Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3762,2,Mod(1,3762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3762, 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("3762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3762.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: | \(30.0397212404\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3762.1 |
$q$-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 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.561553 | −0.212247 | −0.106124 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106124 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.561553 | 0.155747 | 0.0778734 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778734 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(14\) | −0.561553 | −0.150081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.561553 | 0.136197 | 0.0680983 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680983 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.43845 | −0.299937 | −0.149968 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149968 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.561553 | 0.110130 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.561553 | −0.106124 | ||||||||
\(29\) | 5.68466 | 1.05561 | 0.527807 | − | 0.849364i | \(-0.323014\pi\) | ||||
0.527807 | + | 0.849364i | \(0.323014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.561553 | 0.0963055 | ||||||||
\(35\) | 1.12311 | 0.189839 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.12311 | −0.842233 | −0.421117 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421117 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.43845 | −0.212087 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68466 | −0.954951 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.561553 | 0.0778734 | ||||||||
\(53\) | −12.8078 | −1.75928 | −0.879641 | − | 0.475638i | \(-0.842217\pi\) | ||||
−0.879641 | + | 0.475638i | \(0.842217\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | −0.561553 | −0.0750407 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.68466 | 0.746432 | ||||||||
\(59\) | 7.68466 | 1.00046 | 0.500229 | − | 0.865893i | \(-0.333249\pi\) | ||||
0.500229 | + | 0.865893i | \(0.333249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.24621 | 0.799745 | 0.399873 | − | 0.916571i | \(-0.369054\pi\) | ||||
0.399873 | + | 0.916571i | \(0.369054\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.12311 | −0.139304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.68466 | −0.938830 | −0.469415 | − | 0.882978i | \(-0.655535\pi\) | ||||
−0.469415 | + | 0.882978i | \(0.655535\pi\) | |||||||
\(68\) | 0.561553 | 0.0680983 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.12311 | 0.134237 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.68466 | −1.13350 | −0.566752 | − | 0.823889i | \(-0.691800\pi\) | ||||
−0.566752 | + | 0.823889i | \(0.691800\pi\) | |||||||
\(74\) | −5.12311 | −0.595549 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.561553 | 0.0639949 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | −14.2462 | −1.56372 | −0.781862 | − | 0.623451i | \(-0.785730\pi\) | ||||
−0.781862 | + | 0.623451i | \(0.785730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12311 | −0.121818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 0.876894 | 0.0929506 | 0.0464753 | − | 0.998919i | \(-0.485201\pi\) | ||||
0.0464753 | + | 0.998919i | \(0.485201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.315342 | −0.0330568 | ||||||||
\(92\) | −1.43845 | −0.149968 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.12311 | −0.723242 | −0.361621 | − | 0.932325i | \(-0.617777\pi\) | ||||
−0.361621 | + | 0.932325i | \(0.617777\pi\) | |||||||
\(98\) | −6.68466 | −0.675252 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 6.87689 | 0.684277 | 0.342138 | − | 0.939650i | \(-0.388849\pi\) | ||||
0.342138 | + | 0.939650i | \(0.388849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3693 | −1.31732 | −0.658659 | − | 0.752442i | \(-0.728876\pi\) | ||||
−0.658659 | + | 0.752442i | \(0.728876\pi\) | |||||||
\(104\) | 0.561553 | 0.0550648 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.8078 | −1.24400 | ||||||||
\(107\) | 9.93087 | 0.960053 | 0.480027 | − | 0.877254i | \(-0.340627\pi\) | ||||
0.480027 | + | 0.877254i | \(0.340627\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31534 | −0.604900 | −0.302450 | − | 0.953165i | \(-0.597805\pi\) | ||||
−0.302450 | + | 0.953165i | \(0.597805\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.561553 | −0.0530618 | ||||||||
\(113\) | 3.12311 | 0.293797 | 0.146899 | − | 0.989152i | \(-0.453071\pi\) | ||||
0.146899 | + | 0.989152i | \(0.453071\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.87689 | 0.268272 | ||||||||
\(116\) | 5.68466 | 0.527807 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.68466 | 0.707430 | ||||||||
\(119\) | −0.315342 | −0.0289073 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.24621 | 0.565505 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24621 | 0.199319 | 0.0996595 | − | 0.995022i | \(-0.468225\pi\) | ||||
0.0996595 | + | 0.995022i | \(0.468225\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.12311 | −0.0985029 | ||||||||
\(131\) | −1.12311 | −0.0981262 | −0.0490631 | − | 0.998796i | \(-0.515624\pi\) | ||||
−0.0490631 | + | 0.998796i | \(0.515624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.561553 | 0.0486928 | ||||||||
\(134\) | −7.68466 | −0.663853 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.561553 | 0.0481528 | ||||||||
\(137\) | −12.5616 | −1.07321 | −0.536603 | − | 0.843835i | \(-0.680293\pi\) | ||||
−0.536603 | + | 0.843835i | \(0.680293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.36932 | 0.625057 | 0.312529 | − | 0.949908i | \(-0.398824\pi\) | ||||
0.312529 | + | 0.949908i | \(0.398824\pi\) | |||||||
\(140\) | 1.12311 | 0.0949197 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | −0.561553 | −0.0469594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.3693 | −0.944170 | ||||||||
\(146\) | −9.68466 | −0.801508 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.12311 | −0.421117 | ||||||||
\(149\) | 6.87689 | 0.563377 | 0.281689 | − | 0.959506i | \(-0.409106\pi\) | ||||
0.281689 | + | 0.959506i | \(0.409106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.561553 | 0.0452512 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4924 | −1.15662 | −0.578311 | − | 0.815817i | \(-0.696288\pi\) | ||||
−0.578311 | + | 0.815817i | \(0.696288\pi\) | |||||||
\(158\) | −4.00000 | −0.318223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 0.807764 | 0.0636607 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3693 | 0.890514 | 0.445257 | − | 0.895403i | \(-0.353112\pi\) | ||||
0.445257 | + | 0.895403i | \(0.353112\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.2462 | −1.10572 | ||||||||
\(167\) | 0.630683 | 0.0488037 | 0.0244019 | − | 0.999702i | \(-0.492232\pi\) | ||||
0.0244019 | + | 0.999702i | \(0.492232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | −1.12311 | −0.0861383 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.561553 | 0.0424494 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.876894 | 0.0657260 | ||||||||
\(179\) | −5.75379 | −0.430058 | −0.215029 | − | 0.976608i | \(-0.568985\pi\) | ||||
−0.215029 | + | 0.976608i | \(0.568985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8769 | −0.808473 | −0.404237 | − | 0.914654i | \(-0.632463\pi\) | ||||
−0.404237 | + | 0.914654i | \(0.632463\pi\) | |||||||
\(182\) | −0.315342 | −0.0233747 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.43845 | −0.106044 | ||||||||
\(185\) | 10.2462 | 0.753316 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.561553 | −0.0410648 | ||||||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00000 | 0.145095 | ||||||||
\(191\) | 8.31534 | 0.601677 | 0.300838 | − | 0.953675i | \(-0.402733\pi\) | ||||
0.300838 | + | 0.953675i | \(0.402733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.12311 | 0.512732 | 0.256366 | − | 0.966580i | \(-0.417475\pi\) | ||||
0.256366 | + | 0.966580i | \(0.417475\pi\) | |||||||
\(194\) | −7.12311 | −0.511409 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | −18.2462 | −1.29999 | −0.649994 | − | 0.759939i | \(-0.725229\pi\) | ||||
−0.649994 | + | 0.759939i | \(0.725229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6847 | 0.828303 | 0.414152 | − | 0.910208i | \(-0.364078\pi\) | ||||
0.414152 | + | 0.910208i | \(0.364078\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.87689 | 0.483857 | ||||||||
\(203\) | −3.19224 | −0.224051 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | −13.3693 | −0.931484 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.561553 | 0.0389367 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.315342 | −0.0217090 | −0.0108545 | − | 0.999941i | \(-0.503455\pi\) | ||||
−0.0108545 | + | 0.999941i | \(0.503455\pi\) | |||||||
\(212\) | −12.8078 | −0.879641 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.93087 | 0.678860 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.12311 | −0.0762414 | ||||||||
\(218\) | −6.31534 | −0.427729 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 0.315342 | 0.0212122 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.7386 | 1.65662 | 0.828311 | − | 0.560269i | \(-0.189302\pi\) | ||||
0.828311 | + | 0.560269i | \(0.189302\pi\) | |||||||
\(224\) | −0.561553 | −0.0375203 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.12311 | 0.207746 | ||||||||
\(227\) | −28.1771 | −1.87018 | −0.935089 | − | 0.354412i | \(-0.884681\pi\) | ||||
−0.935089 | + | 0.354412i | \(0.884681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8769 | 0.850929 | 0.425465 | − | 0.904975i | \(-0.360111\pi\) | ||||
0.425465 | + | 0.904975i | \(0.360111\pi\) | |||||||
\(230\) | 2.87689 | 0.189697 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.68466 | 0.373216 | ||||||||
\(233\) | 28.7386 | 1.88273 | 0.941365 | − | 0.337389i | \(-0.109544\pi\) | ||||
0.941365 | + | 0.337389i | \(0.109544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 7.68466 | 0.500229 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.315342 | −0.0204406 | ||||||||
\(239\) | −23.9309 | −1.54796 | −0.773980 | − | 0.633210i | \(-0.781737\pi\) | ||||
−0.773980 | + | 0.633210i | \(0.781737\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6155 | −1.26355 | −0.631774 | − | 0.775153i | \(-0.717673\pi\) | ||||
−0.631774 | + | 0.775153i | \(0.717673\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.24621 | 0.399873 | ||||||||
\(245\) | 13.3693 | 0.854134 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.561553 | −0.0357307 | ||||||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | −17.1231 | −1.08080 | −0.540400 | − | 0.841408i | \(-0.681727\pi\) | ||||
−0.540400 | + | 0.841408i | \(0.681727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.43845 | 0.0904344 | ||||||||
\(254\) | 2.24621 | 0.140940 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.87689 | 0.178762 | ||||||||
\(260\) | −1.12311 | −0.0696521 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.12311 | −0.0693857 | ||||||||
\(263\) | −8.87689 | −0.547373 | −0.273686 | − | 0.961819i | \(-0.588243\pi\) | ||||
−0.273686 | + | 0.961819i | \(0.588243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.6155 | 1.57355 | ||||||||
\(266\) | 0.561553 | 0.0344310 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.68466 | −0.469415 | ||||||||
\(269\) | −2.87689 | −0.175407 | −0.0877037 | − | 0.996147i | \(-0.527953\pi\) | ||||
−0.0877037 | + | 0.996147i | \(0.527953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6847 | 1.56023 | 0.780116 | − | 0.625635i | \(-0.215160\pi\) | ||||
0.780116 | + | 0.625635i | \(0.215160\pi\) | |||||||
\(272\) | 0.561553 | 0.0340491 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.5616 | −0.758871 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.49242 | 0.510260 | 0.255130 | − | 0.966907i | \(-0.417882\pi\) | ||||
0.255130 | + | 0.966907i | \(0.417882\pi\) | |||||||
\(278\) | 7.36932 | 0.441982 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.12311 | 0.0671184 | ||||||||
\(281\) | 25.3693 | 1.51341 | 0.756703 | − | 0.653758i | \(-0.226809\pi\) | ||||
0.756703 | + | 0.653758i | \(0.226809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3693 | 0.675836 | 0.337918 | − | 0.941176i | \(-0.390277\pi\) | ||||
0.337918 | + | 0.941176i | \(0.390277\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.561553 | −0.0332053 | ||||||||
\(287\) | 1.12311 | 0.0662948 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6847 | −0.981450 | ||||||||
\(290\) | −11.3693 | −0.667629 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.68466 | −0.566752 | ||||||||
\(293\) | −3.93087 | −0.229644 | −0.114822 | − | 0.993386i | \(-0.536630\pi\) | ||||
−0.114822 | + | 0.993386i | \(0.536630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.3693 | −0.894836 | ||||||||
\(296\) | −5.12311 | −0.297774 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.87689 | 0.398368 | ||||||||
\(299\) | −0.807764 | −0.0467142 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −12.4924 | −0.715314 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.2462 | −1.26966 | −0.634829 | − | 0.772653i | \(-0.718930\pi\) | ||||
−0.634829 | + | 0.772653i | \(0.718930\pi\) | |||||||
\(308\) | 0.561553 | 0.0319974 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.00000 | −0.227185 | ||||||||
\(311\) | 4.80776 | 0.272623 | 0.136312 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136312 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.561553 | −0.0317408 | −0.0158704 | − | 0.999874i | \(-0.505052\pi\) | ||||
−0.0158704 | + | 0.999874i | \(0.505052\pi\) | |||||||
\(314\) | −14.4924 | −0.817855 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 7.05398 | 0.396191 | 0.198095 | − | 0.980183i | \(-0.436524\pi\) | ||||
0.198095 | + | 0.980183i | \(0.436524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.68466 | −0.318280 | ||||||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.807764 | 0.0450149 | ||||||||
\(323\) | −0.561553 | −0.0312456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.561553 | −0.0311493 | ||||||||
\(326\) | 11.3693 | 0.629688 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | 4.49242 | 0.247675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5616 | −0.800375 | −0.400188 | − | 0.916433i | \(-0.631055\pi\) | ||||
−0.400188 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(332\) | −14.2462 | −0.781862 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.630683 | 0.0345094 | ||||||||
\(335\) | 15.3693 | 0.839715 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1231 | 0.605914 | 0.302957 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302957 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(338\) | −12.6847 | −0.689954 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.12311 | −0.0609090 | ||||||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | −9.61553 | −0.516189 | −0.258094 | − | 0.966120i | \(-0.583095\pi\) | ||||
−0.258094 | + | 0.966120i | \(0.583095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.6155 | 1.15705 | 0.578526 | − | 0.815664i | \(-0.303628\pi\) | ||||
0.578526 | + | 0.815664i | \(0.303628\pi\) | |||||||
\(350\) | 0.561553 | 0.0300163 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −22.1771 | −1.18037 | −0.590183 | − | 0.807269i | \(-0.700945\pi\) | ||||
−0.590183 | + | 0.807269i | \(0.700945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | 0.636894 | ||||||||
\(356\) | 0.876894 | 0.0464753 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.75379 | −0.304097 | ||||||||
\(359\) | 15.9309 | 0.840799 | 0.420400 | − | 0.907339i | \(-0.361890\pi\) | ||||
0.420400 | + | 0.907339i | \(0.361890\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −10.8769 | −0.571677 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.315342 | −0.0165284 | ||||||||
\(365\) | 19.3693 | 1.01384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.2462 | 1.57884 | 0.789420 | − | 0.613854i | \(-0.210382\pi\) | ||||
0.789420 | + | 0.613854i | \(0.210382\pi\) | |||||||
\(368\) | −1.43845 | −0.0749842 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.2462 | 0.532675 | ||||||||
\(371\) | 7.19224 | 0.373402 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.43845 | 0.178036 | 0.0890180 | − | 0.996030i | \(-0.471627\pi\) | ||||
0.0890180 | + | 0.996030i | \(0.471627\pi\) | |||||||
\(374\) | −0.561553 | −0.0290372 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 3.19224 | 0.164409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.56155 | 0.337044 | 0.168522 | − | 0.985698i | \(-0.446101\pi\) | ||||
0.168522 | + | 0.985698i | \(0.446101\pi\) | |||||||
\(380\) | 2.00000 | 0.102598 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.31534 | 0.425450 | ||||||||
\(383\) | 2.00000 | 0.102195 | 0.0510976 | − | 0.998694i | \(-0.483728\pi\) | ||||
0.0510976 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.12311 | −0.0572388 | ||||||||
\(386\) | 7.12311 | 0.362557 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.12311 | −0.361621 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.807764 | −0.0408504 | ||||||||
\(392\) | −6.68466 | −0.337626 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.2462 | −0.919231 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.9848 | 1.95659 | 0.978297 | − | 0.207209i | \(-0.0664381\pi\) | ||||
0.978297 | + | 0.207209i | \(0.0664381\pi\) | |||||||
\(398\) | 11.6847 | 0.585699 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 7.75379 | 0.387206 | 0.193603 | − | 0.981080i | \(-0.437983\pi\) | ||||
0.193603 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.12311 | 0.0559459 | ||||||||
\(404\) | 6.87689 | 0.342138 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.19224 | −0.158428 | ||||||||
\(407\) | 5.12311 | 0.253943 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2462 | 0.803323 | 0.401662 | − | 0.915788i | \(-0.368433\pi\) | ||||
0.401662 | + | 0.915788i | \(0.368433\pi\) | |||||||
\(410\) | 4.00000 | 0.197546 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.3693 | −0.658659 | ||||||||
\(413\) | −4.31534 | −0.212344 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.4924 | 1.39864 | ||||||||
\(416\) | 0.561553 | 0.0275324 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.00000 | 0.0489116 | ||||||||
\(419\) | 14.8769 | 0.726784 | 0.363392 | − | 0.931636i | \(-0.381619\pi\) | ||||
0.363392 | + | 0.931636i | \(0.381619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9309 | −1.45874 | −0.729371 | − | 0.684119i | \(-0.760187\pi\) | ||||
−0.729371 | + | 0.684119i | \(0.760187\pi\) | |||||||
\(422\) | −0.315342 | −0.0153506 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.8078 | −0.622000 | ||||||||
\(425\) | −0.561553 | −0.0272393 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.50758 | −0.169744 | ||||||||
\(428\) | 9.93087 | 0.480027 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.8617 | −1.53473 | −0.767363 | − | 0.641213i | \(-0.778432\pi\) | ||||
−0.767363 | + | 0.641213i | \(0.778432\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.63068 | 0.318650 | 0.159325 | − | 0.987226i | \(-0.449068\pi\) | ||||
0.159325 | + | 0.987226i | \(0.449068\pi\) | |||||||
\(434\) | −1.12311 | −0.0539108 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.31534 | −0.302450 | ||||||||
\(437\) | 1.43845 | 0.0688103 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.61553 | −0.458924 | −0.229462 | − | 0.973318i | \(-0.573697\pi\) | ||||
−0.229462 | + | 0.973318i | \(0.573697\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.315342 | 0.0149993 | ||||||||
\(443\) | −39.8617 | −1.89389 | −0.946944 | − | 0.321398i | \(-0.895847\pi\) | ||||
−0.946944 | + | 0.321398i | \(0.895847\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.75379 | −0.0831376 | ||||||||
\(446\) | 24.7386 | 1.17141 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.561553 | −0.0265309 | ||||||||
\(449\) | −23.6155 | −1.11449 | −0.557243 | − | 0.830350i | \(-0.688141\pi\) | ||||
−0.557243 | + | 0.830350i | \(0.688141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | 0.0941763 | ||||||||
\(452\) | 3.12311 | 0.146899 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.1771 | −1.32242 | ||||||||
\(455\) | 0.630683 | 0.0295669 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.5616 | 1.71028 | 0.855139 | − | 0.518399i | \(-0.173472\pi\) | ||||
0.855139 | + | 0.518399i | \(0.173472\pi\) | |||||||
\(458\) | 12.8769 | 0.601698 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.87689 | 0.134136 | ||||||||
\(461\) | −26.7386 | −1.24534 | −0.622671 | − | 0.782484i | \(-0.713953\pi\) | ||||
−0.622671 | + | 0.782484i | \(0.713953\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.50758 | 0.163011 | 0.0815055 | − | 0.996673i | \(-0.474027\pi\) | ||||
0.0815055 | + | 0.996673i | \(0.474027\pi\) | |||||||
\(464\) | 5.68466 | 0.263904 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.7386 | 1.33129 | ||||||||
\(467\) | −9.75379 | −0.451352 | −0.225676 | − | 0.974202i | \(-0.572459\pi\) | ||||
−0.225676 | + | 0.974202i | \(0.572459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.31534 | 0.199264 | ||||||||
\(470\) | 16.0000 | 0.738025 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.68466 | 0.353715 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | −0.315342 | −0.0144537 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.9309 | −1.09457 | ||||||||
\(479\) | 13.3693 | 0.610860 | 0.305430 | − | 0.952215i | \(-0.401200\pi\) | ||||
0.305430 | + | 0.952215i | \(0.401200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.87689 | −0.131175 | ||||||||
\(482\) | −19.6155 | −0.893463 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 14.2462 | 0.646887 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.1231 | 1.41032 | 0.705161 | − | 0.709047i | \(-0.250875\pi\) | ||||
0.705161 | + | 0.709047i | \(0.250875\pi\) | |||||||
\(488\) | 6.24621 | 0.282753 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.3693 | 0.603964 | ||||||||
\(491\) | 39.3693 | 1.77671 | 0.888356 | − | 0.459155i | \(-0.151848\pi\) | ||||
0.888356 | + | 0.459155i | \(0.151848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.19224 | 0.143771 | ||||||||
\(494\) | −0.561553 | −0.0252655 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 3.36932 | 0.151135 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.75379 | 0.436640 | 0.218320 | − | 0.975877i | \(-0.429942\pi\) | ||||
0.218320 | + | 0.975877i | \(0.429942\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.1231 | −0.764242 | ||||||||
\(503\) | −21.6847 | −0.966871 | −0.483436 | − | 0.875380i | \(-0.660611\pi\) | ||||
−0.483436 | + | 0.875380i | \(0.660611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7538 | −0.612036 | ||||||||
\(506\) | 1.43845 | 0.0639468 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.24621 | 0.0996595 | ||||||||
\(509\) | 31.3693 | 1.39042 | 0.695210 | − | 0.718806i | \(-0.255311\pi\) | ||||
0.695210 | + | 0.718806i | \(0.255311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.43845 | 0.240583 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.0000 | 0.970378 | ||||||||
\(515\) | 26.7386 | 1.17824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 2.87689 | 0.126403 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.12311 | −0.0492514 | ||||||||
\(521\) | 7.12311 | 0.312069 | 0.156034 | − | 0.987752i | \(-0.450129\pi\) | ||||
0.156034 | + | 0.987752i | \(0.450129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.0540 | 1.35790 | 0.678948 | − | 0.734187i | \(-0.262436\pi\) | ||||
0.678948 | + | 0.734187i | \(0.262436\pi\) | |||||||
\(524\) | −1.12311 | −0.0490631 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.87689 | −0.387051 | ||||||||
\(527\) | 1.12311 | 0.0489232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9309 | −0.910038 | ||||||||
\(530\) | 25.6155 | 1.11267 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.561553 | 0.0243464 | ||||||||
\(533\) | −1.12311 | −0.0486471 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.8617 | −0.858698 | ||||||||
\(536\) | −7.68466 | −0.331927 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.87689 | −0.124032 | ||||||||
\(539\) | 6.68466 | 0.287929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.2311 | −1.68667 | −0.843337 | − | 0.537384i | \(-0.819412\pi\) | ||||
−0.843337 | + | 0.537384i | \(0.819412\pi\) | |||||||
\(542\) | 25.6847 | 1.10325 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.561553 | 0.0240764 | ||||||||
\(545\) | 12.6307 | 0.541039 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.7386 | −1.82737 | −0.913686 | − | 0.406421i | \(-0.866777\pi\) | ||||
−0.913686 | + | 0.406421i | \(0.866777\pi\) | |||||||
\(548\) | −12.5616 | −0.536603 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −5.68466 | −0.242175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.24621 | 0.0955186 | ||||||||
\(554\) | 8.49242 | 0.360808 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.36932 | 0.312529 | ||||||||
\(557\) | −17.1231 | −0.725529 | −0.362765 | − | 0.931881i | \(-0.618167\pi\) | ||||
−0.362765 | + | 0.931881i | \(0.618167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.12311 | 0.0474599 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.3693 | 1.07014 | ||||||||
\(563\) | 42.7386 | 1.80122 | 0.900609 | − | 0.434630i | \(-0.143121\pi\) | ||||
0.900609 | + | 0.434630i | \(0.143121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.24621 | −0.262780 | ||||||||
\(566\) | 11.3693 | 0.477888 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | 21.3693 | 0.895848 | 0.447924 | − | 0.894072i | \(-0.352163\pi\) | ||||
0.447924 | + | 0.894072i | \(0.352163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.61553 | −0.235003 | −0.117501 | − | 0.993073i | \(-0.537488\pi\) | ||||
−0.117501 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(572\) | −0.561553 | −0.0234797 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.12311 | 0.0468775 | ||||||||
\(575\) | 1.43845 | 0.0599874 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.0540 | 1.70910 | 0.854550 | − | 0.519370i | \(-0.173833\pi\) | ||||
0.854550 | + | 0.519370i | \(0.173833\pi\) | |||||||
\(578\) | −16.6847 | −0.693990 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.3693 | −0.472085 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.8078 | 0.530443 | ||||||||
\(584\) | −9.68466 | −0.400754 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.93087 | −0.162383 | ||||||||
\(587\) | 40.4924 | 1.67130 | 0.835651 | − | 0.549261i | \(-0.185091\pi\) | ||||
0.835651 | + | 0.549261i | \(0.185091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | −15.3693 | −0.632745 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.12311 | −0.210558 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.630683 | 0.0258555 | ||||||||
\(596\) | 6.87689 | 0.281689 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.807764 | −0.0330319 | ||||||||
\(599\) | 17.8617 | 0.729811 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3693 | 0.871673 | 0.435836 | − | 0.900026i | \(-0.356453\pi\) | ||||
0.435836 | + | 0.900026i | \(0.356453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.6155 | −0.552637 | −0.276319 | − | 0.961066i | \(-0.589115\pi\) | ||||
−0.276319 | + | 0.961066i | \(0.589115\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.4924 | −0.505803 | ||||||||
\(611\) | −4.49242 | −0.181744 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2462 | 0.736958 | 0.368479 | − | 0.929636i | \(-0.379879\pi\) | ||||
0.368479 | + | 0.929636i | \(0.379879\pi\) | |||||||
\(614\) | −22.2462 | −0.897784 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.561553 | 0.0226256 | ||||||||
\(617\) | −44.7386 | −1.80111 | −0.900555 | − | 0.434743i | \(-0.856839\pi\) | ||||
−0.900555 | + | 0.434743i | \(0.856839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.75379 | −0.392038 | −0.196019 | − | 0.980600i | \(-0.562801\pi\) | ||||
−0.196019 | + | 0.980600i | \(0.562801\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.80776 | 0.192774 | ||||||||
\(623\) | −0.492423 | −0.0197285 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −0.561553 | −0.0224442 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.4924 | −0.578311 | ||||||||
\(629\) | −2.87689 | −0.114709 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50758 | 0.139634 | 0.0698172 | − | 0.997560i | \(-0.477758\pi\) | ||||
0.0698172 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.05398 | 0.280149 | ||||||||
\(635\) | −4.49242 | −0.178276 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.75379 | −0.148731 | ||||||||
\(638\) | −5.68466 | −0.225058 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.00000 | −0.0790569 | ||||||||
\(641\) | −31.6155 | −1.24874 | −0.624369 | − | 0.781129i | \(-0.714644\pi\) | ||||
−0.624369 | + | 0.781129i | \(0.714644\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6307 | −0.498106 | −0.249053 | − | 0.968490i | \(-0.580119\pi\) | ||||
−0.249053 | + | 0.968490i | \(0.580119\pi\) | |||||||
\(644\) | 0.807764 | 0.0318304 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.561553 | −0.0220940 | ||||||||
\(647\) | 47.5464 | 1.86924 | 0.934621 | − | 0.355646i | \(-0.115739\pi\) | ||||
0.934621 | + | 0.355646i | \(0.115739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.68466 | −0.301649 | ||||||||
\(650\) | −0.561553 | −0.0220259 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.3693 | 0.445257 | ||||||||
\(653\) | 15.6155 | 0.611083 | 0.305541 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305541 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.24621 | 0.0877667 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.49242 | 0.175133 | ||||||||
\(659\) | 14.4233 | 0.561852 | 0.280926 | − | 0.959729i | \(-0.409359\pi\) | ||||
0.280926 | + | 0.959729i | \(0.409359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5616 | −1.03312 | −0.516562 | − | 0.856250i | \(-0.672789\pi\) | ||||
−0.516562 | + | 0.856250i | \(0.672789\pi\) | |||||||
\(662\) | −14.5616 | −0.565951 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.2462 | −0.552860 | ||||||||
\(665\) | −1.12311 | −0.0435522 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.17708 | −0.316618 | ||||||||
\(668\) | 0.630683 | 0.0244019 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.3693 | 0.593769 | ||||||||
\(671\) | −6.24621 | −0.241132 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.1231 | −1.04552 | −0.522759 | − | 0.852480i | \(-0.675097\pi\) | ||||
−0.522759 | + | 0.852480i | \(0.675097\pi\) | |||||||
\(674\) | 11.1231 | 0.428446 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6847 | −0.487871 | ||||||||
\(677\) | −6.17708 | −0.237405 | −0.118702 | − | 0.992930i | \(-0.537873\pi\) | ||||
−0.118702 | + | 0.992930i | \(0.537873\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | −1.12311 | −0.0430691 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | −0.0765840 | ||||||||
\(683\) | −28.4924 | −1.09023 | −0.545116 | − | 0.838361i | \(-0.683514\pi\) | ||||
−0.545116 | + | 0.838361i | \(0.683514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.1231 | 0.959905 | ||||||||
\(686\) | 7.68466 | 0.293402 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.19224 | −0.274002 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.38447 | −0.0907096 | −0.0453548 | − | 0.998971i | \(-0.514442\pi\) | ||||
−0.0453548 | + | 0.998971i | \(0.514442\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.61553 | −0.365000 | ||||||||
\(695\) | −14.7386 | −0.559068 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.12311 | −0.0425407 | ||||||||
\(698\) | 21.6155 | 0.818160 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.561553 | 0.0212247 | ||||||||
\(701\) | 40.9848 | 1.54798 | 0.773988 | − | 0.633200i | \(-0.218259\pi\) | ||||
0.773988 | + | 0.633200i | \(0.218259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.12311 | 0.193222 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.1771 | −0.834645 | ||||||||
\(707\) | −3.86174 | −0.145236 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.4924 | −1.59584 | −0.797918 | − | 0.602766i | \(-0.794065\pi\) | ||||
−0.797918 | + | 0.602766i | \(0.794065\pi\) | |||||||
\(710\) | 12.0000 | 0.450352 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.876894 | 0.0328630 | ||||||||
\(713\) | −2.87689 | −0.107741 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.12311 | 0.0420018 | ||||||||
\(716\) | −5.75379 | −0.215029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.9309 | 0.594535 | ||||||||
\(719\) | 10.5616 | 0.393879 | 0.196940 | − | 0.980416i | \(-0.436900\pi\) | ||||
0.196940 | + | 0.980416i | \(0.436900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.50758 | 0.279597 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.8769 | −0.404237 | ||||||||
\(725\) | −5.68466 | −0.211123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4233 | 0.831634 | 0.415817 | − | 0.909448i | \(-0.363496\pi\) | ||||
0.415817 | + | 0.909448i | \(0.363496\pi\) | |||||||
\(728\) | −0.315342 | −0.0116873 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.3693 | 0.716891 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.1080 | 0.964319 | 0.482160 | − | 0.876083i | \(-0.339853\pi\) | ||||
0.482160 | + | 0.876083i | \(0.339853\pi\) | |||||||
\(734\) | 30.2462 | 1.11641 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.43845 | −0.0530219 | ||||||||
\(737\) | 7.68466 | 0.283068 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.9848 | −1.65479 | −0.827397 | − | 0.561617i | \(-0.810179\pi\) | ||||
−0.827397 | + | 0.561617i | \(0.810179\pi\) | |||||||
\(740\) | 10.2462 | 0.376658 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.19224 | 0.264035 | ||||||||
\(743\) | 42.2462 | 1.54986 | 0.774932 | − | 0.632045i | \(-0.217784\pi\) | ||||
0.774932 | + | 0.632045i | \(0.217784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.7538 | −0.503900 | ||||||||
\(746\) | 3.43845 | 0.125890 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.561553 | −0.0205324 | ||||||||
\(749\) | −5.57671 | −0.203768 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.2311 | 1.50454 | 0.752271 | − | 0.658853i | \(-0.228958\pi\) | ||||
0.752271 | + | 0.658853i | \(0.228958\pi\) | |||||||
\(752\) | −8.00000 | −0.291730 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.19224 | 0.116254 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.4924 | −1.54441 | −0.772207 | − | 0.635371i | \(-0.780847\pi\) | ||||
−0.772207 | + | 0.635371i | \(0.780847\pi\) | |||||||
\(758\) | 6.56155 | 0.238326 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00000 | 0.0725476 | ||||||||
\(761\) | 42.8078 | 1.55178 | 0.775890 | − | 0.630868i | \(-0.217301\pi\) | ||||
0.775890 | + | 0.630868i | \(0.217301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.54640 | 0.128388 | ||||||||
\(764\) | 8.31534 | 0.300838 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | 0.0722629 | ||||||||
\(767\) | 4.31534 | 0.155818 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6847 | −0.493481 | −0.246741 | − | 0.969082i | \(-0.579360\pi\) | ||||
−0.246741 | + | 0.969082i | \(0.579360\pi\) | |||||||
\(770\) | −1.12311 | −0.0404739 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.12311 | 0.256366 | ||||||||
\(773\) | −37.9309 | −1.36428 | −0.682139 | − | 0.731222i | \(-0.738950\pi\) | ||||
−0.682139 | + | 0.731222i | \(0.738950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | −7.12311 | −0.255705 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.0000 | −0.645331 | ||||||||
\(779\) | 2.00000 | 0.0716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | −0.807764 | −0.0288856 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.68466 | −0.238738 | ||||||||
\(785\) | 28.9848 | 1.03451 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.6847 | 0.559098 | 0.279549 | − | 0.960131i | \(-0.409815\pi\) | ||||
0.279549 | + | 0.960131i | \(0.409815\pi\) | |||||||
\(788\) | −18.2462 | −0.649994 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.00000 | 0.284627 | ||||||||
\(791\) | −1.75379 | −0.0623575 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.50758 | 0.124558 | ||||||||
\(794\) | 38.9848 | 1.38352 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.6847 | 0.414152 | ||||||||
\(797\) | 15.1922 | 0.538137 | 0.269068 | − | 0.963121i | \(-0.413284\pi\) | ||||
0.269068 | + | 0.963121i | \(0.413284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.49242 | −0.158930 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.75379 | 0.273796 | ||||||||
\(803\) | 9.68466 | 0.341764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61553 | −0.0569399 | ||||||||
\(806\) | 1.12311 | 0.0395597 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.87689 | 0.241928 | ||||||||
\(809\) | −8.06913 | −0.283696 | −0.141848 | − | 0.989888i | \(-0.545304\pi\) | ||||
−0.141848 | + | 0.989888i | \(0.545304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.31534 | 0.291991 | 0.145996 | − | 0.989285i | \(-0.453361\pi\) | ||||
0.145996 | + | 0.989285i | \(0.453361\pi\) | |||||||
\(812\) | −3.19224 | −0.112026 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.12311 | 0.179565 | ||||||||
\(815\) | −22.7386 | −0.796500 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16.2462 | 0.568035 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 20.9848 | 0.732376 | 0.366188 | − | 0.930541i | \(-0.380663\pi\) | ||||
0.366188 | + | 0.930541i | \(0.380663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9309 | −0.485600 | −0.242800 | − | 0.970076i | \(-0.578066\pi\) | ||||
−0.242800 | + | 0.970076i | \(0.578066\pi\) | |||||||
\(824\) | −13.3693 | −0.465742 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.31534 | −0.150150 | ||||||||
\(827\) | −49.9309 | −1.73627 | −0.868133 | − | 0.496331i | \(-0.834680\pi\) | ||||
−0.868133 | + | 0.496331i | \(0.834680\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1771 | 0.422928 | 0.211464 | − | 0.977386i | \(-0.432177\pi\) | ||||
0.211464 | + | 0.977386i | \(0.432177\pi\) | |||||||
\(830\) | 28.4924 | 0.988986 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.561553 | 0.0194683 | ||||||||
\(833\) | −3.75379 | −0.130061 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.26137 | −0.0436514 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.8769 | 0.513914 | ||||||||
\(839\) | 7.12311 | 0.245917 | 0.122958 | − | 0.992412i | \(-0.460762\pi\) | ||||
0.122958 | + | 0.992412i | \(0.460762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | −29.9309 | −1.03149 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.315342 | −0.0108545 | ||||||||
\(845\) | 25.3693 | 0.872731 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.561553 | −0.0192952 | ||||||||
\(848\) | −12.8078 | −0.439820 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.561553 | −0.0192611 | ||||||||
\(851\) | 7.36932 | 0.252617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.3542 | −1.79257 | −0.896286 | − | 0.443476i | \(-0.853745\pi\) | ||||
−0.896286 | + | 0.443476i | \(0.853745\pi\) | |||||||
\(854\) | −3.50758 | −0.120027 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.93087 | 0.339430 | ||||||||
\(857\) | 10.0000 | 0.341593 | 0.170797 | − | 0.985306i | \(-0.445366\pi\) | ||||
0.170797 | + | 0.985306i | \(0.445366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.8617 | 0.541196 | 0.270598 | − | 0.962692i | \(-0.412779\pi\) | ||||
0.270598 | + | 0.962692i | \(0.412779\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.8617 | −1.08522 | ||||||||
\(863\) | −0.246211 | −0.00838113 | −0.00419056 | − | 0.999991i | \(-0.501334\pi\) | ||||
−0.00419056 | + | 0.999991i | \(0.501334\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 6.63068 | 0.225320 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.12311 | −0.0381207 | ||||||||
\(869\) | 4.00000 | 0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.31534 | −0.146220 | ||||||||
\(872\) | −6.31534 | −0.213864 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.43845 | 0.0486562 | ||||||||
\(875\) | −6.73863 | −0.227807 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.5616 | −1.50474 | −0.752368 | − | 0.658743i | \(-0.771089\pi\) | ||||
−0.752368 | + | 0.658743i | \(0.771089\pi\) | |||||||
\(878\) | −9.61553 | −0.324508 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | 0.0674200 | ||||||||
\(881\) | −20.7386 | −0.698702 | −0.349351 | − | 0.936992i | \(-0.613598\pi\) | ||||
−0.349351 | + | 0.936992i | \(0.613598\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.26137 | −0.177059 | −0.0885295 | − | 0.996074i | \(-0.528217\pi\) | ||||
−0.0885295 | + | 0.996074i | \(0.528217\pi\) | |||||||
\(884\) | 0.315342 | 0.0106061 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.8617 | −1.33918 | ||||||||
\(887\) | 32.0000 | 1.07445 | 0.537227 | − | 0.843437i | \(-0.319472\pi\) | ||||
0.537227 | + | 0.843437i | \(0.319472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.26137 | −0.0423049 | ||||||||
\(890\) | −1.75379 | −0.0587871 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.7386 | 0.828311 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.5076 | 0.384656 | ||||||||
\(896\) | −0.561553 | −0.0187602 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.6155 | −0.788060 | ||||||||
\(899\) | 11.3693 | 0.379188 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.19224 | −0.239608 | ||||||||
\(902\) | 2.00000 | 0.0665927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.12311 | 0.103873 | ||||||||
\(905\) | 21.7538 | 0.723120 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.7926 | −0.989247 | −0.494624 | − | 0.869107i | \(-0.664694\pi\) | ||||
−0.494624 | + | 0.869107i | \(0.664694\pi\) | |||||||
\(908\) | −28.1771 | −0.935089 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.630683 | 0.0209069 | ||||||||
\(911\) | −18.9848 | −0.628996 | −0.314498 | − | 0.949258i | \(-0.601836\pi\) | ||||
−0.314498 | + | 0.949258i | \(0.601836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.2462 | 0.471481 | ||||||||
\(914\) | 36.5616 | 1.20935 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.8769 | 0.425465 | ||||||||
\(917\) | 0.630683 | 0.0208270 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.5616 | 1.07411 | 0.537053 | − | 0.843548i | \(-0.319537\pi\) | ||||
0.537053 | + | 0.843548i | \(0.319537\pi\) | |||||||
\(920\) | 2.87689 | 0.0948484 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.7386 | −0.880590 | ||||||||
\(923\) | −3.36932 | −0.110902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.12311 | 0.168447 | ||||||||
\(926\) | 3.50758 | 0.115266 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.68466 | 0.186608 | ||||||||
\(929\) | −11.9309 | −0.391439 | −0.195720 | − | 0.980660i | \(-0.562704\pi\) | ||||
−0.195720 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.68466 | 0.219081 | ||||||||
\(932\) | 28.7386 | 0.941365 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.75379 | −0.319154 | ||||||||
\(935\) | 1.12311 | 0.0367295 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.699813 | −0.0228619 | −0.0114310 | − | 0.999935i | \(-0.503639\pi\) | ||||
−0.0114310 | + | 0.999935i | \(0.503639\pi\) | |||||||
\(938\) | 4.31534 | 0.140901 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.0000 | 0.521862 | ||||||||
\(941\) | −24.5616 | −0.800684 | −0.400342 | − | 0.916366i | \(-0.631109\pi\) | ||||
−0.400342 | + | 0.916366i | \(0.631109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.87689 | 0.0936846 | ||||||||
\(944\) | 7.68466 | 0.250114 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.9848 | 1.20185 | 0.600923 | − | 0.799307i | \(-0.294800\pi\) | ||||
0.600923 | + | 0.799307i | \(0.294800\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.43845 | −0.176539 | ||||||||
\(950\) | 1.00000 | 0.0324443 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.315342 | −0.0102203 | ||||||||
\(953\) | 0.876894 | 0.0284054 | 0.0142027 | − | 0.999899i | \(-0.495479\pi\) | ||||
0.0142027 | + | 0.999899i | \(0.495479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.6307 | −0.538156 | ||||||||
\(956\) | −23.9309 | −0.773980 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.3693 | 0.431943 | ||||||||
\(959\) | 7.05398 | 0.227785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −2.87689 | −0.0927548 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.6155 | −0.631774 | ||||||||
\(965\) | −14.2462 | −0.458602 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.8617 | 1.73208 | 0.866038 | − | 0.499978i | \(-0.166658\pi\) | ||||
0.866038 | + | 0.499978i | \(0.166658\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.2462 | 0.457418 | ||||||||
\(971\) | −2.24621 | −0.0720843 | −0.0360422 | − | 0.999350i | \(-0.511475\pi\) | ||||
−0.0360422 | + | 0.999350i | \(0.511475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.13826 | −0.132667 | ||||||||
\(974\) | 31.1231 | 0.997249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.24621 | 0.199936 | ||||||||
\(977\) | −30.6307 | −0.979962 | −0.489981 | − | 0.871733i | \(-0.662996\pi\) | ||||
−0.489981 | + | 0.871733i | \(0.662996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.876894 | −0.0280257 | ||||||||
\(980\) | 13.3693 | 0.427067 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.3693 | 1.25633 | ||||||||
\(983\) | 31.7538 | 1.01279 | 0.506394 | − | 0.862302i | \(-0.330978\pi\) | ||||
0.506394 | + | 0.862302i | \(0.330978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.4924 | 1.16275 | ||||||||
\(986\) | 3.19224 | 0.101662 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.561553 | −0.0178654 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8769 | 0.409048 | 0.204524 | − | 0.978862i | \(-0.434435\pi\) | ||||
0.204524 | + | 0.978862i | \(0.434435\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.36932 | 0.106868 | ||||||||
\(995\) | −23.3693 | −0.740857 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.6307 | −0.906743 | −0.453371 | − | 0.891322i | \(-0.649779\pi\) | ||||
−0.453371 | + | 0.891322i | \(0.649779\pi\) | |||||||
\(998\) | 9.75379 | 0.308751 | ||||||||
\(999\) | 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 | 3762.2.a.y.1.1 | 2 | ||
3.2 | odd | 2 | 418.2.a.e.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 3344.2.a.k.1.1 | 2 | |||
33.32 | even | 2 | 4598.2.a.bj.1.2 | 2 | |||
57.56 | even | 2 | 7942.2.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.e.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3344.2.a.k.1.1 | 2 | 12.11 | even | 2 | |||
3762.2.a.y.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4598.2.a.bj.1.2 | 2 | 33.32 | even | 2 | |||
7942.2.a.x.1.1 | 2 | 57.56 | even | 2 |