\) | ||||
−0.777050 | + | 0.629439i | \(0.783285\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.1153 | −1.83317 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.38656 | −0.188087 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5929 | −0.908025 | −0.454013 | − | 0.890995i | \(-0.650008\pi\) | ||||
−0.454013 | + | 0.890995i | \(0.650008\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.94216 | 0.306897 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.17478 | 0.245672 | 0.122836 | − | 0.992427i | \(-0.460801\pi\) | ||||
0.122836 | + | 0.992427i | \(0.460801\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.404508 | −0.0309335 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.10785 | −0.388343 | −0.194171 | − | 0.980968i | \(-0.562202\pi\) | ||||
−0.194171 | + | 0.980968i | \(0.562202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.758347 | −0.0573256 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.4794 | 1.76482 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.7568 | −1.40195 | −0.700974 | − | 0.713187i | \(-0.747251\pi\) | ||||
−0.700974 | + | 0.713187i | \(0.747251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.06001 | 0.227449 | 0.113724 | − | 0.993512i | \(-0.463722\pi\) | ||||
0.113724 | + | 0.993512i | \(0.463722\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.04205 | −0.668408 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.8317 | −0.943408 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.56268 | 0.406783 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.42322 | −0.394481 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.66617 | 0.120560 | 0.0602800 | − | 0.998182i | \(-0.480801\pi\) | ||||
0.0602800 | + | 0.998182i | \(0.480801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.0865 | −1.58982 | −0.794911 | − | 0.606726i | \(-0.792483\pi\) | ||||
−0.794911 | + | 0.606726i | \(0.792483\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.94216 | 0.282304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4822 | 1.10306 | 0.551531 | − | 0.834155i | \(-0.314044\pi\) | ||||
0.551531 | + | 0.834155i | \(0.314044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.49155 | 0.247510 | 0.123755 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123755 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.34976 | 0.659481 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.520193 | 0.0365104 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.63281 | 0.253726 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.718827 | −0.0499619 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.34299 | −0.0928969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.41014 | −0.510135 | −0.255068 | − | 0.966923i | \(-0.582098\pi\) | ||||
−0.255068 | + | 0.966923i | \(0.582098\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.1165 | −1.37836 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.2693 | 1.38236 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.43959 | −0.572916 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.6579 | −1.59865 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.56268 | 0.374186 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.0017 | −1.40638 | −0.703189 | − | 0.711003i | \(-0.748241\pi\) | ||||
−0.703189 | + | 0.711003i | \(0.748241\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.228413 | −0.0152275 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.50544 | −0.166292 | −0.0831459 | − | 0.996537i | \(-0.526497\pi\) | ||||
−0.0831459 | + | 0.996537i | \(0.526497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2660 | 0.744479 | 0.372239 | − | 0.928137i | \(-0.378590\pi\) | ||||
0.372239 | + | 0.928137i | \(0.378590\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.64280 | −0.108089 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.20880 | −0.537776 | −0.268888 | − | 0.963171i | \(-0.586656\pi\) | ||||
−0.268888 | + | 0.963171i | \(0.586656\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.980421 | −0.0639556 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.2271 | 1.76859 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6157 | 0.945411 | 0.472705 | − | 0.881220i | \(-0.343277\pi\) | ||||
0.472705 | + | 0.881220i | \(0.343277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.28925 | −0.211879 | −0.105940 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105940 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.11789 | −0.200013 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.39966 | 0.153308 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.34299 | −0.0854527 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.62454 | 0.609930 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.50916 | 0.221496 | 0.110748 | − | 0.993849i | \(-0.464675\pi\) | ||||
0.110748 | + | 0.993849i | \(0.464675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.38656 | −0.150041 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.9290 | 1.37325 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.4294 | −1.21197 | −0.605985 | − | 0.795476i | \(-0.707221\pi\) | ||||
−0.605985 | + | 0.795476i | \(0.707221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.34732 | 0.332266 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156681 | 0.00969833 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.84088 | 0.360164 | 0.180082 | − | 0.983652i | \(-0.442364\pi\) | ||||
0.180082 | + | 0.983652i | \(0.442364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.7648 | 2.07415 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.9510 | 1.58817 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.75819 | −0.107199 | −0.0535993 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535993 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.64648 | 0.282254 | 0.141127 | − | 0.989992i | \(-0.454927\pi\) | ||||
0.141127 | + | 0.989992i | \(0.454927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.64280 | −0.0994270 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.758347 | −0.0457300 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2026 | 0.613012 | 0.306506 | − | 0.951869i | \(-0.400840\pi\) | ||||
0.306506 | + | 0.951869i | \(0.400840\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.54199 | −0.152185 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.9924 | 1.31196 | 0.655978 | − | 0.754780i | \(-0.272256\pi\) | ||||
0.655978 | + | 0.754780i | \(0.272256\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.24165 | 0.192696 | 0.0963479 | − | 0.995348i | \(-0.469284\pi\) | ||||
0.0963479 | + | 0.995348i | \(0.469284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.29430 | −0.313607 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51389 | −0.0893619 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.9434 | 0.820201 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.9449 | 0.641603 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.1111 | −1.40859 | −0.704293 | − | 0.709909i | \(-0.748736\pi\) | ||||
−0.704293 | + | 0.709909i | \(0.748736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.2966 | −1.99683 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.42322 | −0.314687 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.38656 | −0.138018 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.44676 | −0.486863 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.4959 | 1.17746 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.2078 | 0.756277 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.81645 | 0.103670 | 0.0518350 | − | 0.998656i | \(-0.483493\pi\) | ||||
0.0518350 | + | 0.998656i | \(0.483493\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.61365 | −0.546901 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.76410 | −0.326852 | −0.163426 | − | 0.986556i | \(-0.552255\pi\) | ||||
−0.163426 | + | 0.986556i | \(0.552255\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.4540 | −1.38222 | −0.691111 | − | 0.722749i | \(-0.742878\pi\) | ||||
−0.691111 | + | 0.722749i | \(0.742878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.722772 | 0.0407236 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.6759 | −1.66677 | −0.833383 | − | 0.552695i | \(-0.813599\pi\) | ||||
−0.833383 | + | 0.552695i | \(0.813599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.520193 | 0.0291252 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.718550 | 0.0401055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.47065 | −0.415678 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.758347 | −0.0420655 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.1994 | 0.895830 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.408568 | 0.0225251 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7437 | 1.14017 | 0.570087 | − | 0.821584i | \(-0.306909\pi\) | ||||
0.570087 | + | 0.821584i | \(0.306909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.61060 | 0.0882606 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.6573 | −0.746176 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.30768 | −0.125707 | −0.0628536 | − | 0.998023i | \(-0.520020\pi\) | ||||
−0.0628536 | + | 0.998023i | \(0.520020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.7054 | 1.01594 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.43959 | −0.457029 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.40819 | −0.506520 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.5379 | −0.995167 | −0.497583 | − | 0.867416i | \(-0.665779\pi\) | ||||
−0.497583 | + | 0.867416i | \(0.665779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.6518 | 1.48017 | 0.740084 | − | 0.672514i | \(-0.234786\pi\) | ||||
0.740084 | + | 0.672514i | \(0.234786\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.42322 | −0.289470 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.6831 | −0.728277 | −0.364139 | − | 0.931345i | \(-0.618637\pi\) | ||||
−0.364139 | + | 0.931345i | \(0.618637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.3843 | 1.55956 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.13839 | −0.483655 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.1398 | −1.01016 | −0.505081 | − | 0.863072i | \(-0.668537\pi\) | ||||
−0.505081 | + | 0.863072i | \(0.668537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1964 | −0.905072 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.64280 | −0.0862248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.5573 | 1.80881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.48344 | −0.234033 | −0.117017 | − | 0.993130i | \(-0.537333\pi\) | ||||
−0.117017 | + | 0.993130i | \(0.537333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.455980 | −0.0237374 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0707 | −0.730513 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.6354 | 1.58624 | 0.793120 | − | 0.609065i | \(-0.208455\pi\) | ||||
0.793120 | + | 0.609065i | \(0.208455\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.7213 | 0.863483 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.520193 | 0.0267913 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0887 | 0.518222 | 0.259111 | − | 0.965848i | \(-0.416570\pi\) | ||||
0.259111 | + | 0.965848i | \(0.416570\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.0808 | −1.48985 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.9318 | 1.42725 | 0.713625 | − | 0.700528i | \(-0.247052\pi\) | ||||
0.713625 | + | 0.700528i | \(0.247052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.39966 | 0.122298 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.54415 | −0.129326 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.1525 | 1.73160 | 0.865801 | − | 0.500388i | \(-0.166809\pi\) | ||||
0.865801 | + | 0.500388i | \(0.166809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2756 | −0.671378 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.1132 | −1.16590 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −39.7709 | −2.00109 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2140 | −0.512626 | −0.256313 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256313 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.20628 | 0.110452 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.1600 | −1.20649 | −0.603247 | − | 0.797554i | \(-0.706127\pi\) | ||||
−0.603247 | + | 0.797554i | \(0.706127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.43959 | −0.420406 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.2109 | −0.954597 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.34732 | 0.265057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.1025 | −0.845666 | −0.422833 | − | 0.906208i | \(-0.638964\pi\) | ||||
−0.422833 | + | 0.906208i | \(0.638964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7300 | 0.874556 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.2923 | 0.703278 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0586 | −0.690111 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.95192 | −0.340437 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9863 | 0.829834 | 0.414917 | − | 0.909859i | \(-0.363811\pi\) | ||||
0.414917 | + | 0.909859i | \(0.363811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.8970 | −1.31088 | −0.655439 | − | 0.755248i | \(-0.727516\pi\) | ||||
−0.655439 | + | 0.755248i | \(0.727516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.123060 | 0.00598338 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.21844 | −0.204624 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.50404 | −0.266359 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.64280 | −0.0793153 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.9479 | 1.73155 | 0.865775 | − | 0.500433i | \(-0.166826\pi\) | ||||
0.865775 | + | 0.500433i | \(0.166826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.938349 | −0.0450942 | −0.0225471 | − | 0.999746i | \(-0.507178\pi\) | ||||
−0.0225471 | + | 0.999746i | \(0.507178\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.05069 | 0.0983228 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.20513 | 0.153322 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0850 | −0.624515 | −0.312257 | − | 0.949998i | \(-0.601085\pi\) | ||||
−0.312257 | + | 0.949998i | \(0.601085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.301198 | −0.0143428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.1274 | −1.85900 | −0.929499 | − | 0.368824i | \(-0.879761\pi\) | ||||
−0.929499 | + | 0.368824i | \(0.879761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.9068 | −1.79695 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.4364 | 1.25040 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.62089 | 0.454038 | 0.227019 | − | 0.973890i | \(-0.427102\pi\) | ||||
0.227019 | + | 0.973890i | \(0.427102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.51389 | −0.0712862 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.38356 | −0.346910 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.39966 | 0.112498 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.8035 | −0.645702 | −0.322851 | − | 0.946450i | \(-0.604641\pi\) | ||||
−0.322851 | + | 0.946450i | \(0.604641\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.1676 | −1.40810 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.3567 | 1.50700 | 0.753501 | − | 0.657447i | \(-0.228364\pi\) | ||||
0.753501 | + | 0.657447i | \(0.228364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.5056 | −1.27829 | −0.639147 | − | 0.769084i | \(-0.720713\pi\) | ||||
−0.639147 | + | 0.769084i | \(0.720713\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −33.2702 | −1.54287 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.52725 | −0.0706727 | −0.0353363 | − | 0.999375i | \(-0.511250\pi\) | ||||
−0.0353363 | + | 0.999375i | \(0.511250\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.69135 | 0.262802 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.9900 | 1.47402 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.44676 | −0.388383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.01846 | 0.0467300 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.23806 | −0.194048 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.53266 | 0.344176 | 0.172088 | − | 0.985082i | \(-0.444949\pi\) | ||||
0.172088 | + | 0.985082i | \(0.444949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.34732 | 0.243817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.92064 | 0.178395 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.9874 | −0.725948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.1988 | −1.09655 | −0.548276 | − | 0.836297i | \(-0.684716\pi\) | ||||
−0.548276 | + | 0.836297i | \(0.684716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0448 | 0.861237 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.32992 | −0.150277 | −0.0751385 | − | 0.997173i | \(-0.523940\pi\) | ||||
−0.0751385 | + | 0.997173i | \(0.523940\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.89367 | 0.130324 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.722772 | 0.0324862 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.2452 | −0.549273 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8711 | −1.42675 | −0.713373 | − | 0.700785i | \(-0.752833\pi\) | ||||
−0.713373 | + | 0.700785i | \(0.752833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.21554 | −0.233013 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.79722 | 0.124722 | 0.0623609 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623609 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.9385 | −1.33225 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.64280 | −0.0729594 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.97182 | −0.441993 | −0.220997 | − | 0.975275i | \(-0.570931\pi\) | ||||
−0.220997 | + | 0.975275i | \(0.570931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4010 | −0.637061 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.28335 | 0.321568 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.0427 | 0.618797 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.408568 | 0.0179688 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.39119 | 0.368333 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.63123 | −0.334330 | −0.167165 | − | 0.985929i | \(-0.553461\pi\) | ||||
−0.167165 | + | 0.985929i | \(0.553461\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.93305 | −0.303161 | −0.151581 | − | 0.988445i | \(-0.548436\pi\) | ||||
−0.151581 | + | 0.988445i | \(0.548436\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.24581 | 0.0543718 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −46.9467 | −2.04503 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3044 | −0.752363 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.30482 | 0.186813 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.51389 | −0.0655737 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.04959 | −0.0453778 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.8137 | 1.32971 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.13757 | 0.306868 | 0.153434 | − | 0.988159i | \(-0.450967\pi\) | ||||
0.153434 | + | 0.988159i | \(0.450967\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.02700 | −0.215729 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.6626 | −1.01360 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.6511 | −1.65260 | −0.826301 | − | 0.563228i | \(-0.809559\pi\) | ||||
−0.826301 | + | 0.563228i | \(0.809559\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.65781 | −0.0707535 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.698617 | −0.0297621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.5736 | 0.704780 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.0800 | 0.894796 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.4362 | −1.24725 | −0.623626 | − | 0.781723i | \(-0.714341\pi\) | ||||
−0.623626 | + | 0.781723i | \(0.714341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.44676 | −0.357260 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.13839 | −0.385823 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.9492 | −1.30435 | −0.652177 | − | 0.758066i | \(-0.726144\pi\) | ||||
−0.652177 | + | 0.758066i | \(0.726144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.3231 | −1.14949 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.00568 | 0.336207 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.8226 | 1.29215 | 0.646076 | − | 0.763273i | \(-0.276409\pi\) | ||||
0.646076 | + | 0.763273i | \(0.276409\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.3529 | −1.85611 | −0.928056 | − | 0.372442i | \(-0.878521\pi\) | ||||
−0.928056 | + | 0.372442i | \(0.878521\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.73719 | −0.114348 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.80984 | 0.0754754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.8723 | 0.868925 | 0.434462 | − | 0.900690i | \(-0.356938\pi\) | ||||
0.434462 | + | 0.900690i | \(0.356938\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.2838 | 1.50790 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.85861 | 0.243056 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.0707 | −0.582748 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.722772 | 0.0298830 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.6679 | −0.646682 | −0.323341 | − | 0.946283i | \(-0.604806\pi\) | ||||
−0.323341 | + | 0.946283i | \(0.604806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3343 | 0.467023 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.4342 | −1.04622 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.6491 | 1.01222 | 0.506108 | − | 0.862470i | \(-0.331084\pi\) | ||||
0.506108 | + | 0.862470i | \(0.331084\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.3485 | 0.547236 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.73593 | −0.234756 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.7032 | 1.00934 | 0.504672 | − | 0.863311i | \(-0.331614\pi\) | ||||
0.504672 | + | 0.863311i | \(0.331614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.85788 | −0.198157 | −0.0990785 | − | 0.995080i | \(-0.531590\pi\) | ||||
−0.0990785 | + | 0.995080i | \(0.531590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.71422 | 0.0698086 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.39966 | 0.0975599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.3748 | −0.664633 | −0.332316 | − | 0.943168i | \(-0.607830\pi\) | ||||
−0.332316 | + | 0.943168i | \(0.607830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.854575 | −0.0346291 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.408568 | 0.0165289 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0395 | −0.849779 | −0.424890 | − | 0.905245i | \(-0.639687\pi\) | ||||
−0.424890 | + | 0.905245i | \(0.639687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.96799 | −0.240652 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.6569 | −1.23420 | −0.617101 | − | 0.786884i | \(-0.711693\pi\) | ||||
−0.617101 | + | 0.786884i | \(0.711693\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.5794 | 0.786964 | 0.393482 | − | 0.919332i | \(-0.371270\pi\) | ||||
0.393482 | + | 0.919332i | \(0.371270\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9428 | 0.519377 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.7968 | 0.632883 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.2166 | −1.12867 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.20628 | 0.0881102 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.7454 | 1.18603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.73796 | 0.188615 | 0.0943076 | − | 0.995543i | \(-0.469936\pi\) | ||||
0.0943076 | + | 0.995543i | \(0.469936\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.1734 | 0.483850 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.4785 | 1.68571 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.68824 | −0.145904 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.3647 | −0.527873 | −0.263936 | − | 0.964540i | \(-0.585021\pi\) | ||||
−0.263936 | + | 0.964540i | \(0.585021\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2377 | 1.15302 | 0.576511 | − | 0.817090i | \(-0.304414\pi\) | ||||
0.576511 | + | 0.817090i | \(0.304414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.2985 | −1.31113 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.9618 | −1.41381 | −0.706903 | − | 0.707311i | \(-0.749908\pi\) | ||||
−0.706903 | + | 0.707311i | \(0.749908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.2923 | 0.561022 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.8646 | 0.543396 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.89836 | 0.269954 | 0.134977 | − | 0.990849i | \(-0.456904\pi\) | ||||
0.134977 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.7616 | 1.31917 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.33754 | −0.169224 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0182 | −0.935617 | −0.467808 | − | 0.883830i | \(-0.654956\pi\) | ||||
−0.467808 | + | 0.883830i | \(0.654956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.7016 | 1.23305 | 0.616525 | − | 0.787335i | \(-0.288540\pi\) | ||||
0.616525 | + | 0.787335i | \(0.288540\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.13839 | −0.354906 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.22273 | −0.124972 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.24147 | −0.0480699 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.5017 | 1.33391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.50404 | −0.212481 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.6161 | 1.33435 | 0.667177 | − | 0.744899i | \(-0.267502\pi\) | ||||
0.667177 | + | 0.744899i | \(0.267502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.11268 | 0.158297 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.8616 | 0.993941 | 0.496970 | − | 0.867768i | \(-0.334446\pi\) | ||||
0.496970 | + | 0.867768i | \(0.334446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.66235 | 0.255678 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.11594 | 0.157723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.70904 | 0.103659 | 0.0518293 | − | 0.998656i | \(-0.483495\pi\) | ||||
0.0518293 | + | 0.998656i | \(0.483495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.8984 | −0.989525 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.5078 | −0.706118 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.0707 | −0.536050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0188 | 1.06589 | 0.532944 | − | 0.846151i | \(-0.321086\pi\) | ||||
0.532944 | + | 0.846151i | \(0.321086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.301198 | −0.0114416 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.1547 | 0.385191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.42127 | −0.318978 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.4854 | 0.510066 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.95128 | 0.375855 | 0.187927 | − | 0.982183i | \(-0.439823\pi\) | ||||
0.187927 | + | 0.982183i | \(0.439823\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.18143 | −0.270853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.61064 | 0.0606602 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.4762 | 0.469215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.7166 | −1.60426 | −0.802129 | − | 0.597151i | \(-0.796299\pi\) | ||||
−0.802129 | + | 0.597151i | \(0.796299\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.99193 | 0.187212 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.1415 | 0.754307 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.39966 | 0.0897420 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0107 | −0.896696 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.4226 | −1.24645 | −0.623225 | − | 0.782042i | \(-0.714178\pi\) | ||||
−0.623225 | + | 0.782042i | \(0.714178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.85198 | −0.217939 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.40358 | 0.200961 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.394487 | −0.0146509 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.5522 | 1.09603 | 0.548016 | − | 0.836468i | \(-0.315383\pi\) | ||||
0.548016 | + | 0.836468i | \(0.315383\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.1391 | 1.07923 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.9866 | −1.73786 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.64126 | 0.245300 | 0.122650 | − | 0.992450i | \(-0.460861\pi\) | ||||
0.122650 | + | 0.992450i | \(0.460861\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.94216 | −0.145409 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.69135 | 0.209643 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9747 | 0.771568 | 0.385784 | − | 0.922589i | \(-0.373931\pi\) | ||||
0.385784 | + | 0.922589i | \(0.373931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.20628 | 0.0810496 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.0260 | 0.697995 | 0.348998 | − | 0.937124i | \(-0.386522\pi\) | ||||
0.348998 | + | 0.937124i | \(0.386522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.6159 | −1.41478 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.76460 | 0.0645634 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.437393 | 0.0159820 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.82055 | −0.139414 | −0.0697070 | − | 0.997568i | \(-0.522206\pi\) | ||||
−0.0697070 | + | 0.997568i | \(0.522206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.76486 | −0.210083 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.7852 | 0.392514 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.96730 | −0.362268 | −0.181134 | − | 0.983458i | \(-0.557977\pi\) | ||||
−0.181134 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.92064 | 0.142310 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.1817 | −1.09409 | −0.547043 | − | 0.837105i | \(-0.684246\pi\) | ||||
−0.547043 | + | 0.837105i | \(0.684246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.86084 | 0.356987 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.02055 | 0.145363 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.2923 | 0.516065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.6444 | −1.10507 | −0.552533 | − | 0.833491i | \(-0.686339\pi\) | ||||
−0.552533 | + | 0.833491i | \(0.686339\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.9186 | 1.14952 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.77540 | 0.315629 | 0.157815 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157815 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.40013 | 0.229900 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.78460 | −0.315146 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.03314 | 0.0728449 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.2452 | −0.438168 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.82112 | −0.100819 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.7281 | −1.66780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.6006 | −1.23338 | −0.616690 | − | 0.787206i | \(-0.711527\pi\) | ||||
−0.616690 | + | 0.787206i | \(0.711527\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.59541 | −0.341606 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3863 | 0.404849 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.50404 | −0.195454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55.4688 | −1.96728 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.1131 | 1.31461 | 0.657307 | − | 0.753623i | \(-0.271696\pi\) | ||||
0.657307 | + | 0.753623i | \(0.271696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.27273 | 0.0804034 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.75796 | 0.168114 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4010 | −0.508199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.72691 | −0.201847 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.88836 | 0.101675 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.0435 | −0.669532 | −0.334766 | − | 0.942301i | \(-0.608657\pi\) | ||||
−0.334766 | + | 0.942301i | \(0.608657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.8623 | −0.697460 | −0.348730 | − | 0.937223i | \(-0.613387\pi\) | ||||
−0.348730 | + | 0.937223i | \(0.613387\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.63325 | −0.267710 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.8189 | −0.974455 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.3440 | 0.396875 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.301198 | −0.0105247 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.5743 | 0.752947 | 0.376474 | − | 0.926427i | \(-0.377137\pi\) | ||||
0.376474 | + | 0.926427i | \(0.377137\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.9308 | −0.555312 | −0.277656 | − | 0.960681i | \(-0.589558\pi\) | ||||
−0.277656 | + | 0.960681i | \(0.589558\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.24581 | 0.0433737 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.1864 | −1.81470 | −0.907349 | − | 0.420377i | \(-0.861898\pi\) | ||||
−0.907349 | + | 0.420377i | \(0.861898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.68440 | −0.336353 | −0.168177 | − | 0.985757i | \(-0.553788\pi\) | ||||
−0.168177 | + | 0.985757i | \(0.553788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.7608 | −0.581425 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.56268 | −0.192735 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.61839 | 0.263645 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.7697 | 1.58203 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.47194 | −0.154388 | −0.0771942 | − | 0.997016i | \(-0.524596\pi\) | ||||
−0.0771942 | + | 0.997016i | \(0.524596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7294 | −0.990669 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.1292 | −1.24436 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.39966 | 0.0825507 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.32539 | −0.182767 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.7617 | −0.437465 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.6193 | −1.11686 | −0.558432 | − | 0.829550i | \(-0.688597\pi\) | ||||
−0.558432 | + | 0.829550i | \(0.688597\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.970680 | −0.0331965 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.4158 | 0.902347 | 0.451174 | − | 0.892436i | \(-0.351006\pi\) | ||||
0.451174 | + | 0.892436i | \(0.351006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5661 | 1.07702 | 0.538511 | − | 0.842618i | \(-0.318987\pi\) | ||||
0.538511 | + | 0.842618i | \(0.318987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.48702 | 0.0847574 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.3330 | −0.896385 | −0.448193 | − | 0.893937i | \(-0.647932\pi\) | ||||
−0.448193 | + | 0.893937i | \(0.647932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.2571 | −0.416753 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.9063 | −0.777938 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.5736 | 0.562220 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.69135 | 0.192844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00669 | 0.0679162 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.1785 | 0.344096 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.7176 | 1.67884 | 0.839422 | − | 0.543480i | \(-0.182894\pi\) | ||||
0.839422 | + | 0.543480i | \(0.182894\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 39.6098 | 1.33601 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.8053 | −0.700950 | −0.350475 | − | 0.936572i | \(-0.613980\pi\) | ||||
−0.350475 | + | 0.936572i | \(0.613980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.46311 | 0.0828903 | 0.0414452 | − | 0.999141i | \(-0.486804\pi\) | ||||
0.0414452 | + | 0.999141i | \(0.486804\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.3426 | 1.89393 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.6209 | −1.43107 | −0.715535 | − | 0.698577i | \(-0.753817\pi\) | ||||
−0.715535 | + | 0.698577i | \(0.753817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.7019 | −0.593704 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.00568 | 0.268201 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.548704 | −0.0183617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.0098 | −1.50451 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.92064 | 0.130906 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.39022 | −0.146422 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −78.2706 | −2.60757 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.8764 | 0.461777 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.34298 | 0.244089 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.3137 | 1.70384 | 0.851922 | − | 0.523669i | \(-0.175437\pi\) | ||||
0.851922 | + | 0.523669i | \(0.175437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.75780 | 0.124638 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.21512 | 0.272179 | 0.136089 | − | 0.990697i | \(-0.456547\pi\) | ||||
0.136089 | + | 0.990697i | \(0.456547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.85861 | 0.193892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.6978 | −0.717308 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.0693 | −0.464611 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.84321 | 0.126776 | 0.0633879 | − | 0.997989i | \(-0.479809\pi\) | ||||
0.0633879 | + | 0.997989i | \(0.479809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.98406 | −0.0983282 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2452 | −0.403056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.05513 | −0.133332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.76261 | −0.0578916 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.6152 | 1.20130 | 0.600652 | − | 0.799511i | \(-0.294908\pi\) | ||||
0.600652 | + | 0.799511i | \(0.294908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.34299 | 0.0440149 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.46928 | 0.310010 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.3485 | 0.436543 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.9713 | 0.946451 | 0.473225 | − | 0.880941i | \(-0.343090\pi\) | ||||
0.473225 | + | 0.880941i | \(0.343090\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.1731 | 1.31100 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.6723 | 1.16288 | 0.581441 | − | 0.813588i | \(-0.302489\pi\) | ||||
0.581441 | + | 0.813588i | \(0.302489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.61298 | 0.117655 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.0139 | −0.423341 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.52494 | 0.244528 | 0.122264 | − | 0.992498i | \(-0.460985\pi\) | ||||
0.122264 | + | 0.992498i | \(0.460985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.4010 | −0.467475 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.7517 | 1.58088 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.3891 | −0.984401 | −0.492200 | − | 0.870482i | \(-0.663807\pi\) | ||||
−0.492200 | + | 0.870482i | \(0.663807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.99824 | 0.129380 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.854575 | −0.0276245 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.7925 | 0.348509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.2266 | 1.29763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.131742 | 0.00424532 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53.0000 | −1.70613 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.8860 | −0.768121 | −0.384060 | − | 0.923308i | \(-0.625475\pi\) | ||||
−0.384060 | + | 0.923308i | \(0.625475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.2728 | 0.394259 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6845 | 1.33772 | 0.668860 | − | 0.743388i | \(-0.266783\pi\) | ||||
0.668860 | + | 0.743388i | \(0.266783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.23174 | −0.135663 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.24581 | 0.0398980 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.8330 | −1.27437 | −0.637185 | − | 0.770711i | \(-0.719901\pi\) | ||||
−0.637185 | + | 0.770711i | \(0.719901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7968 | 0.504866 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.97007 | 0.0948271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.2512 | −0.486438 | −0.243219 | − | 0.969971i | \(-0.578203\pi\) | ||||
−0.243219 | + | 0.969971i | \(0.578203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.1519 | 1.18376 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.671196 | −0.0213644 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.1587 | 0.641008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3637 | −0.805705 | −0.402853 | − | 0.915265i | \(-0.631981\pi\) | ||||
−0.402853 | + | 0.915265i | \(0.631981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.0777 | −1.08142 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.37852 | 0.265617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.1588 | −0.986809 | −0.493404 | − | 0.869800i | \(-0.664248\pi\) | ||||
−0.493404 | + | 0.869800i | \(0.664248\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.9997 | −0.917510 |
(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 | 8008.2.a.u.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.u.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial |