Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6534,2,Mod(1,6534)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6534, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6534.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6534.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: | \(52.1742526807\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.493090625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 20x^{4} + 15x^{3} + 115x^{2} + 73x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 594) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.88962\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6534.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.88962 | 1.73949 | 0.869747 | − | 0.493499i | \(-0.164282\pi\) | ||||
0.869747 | + | 0.493499i | \(0.164282\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.72393 | −1.40751 | −0.703756 | − | 0.710441i | \(-0.748495\pi\) | ||||
−0.703756 | + | 0.710441i | \(0.748495\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.88962 | −1.23001 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.50981 | −1.52815 | −0.764074 | − | 0.645129i | \(-0.776804\pi\) | ||||
−0.764074 | + | 0.645129i | \(0.776804\pi\) | |||||||
\(14\) | 3.72393 | 0.995262 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.37189 | 1.06034 | 0.530169 | − | 0.847892i | \(-0.322128\pi\) | ||||
0.530169 | + | 0.847892i | \(0.322128\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.37400 | −1.00346 | −0.501732 | − | 0.865023i | \(-0.667304\pi\) | ||||
−0.501732 | + | 0.865023i | \(0.667304\pi\) | |||||||
\(20\) | 3.88962 | 0.869747 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.169185 | 0.0352775 | 0.0176387 | − | 0.999844i | \(-0.494385\pi\) | ||||
0.0176387 | + | 0.999844i | \(0.494385\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1292 | 2.02584 | ||||||||
\(26\) | 5.50981 | 1.08056 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.72393 | −0.703756 | ||||||||
\(29\) | 8.39728 | 1.55934 | 0.779668 | − | 0.626193i | \(-0.215388\pi\) | ||||
0.779668 | + | 0.626193i | \(0.215388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.337037 | −0.0605337 | −0.0302668 | − | 0.999542i | \(-0.509636\pi\) | ||||
−0.0302668 | + | 0.999542i | \(0.509636\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.37189 | −0.749772 | ||||||||
\(35\) | −14.4847 | −2.44836 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.89975 | 0.312317 | 0.156158 | − | 0.987732i | \(-0.450089\pi\) | ||||
0.156158 | + | 0.987732i | \(0.450089\pi\) | |||||||
\(38\) | 4.37400 | 0.709556 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.88962 | −0.615004 | ||||||||
\(41\) | 4.97703 | 0.777281 | 0.388640 | − | 0.921390i | \(-0.372945\pi\) | ||||
0.388640 | + | 0.921390i | \(0.372945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.84121 | 0.585779 | 0.292889 | − | 0.956146i | \(-0.405383\pi\) | ||||
0.292889 | + | 0.956146i | \(0.405383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.169185 | −0.0249449 | ||||||||
\(47\) | −1.03768 | −0.151361 | −0.0756805 | − | 0.997132i | \(-0.524113\pi\) | ||||
−0.0756805 | + | 0.997132i | \(0.524113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.86764 | 0.981092 | ||||||||
\(50\) | −10.1292 | −1.43248 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.50981 | −0.764074 | ||||||||
\(53\) | −6.91374 | −0.949675 | −0.474837 | − | 0.880074i | \(-0.657493\pi\) | ||||
−0.474837 | + | 0.880074i | \(0.657493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.72393 | 0.497631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.39728 | −1.10262 | ||||||||
\(59\) | −2.69189 | −0.350455 | −0.175227 | − | 0.984528i | \(-0.556066\pi\) | ||||
−0.175227 | + | 0.984528i | \(0.556066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6852 | −1.36810 | −0.684052 | − | 0.729434i | \(-0.739784\pi\) | ||||
−0.684052 | + | 0.729434i | \(0.739784\pi\) | |||||||
\(62\) | 0.337037 | 0.0428038 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −21.4311 | −2.65820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4875 | −1.40342 | −0.701708 | − | 0.712465i | \(-0.747579\pi\) | ||||
−0.701708 | + | 0.712465i | \(0.747579\pi\) | |||||||
\(68\) | 4.37189 | 0.530169 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 14.4847 | 1.73125 | ||||||||
\(71\) | 12.7472 | 1.51281 | 0.756406 | − | 0.654102i | \(-0.226953\pi\) | ||||
0.756406 | + | 0.654102i | \(0.226953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.27159 | 0.616993 | 0.308497 | − | 0.951225i | \(-0.400174\pi\) | ||||
0.308497 | + | 0.951225i | \(0.400174\pi\) | |||||||
\(74\) | −1.89975 | −0.220841 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.37400 | −0.501732 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2281 | 1.15075 | 0.575376 | − | 0.817889i | \(-0.304856\pi\) | ||||
0.575376 | + | 0.817889i | \(0.304856\pi\) | |||||||
\(80\) | 3.88962 | 0.434873 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.97703 | −0.549621 | ||||||||
\(83\) | 6.65182 | 0.730132 | 0.365066 | − | 0.930982i | \(-0.381046\pi\) | ||||
0.365066 | + | 0.930982i | \(0.381046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.0050 | 1.84445 | ||||||||
\(86\) | −3.84121 | −0.414208 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2110 | −1.29436 | −0.647181 | − | 0.762337i | \(-0.724052\pi\) | ||||
−0.647181 | + | 0.762337i | \(0.724052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.5182 | 2.15089 | ||||||||
\(92\) | 0.169185 | 0.0176387 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.03768 | 0.107028 | ||||||||
\(95\) | −17.0132 | −1.74552 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.5359 | 1.78050 | 0.890249 | − | 0.455474i | \(-0.150530\pi\) | ||||
0.890249 | + | 0.455474i | \(0.150530\pi\) | |||||||
\(98\) | −6.86764 | −0.693737 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.1292 | 1.01292 | ||||||||
\(101\) | 6.73880 | 0.670536 | 0.335268 | − | 0.942123i | \(-0.391173\pi\) | ||||
0.335268 | + | 0.942123i | \(0.391173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9510 | −1.47317 | −0.736583 | − | 0.676347i | \(-0.763562\pi\) | ||||
−0.736583 | + | 0.676347i | \(0.763562\pi\) | |||||||
\(104\) | 5.50981 | 0.540282 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.91374 | 0.671521 | ||||||||
\(107\) | −4.06329 | −0.392813 | −0.196407 | − | 0.980523i | \(-0.562927\pi\) | ||||
−0.196407 | + | 0.980523i | \(0.562927\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7612 | 1.50965 | 0.754825 | − | 0.655927i | \(-0.227722\pi\) | ||||
0.754825 | + | 0.655927i | \(0.227722\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.72393 | −0.351878 | ||||||||
\(113\) | 0.634344 | 0.0596741 | 0.0298370 | − | 0.999555i | \(-0.490501\pi\) | ||||
0.0298370 | + | 0.999555i | \(0.490501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.658065 | 0.0613649 | ||||||||
\(116\) | 8.39728 | 0.779668 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.69189 | 0.247809 | ||||||||
\(119\) | −16.2806 | −1.49244 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.6852 | 0.967395 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.337037 | −0.0302668 | ||||||||
\(125\) | 19.9506 | 1.78444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.64282 | 0.766926 | 0.383463 | − | 0.923556i | \(-0.374731\pi\) | ||||
0.383463 | + | 0.923556i | \(0.374731\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 21.4311 | 1.87963 | ||||||||
\(131\) | −0.692672 | −0.0605191 | −0.0302595 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302595 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.2885 | 1.41239 | ||||||||
\(134\) | 11.4875 | 0.992365 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.37189 | −0.374886 | ||||||||
\(137\) | 9.77714 | 0.835317 | 0.417659 | − | 0.908604i | \(-0.362851\pi\) | ||||
0.417659 | + | 0.908604i | \(0.362851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00759 | 0.255100 | 0.127550 | − | 0.991832i | \(-0.459289\pi\) | ||||
0.127550 | + | 0.991832i | \(0.459289\pi\) | |||||||
\(140\) | −14.4847 | −1.22418 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.7472 | −1.06972 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32.6623 | 2.71245 | ||||||||
\(146\) | −5.27159 | −0.436280 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.89975 | 0.156158 | ||||||||
\(149\) | 9.16847 | 0.751110 | 0.375555 | − | 0.926800i | \(-0.377452\pi\) | ||||
0.375555 | + | 0.926800i | \(0.377452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.84056 | 0.149783 | 0.0748914 | − | 0.997192i | \(-0.476139\pi\) | ||||
0.0748914 | + | 0.997192i | \(0.476139\pi\) | |||||||
\(152\) | 4.37400 | 0.354778 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.31095 | −0.105298 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.95486 | −0.634867 | −0.317433 | − | 0.948281i | \(-0.602821\pi\) | ||||
−0.317433 | + | 0.948281i | \(0.602821\pi\) | |||||||
\(158\) | −10.2281 | −0.813704 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.88962 | −0.307502 | ||||||||
\(161\) | −0.630032 | −0.0496535 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.10949 | −0.0869017 | −0.0434509 | − | 0.999056i | \(-0.513835\pi\) | ||||
−0.0434509 | + | 0.999056i | \(0.513835\pi\) | |||||||
\(164\) | 4.97703 | 0.388640 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.65182 | −0.516281 | ||||||||
\(167\) | 5.03898 | 0.389928 | 0.194964 | − | 0.980810i | \(-0.437541\pi\) | ||||
0.194964 | + | 0.980810i | \(0.437541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.3581 | 1.33524 | ||||||||
\(170\) | −17.0050 | −1.30422 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.84121 | 0.292889 | ||||||||
\(173\) | 2.21200 | 0.168175 | 0.0840877 | − | 0.996458i | \(-0.473202\pi\) | ||||
0.0840877 | + | 0.996458i | \(0.473202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −37.7203 | −2.85139 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.2110 | 0.915252 | ||||||||
\(179\) | 20.1845 | 1.50866 | 0.754332 | − | 0.656493i | \(-0.227961\pi\) | ||||
0.754332 | + | 0.656493i | \(0.227961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3099 | 1.36097 | 0.680483 | − | 0.732764i | \(-0.261770\pi\) | ||||
0.680483 | + | 0.732764i | \(0.261770\pi\) | |||||||
\(182\) | −20.5182 | −1.52091 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.169185 | −0.0124725 | ||||||||
\(185\) | 7.38931 | 0.543273 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.03768 | −0.0756805 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.0132 | 1.23427 | ||||||||
\(191\) | −5.91014 | −0.427643 | −0.213821 | − | 0.976873i | \(-0.568591\pi\) | ||||
−0.213821 | + | 0.976873i | \(0.568591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.16369 | −0.515654 | −0.257827 | − | 0.966191i | \(-0.583006\pi\) | ||||
−0.257827 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(194\) | −17.5359 | −1.25900 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.86764 | 0.490546 | ||||||||
\(197\) | 18.0381 | 1.28516 | 0.642581 | − | 0.766218i | \(-0.277864\pi\) | ||||
0.642581 | + | 0.766218i | \(0.277864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5714 | −0.891166 | −0.445583 | − | 0.895241i | \(-0.647004\pi\) | ||||
−0.445583 | + | 0.895241i | \(0.647004\pi\) | |||||||
\(200\) | −10.1292 | −0.716241 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.73880 | −0.474140 | ||||||||
\(203\) | −31.2709 | −2.19479 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.3588 | 1.35207 | ||||||||
\(206\) | 14.9510 | 1.04169 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.50981 | −0.382037 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5656 | 1.55348 | 0.776741 | − | 0.629820i | \(-0.216871\pi\) | ||||
0.776741 | + | 0.629820i | \(0.216871\pi\) | |||||||
\(212\) | −6.91374 | −0.474837 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.06329 | 0.277761 | ||||||||
\(215\) | 14.9409 | 1.01896 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.25510 | 0.0852019 | ||||||||
\(218\) | −15.7612 | −1.06748 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0883 | −1.62035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.6187 | 1.71556 | 0.857778 | − | 0.514020i | \(-0.171844\pi\) | ||||
0.857778 | + | 0.514020i | \(0.171844\pi\) | |||||||
\(224\) | 3.72393 | 0.248815 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.634344 | −0.0421959 | ||||||||
\(227\) | −9.61057 | −0.637876 | −0.318938 | − | 0.947776i | \(-0.603326\pi\) | ||||
−0.318938 | + | 0.947776i | \(0.603326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.14702 | −0.207961 | −0.103980 | − | 0.994579i | \(-0.533158\pi\) | ||||
−0.103980 | + | 0.994579i | \(0.533158\pi\) | |||||||
\(230\) | −0.658065 | −0.0433915 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.39728 | −0.551309 | ||||||||
\(233\) | 3.37892 | 0.221361 | 0.110680 | − | 0.993856i | \(-0.464697\pi\) | ||||
0.110680 | + | 0.993856i | \(0.464697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.03618 | −0.263291 | ||||||||
\(236\) | −2.69189 | −0.175227 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.2806 | 1.05531 | ||||||||
\(239\) | −2.96663 | −0.191896 | −0.0959478 | − | 0.995386i | \(-0.530588\pi\) | ||||
−0.0959478 | + | 0.995386i | \(0.530588\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0533 | 1.42058 | 0.710289 | − | 0.703910i | \(-0.248564\pi\) | ||||
0.710289 | + | 0.703910i | \(0.248564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.6852 | −0.684052 | ||||||||
\(245\) | 26.7126 | 1.70660 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0999 | 1.53344 | ||||||||
\(248\) | 0.337037 | 0.0214019 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −19.9506 | −1.26179 | ||||||||
\(251\) | 15.6905 | 0.990378 | 0.495189 | − | 0.868785i | \(-0.335099\pi\) | ||||
0.495189 | + | 0.868785i | \(0.335099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.64282 | −0.542299 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.3955 | −0.897969 | −0.448985 | − | 0.893539i | \(-0.648214\pi\) | ||||
−0.448985 | + | 0.893539i | \(0.648214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.07453 | −0.439590 | ||||||||
\(260\) | −21.4311 | −1.32910 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.692672 | 0.0427934 | ||||||||
\(263\) | 19.2655 | 1.18796 | 0.593980 | − | 0.804480i | \(-0.297556\pi\) | ||||
0.593980 | + | 0.804480i | \(0.297556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.8918 | −1.65195 | ||||||||
\(266\) | −16.2885 | −0.998709 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.4875 | −0.701708 | ||||||||
\(269\) | 28.9688 | 1.76626 | 0.883130 | − | 0.469128i | \(-0.155432\pi\) | ||||
0.883130 | + | 0.469128i | \(0.155432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8648 | −1.20670 | −0.603351 | − | 0.797476i | \(-0.706168\pi\) | ||||
−0.603351 | + | 0.797476i | \(0.706168\pi\) | |||||||
\(272\) | 4.37189 | 0.265085 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.77714 | −0.590659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.9415 | 0.957829 | 0.478915 | − | 0.877861i | \(-0.341030\pi\) | ||||
0.478915 | + | 0.877861i | \(0.341030\pi\) | |||||||
\(278\) | −3.00759 | −0.180383 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.4847 | 0.865625 | ||||||||
\(281\) | −8.07105 | −0.481478 | −0.240739 | − | 0.970590i | \(-0.577390\pi\) | ||||
−0.240739 | + | 0.970590i | \(0.577390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.0217 | −1.24961 | −0.624806 | − | 0.780780i | \(-0.714822\pi\) | ||||
−0.624806 | + | 0.780780i | \(0.714822\pi\) | |||||||
\(284\) | 12.7472 | 0.756406 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.5341 | −1.09403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.11339 | 0.124317 | ||||||||
\(290\) | −32.6623 | −1.91800 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.27159 | 0.308497 | ||||||||
\(293\) | 10.8568 | 0.634259 | 0.317130 | − | 0.948382i | \(-0.397281\pi\) | ||||
0.317130 | + | 0.948382i | \(0.397281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.4705 | −0.609614 | ||||||||
\(296\) | −1.89975 | −0.110421 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.16847 | −0.531115 | ||||||||
\(299\) | −0.932177 | −0.0539092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3044 | −0.824491 | ||||||||
\(302\) | −1.84056 | −0.105912 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.37400 | −0.250866 | ||||||||
\(305\) | −41.5615 | −2.37981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3580 | −0.648235 | −0.324118 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324118 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.31095 | 0.0744568 | ||||||||
\(311\) | −0.830666 | −0.0471027 | −0.0235514 | − | 0.999723i | \(-0.507497\pi\) | ||||
−0.0235514 | + | 0.999723i | \(0.507497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.68426 | 0.0951999 | 0.0476000 | − | 0.998866i | \(-0.484843\pi\) | ||||
0.0476000 | + | 0.998866i | \(0.484843\pi\) | |||||||
\(314\) | 7.95486 | 0.448919 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2281 | 0.575376 | ||||||||
\(317\) | −18.1677 | −1.02040 | −0.510199 | − | 0.860056i | \(-0.670428\pi\) | ||||
−0.510199 | + | 0.860056i | \(0.670428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.88962 | 0.217437 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.630032 | 0.0351103 | ||||||||
\(323\) | −19.1226 | −1.06401 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −55.8099 | −3.09578 | ||||||||
\(326\) | 1.10949 | 0.0614488 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.97703 | −0.274810 | ||||||||
\(329\) | 3.86424 | 0.213043 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.1155 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(332\) | 6.65182 | 0.365066 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.03898 | −0.275721 | ||||||||
\(335\) | −44.6819 | −2.44123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.15948 | 0.390002 | 0.195001 | − | 0.980803i | \(-0.437529\pi\) | ||||
0.195001 | + | 0.980803i | \(0.437529\pi\) | |||||||
\(338\) | −17.3581 | −0.944154 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 17.0050 | 0.922225 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.492889 | 0.0266135 | ||||||||
\(344\) | −3.84121 | −0.207104 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.21200 | −0.118918 | ||||||||
\(347\) | −1.98859 | −0.106753 | −0.0533765 | − | 0.998574i | \(-0.516998\pi\) | ||||
−0.0533765 | + | 0.998574i | \(0.516998\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3795 | 0.716187 | 0.358093 | − | 0.933686i | \(-0.383427\pi\) | ||||
0.358093 | + | 0.933686i | \(0.383427\pi\) | |||||||
\(350\) | 37.7203 | 2.01624 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.543932 | −0.0289506 | −0.0144753 | − | 0.999895i | \(-0.504608\pi\) | ||||
−0.0144753 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.5818 | 2.63153 | ||||||||
\(356\) | −12.2110 | −0.647181 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.1845 | −1.06679 | ||||||||
\(359\) | −18.6625 | −0.984967 | −0.492483 | − | 0.870322i | \(-0.663911\pi\) | ||||
−0.492483 | + | 0.870322i | \(0.663911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.131848 | 0.00693939 | ||||||||
\(362\) | −18.3099 | −0.962348 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.5182 | 1.07544 | ||||||||
\(365\) | 20.5045 | 1.07326 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.70810 | 0.297960 | 0.148980 | − | 0.988840i | \(-0.452401\pi\) | ||||
0.148980 | + | 0.988840i | \(0.452401\pi\) | |||||||
\(368\) | 0.169185 | 0.00881937 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.38931 | −0.384152 | ||||||||
\(371\) | 25.7463 | 1.33668 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.6045 | −1.94709 | −0.973544 | − | 0.228498i | \(-0.926619\pi\) | ||||
−0.973544 | + | 0.228498i | \(0.926619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.03768 | 0.0535142 | ||||||||
\(377\) | −46.2675 | −2.38290 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4100 | 1.09976 | 0.549878 | − | 0.835245i | \(-0.314674\pi\) | ||||
0.549878 | + | 0.835245i | \(0.314674\pi\) | |||||||
\(380\) | −17.0132 | −0.872759 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.91014 | 0.302389 | ||||||||
\(383\) | 34.7444 | 1.77536 | 0.887678 | − | 0.460465i | \(-0.152317\pi\) | ||||
0.887678 | + | 0.460465i | \(0.152317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.16369 | 0.364622 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.5359 | 0.890249 | ||||||||
\(389\) | 8.66923 | 0.439547 | 0.219774 | − | 0.975551i | \(-0.429468\pi\) | ||||
0.219774 | + | 0.975551i | \(0.429468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.739657 | 0.0374060 | ||||||||
\(392\) | −6.86764 | −0.346868 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0381 | −0.908746 | ||||||||
\(395\) | 39.7835 | 2.00172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0635 | 0.655640 | 0.327820 | − | 0.944740i | \(-0.393686\pi\) | ||||
0.327820 | + | 0.944740i | \(0.393686\pi\) | |||||||
\(398\) | 12.5714 | 0.630149 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.1292 | 0.506459 | ||||||||
\(401\) | 3.29858 | 0.164723 | 0.0823616 | − | 0.996603i | \(-0.473754\pi\) | ||||
0.0823616 | + | 0.996603i | \(0.473754\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.85701 | 0.0925044 | ||||||||
\(404\) | 6.73880 | 0.335268 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.2709 | 1.55195 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0301 | −1.28710 | −0.643552 | − | 0.765402i | \(-0.722540\pi\) | ||||
−0.643552 | + | 0.765402i | \(0.722540\pi\) | |||||||
\(410\) | −19.3588 | −0.956061 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.9510 | −0.736583 | ||||||||
\(413\) | 10.0244 | 0.493269 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.8731 | 1.27006 | ||||||||
\(416\) | 5.50981 | 0.270141 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.7916 | −1.11344 | −0.556722 | − | 0.830699i | \(-0.687941\pi\) | ||||
−0.556722 | + | 0.830699i | \(0.687941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.59051 | −0.321202 | −0.160601 | − | 0.987019i | \(-0.551343\pi\) | ||||
−0.160601 | + | 0.987019i | \(0.551343\pi\) | |||||||
\(422\) | −22.5656 | −1.09848 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.91374 | 0.335761 | ||||||||
\(425\) | 44.2836 | 2.14807 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.7910 | 1.92562 | ||||||||
\(428\) | −4.06329 | −0.196407 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.9409 | −0.720512 | ||||||||
\(431\) | −3.62968 | −0.174836 | −0.0874178 | − | 0.996172i | \(-0.527862\pi\) | ||||
−0.0874178 | + | 0.996172i | \(0.527862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.05071 | 0.0504938 | 0.0252469 | − | 0.999681i | \(-0.491963\pi\) | ||||
0.0252469 | + | 0.999681i | \(0.491963\pi\) | |||||||
\(434\) | −1.25510 | −0.0602468 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.7612 | 0.754825 | ||||||||
\(437\) | −0.740014 | −0.0353997 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.1100 | −1.67571 | −0.837854 | − | 0.545894i | \(-0.816190\pi\) | ||||
−0.837854 | + | 0.545894i | \(0.816190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.0883 | 1.14576 | ||||||||
\(443\) | 24.6020 | 1.16888 | 0.584438 | − | 0.811439i | \(-0.301315\pi\) | ||||
0.584438 | + | 0.811439i | \(0.301315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.4961 | −2.25153 | ||||||||
\(446\) | −25.6187 | −1.21308 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.72393 | −0.175939 | ||||||||
\(449\) | −22.6302 | −1.06799 | −0.533993 | − | 0.845489i | \(-0.679309\pi\) | ||||
−0.533993 | + | 0.845489i | \(0.679309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.634344 | 0.0298370 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.61057 | 0.451046 | ||||||||
\(455\) | 79.8079 | 3.74145 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.46787 | −0.0686640 | −0.0343320 | − | 0.999410i | \(-0.510930\pi\) | ||||
−0.0343320 | + | 0.999410i | \(0.510930\pi\) | |||||||
\(458\) | 3.14702 | 0.147050 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.658065 | 0.0306825 | ||||||||
\(461\) | 3.89222 | 0.181279 | 0.0906393 | − | 0.995884i | \(-0.471109\pi\) | ||||
0.0906393 | + | 0.995884i | \(0.471109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.722010 | 0.0335547 | 0.0167773 | − | 0.999859i | \(-0.494659\pi\) | ||||
0.0167773 | + | 0.999859i | \(0.494659\pi\) | |||||||
\(464\) | 8.39728 | 0.389834 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.37892 | −0.156526 | ||||||||
\(467\) | −10.4531 | −0.483713 | −0.241857 | − | 0.970312i | \(-0.577756\pi\) | ||||
−0.241857 | + | 0.970312i | \(0.577756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.7785 | 1.97533 | ||||||||
\(470\) | 4.03618 | 0.186175 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.69189 | 0.123904 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −44.3050 | −2.03285 | ||||||||
\(476\) | −16.2806 | −0.746220 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.96663 | 0.135691 | ||||||||
\(479\) | −21.5459 | −0.984459 | −0.492230 | − | 0.870465i | \(-0.663818\pi\) | ||||
−0.492230 | + | 0.870465i | \(0.663818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.4673 | −0.477266 | ||||||||
\(482\) | −22.0533 | −1.00450 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 68.2080 | 3.09716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.32816 | 0.105499 | 0.0527496 | − | 0.998608i | \(-0.483201\pi\) | ||||
0.0527496 | + | 0.998608i | \(0.483201\pi\) | |||||||
\(488\) | 10.6852 | 0.483698 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −26.7126 | −1.20675 | ||||||||
\(491\) | 13.4826 | 0.608462 | 0.304231 | − | 0.952598i | \(-0.401601\pi\) | ||||
0.304231 | + | 0.952598i | \(0.401601\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.7120 | 1.65342 | ||||||||
\(494\) | −24.0999 | −1.08431 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.337037 | −0.0151334 | ||||||||
\(497\) | −47.4696 | −2.12930 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.6919 | 1.91115 | 0.955575 | − | 0.294747i | \(-0.0952355\pi\) | ||||
0.955575 | + | 0.294747i | \(0.0952355\pi\) | |||||||
\(500\) | 19.9506 | 0.892218 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.6905 | −0.700303 | ||||||||
\(503\) | −29.1100 | −1.29795 | −0.648976 | − | 0.760809i | \(-0.724802\pi\) | ||||
−0.648976 | + | 0.760809i | \(0.724802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.2114 | 1.16639 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.64282 | 0.383463 | ||||||||
\(509\) | 19.2578 | 0.853586 | 0.426793 | − | 0.904349i | \(-0.359643\pi\) | ||||
0.426793 | + | 0.904349i | \(0.359643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.6310 | −0.868425 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.3955 | 0.634960 | ||||||||
\(515\) | −58.1538 | −2.56256 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.07453 | 0.310837 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.4311 | 0.939816 | ||||||||
\(521\) | 29.7366 | 1.30279 | 0.651393 | − | 0.758740i | \(-0.274185\pi\) | ||||
0.651393 | + | 0.758740i | \(0.274185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4944 | −0.590070 | −0.295035 | − | 0.955486i | \(-0.595331\pi\) | ||||
−0.295035 | + | 0.955486i | \(0.595331\pi\) | |||||||
\(524\) | −0.692672 | −0.0302595 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.2655 | −0.840015 | ||||||||
\(527\) | −1.47349 | −0.0641861 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9714 | −0.998756 | ||||||||
\(530\) | 26.8918 | 1.16811 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.2885 | 0.706194 | ||||||||
\(533\) | −27.4225 | −1.18780 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8047 | −0.683296 | ||||||||
\(536\) | 11.4875 | 0.496182 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.9688 | −1.24893 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5154 | 0.581074 | 0.290537 | − | 0.956864i | \(-0.406166\pi\) | ||||
0.290537 | + | 0.956864i | \(0.406166\pi\) | |||||||
\(542\) | 19.8648 | 0.853267 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.37189 | −0.187443 | ||||||||
\(545\) | 61.3052 | 2.62602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7611 | −0.973193 | −0.486596 | − | 0.873627i | \(-0.661762\pi\) | ||||
−0.486596 | + | 0.873627i | \(0.661762\pi\) | |||||||
\(548\) | 9.77714 | 0.417659 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.7297 | −1.56474 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.0887 | −1.61970 | ||||||||
\(554\) | −15.9415 | −0.677288 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.00759 | 0.127550 | ||||||||
\(557\) | −6.41046 | −0.271620 | −0.135810 | − | 0.990735i | \(-0.543364\pi\) | ||||
−0.135810 | + | 0.990735i | \(0.543364\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.1643 | −0.895156 | ||||||||
\(560\) | −14.4847 | −0.612090 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.07105 | 0.340457 | ||||||||
\(563\) | −6.52972 | −0.275195 | −0.137597 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137597 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.46736 | 0.103803 | ||||||||
\(566\) | 21.0217 | 0.883610 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7472 | −0.534860 | ||||||||
\(569\) | 32.1193 | 1.34651 | 0.673255 | − | 0.739411i | \(-0.264896\pi\) | ||||
0.673255 | + | 0.739411i | \(0.264896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.178273 | 0.00746047 | 0.00373024 | − | 0.999993i | \(-0.498813\pi\) | ||||
0.00373024 | + | 0.999993i | \(0.498813\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.5341 | 0.773598 | ||||||||
\(575\) | 1.71370 | 0.0714664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.2692 | −1.55154 | −0.775769 | − | 0.631017i | \(-0.782638\pi\) | ||||
−0.775769 | + | 0.631017i | \(0.782638\pi\) | |||||||
\(578\) | −2.11339 | −0.0879053 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 32.6623 | 1.35623 | ||||||||
\(581\) | −24.7709 | −1.02767 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.27159 | −0.218140 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.8568 | −0.448489 | ||||||||
\(587\) | 17.4735 | 0.721208 | 0.360604 | − | 0.932719i | \(-0.382571\pi\) | ||||
0.360604 | + | 0.932719i | \(0.382571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.47420 | 0.0607433 | ||||||||
\(590\) | 10.4705 | 0.431062 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.89975 | 0.0780792 | ||||||||
\(593\) | −33.4398 | −1.37321 | −0.686603 | − | 0.727032i | \(-0.740899\pi\) | ||||
−0.686603 | + | 0.727032i | \(0.740899\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −63.3254 | −2.59609 | ||||||||
\(596\) | 9.16847 | 0.375555 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.932177 | 0.0381195 | ||||||||
\(599\) | 22.4464 | 0.917136 | 0.458568 | − | 0.888659i | \(-0.348363\pi\) | ||||
0.458568 | + | 0.888659i | \(0.348363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1280 | 1.02499 | 0.512497 | − | 0.858689i | \(-0.328721\pi\) | ||||
0.512497 | + | 0.858689i | \(0.328721\pi\) | |||||||
\(602\) | 14.3044 | 0.583003 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.84056 | 0.0748914 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7513 | 0.476971 | 0.238485 | − | 0.971146i | \(-0.423349\pi\) | ||||
0.238485 | + | 0.971146i | \(0.423349\pi\) | |||||||
\(608\) | 4.37400 | 0.177389 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 41.5615 | 1.68278 | ||||||||
\(611\) | 5.71742 | 0.231302 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8488 | 0.680517 | 0.340258 | − | 0.940332i | \(-0.389486\pi\) | ||||
0.340258 | + | 0.940332i | \(0.389486\pi\) | |||||||
\(614\) | 11.3580 | 0.458372 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.4952 | 1.18743 | 0.593716 | − | 0.804675i | \(-0.297660\pi\) | ||||
0.593716 | + | 0.804675i | \(0.297660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.0347 | −0.765068 | −0.382534 | − | 0.923941i | \(-0.624948\pi\) | ||||
−0.382534 | + | 0.923941i | \(0.624948\pi\) | |||||||
\(620\) | −1.31095 | −0.0526489 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.830666 | 0.0333067 | ||||||||
\(623\) | 45.4728 | 1.82183 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26.9544 | 1.07818 | ||||||||
\(626\) | −1.68426 | −0.0673165 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.95486 | −0.317433 | ||||||||
\(629\) | 8.30549 | 0.331162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.464051 | 0.0184736 | 0.00923679 | − | 0.999957i | \(-0.497060\pi\) | ||||
0.00923679 | + | 0.999957i | \(0.497060\pi\) | |||||||
\(632\) | −10.2281 | −0.406852 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.1677 | 0.721531 | ||||||||
\(635\) | 33.6173 | 1.33406 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.8394 | −1.49925 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.88962 | −0.153751 | ||||||||
\(641\) | −48.0978 | −1.89975 | −0.949874 | − | 0.312633i | \(-0.898789\pi\) | ||||
−0.949874 | + | 0.312633i | \(0.898789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.91559 | 0.391033 | 0.195516 | − | 0.980700i | \(-0.437362\pi\) | ||||
0.195516 | + | 0.980700i | \(0.437362\pi\) | |||||||
\(644\) | −0.630032 | −0.0248267 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.1226 | 0.752369 | ||||||||
\(647\) | 45.0843 | 1.77245 | 0.886224 | − | 0.463257i | \(-0.153319\pi\) | ||||
0.886224 | + | 0.463257i | \(0.153319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 55.8099 | 2.18904 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.10949 | −0.0434509 | ||||||||
\(653\) | 7.67438 | 0.300322 | 0.150161 | − | 0.988662i | \(-0.452021\pi\) | ||||
0.150161 | + | 0.988662i | \(0.452021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.69424 | −0.105273 | ||||||||
\(656\) | 4.97703 | 0.194320 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.86424 | −0.150644 | ||||||||
\(659\) | −21.4800 | −0.836743 | −0.418372 | − | 0.908276i | \(-0.637399\pi\) | ||||
−0.418372 | + | 0.908276i | \(0.637399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.0869 | 1.36472 | 0.682362 | − | 0.731015i | \(-0.260953\pi\) | ||||
0.682362 | + | 0.731015i | \(0.260953\pi\) | |||||||
\(662\) | −24.1155 | −0.937276 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.65182 | −0.258141 | ||||||||
\(665\) | 63.3560 | 2.45684 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.42069 | 0.0550094 | ||||||||
\(668\) | 5.03898 | 0.194964 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 44.6819 | 1.72621 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.43001 | −0.324953 | −0.162476 | − | 0.986712i | \(-0.551948\pi\) | ||||
−0.162476 | + | 0.986712i | \(0.551948\pi\) | |||||||
\(674\) | −7.15948 | −0.275773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.3581 | 0.667618 | ||||||||
\(677\) | 14.4454 | 0.555184 | 0.277592 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277592 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −65.3023 | −2.50607 | ||||||||
\(680\) | −17.0050 | −0.652112 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.5728 | 1.39942 | 0.699710 | − | 0.714427i | \(-0.253312\pi\) | ||||
0.699710 | + | 0.714427i | \(0.253312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.0294 | 1.45303 | ||||||||
\(686\) | −0.492889 | −0.0188186 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.84121 | 0.146445 | ||||||||
\(689\) | 38.0934 | 1.45124 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1400 | 0.728120 | 0.364060 | − | 0.931376i | \(-0.381390\pi\) | ||||
0.364060 | + | 0.931376i | \(0.381390\pi\) | |||||||
\(692\) | 2.21200 | 0.0840877 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.98859 | 0.0754857 | ||||||||
\(695\) | 11.6984 | 0.443745 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.7590 | 0.824180 | ||||||||
\(698\) | −13.3795 | −0.506421 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −37.7203 | −1.42570 | ||||||||
\(701\) | 23.1812 | 0.875543 | 0.437771 | − | 0.899086i | \(-0.355768\pi\) | ||||
0.437771 | + | 0.899086i | \(0.355768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.30950 | −0.313399 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.543932 | 0.0204712 | ||||||||
\(707\) | −25.0948 | −0.943788 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.3651 | 1.70372 | 0.851860 | − | 0.523769i | \(-0.175475\pi\) | ||||
0.851860 | + | 0.523769i | \(0.175475\pi\) | |||||||
\(710\) | −49.5818 | −1.86077 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.2110 | 0.457626 | ||||||||
\(713\) | −0.0570216 | −0.00213547 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.1845 | 0.754332 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.6625 | 0.696477 | ||||||||
\(719\) | 0.559793 | 0.0208767 | 0.0104384 | − | 0.999946i | \(-0.496677\pi\) | ||||
0.0104384 | + | 0.999946i | \(0.496677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.6765 | 2.07350 | ||||||||
\(722\) | −0.131848 | −0.00490689 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.3099 | 0.680483 | ||||||||
\(725\) | 85.0576 | 3.15896 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.5446 | −0.799045 | −0.399523 | − | 0.916723i | \(-0.630824\pi\) | ||||
−0.399523 | + | 0.916723i | \(0.630824\pi\) | |||||||
\(728\) | −20.5182 | −0.760453 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.5045 | −0.758906 | ||||||||
\(731\) | 16.7933 | 0.621123 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.2240 | −1.19022 | −0.595111 | − | 0.803643i | \(-0.702892\pi\) | ||||
−0.595111 | + | 0.803643i | \(0.702892\pi\) | |||||||
\(734\) | −5.70810 | −0.210690 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.169185 | −0.00623623 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.79513 | −0.0660350 | −0.0330175 | − | 0.999455i | \(-0.510512\pi\) | ||||
−0.0330175 | + | 0.999455i | \(0.510512\pi\) | |||||||
\(740\) | 7.38931 | 0.271637 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.7463 | −0.945175 | ||||||||
\(743\) | 42.3582 | 1.55397 | 0.776986 | − | 0.629518i | \(-0.216747\pi\) | ||||
0.776986 | + | 0.629518i | \(0.216747\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.6619 | 1.30655 | ||||||||
\(746\) | 37.6045 | 1.37680 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1314 | 0.552889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.2172 | 1.06615 | 0.533075 | − | 0.846068i | \(-0.321036\pi\) | ||||
0.533075 | + | 0.846068i | \(0.321036\pi\) | |||||||
\(752\) | −1.03768 | −0.0378403 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46.2675 | 1.68496 | ||||||||
\(755\) | 7.15909 | 0.260546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.7290 | 1.08052 | 0.540259 | − | 0.841499i | \(-0.318326\pi\) | ||||
0.540259 | + | 0.841499i | \(0.318326\pi\) | |||||||
\(758\) | −21.4100 | −0.777645 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.0132 | 0.617134 | ||||||||
\(761\) | −15.8628 | −0.575024 | −0.287512 | − | 0.957777i | \(-0.592828\pi\) | ||||
−0.287512 | + | 0.957777i | \(0.592828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −58.6936 | −2.12485 | ||||||||
\(764\) | −5.91014 | −0.213821 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.7444 | −1.25537 | ||||||||
\(767\) | 14.8318 | 0.535547 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0451 | 0.722845 | 0.361423 | − | 0.932402i | \(-0.382291\pi\) | ||||
0.361423 | + | 0.932402i | \(0.382291\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.16369 | −0.257827 | ||||||||
\(773\) | 12.0655 | 0.433967 | 0.216984 | − | 0.976175i | \(-0.430378\pi\) | ||||
0.216984 | + | 0.976175i | \(0.430378\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.41391 | −0.122631 | ||||||||
\(776\) | −17.5359 | −0.629501 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.66923 | −0.310807 | ||||||||
\(779\) | −21.7695 | −0.779973 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.739657 | −0.0264501 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.86764 | 0.245273 | ||||||||
\(785\) | −30.9414 | −1.10435 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.8997 | −0.851933 | −0.425967 | − | 0.904739i | \(-0.640066\pi\) | ||||
−0.425967 | + | 0.904739i | \(0.640066\pi\) | |||||||
\(788\) | 18.0381 | 0.642581 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −39.7835 | −1.41543 | ||||||||
\(791\) | −2.36225 | −0.0839920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58.8736 | 2.09066 | ||||||||
\(794\) | −13.0635 | −0.463608 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.5714 | −0.445583 | ||||||||
\(797\) | 39.4934 | 1.39893 | 0.699463 | − | 0.714669i | \(-0.253422\pi\) | ||||
0.699463 | + | 0.714669i | \(0.253422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.53661 | −0.160494 | ||||||||
\(800\) | −10.1292 | −0.358121 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.29858 | −0.116477 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.45059 | −0.0863719 | ||||||||
\(806\) | −1.85701 | −0.0654105 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.73880 | −0.237070 | ||||||||
\(809\) | 15.8885 | 0.558609 | 0.279304 | − | 0.960203i | \(-0.409896\pi\) | ||||
0.279304 | + | 0.960203i | \(0.409896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0176 | −0.351765 | −0.175882 | − | 0.984411i | \(-0.556278\pi\) | ||||
−0.175882 | + | 0.984411i | \(0.556278\pi\) | |||||||
\(812\) | −31.2709 | −1.09739 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.31549 | −0.151165 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.8014 | −0.587808 | ||||||||
\(818\) | 26.0301 | 0.910120 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.3588 | 0.676037 | ||||||||
\(821\) | 43.6797 | 1.52443 | 0.762217 | − | 0.647322i | \(-0.224111\pi\) | ||||
0.762217 | + | 0.647322i | \(0.224111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.5753 | −1.13550 | −0.567751 | − | 0.823200i | \(-0.692186\pi\) | ||||
−0.567751 | + | 0.823200i | \(0.692186\pi\) | |||||||
\(824\) | 14.9510 | 0.520843 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.0244 | −0.348794 | ||||||||
\(827\) | −25.8332 | −0.898308 | −0.449154 | − | 0.893454i | \(-0.648275\pi\) | ||||
−0.449154 | + | 0.893454i | \(0.648275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.4608 | −0.884289 | −0.442145 | − | 0.896944i | \(-0.645782\pi\) | ||||
−0.442145 | + | 0.896944i | \(0.645782\pi\) | |||||||
\(830\) | −25.8731 | −0.898068 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.50981 | −0.191018 | ||||||||
\(833\) | 30.0246 | 1.04029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5998 | 0.678277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.7916 | 0.787323 | ||||||||
\(839\) | 17.1512 | 0.592125 | 0.296063 | − | 0.955169i | \(-0.404326\pi\) | ||||
0.296063 | + | 0.955169i | \(0.404326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.5144 | 1.43153 | ||||||||
\(842\) | 6.59051 | 0.227124 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.5656 | 0.776741 | ||||||||
\(845\) | 67.5163 | 2.32263 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.91374 | −0.237419 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −44.2836 | −1.51892 | ||||||||
\(851\) | 0.321409 | 0.0110178 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.71717 | 0.195752 | 0.0978760 | − | 0.995199i | \(-0.468795\pi\) | ||||
0.0978760 | + | 0.995199i | \(0.468795\pi\) | |||||||
\(854\) | −39.7910 | −1.36162 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.06329 | 0.138880 | ||||||||
\(857\) | −13.0129 | −0.444511 | −0.222256 | − | 0.974988i | \(-0.571342\pi\) | ||||
−0.222256 | + | 0.974988i | \(0.571342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.5028 | −1.24546 | −0.622729 | − | 0.782437i | \(-0.713976\pi\) | ||||
−0.622729 | + | 0.782437i | \(0.713976\pi\) | |||||||
\(860\) | 14.9409 | 0.509479 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.62968 | 0.123627 | ||||||||
\(863\) | −7.72911 | −0.263102 | −0.131551 | − | 0.991309i | \(-0.541996\pi\) | ||||
−0.131551 | + | 0.991309i | \(0.541996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.60386 | 0.292540 | ||||||||
\(866\) | −1.05071 | −0.0357045 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.25510 | 0.0426009 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.2937 | 2.14463 | ||||||||
\(872\) | −15.7612 | −0.533742 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.740014 | 0.0250313 | ||||||||
\(875\) | −74.2946 | −2.51161 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.5327 | −1.60507 | −0.802533 | − | 0.596607i | \(-0.796515\pi\) | ||||
−0.802533 | + | 0.596607i | \(0.796515\pi\) | |||||||
\(878\) | 35.1100 | 1.18490 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.3262 | −1.52708 | −0.763539 | − | 0.645761i | \(-0.776540\pi\) | ||||
−0.763539 | + | 0.645761i | \(0.776540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.8274 | −1.50856 | −0.754281 | − | 0.656552i | \(-0.772014\pi\) | ||||
−0.754281 | + | 0.656552i | \(0.772014\pi\) | |||||||
\(884\) | −24.0883 | −0.810177 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6020 | −0.826519 | ||||||||
\(887\) | 12.7328 | 0.427526 | 0.213763 | − | 0.976886i | \(-0.431428\pi\) | ||||
0.213763 | + | 0.976886i | \(0.431428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.1852 | −1.07946 | ||||||||
\(890\) | 47.4961 | 1.59207 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.6187 | 0.857778 | ||||||||
\(893\) | 4.53880 | 0.151885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 78.5103 | 2.62431 | ||||||||
\(896\) | 3.72393 | 0.124408 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.6302 | 0.755181 | ||||||||
\(899\) | −2.83020 | −0.0943923 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.2261 | −1.00698 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.634344 | −0.0210980 | ||||||||
\(905\) | 71.2187 | 2.36739 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.83861 | 0.260277 | 0.130138 | − | 0.991496i | \(-0.458458\pi\) | ||||
0.130138 | + | 0.991496i | \(0.458458\pi\) | |||||||
\(908\) | −9.61057 | −0.318938 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −79.8079 | −2.64561 | ||||||||
\(911\) | −23.6254 | −0.782746 | −0.391373 | − | 0.920232i | \(-0.628000\pi\) | ||||
−0.391373 | + | 0.920232i | \(0.628000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.46787 | 0.0485528 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.14702 | −0.103980 | ||||||||
\(917\) | 2.57946 | 0.0851814 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.7167 | 1.87091 | 0.935456 | − | 0.353442i | \(-0.114989\pi\) | ||||
0.935456 | + | 0.353442i | \(0.114989\pi\) | |||||||
\(920\) | −0.658065 | −0.0216958 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.89222 | −0.128183 | ||||||||
\(923\) | −70.2346 | −2.31180 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2429 | 0.632703 | ||||||||
\(926\) | −0.722010 | −0.0237267 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.39728 | −0.275654 | ||||||||
\(929\) | −7.36655 | −0.241689 | −0.120844 | − | 0.992671i | \(-0.538560\pi\) | ||||
−0.120844 | + | 0.992671i | \(0.538560\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.0390 | −0.984490 | ||||||||
\(932\) | 3.37892 | 0.110680 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.4531 | 0.342037 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5554 | −0.900194 | −0.450097 | − | 0.892980i | \(-0.648611\pi\) | ||||
−0.450097 | + | 0.892980i | \(0.648611\pi\) | |||||||
\(938\) | −42.7785 | −1.39677 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.03618 | −0.131646 | ||||||||
\(941\) | −25.8859 | −0.843856 | −0.421928 | − | 0.906629i | \(-0.638646\pi\) | ||||
−0.421928 | + | 0.906629i | \(0.638646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.842037 | 0.0274205 | ||||||||
\(944\) | −2.69189 | −0.0876137 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.0180 | −1.30041 | −0.650206 | − | 0.759758i | \(-0.725317\pi\) | ||||
−0.650206 | + | 0.759758i | \(0.725317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.0455 | −0.942856 | ||||||||
\(950\) | 44.3050 | 1.43744 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.2806 | 0.527657 | ||||||||
\(953\) | −14.8324 | −0.480468 | −0.240234 | − | 0.970715i | \(-0.577224\pi\) | ||||
−0.240234 | + | 0.970715i | \(0.577224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.9882 | −0.743882 | ||||||||
\(956\) | −2.96663 | −0.0959478 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.5459 | 0.696118 | ||||||||
\(959\) | −36.4094 | −1.17572 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8864 | −0.996336 | ||||||||
\(962\) | 10.4673 | 0.337478 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.0533 | 0.710289 | ||||||||
\(965\) | −27.8641 | −0.896976 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.6333 | 1.72473 | 0.862366 | − | 0.506286i | \(-0.168982\pi\) | ||||
0.862366 | + | 0.506286i | \(0.168982\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −68.2080 | −2.19003 | ||||||||
\(971\) | −8.30534 | −0.266531 | −0.133265 | − | 0.991080i | \(-0.542546\pi\) | ||||
−0.133265 | + | 0.991080i | \(0.542546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2001 | −0.359057 | ||||||||
\(974\) | −2.32816 | −0.0745992 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.6852 | −0.342026 | ||||||||
\(977\) | −1.11029 | −0.0355214 | −0.0177607 | − | 0.999842i | \(-0.505654\pi\) | ||||
−0.0177607 | + | 0.999842i | \(0.505654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 26.7126 | 0.853301 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.4826 | −0.430248 | ||||||||
\(983\) | −41.7968 | −1.33311 | −0.666556 | − | 0.745455i | \(-0.732232\pi\) | ||||
−0.666556 | + | 0.745455i | \(0.732232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 70.1614 | 2.23553 | ||||||||
\(986\) | −36.7120 | −1.16915 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0999 | 0.766720 | ||||||||
\(989\) | 0.649874 | 0.0206648 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.5023 | 1.44543 | 0.722715 | − | 0.691147i | \(-0.242894\pi\) | ||||
0.722715 | + | 0.691147i | \(0.242894\pi\) | |||||||
\(992\) | 0.337037 | 0.0107009 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 47.4696 | 1.50564 | ||||||||
\(995\) | −48.8982 | −1.55018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2855 | 0.452427 | 0.226213 | − | 0.974078i | \(-0.427365\pi\) | ||||
0.226213 | + | 0.974078i | \(0.427365\pi\) | |||||||
\(998\) | −42.6919 | −1.35139 | ||||||||
\(999\) | 0 | 0 |
(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 | 6534.2.a.cv.1.5 | 6 | ||
3.2 | odd | 2 | 6534.2.a.cw.1.2 | 6 | |||
11.2 | odd | 10 | 594.2.f.k.433.1 | ✓ | 12 | ||
11.6 | odd | 10 | 594.2.f.k.487.1 | yes | 12 | ||
11.10 | odd | 2 | 6534.2.a.cx.1.5 | 6 | |||
33.2 | even | 10 | 594.2.f.l.433.3 | yes | 12 | ||
33.17 | even | 10 | 594.2.f.l.487.3 | yes | 12 | ||
33.32 | even | 2 | 6534.2.a.cu.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
594.2.f.k.433.1 | ✓ | 12 | 11.2 | odd | 10 | ||
594.2.f.k.487.1 | yes | 12 | 11.6 | odd | 10 | ||
594.2.f.l.433.3 | yes | 12 | 33.2 | even | 10 | ||
594.2.f.l.487.3 | yes | 12 | 33.17 | even | 10 | ||
6534.2.a.cu.1.2 | 6 | 33.32 | even | 2 | |||
6534.2.a.cv.1.5 | 6 | 1.1 | even | 1 | trivial | ||
6534.2.a.cw.1.2 | 6 | 3.2 | odd | 2 | |||
6534.2.a.cx.1.5 | 6 | 11.10 | odd | 2 |