Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.14336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.60804\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.27411 | 1.01701 | 0.508506 | − | 0.861058i | \(-0.330198\pi\) | ||||
0.508506 | + | 0.861058i | \(0.330198\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.27411 | −0.719136 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.63029 | 1.28421 | 0.642106 | − | 0.766616i | \(-0.278061\pi\) | ||||
0.642106 | + | 0.766616i | \(0.278061\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.27411 | −0.587172 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.554318 | −0.134442 | −0.0672209 | − | 0.997738i | \(-0.521413\pi\) | ||||
−0.0672209 | + | 0.997738i | \(0.521413\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.07597 | −0.935092 | −0.467546 | − | 0.883969i | \(-0.654862\pi\) | ||||
−0.467546 | + | 0.883969i | \(0.654862\pi\) | |||||||
\(20\) | 2.27411 | 0.508506 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −6.93587 | −1.44623 | −0.723114 | − | 0.690729i | \(-0.757290\pi\) | ||||
−0.723114 | + | 0.690729i | \(0.757290\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.171573 | 0.0343146 | ||||||||
\(26\) | −4.63029 | −0.908075 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | 2.27411 | 0.415194 | ||||||||
\(31\) | −7.68832 | −1.38086 | −0.690432 | − | 0.723398i | \(-0.742579\pi\) | ||||
−0.690432 | + | 0.723398i | \(0.742579\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0.554318 | 0.0950647 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.8729 | 1.78750 | 0.893749 | − | 0.448567i | \(-0.148065\pi\) | ||||
0.893749 | + | 0.448567i | \(0.148065\pi\) | |||||||
\(38\) | 4.07597 | 0.661210 | ||||||||
\(39\) | −4.63029 | −0.741440 | ||||||||
\(40\) | −2.27411 | −0.359568 | ||||||||
\(41\) | 0.554318 | 0.0865699 | 0.0432850 | − | 0.999063i | \(-0.486218\pi\) | ||||
0.0432850 | + | 0.999063i | \(0.486218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.59272 | −1.31038 | −0.655189 | − | 0.755465i | \(-0.727411\pi\) | ||||
−0.655189 | + | 0.755465i | \(0.727411\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.27411 | 0.339004 | ||||||||
\(46\) | 6.93587 | 1.02264 | ||||||||
\(47\) | −10.9044 | −1.59057 | −0.795285 | − | 0.606236i | \(-0.792679\pi\) | ||||
−0.795285 | + | 0.606236i | \(0.792679\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.171573 | −0.0242641 | ||||||||
\(51\) | 0.554318 | 0.0776200 | ||||||||
\(52\) | 4.63029 | 0.642106 | ||||||||
\(53\) | −0.440778 | −0.0605455 | −0.0302728 | − | 0.999542i | \(-0.509638\pi\) | ||||
−0.0302728 | + | 0.999542i | \(0.509638\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.27411 | −0.306641 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.07597 | 0.539876 | ||||||||
\(58\) | 2.82843 | 0.371391 | ||||||||
\(59\) | −5.17157 | −0.673281 | −0.336641 | − | 0.941633i | \(-0.609291\pi\) | ||||
−0.336641 | + | 0.941633i | \(0.609291\pi\) | |||||||
\(60\) | −2.27411 | −0.293586 | ||||||||
\(61\) | −2.19814 | −0.281443 | −0.140721 | − | 0.990049i | \(-0.544942\pi\) | ||||
−0.140721 | + | 0.990049i | \(0.544942\pi\) | |||||||
\(62\) | 7.68832 | 0.976418 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.5298 | 1.30606 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −11.1409 | −1.36108 | −0.680541 | − | 0.732710i | \(-0.738255\pi\) | ||||
−0.680541 | + | 0.732710i | \(0.738255\pi\) | |||||||
\(68\) | −0.554318 | −0.0672209 | ||||||||
\(69\) | 6.93587 | 0.834980 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.60373 | 0.427683 | 0.213842 | − | 0.976868i | \(-0.431402\pi\) | ||||
0.213842 | + | 0.976868i | \(0.431402\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −14.3631 | −1.68108 | −0.840538 | − | 0.541753i | \(-0.817761\pi\) | ||||
−0.840538 | + | 0.541753i | \(0.817761\pi\) | |||||||
\(74\) | −10.8729 | −1.26395 | ||||||||
\(75\) | −0.171573 | −0.0198115 | ||||||||
\(76\) | −4.07597 | −0.467546 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.63029 | 0.524277 | ||||||||
\(79\) | 15.7014 | 1.76654 | 0.883270 | − | 0.468864i | \(-0.155337\pi\) | ||||
0.883270 | + | 0.468864i | \(0.155337\pi\) | |||||||
\(80\) | 2.27411 | 0.254253 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.554318 | −0.0612142 | ||||||||
\(83\) | 6.51675 | 0.715306 | 0.357653 | − | 0.933855i | \(-0.383577\pi\) | ||||
0.357653 | + | 0.933855i | \(0.383577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.26058 | −0.136729 | ||||||||
\(86\) | 8.59272 | 0.926577 | ||||||||
\(87\) | 2.82843 | 0.303239 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 4.23401 | 0.448805 | 0.224402 | − | 0.974497i | \(-0.427957\pi\) | ||||
0.224402 | + | 0.974497i | \(0.427957\pi\) | |||||||
\(90\) | −2.27411 | −0.239712 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.93587 | −0.723114 | ||||||||
\(93\) | 7.68832 | 0.797242 | ||||||||
\(94\) | 10.9044 | 1.12470 | ||||||||
\(95\) | −9.26921 | −0.951000 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −3.84637 | −0.390539 | −0.195270 | − | 0.980750i | \(-0.562558\pi\) | ||||
−0.195270 | + | 0.980750i | \(0.562558\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0.171573 | 0.0171573 | ||||||||
\(101\) | −10.7377 | −1.06844 | −0.534222 | − | 0.845344i | \(-0.679395\pi\) | ||||
−0.534222 | + | 0.845344i | \(0.679395\pi\) | |||||||
\(102\) | −0.554318 | −0.0548856 | ||||||||
\(103\) | 9.49712 | 0.935779 | 0.467890 | − | 0.883787i | \(-0.345015\pi\) | ||||
0.467890 | + | 0.883787i | \(0.345015\pi\) | |||||||
\(104\) | −4.63029 | −0.454037 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.440778 | 0.0428122 | ||||||||
\(107\) | −7.64823 | −0.739382 | −0.369691 | − | 0.929155i | \(-0.620536\pi\) | ||||
−0.369691 | + | 0.929155i | \(0.620536\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.22470 | −0.117305 | −0.0586526 | − | 0.998278i | \(-0.518680\pi\) | ||||
−0.0586526 | + | 0.998278i | \(0.518680\pi\) | |||||||
\(110\) | 2.27411 | 0.216828 | ||||||||
\(111\) | −10.8729 | −1.03201 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.37665 | 0.317648 | 0.158824 | − | 0.987307i | \(-0.449230\pi\) | ||||
0.158824 | + | 0.987307i | \(0.449230\pi\) | |||||||
\(114\) | −4.07597 | −0.381750 | ||||||||
\(115\) | −15.7729 | −1.47083 | ||||||||
\(116\) | −2.82843 | −0.262613 | ||||||||
\(117\) | 4.63029 | 0.428070 | ||||||||
\(118\) | 5.17157 | 0.476082 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.27411 | 0.207597 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.19814 | 0.199010 | ||||||||
\(123\) | −0.554318 | −0.0499812 | ||||||||
\(124\) | −7.68832 | −0.690432 | ||||||||
\(125\) | −10.9804 | −0.982114 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.3656 | 1.62969 | 0.814844 | − | 0.579681i | \(-0.196823\pi\) | ||||
0.814844 | + | 0.579681i | \(0.196823\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.59272 | 0.756547 | ||||||||
\(130\) | −10.5298 | −0.923523 | ||||||||
\(131\) | −10.5167 | −0.918853 | −0.459426 | − | 0.888216i | \(-0.651945\pi\) | ||||
−0.459426 | + | 0.888216i | \(0.651945\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1409 | 0.962431 | ||||||||
\(135\) | −2.27411 | −0.195724 | ||||||||
\(136\) | 0.554318 | 0.0475324 | ||||||||
\(137\) | −1.60373 | −0.137015 | −0.0685077 | − | 0.997651i | \(-0.521824\pi\) | ||||
−0.0685077 | + | 0.997651i | \(0.521824\pi\) | |||||||
\(138\) | −6.93587 | −0.590420 | ||||||||
\(139\) | 11.4526 | 0.971398 | 0.485699 | − | 0.874126i | \(-0.338565\pi\) | ||||
0.485699 | + | 0.874126i | \(0.338565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9044 | 0.918316 | ||||||||
\(142\) | −3.60373 | −0.302418 | ||||||||
\(143\) | −4.63029 | −0.387204 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.43215 | −0.534161 | ||||||||
\(146\) | 14.3631 | 1.18870 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.8729 | 0.893749 | ||||||||
\(149\) | −6.99257 | −0.572854 | −0.286427 | − | 0.958102i | \(-0.592468\pi\) | ||||
−0.286427 | + | 0.958102i | \(0.592468\pi\) | |||||||
\(150\) | 0.171573 | 0.0140089 | ||||||||
\(151\) | 19.5286 | 1.58921 | 0.794607 | − | 0.607124i | \(-0.207677\pi\) | ||||
0.794607 | + | 0.607124i | \(0.207677\pi\) | |||||||
\(152\) | 4.07597 | 0.330605 | ||||||||
\(153\) | −0.554318 | −0.0448139 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.4841 | −1.40436 | ||||||||
\(156\) | −4.63029 | −0.370720 | ||||||||
\(157\) | −9.81490 | −0.783314 | −0.391657 | − | 0.920111i | \(-0.628098\pi\) | ||||
−0.391657 | + | 0.920111i | \(0.628098\pi\) | |||||||
\(158\) | −15.7014 | −1.24913 | ||||||||
\(159\) | 0.440778 | 0.0349560 | ||||||||
\(160\) | −2.27411 | −0.179784 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 13.6569 | 1.06969 | 0.534844 | − | 0.844951i | \(-0.320370\pi\) | ||||
0.534844 | + | 0.844951i | \(0.320370\pi\) | |||||||
\(164\) | 0.554318 | 0.0432850 | ||||||||
\(165\) | 2.27411 | 0.177039 | ||||||||
\(166\) | −6.51675 | −0.505798 | ||||||||
\(167\) | 6.03588 | 0.467070 | 0.233535 | − | 0.972348i | \(-0.424971\pi\) | ||||
0.233535 | + | 0.972348i | \(0.424971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.43958 | 0.649199 | ||||||||
\(170\) | 1.26058 | 0.0966820 | ||||||||
\(171\) | −4.07597 | −0.311697 | ||||||||
\(172\) | −8.59272 | −0.655189 | ||||||||
\(173\) | −3.68222 | −0.279954 | −0.139977 | − | 0.990155i | \(-0.544703\pi\) | ||||
−0.139977 | + | 0.990155i | \(0.544703\pi\) | |||||||
\(174\) | −2.82843 | −0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 5.17157 | 0.388719 | ||||||||
\(178\) | −4.23401 | −0.317353 | ||||||||
\(179\) | −10.6049 | −0.792649 | −0.396324 | − | 0.918111i | \(-0.629714\pi\) | ||||
−0.396324 | + | 0.918111i | \(0.629714\pi\) | |||||||
\(180\) | 2.27411 | 0.169502 | ||||||||
\(181\) | −20.7692 | −1.54376 | −0.771881 | − | 0.635767i | \(-0.780684\pi\) | ||||
−0.771881 | + | 0.635767i | \(0.780684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.19814 | 0.162491 | ||||||||
\(184\) | 6.93587 | 0.511319 | ||||||||
\(185\) | 24.7262 | 1.81791 | ||||||||
\(186\) | −7.68832 | −0.563735 | ||||||||
\(187\) | 0.554318 | 0.0405357 | ||||||||
\(188\) | −10.9044 | −0.795285 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.26921 | 0.672459 | ||||||||
\(191\) | 16.6817 | 1.20705 | 0.603524 | − | 0.797345i | \(-0.293763\pi\) | ||||
0.603524 | + | 0.797345i | \(0.293763\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 5.43958 | 0.391550 | 0.195775 | − | 0.980649i | \(-0.437278\pi\) | ||||
0.195775 | + | 0.980649i | \(0.437278\pi\) | |||||||
\(194\) | 3.84637 | 0.276153 | ||||||||
\(195\) | −10.5298 | −0.754054 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3963 | −0.740704 | −0.370352 | − | 0.928892i | \(-0.620763\pi\) | ||||
−0.370352 | + | 0.928892i | \(0.620763\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −6.03147 | −0.427559 | −0.213780 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213780 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(200\) | −0.171573 | −0.0121320 | ||||||||
\(201\) | 11.1409 | 0.785821 | ||||||||
\(202\) | 10.7377 | 0.755504 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.554318 | 0.0388100 | ||||||||
\(205\) | 1.26058 | 0.0880427 | ||||||||
\(206\) | −9.49712 | −0.661696 | ||||||||
\(207\) | −6.93587 | −0.482076 | ||||||||
\(208\) | 4.63029 | 0.321053 | ||||||||
\(209\) | 4.07597 | 0.281941 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.16057 | −0.148740 | −0.0743699 | − | 0.997231i | \(-0.523695\pi\) | ||||
−0.0743699 | + | 0.997231i | \(0.523695\pi\) | |||||||
\(212\) | −0.440778 | −0.0302728 | ||||||||
\(213\) | −3.60373 | −0.246923 | ||||||||
\(214\) | 7.64823 | 0.522822 | ||||||||
\(215\) | −19.5408 | −1.33267 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.22470 | 0.0829473 | ||||||||
\(219\) | 14.3631 | 0.970569 | ||||||||
\(220\) | −2.27411 | −0.153320 | ||||||||
\(221\) | −2.56665 | −0.172652 | ||||||||
\(222\) | 10.8729 | 0.729743 | ||||||||
\(223\) | 1.17598 | 0.0787496 | 0.0393748 | − | 0.999225i | \(-0.487463\pi\) | ||||
0.0393748 | + | 0.999225i | \(0.487463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.171573 | 0.0114382 | ||||||||
\(226\) | −3.37665 | −0.224611 | ||||||||
\(227\) | 22.0453 | 1.46320 | 0.731600 | − | 0.681734i | \(-0.238774\pi\) | ||||
0.731600 | + | 0.681734i | \(0.238774\pi\) | |||||||
\(228\) | 4.07597 | 0.269938 | ||||||||
\(229\) | 0.554318 | 0.0366304 | 0.0183152 | − | 0.999832i | \(-0.494170\pi\) | ||||
0.0183152 | + | 0.999832i | \(0.494170\pi\) | |||||||
\(230\) | 15.7729 | 1.04004 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.82843 | 0.185695 | ||||||||
\(233\) | −0.343146 | −0.0224802 | −0.0112401 | − | 0.999937i | \(-0.503578\pi\) | ||||
−0.0112401 | + | 0.999937i | \(0.503578\pi\) | |||||||
\(234\) | −4.63029 | −0.302692 | ||||||||
\(235\) | −24.7978 | −1.61763 | ||||||||
\(236\) | −5.17157 | −0.336641 | ||||||||
\(237\) | −15.7014 | −1.01991 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.56785 | −0.360154 | −0.180077 | − | 0.983653i | \(-0.557635\pi\) | ||||
−0.180077 | + | 0.983653i | \(0.557635\pi\) | |||||||
\(240\) | −2.27411 | −0.146793 | ||||||||
\(241\) | 1.94077 | 0.125016 | 0.0625080 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625080 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.19814 | −0.140721 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.554318 | 0.0353420 | ||||||||
\(247\) | −18.8729 | −1.20086 | ||||||||
\(248\) | 7.68832 | 0.488209 | ||||||||
\(249\) | −6.51675 | −0.412982 | ||||||||
\(250\) | 10.9804 | 0.694460 | ||||||||
\(251\) | −23.4657 | −1.48114 | −0.740569 | − | 0.671980i | \(-0.765444\pi\) | ||||
−0.740569 | + | 0.671980i | \(0.765444\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.93587 | 0.436054 | ||||||||
\(254\) | −18.3656 | −1.15236 | ||||||||
\(255\) | 1.26058 | 0.0789405 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.6083 | −1.41027 | −0.705133 | − | 0.709075i | \(-0.749113\pi\) | ||||
−0.705133 | + | 0.709075i | \(0.749113\pi\) | |||||||
\(258\) | −8.59272 | −0.534959 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.5298 | 0.653030 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | 10.5167 | 0.649727 | ||||||||
\(263\) | −31.2299 | −1.92572 | −0.962861 | − | 0.269999i | \(-0.912977\pi\) | ||||
−0.962861 | + | 0.269999i | \(0.912977\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −1.00238 | −0.0615756 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.23401 | −0.259118 | ||||||||
\(268\) | −11.1409 | −0.680541 | ||||||||
\(269\) | −28.4792 | −1.73641 | −0.868203 | − | 0.496209i | \(-0.834725\pi\) | ||||
−0.868203 | + | 0.496209i | \(0.834725\pi\) | |||||||
\(270\) | 2.27411 | 0.138398 | ||||||||
\(271\) | −9.94687 | −0.604229 | −0.302115 | − | 0.953272i | \(-0.597693\pi\) | ||||
−0.302115 | + | 0.953272i | \(0.597693\pi\) | |||||||
\(272\) | −0.554318 | −0.0336105 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.60373 | 0.0968846 | ||||||||
\(275\) | −0.171573 | −0.0103462 | ||||||||
\(276\) | 6.93587 | 0.417490 | ||||||||
\(277\) | 26.5262 | 1.59381 | 0.796903 | − | 0.604108i | \(-0.206470\pi\) | ||||
0.796903 | + | 0.604108i | \(0.206470\pi\) | |||||||
\(278\) | −11.4526 | −0.686882 | ||||||||
\(279\) | −7.68832 | −0.460288 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.11844 | −0.305341 | −0.152670 | − | 0.988277i | \(-0.548787\pi\) | ||||
−0.152670 | + | 0.988277i | \(0.548787\pi\) | |||||||
\(282\) | −10.9044 | −0.649348 | ||||||||
\(283\) | 2.48205 | 0.147543 | 0.0737714 | − | 0.997275i | \(-0.476496\pi\) | ||||
0.0737714 | + | 0.997275i | \(0.476496\pi\) | |||||||
\(284\) | 3.60373 | 0.213842 | ||||||||
\(285\) | 9.26921 | 0.549060 | ||||||||
\(286\) | 4.63029 | 0.273795 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.6927 | −0.981925 | ||||||||
\(290\) | 6.43215 | 0.377709 | ||||||||
\(291\) | 3.84637 | 0.225478 | ||||||||
\(292\) | −14.3631 | −0.840538 | ||||||||
\(293\) | −2.02537 | −0.118323 | −0.0591617 | − | 0.998248i | \(-0.518843\pi\) | ||||
−0.0591617 | + | 0.998248i | \(0.518843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7607 | −0.684736 | ||||||||
\(296\) | −10.8729 | −0.631976 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 6.99257 | 0.405069 | ||||||||
\(299\) | −32.1151 | −1.85726 | ||||||||
\(300\) | −0.171573 | −0.00990576 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.5286 | −1.12374 | ||||||||
\(303\) | 10.7377 | 0.616866 | ||||||||
\(304\) | −4.07597 | −0.233773 | ||||||||
\(305\) | −4.99880 | −0.286231 | ||||||||
\(306\) | 0.554318 | 0.0316882 | ||||||||
\(307\) | −5.88477 | −0.335862 | −0.167931 | − | 0.985799i | \(-0.553709\pi\) | ||||
−0.167931 | + | 0.985799i | \(0.553709\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.49712 | −0.540272 | ||||||||
\(310\) | 17.4841 | 0.993029 | ||||||||
\(311\) | −17.4624 | −0.990203 | −0.495102 | − | 0.868835i | \(-0.664869\pi\) | ||||
−0.495102 | + | 0.868835i | \(0.664869\pi\) | |||||||
\(312\) | 4.63029 | 0.262139 | ||||||||
\(313\) | 8.87987 | 0.501920 | 0.250960 | − | 0.967997i | \(-0.419254\pi\) | ||||
0.250960 | + | 0.967997i | \(0.419254\pi\) | |||||||
\(314\) | 9.81490 | 0.553887 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.7014 | 0.883270 | ||||||||
\(317\) | −3.96937 | −0.222942 | −0.111471 | − | 0.993768i | \(-0.535556\pi\) | ||||
−0.111471 | + | 0.993768i | \(0.535556\pi\) | |||||||
\(318\) | −0.440778 | −0.0247176 | ||||||||
\(319\) | 2.82843 | 0.158362 | ||||||||
\(320\) | 2.27411 | 0.127127 | ||||||||
\(321\) | 7.64823 | 0.426882 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.25938 | 0.125715 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.794432 | 0.0440672 | ||||||||
\(326\) | −13.6569 | −0.756383 | ||||||||
\(327\) | 1.22470 | 0.0677262 | ||||||||
\(328\) | −0.554318 | −0.0306071 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.27411 | −0.125186 | ||||||||
\(331\) | −13.2692 | −0.729341 | −0.364671 | − | 0.931137i | \(-0.618818\pi\) | ||||
−0.364671 | + | 0.931137i | \(0.618818\pi\) | |||||||
\(332\) | 6.51675 | 0.357653 | ||||||||
\(333\) | 10.8729 | 0.595833 | ||||||||
\(334\) | −6.03588 | −0.330269 | ||||||||
\(335\) | −25.3357 | −1.38424 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.88036 | −0.211377 | −0.105688 | − | 0.994399i | \(-0.533705\pi\) | ||||
−0.105688 | + | 0.994399i | \(0.533705\pi\) | |||||||
\(338\) | −8.43958 | −0.459053 | ||||||||
\(339\) | −3.37665 | −0.183394 | ||||||||
\(340\) | −1.26058 | −0.0683645 | ||||||||
\(341\) | 7.68832 | 0.416346 | ||||||||
\(342\) | 4.07597 | 0.220403 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.59272 | 0.463289 | ||||||||
\(345\) | 15.7729 | 0.849185 | ||||||||
\(346\) | 3.68222 | 0.197958 | ||||||||
\(347\) | 19.1768 | 1.02947 | 0.514733 | − | 0.857351i | \(-0.327891\pi\) | ||||
0.514733 | + | 0.857351i | \(0.327891\pi\) | |||||||
\(348\) | 2.82843 | 0.151620 | ||||||||
\(349\) | 30.7602 | 1.64656 | 0.823279 | − | 0.567638i | \(-0.192142\pi\) | ||||
0.823279 | + | 0.567638i | \(0.192142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.63029 | −0.247147 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 1.19071 | 0.0633749 | 0.0316875 | − | 0.999498i | \(-0.489912\pi\) | ||||
0.0316875 | + | 0.999498i | \(0.489912\pi\) | |||||||
\(354\) | −5.17157 | −0.274866 | ||||||||
\(355\) | 8.19526 | 0.434959 | ||||||||
\(356\) | 4.23401 | 0.224402 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.6049 | 0.560487 | ||||||||
\(359\) | −24.6915 | −1.30317 | −0.651585 | − | 0.758576i | \(-0.725895\pi\) | ||||
−0.651585 | + | 0.758576i | \(0.725895\pi\) | |||||||
\(360\) | −2.27411 | −0.119856 | ||||||||
\(361\) | −2.38645 | −0.125603 | ||||||||
\(362\) | 20.7692 | 1.09160 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.6633 | −1.70967 | ||||||||
\(366\) | −2.19814 | −0.114898 | ||||||||
\(367\) | 7.21691 | 0.376720 | 0.188360 | − | 0.982100i | \(-0.439683\pi\) | ||||
0.188360 | + | 0.982100i | \(0.439683\pi\) | |||||||
\(368\) | −6.93587 | −0.361557 | ||||||||
\(369\) | 0.554318 | 0.0288566 | ||||||||
\(370\) | −24.7262 | −1.28546 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.68832 | 0.398621 | ||||||||
\(373\) | 1.70998 | 0.0885396 | 0.0442698 | − | 0.999020i | \(-0.485904\pi\) | ||||
0.0442698 | + | 0.999020i | \(0.485904\pi\) | |||||||
\(374\) | −0.554318 | −0.0286631 | ||||||||
\(375\) | 10.9804 | 0.567024 | ||||||||
\(376\) | 10.9044 | 0.562351 | ||||||||
\(377\) | −13.0964 | −0.674501 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.2745 | −1.91466 | −0.957330 | − | 0.288997i | \(-0.906678\pi\) | ||||
−0.957330 | + | 0.288997i | \(0.906678\pi\) | |||||||
\(380\) | −9.26921 | −0.475500 | ||||||||
\(381\) | −18.3656 | −0.940900 | ||||||||
\(382\) | −16.6817 | −0.853511 | ||||||||
\(383\) | −11.4019 | −0.582609 | −0.291304 | − | 0.956630i | \(-0.594089\pi\) | ||||
−0.291304 | + | 0.956630i | \(0.594089\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.43958 | −0.276867 | ||||||||
\(387\) | −8.59272 | −0.436793 | ||||||||
\(388\) | −3.84637 | −0.195270 | ||||||||
\(389\) | 38.6250 | 1.95837 | 0.979183 | − | 0.202978i | \(-0.0650620\pi\) | ||||
0.979183 | + | 0.202978i | \(0.0650620\pi\) | |||||||
\(390\) | 10.5298 | 0.533196 | ||||||||
\(391\) | 3.84468 | 0.194434 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.5167 | 0.530500 | ||||||||
\(394\) | 10.3963 | 0.523757 | ||||||||
\(395\) | 35.7066 | 1.79659 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −15.7929 | −0.792622 | −0.396311 | − | 0.918116i | \(-0.629710\pi\) | ||||
−0.396311 | + | 0.918116i | \(0.629710\pi\) | |||||||
\(398\) | 6.03147 | 0.302330 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.171573 | 0.00857864 | ||||||||
\(401\) | −21.7100 | −1.08414 | −0.542072 | − | 0.840332i | \(-0.682360\pi\) | ||||
−0.542072 | + | 0.840332i | \(0.682360\pi\) | |||||||
\(402\) | −11.1409 | −0.555660 | ||||||||
\(403\) | −35.5992 | −1.77332 | ||||||||
\(404\) | −10.7377 | −0.534222 | ||||||||
\(405\) | 2.27411 | 0.113001 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.8729 | −0.538951 | ||||||||
\(408\) | −0.554318 | −0.0274428 | ||||||||
\(409\) | −37.7520 | −1.86671 | −0.933357 | − | 0.358949i | \(-0.883135\pi\) | ||||
−0.933357 | + | 0.358949i | \(0.883135\pi\) | |||||||
\(410\) | −1.26058 | −0.0622556 | ||||||||
\(411\) | 1.60373 | 0.0791059 | ||||||||
\(412\) | 9.49712 | 0.467890 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.93587 | 0.340879 | ||||||||
\(415\) | 14.8198 | 0.727475 | ||||||||
\(416\) | −4.63029 | −0.227019 | ||||||||
\(417\) | −11.4526 | −0.560837 | ||||||||
\(418\) | −4.07597 | −0.199362 | ||||||||
\(419\) | −15.5408 | −0.759217 | −0.379609 | − | 0.925147i | \(-0.623941\pi\) | ||||
−0.379609 | + | 0.925147i | \(0.623941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.6176 | 1.44347 | 0.721737 | − | 0.692168i | \(-0.243344\pi\) | ||||
0.721737 | + | 0.692168i | \(0.243344\pi\) | |||||||
\(422\) | 2.16057 | 0.105175 | ||||||||
\(423\) | −10.9044 | −0.530190 | ||||||||
\(424\) | 0.440778 | 0.0214061 | ||||||||
\(425\) | −0.0951059 | −0.00461331 | ||||||||
\(426\) | 3.60373 | 0.174601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.64823 | −0.369691 | ||||||||
\(429\) | 4.63029 | 0.223552 | ||||||||
\(430\) | 19.5408 | 0.942340 | ||||||||
\(431\) | 24.7978 | 1.19447 | 0.597234 | − | 0.802067i | \(-0.296266\pi\) | ||||
0.597234 | + | 0.802067i | \(0.296266\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 11.2859 | 0.542368 | 0.271184 | − | 0.962528i | \(-0.412585\pi\) | ||||
0.271184 | + | 0.962528i | \(0.412585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.43215 | 0.308398 | ||||||||
\(436\) | −1.22470 | −0.0586526 | ||||||||
\(437\) | 28.2704 | 1.35236 | ||||||||
\(438\) | −14.3631 | −0.686296 | ||||||||
\(439\) | 1.17157 | 0.0559161 | 0.0279581 | − | 0.999609i | \(-0.491100\pi\) | ||||
0.0279581 | + | 0.999609i | \(0.491100\pi\) | |||||||
\(440\) | 2.27411 | 0.108414 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.56665 | 0.122083 | ||||||||
\(443\) | 16.6915 | 0.793039 | 0.396519 | − | 0.918026i | \(-0.370218\pi\) | ||||
0.396519 | + | 0.918026i | \(0.370218\pi\) | |||||||
\(444\) | −10.8729 | −0.516006 | ||||||||
\(445\) | 9.62861 | 0.456440 | ||||||||
\(446\) | −1.17598 | −0.0556844 | ||||||||
\(447\) | 6.99257 | 0.330737 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.5547 | −1.30038 | −0.650192 | − | 0.759770i | \(-0.725312\pi\) | ||||
−0.650192 | + | 0.759770i | \(0.725312\pi\) | |||||||
\(450\) | −0.171573 | −0.00808802 | ||||||||
\(451\) | −0.554318 | −0.0261018 | ||||||||
\(452\) | 3.37665 | 0.158824 | ||||||||
\(453\) | −19.5286 | −0.917533 | ||||||||
\(454\) | −22.0453 | −1.03464 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.07597 | −0.190875 | ||||||||
\(457\) | −18.1953 | −0.851139 | −0.425569 | − | 0.904926i | \(-0.639926\pi\) | ||||
−0.425569 | + | 0.904926i | \(0.639926\pi\) | |||||||
\(458\) | −0.554318 | −0.0259016 | ||||||||
\(459\) | 0.554318 | 0.0258733 | ||||||||
\(460\) | −15.7729 | −0.735416 | ||||||||
\(461\) | 19.6193 | 0.913761 | 0.456881 | − | 0.889528i | \(-0.348967\pi\) | ||||
0.456881 | + | 0.889528i | \(0.348967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.6176 | 1.65529 | 0.827645 | − | 0.561252i | \(-0.189680\pi\) | ||||
0.827645 | + | 0.561252i | \(0.189680\pi\) | |||||||
\(464\) | −2.82843 | −0.131306 | ||||||||
\(465\) | 17.4841 | 0.810805 | ||||||||
\(466\) | 0.343146 | 0.0158959 | ||||||||
\(467\) | −35.0744 | −1.62305 | −0.811526 | − | 0.584317i | \(-0.801362\pi\) | ||||
−0.811526 | + | 0.584317i | \(0.801362\pi\) | |||||||
\(468\) | 4.63029 | 0.214035 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.7978 | 1.14384 | ||||||||
\(471\) | 9.81490 | 0.452247 | ||||||||
\(472\) | 5.17157 | 0.238041 | ||||||||
\(473\) | 8.59272 | 0.395094 | ||||||||
\(474\) | 15.7014 | 0.721187 | ||||||||
\(475\) | −0.699326 | −0.0320873 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.440778 | −0.0201818 | ||||||||
\(478\) | 5.56785 | 0.254667 | ||||||||
\(479\) | −18.7482 | −0.856629 | −0.428314 | − | 0.903630i | \(-0.640892\pi\) | ||||
−0.428314 | + | 0.903630i | \(0.640892\pi\) | |||||||
\(480\) | 2.27411 | 0.103798 | ||||||||
\(481\) | 50.3448 | 2.29553 | ||||||||
\(482\) | −1.94077 | −0.0883997 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −8.74706 | −0.397183 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 29.9301 | 1.35626 | 0.678131 | − | 0.734941i | \(-0.262790\pi\) | ||||
0.678131 | + | 0.734941i | \(0.262790\pi\) | |||||||
\(488\) | 2.19814 | 0.0995050 | ||||||||
\(489\) | −13.6569 | −0.617584 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.68629 | −0.392007 | −0.196003 | − | 0.980603i | \(-0.562796\pi\) | ||||
−0.196003 | + | 0.980603i | \(0.562796\pi\) | |||||||
\(492\) | −0.554318 | −0.0249906 | ||||||||
\(493\) | 1.56785 | 0.0706123 | ||||||||
\(494\) | 18.8729 | 0.849133 | ||||||||
\(495\) | −2.27411 | −0.102214 | ||||||||
\(496\) | −7.68832 | −0.345216 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.51675 | 0.292023 | ||||||||
\(499\) | 23.8076 | 1.06578 | 0.532888 | − | 0.846186i | \(-0.321107\pi\) | ||||
0.532888 | + | 0.846186i | \(0.321107\pi\) | |||||||
\(500\) | −10.9804 | −0.491057 | ||||||||
\(501\) | −6.03588 | −0.269663 | ||||||||
\(502\) | 23.4657 | 1.04732 | ||||||||
\(503\) | 32.2531 | 1.43810 | 0.719048 | − | 0.694960i | \(-0.244578\pi\) | ||||
0.719048 | + | 0.694960i | \(0.244578\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.4188 | −1.08662 | ||||||||
\(506\) | −6.93587 | −0.308337 | ||||||||
\(507\) | −8.43958 | −0.374815 | ||||||||
\(508\) | 18.3656 | 0.814844 | ||||||||
\(509\) | −35.1066 | −1.55607 | −0.778036 | − | 0.628219i | \(-0.783784\pi\) | ||||
−0.778036 | + | 0.628219i | \(0.783784\pi\) | |||||||
\(510\) | −1.26058 | −0.0558194 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.07597 | 0.179959 | ||||||||
\(514\) | 22.6083 | 0.997209 | ||||||||
\(515\) | 21.5975 | 0.951699 | ||||||||
\(516\) | 8.59272 | 0.378273 | ||||||||
\(517\) | 10.9044 | 0.479575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.68222 | 0.161632 | ||||||||
\(520\) | −10.5298 | −0.461762 | ||||||||
\(521\) | −31.0763 | −1.36148 | −0.680739 | − | 0.732526i | \(-0.738341\pi\) | ||||
−0.680739 | + | 0.732526i | \(0.738341\pi\) | |||||||
\(522\) | 2.82843 | 0.123797 | ||||||||
\(523\) | 18.3822 | 0.803800 | 0.401900 | − | 0.915684i | \(-0.368350\pi\) | ||||
0.401900 | + | 0.915684i | \(0.368350\pi\) | |||||||
\(524\) | −10.5167 | −0.459426 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.2299 | 1.36169 | ||||||||
\(527\) | 4.26177 | 0.185646 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 25.1063 | 1.09158 | ||||||||
\(530\) | 1.00238 | 0.0435405 | ||||||||
\(531\) | −5.17157 | −0.224427 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.56665 | 0.111174 | ||||||||
\(534\) | 4.23401 | 0.183224 | ||||||||
\(535\) | −17.3929 | −0.751961 | ||||||||
\(536\) | 11.1409 | 0.481215 | ||||||||
\(537\) | 10.6049 | 0.457636 | ||||||||
\(538\) | 28.4792 | 1.22782 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.27411 | −0.0978621 | ||||||||
\(541\) | −20.2311 | −0.869805 | −0.434902 | − | 0.900478i | \(-0.643217\pi\) | ||||
−0.434902 | + | 0.900478i | \(0.643217\pi\) | |||||||
\(542\) | 9.94687 | 0.427255 | ||||||||
\(543\) | 20.7692 | 0.891292 | ||||||||
\(544\) | 0.554318 | 0.0237662 | ||||||||
\(545\) | −2.78511 | −0.119301 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.9249 | 1.36501 | 0.682504 | − | 0.730882i | \(-0.260891\pi\) | ||||
0.682504 | + | 0.730882i | \(0.260891\pi\) | |||||||
\(548\) | −1.60373 | −0.0685077 | ||||||||
\(549\) | −2.19814 | −0.0938142 | ||||||||
\(550\) | 0.171573 | 0.00731589 | ||||||||
\(551\) | 11.5286 | 0.491134 | ||||||||
\(552\) | −6.93587 | −0.295210 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.5262 | −1.12699 | ||||||||
\(555\) | −24.7262 | −1.04957 | ||||||||
\(556\) | 11.4526 | 0.485699 | ||||||||
\(557\) | 39.4386 | 1.67107 | 0.835533 | − | 0.549440i | \(-0.185159\pi\) | ||||
0.835533 | + | 0.549440i | \(0.185159\pi\) | |||||||
\(558\) | 7.68832 | 0.325473 | ||||||||
\(559\) | −39.7868 | −1.68280 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.554318 | −0.0234033 | ||||||||
\(562\) | 5.11844 | 0.215909 | ||||||||
\(563\) | 44.6098 | 1.88008 | 0.940040 | − | 0.341065i | \(-0.110787\pi\) | ||||
0.940040 | + | 0.341065i | \(0.110787\pi\) | |||||||
\(564\) | 10.9044 | 0.459158 | ||||||||
\(565\) | 7.67886 | 0.323052 | ||||||||
\(566\) | −2.48205 | −0.104329 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.60373 | −0.151209 | ||||||||
\(569\) | 35.1682 | 1.47433 | 0.737164 | − | 0.675714i | \(-0.236165\pi\) | ||||
0.737164 | + | 0.675714i | \(0.236165\pi\) | |||||||
\(570\) | −9.26921 | −0.388244 | ||||||||
\(571\) | −9.96412 | −0.416986 | −0.208493 | − | 0.978024i | \(-0.566856\pi\) | ||||
−0.208493 | + | 0.978024i | \(0.566856\pi\) | |||||||
\(572\) | −4.63029 | −0.193602 | ||||||||
\(573\) | −16.6817 | −0.696889 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.19001 | −0.0496267 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −2.12657 | −0.0885305 | −0.0442652 | − | 0.999020i | \(-0.514095\pi\) | ||||
−0.0442652 | + | 0.999020i | \(0.514095\pi\) | |||||||
\(578\) | 16.6927 | 0.694326 | ||||||||
\(579\) | −5.43958 | −0.226061 | ||||||||
\(580\) | −6.43215 | −0.267081 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.84637 | −0.159437 | ||||||||
\(583\) | 0.440778 | 0.0182552 | ||||||||
\(584\) | 14.3631 | 0.594350 | ||||||||
\(585\) | 10.5298 | 0.435353 | ||||||||
\(586\) | 2.02537 | 0.0836672 | ||||||||
\(587\) | 25.8260 | 1.06596 | 0.532978 | − | 0.846129i | \(-0.321073\pi\) | ||||
0.532978 | + | 0.846129i | \(0.321073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3374 | 1.29123 | ||||||||
\(590\) | 11.7607 | 0.484181 | ||||||||
\(591\) | 10.3963 | 0.427646 | ||||||||
\(592\) | 10.8729 | 0.446875 | ||||||||
\(593\) | 18.8975 | 0.776026 | 0.388013 | − | 0.921654i | \(-0.373162\pi\) | ||||
0.388013 | + | 0.921654i | \(0.373162\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.99257 | −0.286427 | ||||||||
\(597\) | 6.03147 | 0.246852 | ||||||||
\(598\) | 32.1151 | 1.31328 | ||||||||
\(599\) | 3.49510 | 0.142806 | 0.0714030 | − | 0.997448i | \(-0.477252\pi\) | ||||
0.0714030 | + | 0.997448i | \(0.477252\pi\) | |||||||
\(600\) | 0.171573 | 0.00700443 | ||||||||
\(601\) | 23.6409 | 0.964334 | 0.482167 | − | 0.876079i | \(-0.339850\pi\) | ||||
0.482167 | + | 0.876079i | \(0.339850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.1409 | −0.453694 | ||||||||
\(604\) | 19.5286 | 0.794607 | ||||||||
\(605\) | 2.27411 | 0.0924557 | ||||||||
\(606\) | −10.7377 | −0.436190 | ||||||||
\(607\) | 8.19526 | 0.332636 | 0.166318 | − | 0.986072i | \(-0.446812\pi\) | ||||
0.166318 | + | 0.986072i | \(0.446812\pi\) | |||||||
\(608\) | 4.07597 | 0.165302 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.99880 | 0.202396 | ||||||||
\(611\) | −50.4905 | −2.04263 | ||||||||
\(612\) | −0.554318 | −0.0224070 | ||||||||
\(613\) | 26.3692 | 1.06504 | 0.532521 | − | 0.846417i | \(-0.321245\pi\) | ||||
0.532521 | + | 0.846417i | \(0.321245\pi\) | |||||||
\(614\) | 5.88477 | 0.237490 | ||||||||
\(615\) | −1.26058 | −0.0508315 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.35534 | −0.0948226 | −0.0474113 | − | 0.998875i | \(-0.515097\pi\) | ||||
−0.0474113 | + | 0.998875i | \(0.515097\pi\) | |||||||
\(618\) | 9.49712 | 0.382030 | ||||||||
\(619\) | −10.2051 | −0.410177 | −0.205088 | − | 0.978743i | \(-0.565748\pi\) | ||||
−0.205088 | + | 0.978743i | \(0.565748\pi\) | |||||||
\(620\) | −17.4841 | −0.702178 | ||||||||
\(621\) | 6.93587 | 0.278327 | ||||||||
\(622\) | 17.4624 | 0.700179 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.63029 | −0.185360 | ||||||||
\(625\) | −25.8284 | −1.03314 | ||||||||
\(626\) | −8.87987 | −0.354911 | ||||||||
\(627\) | −4.07597 | −0.162779 | ||||||||
\(628\) | −9.81490 | −0.391657 | ||||||||
\(629\) | −6.02706 | −0.240315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.86550 | −0.392739 | −0.196370 | − | 0.980530i | \(-0.562915\pi\) | ||||
−0.196370 | + | 0.980530i | \(0.562915\pi\) | |||||||
\(632\) | −15.7014 | −0.624566 | ||||||||
\(633\) | 2.16057 | 0.0858749 | ||||||||
\(634\) | 3.96937 | 0.157644 | ||||||||
\(635\) | 41.7655 | 1.65741 | ||||||||
\(636\) | 0.440778 | 0.0174780 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.82843 | −0.111979 | ||||||||
\(639\) | 3.60373 | 0.142561 | ||||||||
\(640\) | −2.27411 | −0.0898921 | ||||||||
\(641\) | −13.3063 | −0.525566 | −0.262783 | − | 0.964855i | \(-0.584640\pi\) | ||||
−0.262783 | + | 0.964855i | \(0.584640\pi\) | |||||||
\(642\) | −7.64823 | −0.301851 | ||||||||
\(643\) | −12.2531 | −0.483217 | −0.241609 | − | 0.970374i | \(-0.577675\pi\) | ||||
−0.241609 | + | 0.970374i | \(0.577675\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.5408 | 0.769418 | ||||||||
\(646\) | −2.25938 | −0.0888943 | ||||||||
\(647\) | 22.3873 | 0.880136 | 0.440068 | − | 0.897965i | \(-0.354954\pi\) | ||||
0.440068 | + | 0.897965i | \(0.354954\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 5.17157 | 0.203002 | ||||||||
\(650\) | −0.794432 | −0.0311602 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.6569 | 0.534844 | ||||||||
\(653\) | 14.1953 | 0.555504 | 0.277752 | − | 0.960653i | \(-0.410411\pi\) | ||||
0.277752 | + | 0.960653i | \(0.410411\pi\) | |||||||
\(654\) | −1.22470 | −0.0478896 | ||||||||
\(655\) | −23.9162 | −0.934485 | ||||||||
\(656\) | 0.554318 | 0.0216425 | ||||||||
\(657\) | −14.3631 | −0.560359 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.7152 | −0.845905 | −0.422953 | − | 0.906152i | \(-0.639006\pi\) | ||||
−0.422953 | + | 0.906152i | \(0.639006\pi\) | |||||||
\(660\) | 2.27411 | 0.0885196 | ||||||||
\(661\) | 46.5029 | 1.80875 | 0.904376 | − | 0.426737i | \(-0.140337\pi\) | ||||
0.904376 | + | 0.426737i | \(0.140337\pi\) | |||||||
\(662\) | 13.2692 | 0.515722 | ||||||||
\(663\) | 2.56665 | 0.0996805 | ||||||||
\(664\) | −6.51675 | −0.252899 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.8729 | −0.421317 | ||||||||
\(667\) | 19.6176 | 0.759596 | ||||||||
\(668\) | 6.03588 | 0.233535 | ||||||||
\(669\) | −1.17598 | −0.0454661 | ||||||||
\(670\) | 25.3357 | 0.978804 | ||||||||
\(671\) | 2.19814 | 0.0848582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.7152 | −1.14544 | −0.572719 | − | 0.819752i | \(-0.694111\pi\) | ||||
−0.572719 | + | 0.819752i | \(0.694111\pi\) | |||||||
\(674\) | 3.88036 | 0.149466 | ||||||||
\(675\) | −0.171573 | −0.00660384 | ||||||||
\(676\) | 8.43958 | 0.324599 | ||||||||
\(677\) | 43.5147 | 1.67241 | 0.836203 | − | 0.548420i | \(-0.184771\pi\) | ||||
0.836203 | + | 0.548420i | \(0.184771\pi\) | |||||||
\(678\) | 3.37665 | 0.129679 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.26058 | 0.0483410 | ||||||||
\(681\) | −22.0453 | −0.844779 | ||||||||
\(682\) | −7.68832 | −0.294401 | ||||||||
\(683\) | −29.3582 | −1.12336 | −0.561680 | − | 0.827354i | \(-0.689845\pi\) | ||||
−0.561680 | + | 0.827354i | \(0.689845\pi\) | |||||||
\(684\) | −4.07597 | −0.155849 | ||||||||
\(685\) | −3.64705 | −0.139346 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.554318 | −0.0211485 | ||||||||
\(688\) | −8.59272 | −0.327594 | ||||||||
\(689\) | −2.04093 | −0.0777533 | ||||||||
\(690\) | −15.7729 | −0.600465 | ||||||||
\(691\) | 6.84063 | 0.260230 | 0.130115 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130115 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(692\) | −3.68222 | −0.139977 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.1768 | −0.727942 | ||||||||
\(695\) | 26.0445 | 0.987924 | ||||||||
\(696\) | −2.82843 | −0.107211 | ||||||||
\(697\) | −0.307268 | −0.0116386 | ||||||||
\(698\) | −30.7602 | −1.16429 | ||||||||
\(699\) | 0.343146 | 0.0129790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.1929 | −0.913752 | −0.456876 | − | 0.889530i | \(-0.651032\pi\) | ||||
−0.456876 | + | 0.889530i | \(0.651032\pi\) | |||||||
\(702\) | 4.63029 | 0.174759 | ||||||||
\(703\) | −44.3178 | −1.67148 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 24.7978 | 0.933939 | ||||||||
\(706\) | −1.19071 | −0.0448128 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.17157 | 0.194360 | ||||||||
\(709\) | −32.8509 | −1.23374 | −0.616871 | − | 0.787064i | \(-0.711600\pi\) | ||||
−0.616871 | + | 0.787064i | \(0.711600\pi\) | |||||||
\(710\) | −8.19526 | −0.307563 | ||||||||
\(711\) | 15.7014 | 0.588847 | ||||||||
\(712\) | −4.23401 | −0.158676 | ||||||||
\(713\) | 53.3252 | 1.99704 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5298 | −0.393792 | ||||||||
\(716\) | −10.6049 | −0.396324 | ||||||||
\(717\) | 5.56785 | 0.207935 | ||||||||
\(718\) | 24.6915 | 0.921480 | ||||||||
\(719\) | 6.43132 | 0.239848 | 0.119924 | − | 0.992783i | \(-0.461735\pi\) | ||||
0.119924 | + | 0.992783i | \(0.461735\pi\) | |||||||
\(720\) | 2.27411 | 0.0847510 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.38645 | 0.0888146 | ||||||||
\(723\) | −1.94077 | −0.0721781 | ||||||||
\(724\) | −20.7692 | −0.771881 | ||||||||
\(725\) | −0.485281 | −0.0180229 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −2.71776 | −0.100796 | −0.0503981 | − | 0.998729i | \(-0.516049\pi\) | ||||
−0.0503981 | + | 0.998729i | \(0.516049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 32.6633 | 1.20892 | ||||||||
\(731\) | 4.76310 | 0.176170 | ||||||||
\(732\) | 2.19814 | 0.0812455 | ||||||||
\(733\) | 47.7799 | 1.76479 | 0.882395 | − | 0.470510i | \(-0.155930\pi\) | ||||
0.882395 | + | 0.470510i | \(0.155930\pi\) | |||||||
\(734\) | −7.21691 | −0.266381 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.93587 | 0.255659 | ||||||||
\(737\) | 11.1409 | 0.410382 | ||||||||
\(738\) | −0.554318 | −0.0204047 | ||||||||
\(739\) | −35.5425 | −1.30745 | −0.653725 | − | 0.756732i | \(-0.726795\pi\) | ||||
−0.653725 | + | 0.756732i | \(0.726795\pi\) | |||||||
\(740\) | 24.7262 | 0.908954 | ||||||||
\(741\) | 18.8729 | 0.693314 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.4992 | 0.752041 | 0.376020 | − | 0.926611i | \(-0.377292\pi\) | ||||
0.376020 | + | 0.926611i | \(0.377292\pi\) | |||||||
\(744\) | −7.68832 | −0.281868 | ||||||||
\(745\) | −15.9019 | −0.582599 | ||||||||
\(746\) | −1.70998 | −0.0626069 | ||||||||
\(747\) | 6.51675 | 0.238435 | ||||||||
\(748\) | 0.554318 | 0.0202679 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.9804 | −0.400946 | ||||||||
\(751\) | −45.2682 | −1.65186 | −0.825930 | − | 0.563772i | \(-0.809350\pi\) | ||||
−0.825930 | + | 0.563772i | \(0.809350\pi\) | |||||||
\(752\) | −10.9044 | −0.397643 | ||||||||
\(753\) | 23.4657 | 0.855136 | ||||||||
\(754\) | 13.0964 | 0.476944 | ||||||||
\(755\) | 44.4101 | 1.61625 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.6188 | −1.47632 | −0.738158 | − | 0.674628i | \(-0.764304\pi\) | ||||
−0.738158 | + | 0.674628i | \(0.764304\pi\) | |||||||
\(758\) | 37.2745 | 1.35387 | ||||||||
\(759\) | −6.93587 | −0.251756 | ||||||||
\(760\) | 9.26921 | 0.336229 | ||||||||
\(761\) | −29.1164 | −1.05547 | −0.527734 | − | 0.849409i | \(-0.676958\pi\) | ||||
−0.527734 | + | 0.849409i | \(0.676958\pi\) | |||||||
\(762\) | 18.3656 | 0.665317 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.6817 | 0.603524 | ||||||||
\(765\) | −1.26058 | −0.0455763 | ||||||||
\(766\) | 11.4019 | 0.411967 | ||||||||
\(767\) | −23.9459 | −0.864636 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 22.9987 | 0.829353 | 0.414677 | − | 0.909969i | \(-0.363895\pi\) | ||||
0.414677 | + | 0.909969i | \(0.363895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.6083 | 0.814217 | ||||||||
\(772\) | 5.43958 | 0.195775 | ||||||||
\(773\) | 51.0755 | 1.83706 | 0.918529 | − | 0.395355i | \(-0.129378\pi\) | ||||
0.918529 | + | 0.395355i | \(0.129378\pi\) | |||||||
\(774\) | 8.59272 | 0.308859 | ||||||||
\(775\) | −1.31911 | −0.0473837 | ||||||||
\(776\) | 3.84637 | 0.138076 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.6250 | −1.38477 | ||||||||
\(779\) | −2.25938 | −0.0809508 | ||||||||
\(780\) | −10.5298 | −0.377027 | ||||||||
\(781\) | −3.60373 | −0.128951 | ||||||||
\(782\) | −3.84468 | −0.137485 | ||||||||
\(783\) | 2.82843 | 0.101080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.3201 | −0.796640 | ||||||||
\(786\) | −10.5167 | −0.375120 | ||||||||
\(787\) | −29.5024 | −1.05165 | −0.525823 | − | 0.850594i | \(-0.676243\pi\) | ||||
−0.525823 | + | 0.850594i | \(0.676243\pi\) | |||||||
\(788\) | −10.3963 | −0.370352 | ||||||||
\(789\) | 31.2299 | 1.11182 | ||||||||
\(790\) | −35.7066 | −1.27038 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −10.1780 | −0.361432 | ||||||||
\(794\) | 15.7929 | 0.560469 | ||||||||
\(795\) | 1.00238 | 0.0355507 | ||||||||
\(796\) | −6.03147 | −0.213780 | ||||||||
\(797\) | 16.3990 | 0.580882 | 0.290441 | − | 0.956893i | \(-0.406198\pi\) | ||||
0.290441 | + | 0.956893i | \(0.406198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.04450 | 0.213839 | ||||||||
\(800\) | −0.171573 | −0.00606602 | ||||||||
\(801\) | 4.23401 | 0.149602 | ||||||||
\(802\) | 21.7100 | 0.766606 | ||||||||
\(803\) | 14.3631 | 0.506863 | ||||||||
\(804\) | 11.1409 | 0.392911 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35.5992 | 1.25393 | ||||||||
\(807\) | 28.4792 | 1.00251 | ||||||||
\(808\) | 10.7377 | 0.377752 | ||||||||
\(809\) | 17.0730 | 0.600253 | 0.300126 | − | 0.953899i | \(-0.402971\pi\) | ||||
0.300126 | + | 0.953899i | \(0.402971\pi\) | |||||||
\(810\) | −2.27411 | −0.0799041 | ||||||||
\(811\) | 26.9166 | 0.945170 | 0.472585 | − | 0.881285i | \(-0.343321\pi\) | ||||
0.472585 | + | 0.881285i | \(0.343321\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.94687 | 0.348852 | ||||||||
\(814\) | 10.8729 | 0.381096 | ||||||||
\(815\) | 31.0572 | 1.08789 | ||||||||
\(816\) | 0.554318 | 0.0194050 | ||||||||
\(817\) | 35.0237 | 1.22532 | ||||||||
\(818\) | 37.7520 | 1.31997 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.26058 | 0.0440213 | ||||||||
\(821\) | −21.2917 | −0.743086 | −0.371543 | − | 0.928416i | \(-0.621171\pi\) | ||||
−0.371543 | + | 0.928416i | \(0.621171\pi\) | |||||||
\(822\) | −1.60373 | −0.0559363 | ||||||||
\(823\) | 4.18425 | 0.145854 | 0.0729269 | − | 0.997337i | \(-0.476766\pi\) | ||||
0.0729269 | + | 0.997337i | \(0.476766\pi\) | |||||||
\(824\) | −9.49712 | −0.330848 | ||||||||
\(825\) | 0.171573 | 0.00597340 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.23213 | −0.286259 | −0.143130 | − | 0.989704i | \(-0.545717\pi\) | ||||
−0.143130 | + | 0.989704i | \(0.545717\pi\) | |||||||
\(828\) | −6.93587 | −0.241038 | ||||||||
\(829\) | 42.4954 | 1.47593 | 0.737964 | − | 0.674840i | \(-0.235787\pi\) | ||||
0.737964 | + | 0.674840i | \(0.235787\pi\) | |||||||
\(830\) | −14.8198 | −0.514403 | ||||||||
\(831\) | −26.5262 | −0.920184 | ||||||||
\(832\) | 4.63029 | 0.160526 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.4526 | 0.396572 | ||||||||
\(835\) | 13.7262 | 0.475016 | ||||||||
\(836\) | 4.07597 | 0.140970 | ||||||||
\(837\) | 7.68832 | 0.265747 | ||||||||
\(838\) | 15.5408 | 0.536848 | ||||||||
\(839\) | 14.4330 | 0.498282 | 0.249141 | − | 0.968467i | \(-0.419852\pi\) | ||||
0.249141 | + | 0.968467i | \(0.419852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | −29.6176 | −1.02069 | ||||||||
\(843\) | 5.11844 | 0.176289 | ||||||||
\(844\) | −2.16057 | −0.0743699 | ||||||||
\(845\) | 19.1925 | 0.660243 | ||||||||
\(846\) | 10.9044 | 0.374901 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.440778 | −0.0151364 | ||||||||
\(849\) | −2.48205 | −0.0851839 | ||||||||
\(850\) | 0.0951059 | 0.00326211 | ||||||||
\(851\) | −75.4132 | −2.58513 | ||||||||
\(852\) | −3.60373 | −0.123462 | ||||||||
\(853\) | −52.1866 | −1.78684 | −0.893418 | − | 0.449226i | \(-0.851700\pi\) | ||||
−0.893418 | + | 0.449226i | \(0.851700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.26921 | −0.317000 | ||||||||
\(856\) | 7.64823 | 0.261411 | ||||||||
\(857\) | −25.6474 | −0.876098 | −0.438049 | − | 0.898951i | \(-0.644330\pi\) | ||||
−0.438049 | + | 0.898951i | \(0.644330\pi\) | |||||||
\(858\) | −4.63029 | −0.158075 | ||||||||
\(859\) | −2.32928 | −0.0794738 | −0.0397369 | − | 0.999210i | \(-0.512652\pi\) | ||||
−0.0397369 | + | 0.999210i | \(0.512652\pi\) | |||||||
\(860\) | −19.5408 | −0.666335 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.7978 | −0.844616 | ||||||||
\(863\) | −4.46685 | −0.152053 | −0.0760266 | − | 0.997106i | \(-0.524223\pi\) | ||||
−0.0760266 | + | 0.997106i | \(0.524223\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −8.37378 | −0.284717 | ||||||||
\(866\) | −11.2859 | −0.383512 | ||||||||
\(867\) | 16.6927 | 0.566915 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.7014 | −0.532632 | ||||||||
\(870\) | −6.43215 | −0.218070 | ||||||||
\(871\) | −51.5858 | −1.74792 | ||||||||
\(872\) | 1.22470 | 0.0414736 | ||||||||
\(873\) | −3.84637 | −0.130180 | ||||||||
\(874\) | −28.2704 | −0.956261 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.3631 | 0.485285 | ||||||||
\(877\) | −45.8497 | −1.54824 | −0.774118 | − | 0.633042i | \(-0.781806\pi\) | ||||
−0.774118 | + | 0.633042i | \(0.781806\pi\) | |||||||
\(878\) | −1.17157 | −0.0395387 | ||||||||
\(879\) | 2.02537 | 0.0683140 | ||||||||
\(880\) | −2.27411 | −0.0766602 | ||||||||
\(881\) | −39.6418 | −1.33557 | −0.667783 | − | 0.744356i | \(-0.732756\pi\) | ||||
−0.667783 | + | 0.744356i | \(0.732756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.2843 | 1.08645 | 0.543226 | − | 0.839586i | \(-0.317203\pi\) | ||||
0.543226 | + | 0.839586i | \(0.317203\pi\) | |||||||
\(884\) | −2.56665 | −0.0863259 | ||||||||
\(885\) | 11.7607 | 0.395332 | ||||||||
\(886\) | −16.6915 | −0.560763 | ||||||||
\(887\) | −23.4027 | −0.785786 | −0.392893 | − | 0.919584i | \(-0.628526\pi\) | ||||
−0.392893 | + | 0.919584i | \(0.628526\pi\) | |||||||
\(888\) | 10.8729 | 0.364872 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.62861 | −0.322752 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 1.17598 | 0.0393748 | ||||||||
\(893\) | 44.4460 | 1.48733 | ||||||||
\(894\) | −6.99257 | −0.233867 | ||||||||
\(895\) | −24.1167 | −0.806134 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.1151 | 1.07229 | ||||||||
\(898\) | 27.5547 | 0.919511 | ||||||||
\(899\) | 21.7459 | 0.725265 | ||||||||
\(900\) | 0.171573 | 0.00571910 | ||||||||
\(901\) | 0.244331 | 0.00813985 | ||||||||
\(902\) | 0.554318 | 0.0184568 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.37665 | −0.112306 | ||||||||
\(905\) | −47.2314 | −1.57003 | ||||||||
\(906\) | 19.5286 | 0.648794 | ||||||||
\(907\) | 11.4692 | 0.380829 | 0.190415 | − | 0.981704i | \(-0.439017\pi\) | ||||
0.190415 | + | 0.981704i | \(0.439017\pi\) | |||||||
\(908\) | 22.0453 | 0.731600 | ||||||||
\(909\) | −10.7377 | −0.356148 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.1213 | 1.06423 | 0.532113 | − | 0.846673i | \(-0.321398\pi\) | ||||
0.532113 | + | 0.846673i | \(0.321398\pi\) | |||||||
\(912\) | 4.07597 | 0.134969 | ||||||||
\(913\) | −6.51675 | −0.215673 | ||||||||
\(914\) | 18.1953 | 0.601846 | ||||||||
\(915\) | 4.99880 | 0.165255 | ||||||||
\(916\) | 0.554318 | 0.0183152 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.554318 | −0.0182952 | ||||||||
\(919\) | 35.2965 | 1.16432 | 0.582161 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582161 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(920\) | 15.7729 | 0.520018 | ||||||||
\(921\) | 5.88477 | 0.193910 | ||||||||
\(922\) | −19.6193 | −0.646127 | ||||||||
\(923\) | 16.6863 | 0.549236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.86550 | 0.0613373 | ||||||||
\(926\) | −35.6176 | −1.17047 | ||||||||
\(927\) | 9.49712 | 0.311926 | ||||||||
\(928\) | 2.82843 | 0.0928477 | ||||||||
\(929\) | 28.6614 | 0.940350 | 0.470175 | − | 0.882573i | \(-0.344191\pi\) | ||||
0.470175 | + | 0.882573i | \(0.344191\pi\) | |||||||
\(930\) | −17.4841 | −0.573326 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.343146 | −0.0112401 | ||||||||
\(933\) | 17.4624 | 0.571694 | ||||||||
\(934\) | 35.0744 | 1.14767 | ||||||||
\(935\) | 1.26058 | 0.0412254 | ||||||||
\(936\) | −4.63029 | −0.151346 | ||||||||
\(937\) | −12.1753 | −0.397750 | −0.198875 | − | 0.980025i | \(-0.563729\pi\) | ||||
−0.198875 | + | 0.980025i | \(0.563729\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.87987 | −0.289783 | ||||||||
\(940\) | −24.7978 | −0.808815 | ||||||||
\(941\) | 32.9935 | 1.07556 | 0.537779 | − | 0.843086i | \(-0.319263\pi\) | ||||
0.537779 | + | 0.843086i | \(0.319263\pi\) | |||||||
\(942\) | −9.81490 | −0.319787 | ||||||||
\(943\) | −3.84468 | −0.125200 | ||||||||
\(944\) | −5.17157 | −0.168320 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.59272 | −0.279373 | ||||||||
\(947\) | 54.6748 | 1.77669 | 0.888346 | − | 0.459175i | \(-0.151855\pi\) | ||||
0.888346 | + | 0.459175i | \(0.151855\pi\) | |||||||
\(948\) | −15.7014 | −0.509956 | ||||||||
\(949\) | −66.5054 | −2.15886 | ||||||||
\(950\) | 0.699326 | 0.0226891 | ||||||||
\(951\) | 3.96937 | 0.128716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.9122 | 0.418267 | 0.209133 | − | 0.977887i | \(-0.432936\pi\) | ||||
0.209133 | + | 0.977887i | \(0.432936\pi\) | |||||||
\(954\) | 0.440778 | 0.0142707 | ||||||||
\(955\) | 37.9361 | 1.22758 | ||||||||
\(956\) | −5.56785 | −0.180077 | ||||||||
\(957\) | −2.82843 | −0.0914301 | ||||||||
\(958\) | 18.7482 | 0.605728 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.27411 | −0.0733966 | ||||||||
\(961\) | 28.1103 | 0.906784 | ||||||||
\(962\) | −50.3448 | −1.62318 | ||||||||
\(963\) | −7.64823 | −0.246461 | ||||||||
\(964\) | 1.94077 | 0.0625080 | ||||||||
\(965\) | 12.3702 | 0.398211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.6003 | −1.65936 | −0.829678 | − | 0.558243i | \(-0.811476\pi\) | ||||
−0.829678 | + | 0.558243i | \(0.811476\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −2.25938 | −0.0725819 | ||||||||
\(970\) | 8.74706 | 0.280851 | ||||||||
\(971\) | −45.9485 | −1.47456 | −0.737279 | − | 0.675588i | \(-0.763890\pi\) | ||||
−0.737279 | + | 0.675588i | \(0.763890\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.9301 | −0.959023 | ||||||||
\(975\) | −0.794432 | −0.0254422 | ||||||||
\(976\) | −2.19814 | −0.0703607 | ||||||||
\(977\) | 62.2328 | 1.99100 | 0.995502 | − | 0.0947399i | \(-0.0302020\pi\) | ||||
0.995502 | + | 0.0947399i | \(0.0302020\pi\) | |||||||
\(978\) | 13.6569 | 0.436698 | ||||||||
\(979\) | −4.23401 | −0.135320 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.22470 | −0.0391017 | ||||||||
\(982\) | 8.68629 | 0.277191 | ||||||||
\(983\) | −26.4763 | −0.844463 | −0.422232 | − | 0.906488i | \(-0.638753\pi\) | ||||
−0.422232 | + | 0.906488i | \(0.638753\pi\) | |||||||
\(984\) | 0.554318 | 0.0176710 | ||||||||
\(985\) | −23.6423 | −0.753305 | ||||||||
\(986\) | −1.56785 | −0.0499304 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.8729 | −0.600428 | ||||||||
\(989\) | 59.5980 | 1.89511 | ||||||||
\(990\) | 2.27411 | 0.0722759 | ||||||||
\(991\) | 46.5858 | 1.47985 | 0.739923 | − | 0.672692i | \(-0.234862\pi\) | ||||
0.739923 | + | 0.672692i | \(0.234862\pi\) | |||||||
\(992\) | 7.68832 | 0.244104 | ||||||||
\(993\) | 13.2692 | 0.421086 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.7162 | −0.434833 | ||||||||
\(996\) | −6.51675 | −0.206491 | ||||||||
\(997\) | 54.1457 | 1.71481 | 0.857406 | − | 0.514641i | \(-0.172075\pi\) | ||||
0.857406 | + | 0.514641i | \(0.172075\pi\) | |||||||
\(998\) | −23.8076 | −0.753617 | ||||||||
\(999\) | −10.8729 | −0.344004 |
(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 | 3234.2.a.bj.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 9702.2.a.eb.1.2 | 4 | |||
7.6 | odd | 2 | 3234.2.a.bk.1.2 | yes | 4 | ||
21.20 | even | 2 | 9702.2.a.ec.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bj.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3234.2.a.bk.1.2 | yes | 4 | 7.6 | odd | 2 | ||
9702.2.a.eb.1.2 | 4 | 3.2 | odd | 2 | |||
9702.2.a.ec.1.3 | 4 | 21.20 | even | 2 |