Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2898,2,Mod(1,2898)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, 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("2898.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2898.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: | \(23.1406465058\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2898.1 |
$q$-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 | ||||||||
\(5\) | −2.56155 | −1.14556 | −0.572781 | − | 0.819709i | \(-0.694135\pi\) | ||||
−0.572781 | + | 0.819709i | \(0.694135\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.56155 | −0.810034 | ||||||||
\(11\) | 3.12311 | 0.941652 | 0.470826 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.561553 | 0.155747 | 0.0778734 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778734 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.12311 | −1.72761 | −0.863803 | − | 0.503829i | \(-0.831924\pi\) | ||||
−0.863803 | + | 0.503829i | \(0.831924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12311 | 0.716490 | 0.358245 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358245 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(20\) | −2.56155 | −0.572781 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.12311 | 0.665848 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 0.561553 | 0.110130 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −3.43845 | −0.638504 | −0.319252 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319252 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12311 | −0.920137 | −0.460068 | − | 0.887883i | \(-0.652175\pi\) | ||||
−0.460068 | + | 0.887883i | \(0.652175\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.12311 | −1.22160 | ||||||||
\(35\) | 2.56155 | 0.432981 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.56155 | 0.421117 | 0.210558 | − | 0.977581i | \(-0.432472\pi\) | ||||
0.210558 | + | 0.977581i | \(0.432472\pi\) | |||||||
\(38\) | 3.12311 | 0.506635 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.56155 | −0.405017 | ||||||||
\(41\) | 0.561553 | 0.0876998 | 0.0438499 | − | 0.999038i | \(-0.486038\pi\) | ||||
0.0438499 | + | 0.999038i | \(0.486038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.68466 | −0.866902 | −0.433451 | − | 0.901177i | \(-0.642704\pi\) | ||||
−0.433451 | + | 0.901177i | \(0.642704\pi\) | |||||||
\(44\) | 3.12311 | 0.470826 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.56155 | −0.957101 | −0.478550 | − | 0.878060i | \(-0.658838\pi\) | ||||
−0.478550 | + | 0.878060i | \(0.658838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.56155 | 0.220837 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.561553 | 0.0778734 | ||||||||
\(53\) | 2.24621 | 0.308541 | 0.154270 | − | 0.988029i | \(-0.450697\pi\) | ||||
0.154270 | + | 0.988029i | \(0.450697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.43845 | −0.451490 | ||||||||
\(59\) | −13.1231 | −1.70848 | −0.854241 | − | 0.519877i | \(-0.825978\pi\) | ||||
−0.854241 | + | 0.519877i | \(0.825978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.12311 | 1.16809 | 0.584047 | − | 0.811720i | \(-0.301468\pi\) | ||||
0.584047 | + | 0.811720i | \(0.301468\pi\) | |||||||
\(62\) | −5.12311 | −0.650635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.43845 | −0.178417 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.12311 | 0.870226 | 0.435113 | − | 0.900376i | \(-0.356708\pi\) | ||||
0.435113 | + | 0.900376i | \(0.356708\pi\) | |||||||
\(68\) | −7.12311 | −0.863803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.56155 | 0.306164 | ||||||||
\(71\) | −15.3693 | −1.82400 | −0.912001 | − | 0.410188i | \(-0.865463\pi\) | ||||
−0.912001 | + | 0.410188i | \(0.865463\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.876894 | 0.102633 | 0.0513164 | − | 0.998682i | \(-0.483658\pi\) | ||||
0.0513164 | + | 0.998682i | \(0.483658\pi\) | |||||||
\(74\) | 2.56155 | 0.297774 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.12311 | 0.358245 | ||||||||
\(77\) | −3.12311 | −0.355911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.24621 | −0.252719 | −0.126359 | − | 0.991985i | \(-0.540329\pi\) | ||||
−0.126359 | + | 0.991985i | \(0.540329\pi\) | |||||||
\(80\) | −2.56155 | −0.286390 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.561553 | 0.0620131 | ||||||||
\(83\) | 0.876894 | 0.0962517 | 0.0481258 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481258 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.2462 | 1.97908 | ||||||||
\(86\) | −5.68466 | −0.612992 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.12311 | 0.332924 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.561553 | −0.0588667 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.56155 | −0.676772 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5616 | −1.68157 | −0.840785 | − | 0.541368i | \(-0.817906\pi\) | ||||
−0.840785 | + | 0.541368i | \(0.817906\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.56155 | 0.156155 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.93087 | −0.978518 | −0.489259 | − | 0.872139i | \(-0.662733\pi\) | ||||
−0.489259 | + | 0.872139i | \(0.662733\pi\) | |||||||
\(104\) | 0.561553 | 0.0550648 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.24621 | 0.218171 | ||||||||
\(107\) | −3.12311 | −0.301922 | −0.150961 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150961 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5616 | 1.39474 | 0.697372 | − | 0.716709i | \(-0.254353\pi\) | ||||
0.697372 | + | 0.716709i | \(0.254353\pi\) | |||||||
\(110\) | −8.00000 | −0.762770 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −9.68466 | −0.911056 | −0.455528 | − | 0.890221i | \(-0.650550\pi\) | ||||
−0.455528 | + | 0.890221i | \(0.650550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.56155 | 0.238866 | ||||||||
\(116\) | −3.43845 | −0.319252 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.1231 | −1.20808 | ||||||||
\(119\) | 7.12311 | 0.652974 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 9.12311 | 0.825967 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.12311 | −0.460068 | ||||||||
\(125\) | 8.80776 | 0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.31534 | −0.382925 | −0.191462 | − | 0.981500i | \(-0.561323\pi\) | ||||
−0.191462 | + | 0.981500i | \(0.561323\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.43845 | −0.126160 | ||||||||
\(131\) | −13.1231 | −1.14657 | −0.573286 | − | 0.819356i | \(-0.694331\pi\) | ||||
−0.573286 | + | 0.819356i | \(0.694331\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12311 | −0.270808 | ||||||||
\(134\) | 7.12311 | 0.615343 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.12311 | −0.610801 | ||||||||
\(137\) | 4.56155 | 0.389720 | 0.194860 | − | 0.980831i | \(-0.437575\pi\) | ||||
0.194860 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8078 | −1.42562 | −0.712808 | − | 0.701359i | \(-0.752577\pi\) | ||||
−0.712808 | + | 0.701359i | \(0.752577\pi\) | |||||||
\(140\) | 2.56155 | 0.216491 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.3693 | −1.28976 | ||||||||
\(143\) | 1.75379 | 0.146659 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.80776 | 0.731445 | ||||||||
\(146\) | 0.876894 | 0.0725723 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.56155 | 0.210558 | ||||||||
\(149\) | −10.2462 | −0.839402 | −0.419701 | − | 0.907662i | \(-0.637865\pi\) | ||||
−0.419701 | + | 0.907662i | \(0.637865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.6847 | 1.60191 | 0.800957 | − | 0.598721i | \(-0.204324\pi\) | ||||
0.800957 | + | 0.598721i | \(0.204324\pi\) | |||||||
\(152\) | 3.12311 | 0.253317 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.12311 | −0.251667 | ||||||||
\(155\) | 13.1231 | 1.05407 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24621 | −0.179267 | −0.0896336 | − | 0.995975i | \(-0.528570\pi\) | ||||
−0.0896336 | + | 0.995975i | \(0.528570\pi\) | |||||||
\(158\) | −2.24621 | −0.178699 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.56155 | −0.202509 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 0.561553 | 0.0438499 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.876894 | 0.0680602 | ||||||||
\(167\) | −2.24621 | −0.173817 | −0.0869085 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869085 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | 18.2462 | 1.39942 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.68466 | −0.433451 | ||||||||
\(173\) | 14.4924 | 1.10184 | 0.550919 | − | 0.834559i | \(-0.314277\pi\) | ||||
0.550919 | + | 0.834559i | \(0.314277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56155 | −0.118042 | ||||||||
\(176\) | 3.12311 | 0.235413 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.0000 | −1.04934 | ||||||||
\(179\) | −16.8078 | −1.25627 | −0.628136 | − | 0.778104i | \(-0.716182\pi\) | ||||
−0.628136 | + | 0.778104i | \(0.716182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.87689 | −0.511156 | −0.255578 | − | 0.966789i | \(-0.582266\pi\) | ||||
−0.255578 | + | 0.966789i | \(0.582266\pi\) | |||||||
\(182\) | −0.561553 | −0.0416251 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −6.56155 | −0.482415 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.2462 | −1.62680 | ||||||||
\(188\) | −6.56155 | −0.478550 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.00000 | −0.580381 | ||||||||
\(191\) | 20.0000 | 1.44715 | 0.723575 | − | 0.690246i | \(-0.242498\pi\) | ||||
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.68466 | −0.697117 | −0.348558 | − | 0.937287i | \(-0.613329\pi\) | ||||
−0.348558 | + | 0.937287i | \(0.613329\pi\) | |||||||
\(194\) | −16.5616 | −1.18905 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.93087 | 0.280063 | 0.140031 | − | 0.990147i | \(-0.455280\pi\) | ||||
0.140031 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.1771 | 1.71387 | 0.856934 | − | 0.515426i | \(-0.172366\pi\) | ||||
0.856934 | + | 0.515426i | \(0.172366\pi\) | |||||||
\(200\) | 1.56155 | 0.110418 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.246211 | 0.0173234 | ||||||||
\(203\) | 3.43845 | 0.241332 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.43845 | −0.100466 | ||||||||
\(206\) | −9.93087 | −0.691916 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.561553 | 0.0389367 | ||||||||
\(209\) | 9.75379 | 0.674684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4924 | 1.13539 | 0.567693 | − | 0.823241i | \(-0.307836\pi\) | ||||
0.567693 | + | 0.823241i | \(0.307836\pi\) | |||||||
\(212\) | 2.24621 | 0.154270 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.12311 | −0.213491 | ||||||||
\(215\) | 14.5616 | 0.993090 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.12311 | 0.347779 | ||||||||
\(218\) | 14.5616 | 0.986233 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.00000 | −0.539360 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.12311 | −0.343069 | −0.171534 | − | 0.985178i | \(-0.554872\pi\) | ||||
−0.171534 | + | 0.985178i | \(0.554872\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.68466 | −0.644214 | ||||||||
\(227\) | 26.8078 | 1.77929 | 0.889647 | − | 0.456649i | \(-0.150951\pi\) | ||||
0.889647 | + | 0.456649i | \(0.150951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.2462 | −0.941416 | −0.470708 | − | 0.882289i | \(-0.656001\pi\) | ||||
−0.470708 | + | 0.882289i | \(0.656001\pi\) | |||||||
\(230\) | 2.56155 | 0.168904 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.43845 | −0.225745 | ||||||||
\(233\) | −14.4924 | −0.949430 | −0.474715 | − | 0.880140i | \(-0.657449\pi\) | ||||
−0.474715 | + | 0.880140i | \(0.657449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.8078 | 1.09642 | ||||||||
\(236\) | −13.1231 | −0.854241 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.12311 | 0.461722 | ||||||||
\(239\) | 28.4924 | 1.84302 | 0.921511 | − | 0.388353i | \(-0.126956\pi\) | ||||
0.921511 | + | 0.388353i | \(0.126956\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0540 | 1.09854 | 0.549272 | − | 0.835644i | \(-0.314905\pi\) | ||||
0.549272 | + | 0.835644i | \(0.314905\pi\) | |||||||
\(242\) | −1.24621 | −0.0801095 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.12311 | 0.584047 | ||||||||
\(245\) | −2.56155 | −0.163652 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.75379 | 0.111591 | ||||||||
\(248\) | −5.12311 | −0.325318 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.80776 | 0.557052 | ||||||||
\(251\) | 4.56155 | 0.287923 | 0.143961 | − | 0.989583i | \(-0.454016\pi\) | ||||
0.143961 | + | 0.989583i | \(0.454016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.12311 | −0.196348 | ||||||||
\(254\) | −4.31534 | −0.270769 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.56155 | −0.159167 | ||||||||
\(260\) | −1.43845 | −0.0892087 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.1231 | −0.810748 | ||||||||
\(263\) | 5.93087 | 0.365713 | 0.182857 | − | 0.983140i | \(-0.441466\pi\) | ||||
0.182857 | + | 0.983140i | \(0.441466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.75379 | −0.353452 | ||||||||
\(266\) | −3.12311 | −0.191490 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.12311 | 0.435113 | ||||||||
\(269\) | 4.24621 | 0.258896 | 0.129448 | − | 0.991586i | \(-0.458679\pi\) | ||||
0.129448 | + | 0.991586i | \(0.458679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.24621 | −0.136448 | −0.0682238 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682238 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(272\) | −7.12311 | −0.431902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.56155 | 0.275573 | ||||||||
\(275\) | 4.87689 | 0.294088 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.87689 | 0.293024 | 0.146512 | − | 0.989209i | \(-0.453195\pi\) | ||||
0.146512 | + | 0.989209i | \(0.453195\pi\) | |||||||
\(278\) | −16.8078 | −1.00806 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.56155 | 0.153082 | ||||||||
\(281\) | 23.9309 | 1.42760 | 0.713798 | − | 0.700352i | \(-0.246973\pi\) | ||||
0.713798 | + | 0.700352i | \(0.246973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4924 | 1.33704 | 0.668518 | − | 0.743696i | \(-0.266929\pi\) | ||||
0.668518 | + | 0.743696i | \(0.266929\pi\) | |||||||
\(284\) | −15.3693 | −0.912001 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.75379 | 0.103704 | ||||||||
\(287\) | −0.561553 | −0.0331474 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.7386 | 1.98463 | ||||||||
\(290\) | 8.80776 | 0.517210 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.876894 | 0.0513164 | ||||||||
\(293\) | 13.6155 | 0.795428 | 0.397714 | − | 0.917510i | \(-0.369804\pi\) | ||||
0.397714 | + | 0.917510i | \(0.369804\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.6155 | 1.95717 | ||||||||
\(296\) | 2.56155 | 0.148887 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.2462 | −0.593547 | ||||||||
\(299\) | −0.561553 | −0.0324754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.68466 | 0.327658 | ||||||||
\(302\) | 19.6847 | 1.13272 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.12311 | 0.179122 | ||||||||
\(305\) | −23.3693 | −1.33812 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9309 | −1.47995 | −0.739976 | − | 0.672633i | \(-0.765163\pi\) | ||||
−0.739976 | + | 0.672633i | \(0.765163\pi\) | |||||||
\(308\) | −3.12311 | −0.177955 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.1231 | 0.745342 | ||||||||
\(311\) | 30.7386 | 1.74303 | 0.871514 | − | 0.490371i | \(-0.163139\pi\) | ||||
0.871514 | + | 0.490371i | \(0.163139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2462 | −0.692197 | −0.346098 | − | 0.938198i | \(-0.612494\pi\) | ||||
−0.346098 | + | 0.938198i | \(0.612494\pi\) | |||||||
\(314\) | −2.24621 | −0.126761 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.24621 | −0.126359 | ||||||||
\(317\) | −2.80776 | −0.157700 | −0.0788499 | − | 0.996887i | \(-0.525125\pi\) | ||||
−0.0788499 | + | 0.996887i | \(0.525125\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.7386 | −0.601248 | ||||||||
\(320\) | −2.56155 | −0.143195 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | −22.2462 | −1.23781 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.876894 | 0.0486413 | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.561553 | 0.0310066 | ||||||||
\(329\) | 6.56155 | 0.361750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.49242 | 0.466786 | 0.233393 | − | 0.972383i | \(-0.425017\pi\) | ||||
0.233393 | + | 0.972383i | \(0.425017\pi\) | |||||||
\(332\) | 0.876894 | 0.0481258 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.24621 | −0.122907 | ||||||||
\(335\) | −18.2462 | −0.996897 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.63068 | 0.143302 | 0.0716512 | − | 0.997430i | \(-0.477173\pi\) | ||||
0.0716512 | + | 0.997430i | \(0.477173\pi\) | |||||||
\(338\) | −12.6847 | −0.689954 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.2462 | 0.989540 | ||||||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.68466 | −0.306496 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.4924 | 0.779117 | ||||||||
\(347\) | 13.9309 | 0.747848 | 0.373924 | − | 0.927459i | \(-0.378012\pi\) | ||||
0.373924 | + | 0.927459i | \(0.378012\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.246211 | 0.0131794 | 0.00658969 | − | 0.999978i | \(-0.497902\pi\) | ||||
0.00658969 | + | 0.999978i | \(0.497902\pi\) | |||||||
\(350\) | −1.56155 | −0.0834685 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.12311 | 0.166462 | ||||||||
\(353\) | 13.1922 | 0.702152 | 0.351076 | − | 0.936347i | \(-0.385816\pi\) | ||||
0.351076 | + | 0.936347i | \(0.385816\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.3693 | 2.08951 | ||||||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.8078 | −0.888318 | ||||||||
\(359\) | 10.5616 | 0.557417 | 0.278709 | − | 0.960376i | \(-0.410094\pi\) | ||||
0.278709 | + | 0.960376i | \(0.410094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | −6.87689 | −0.361442 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.561553 | −0.0294334 | ||||||||
\(365\) | −2.24621 | −0.117572 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5616 | −1.17770 | −0.588852 | − | 0.808241i | \(-0.700420\pi\) | ||||
−0.588852 | + | 0.808241i | \(0.700420\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.56155 | −0.341119 | ||||||||
\(371\) | −2.24621 | −0.116617 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.87689 | 0.356072 | 0.178036 | − | 0.984024i | \(-0.443026\pi\) | ||||
0.178036 | + | 0.984024i | \(0.443026\pi\) | |||||||
\(374\) | −22.2462 | −1.15032 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.56155 | −0.338386 | ||||||||
\(377\) | −1.93087 | −0.0994448 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0540 | −0.876004 | −0.438002 | − | 0.898974i | \(-0.644314\pi\) | ||||
−0.438002 | + | 0.898974i | \(0.644314\pi\) | |||||||
\(380\) | −8.00000 | −0.410391 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.0000 | 1.02329 | ||||||||
\(383\) | −10.2462 | −0.523557 | −0.261778 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261778 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | 0.407718 | ||||||||
\(386\) | −9.68466 | −0.492936 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.5616 | −0.840785 | ||||||||
\(389\) | 4.63068 | 0.234785 | 0.117392 | − | 0.993086i | \(-0.462546\pi\) | ||||
0.117392 | + | 0.993086i | \(0.462546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.12311 | 0.360231 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.93087 | 0.198034 | ||||||||
\(395\) | 5.75379 | 0.289505 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.2462 | −1.21688 | −0.608441 | − | 0.793599i | \(-0.708205\pi\) | ||||
−0.608441 | + | 0.793599i | \(0.708205\pi\) | |||||||
\(398\) | 24.1771 | 1.21189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.56155 | 0.0780776 | ||||||||
\(401\) | 0.246211 | 0.0122952 | 0.00614760 | − | 0.999981i | \(-0.498043\pi\) | ||||
0.00614760 | + | 0.999981i | \(0.498043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.87689 | −0.143308 | ||||||||
\(404\) | 0.246211 | 0.0122495 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.43845 | 0.170647 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.61553 | −0.376564 | −0.188282 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188282 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(410\) | −1.43845 | −0.0710398 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.93087 | −0.489259 | ||||||||
\(413\) | 13.1231 | 0.645746 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.24621 | −0.110262 | ||||||||
\(416\) | 0.561553 | 0.0275324 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.75379 | 0.477073 | ||||||||
\(419\) | 33.8617 | 1.65425 | 0.827127 | − | 0.562015i | \(-0.189974\pi\) | ||||
0.827127 | + | 0.562015i | \(0.189974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.1771 | −0.593475 | −0.296737 | − | 0.954959i | \(-0.595899\pi\) | ||||
−0.296737 | + | 0.954959i | \(0.595899\pi\) | |||||||
\(422\) | 16.4924 | 0.802839 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.24621 | 0.109086 | ||||||||
\(425\) | −11.1231 | −0.539550 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.12311 | −0.441498 | ||||||||
\(428\) | −3.12311 | −0.150961 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.5616 | 0.702220 | ||||||||
\(431\) | 15.6847 | 0.755503 | 0.377752 | − | 0.925907i | \(-0.376697\pi\) | ||||
0.377752 | + | 0.925907i | \(0.376697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.31534 | 0.111268 | 0.0556341 | − | 0.998451i | \(-0.482282\pi\) | ||||
0.0556341 | + | 0.998451i | \(0.482282\pi\) | |||||||
\(434\) | 5.12311 | 0.245917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.5616 | 0.697372 | ||||||||
\(437\) | −3.12311 | −0.149398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6155 | 0.840743 | 0.420372 | − | 0.907352i | \(-0.361900\pi\) | ||||
0.420372 | + | 0.907352i | \(0.361900\pi\) | |||||||
\(440\) | −8.00000 | −0.381385 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | −0.190261 | ||||||||
\(443\) | −37.9309 | −1.80215 | −0.901075 | − | 0.433663i | \(-0.857221\pi\) | ||||
−0.901075 | + | 0.433663i | \(0.857221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.8617 | 1.70001 | ||||||||
\(446\) | −5.12311 | −0.242586 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −16.2462 | −0.766706 | −0.383353 | − | 0.923602i | \(-0.625231\pi\) | ||||
−0.383353 | + | 0.923602i | \(0.625231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75379 | 0.0825827 | ||||||||
\(452\) | −9.68466 | −0.455528 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.8078 | 1.25815 | ||||||||
\(455\) | 1.43845 | 0.0674354 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3693 | −0.812502 | −0.406251 | − | 0.913761i | \(-0.633164\pi\) | ||||
−0.406251 | + | 0.913761i | \(0.633164\pi\) | |||||||
\(458\) | −14.2462 | −0.665682 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.56155 | 0.119433 | ||||||||
\(461\) | 8.73863 | 0.406999 | 0.203499 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203499 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.43845 | −0.438642 | −0.219321 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219321 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(464\) | −3.43845 | −0.159626 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.4924 | −0.671349 | ||||||||
\(467\) | 9.68466 | 0.448153 | 0.224076 | − | 0.974572i | \(-0.428064\pi\) | ||||
0.224076 | + | 0.974572i | \(0.428064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.12311 | −0.328914 | ||||||||
\(470\) | 16.8078 | 0.775284 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.1231 | −0.604040 | ||||||||
\(473\) | −17.7538 | −0.816320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.87689 | 0.223767 | ||||||||
\(476\) | 7.12311 | 0.326487 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.4924 | 1.30321 | ||||||||
\(479\) | 9.61553 | 0.439345 | 0.219672 | − | 0.975574i | \(-0.429501\pi\) | ||||
0.219672 | + | 0.975574i | \(0.429501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.43845 | 0.0655875 | ||||||||
\(482\) | 17.0540 | 0.776787 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.24621 | −0.0566460 | ||||||||
\(485\) | 42.4233 | 1.92634 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.43845 | −0.0651823 | −0.0325911 | − | 0.999469i | \(-0.510376\pi\) | ||||
−0.0325911 | + | 0.999469i | \(0.510376\pi\) | |||||||
\(488\) | 9.12311 | 0.412984 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.56155 | −0.115719 | ||||||||
\(491\) | −22.7386 | −1.02618 | −0.513090 | − | 0.858335i | \(-0.671499\pi\) | ||||
−0.513090 | + | 0.858335i | \(0.671499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.4924 | 1.10308 | ||||||||
\(494\) | 1.75379 | 0.0789067 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.12311 | −0.230034 | ||||||||
\(497\) | 15.3693 | 0.689408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6307 | 0.744492 | 0.372246 | − | 0.928134i | \(-0.378588\pi\) | ||||
0.372246 | + | 0.928134i | \(0.378588\pi\) | |||||||
\(500\) | 8.80776 | 0.393895 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.56155 | 0.203592 | ||||||||
\(503\) | −42.1080 | −1.87750 | −0.938750 | − | 0.344598i | \(-0.888015\pi\) | ||||
−0.938750 | + | 0.344598i | \(0.888015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.630683 | −0.0280650 | ||||||||
\(506\) | −3.12311 | −0.138839 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.31534 | −0.191462 | ||||||||
\(509\) | −21.3693 | −0.947178 | −0.473589 | − | 0.880746i | \(-0.657042\pi\) | ||||
−0.473589 | + | 0.880746i | \(0.657042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.876894 | −0.0387915 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.00000 | 0.0882162 | ||||||||
\(515\) | 25.4384 | 1.12095 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4924 | −0.901256 | ||||||||
\(518\) | −2.56155 | −0.112548 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.43845 | −0.0630801 | ||||||||
\(521\) | 16.2462 | 0.711759 | 0.355880 | − | 0.934532i | \(-0.384181\pi\) | ||||
0.355880 | + | 0.934532i | \(0.384181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0000 | 0.612177 | 0.306089 | − | 0.952003i | \(-0.400980\pi\) | ||||
0.306089 | + | 0.952003i | \(0.400980\pi\) | |||||||
\(524\) | −13.1231 | −0.573286 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.93087 | 0.258598 | ||||||||
\(527\) | 36.4924 | 1.58963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −5.75379 | −0.249929 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.12311 | −0.135404 | ||||||||
\(533\) | 0.315342 | 0.0136590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 7.12311 | 0.307671 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.24621 | 0.183067 | ||||||||
\(539\) | 3.12311 | 0.134522 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.36932 | 0.402818 | 0.201409 | − | 0.979507i | \(-0.435448\pi\) | ||||
0.201409 | + | 0.979507i | \(0.435448\pi\) | |||||||
\(542\) | −2.24621 | −0.0964830 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.12311 | −0.305401 | ||||||||
\(545\) | −37.3002 | −1.59776 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.6155 | 1.60832 | 0.804162 | − | 0.594410i | \(-0.202614\pi\) | ||||
0.804162 | + | 0.594410i | \(0.202614\pi\) | |||||||
\(548\) | 4.56155 | 0.194860 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.87689 | 0.207951 | ||||||||
\(551\) | −10.7386 | −0.457481 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.24621 | 0.0955186 | ||||||||
\(554\) | 4.87689 | 0.207199 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8078 | −0.712808 | ||||||||
\(557\) | −36.9848 | −1.56710 | −0.783549 | − | 0.621330i | \(-0.786593\pi\) | ||||
−0.783549 | + | 0.621330i | \(0.786593\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.19224 | −0.135017 | ||||||||
\(560\) | 2.56155 | 0.108245 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.9309 | 1.00946 | ||||||||
\(563\) | −15.4384 | −0.650653 | −0.325326 | − | 0.945602i | \(-0.605474\pi\) | ||||
−0.325326 | + | 0.945602i | \(0.605474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.8078 | 1.04367 | ||||||||
\(566\) | 22.4924 | 0.945427 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.3693 | −0.644882 | ||||||||
\(569\) | −25.5464 | −1.07096 | −0.535480 | − | 0.844548i | \(-0.679869\pi\) | ||||
−0.535480 | + | 0.844548i | \(0.679869\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.6307 | 0.779670 | 0.389835 | − | 0.920885i | \(-0.372532\pi\) | ||||
0.389835 | + | 0.920885i | \(0.372532\pi\) | |||||||
\(572\) | 1.75379 | 0.0733296 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.561553 | −0.0234388 | ||||||||
\(575\) | −1.56155 | −0.0651213 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.2462 | −1.50895 | −0.754475 | − | 0.656329i | \(-0.772108\pi\) | ||||
−0.754475 | + | 0.656329i | \(0.772108\pi\) | |||||||
\(578\) | 33.7386 | 1.40334 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.80776 | 0.365722 | ||||||||
\(581\) | −0.876894 | −0.0363797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.01515 | 0.290538 | ||||||||
\(584\) | 0.876894 | 0.0362861 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.6155 | 0.562452 | ||||||||
\(587\) | −40.9848 | −1.69163 | −0.845813 | − | 0.533480i | \(-0.820884\pi\) | ||||
−0.845813 | + | 0.533480i | \(0.820884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 33.6155 | 1.38393 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.56155 | 0.105279 | ||||||||
\(593\) | 23.3002 | 0.956824 | 0.478412 | − | 0.878136i | \(-0.341213\pi\) | ||||
0.478412 | + | 0.878136i | \(0.341213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.2462 | −0.748022 | ||||||||
\(596\) | −10.2462 | −0.419701 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.561553 | −0.0229636 | ||||||||
\(599\) | −38.7386 | −1.58282 | −0.791409 | − | 0.611287i | \(-0.790652\pi\) | ||||
−0.791409 | + | 0.611287i | \(0.790652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3693 | 0.871673 | 0.435836 | − | 0.900026i | \(-0.356453\pi\) | ||||
0.435836 | + | 0.900026i | \(0.356453\pi\) | |||||||
\(602\) | 5.68466 | 0.231689 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.6847 | 0.800957 | ||||||||
\(605\) | 3.19224 | 0.129783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.38447 | −0.259138 | −0.129569 | − | 0.991570i | \(-0.541359\pi\) | ||||
−0.129569 | + | 0.991570i | \(0.541359\pi\) | |||||||
\(608\) | 3.12311 | 0.126659 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.3693 | −0.946196 | ||||||||
\(611\) | −3.68466 | −0.149065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.8078 | −0.678859 | −0.339430 | − | 0.940631i | \(-0.610234\pi\) | ||||
−0.339430 | + | 0.940631i | \(0.610234\pi\) | |||||||
\(614\) | −25.9309 | −1.04648 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.12311 | −0.125834 | ||||||||
\(617\) | −48.2462 | −1.94232 | −0.971160 | − | 0.238430i | \(-0.923367\pi\) | ||||
−0.971160 | + | 0.238430i | \(0.923367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.24621 | −0.331443 | −0.165722 | − | 0.986173i | \(-0.552995\pi\) | ||||
−0.165722 | + | 0.986173i | \(0.552995\pi\) | |||||||
\(620\) | 13.1231 | 0.527037 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.7386 | 1.23251 | ||||||||
\(623\) | 14.0000 | 0.560898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | −12.2462 | −0.489457 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.24621 | −0.0896336 | ||||||||
\(629\) | −18.2462 | −0.727524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4924 | −0.975028 | −0.487514 | − | 0.873115i | \(-0.662096\pi\) | ||||
−0.487514 | + | 0.873115i | \(0.662096\pi\) | |||||||
\(632\) | −2.24621 | −0.0893495 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.80776 | −0.111511 | ||||||||
\(635\) | 11.0540 | 0.438664 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.561553 | 0.0222495 | ||||||||
\(638\) | −10.7386 | −0.425147 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.56155 | −0.101254 | ||||||||
\(641\) | 25.6847 | 1.01448 | 0.507242 | − | 0.861804i | \(-0.330665\pi\) | ||||
0.507242 | + | 0.861804i | \(0.330665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.0000 | −1.49857 | −0.749287 | − | 0.662246i | \(-0.769604\pi\) | ||||
−0.749287 | + | 0.662246i | \(0.769604\pi\) | |||||||
\(644\) | 1.00000 | 0.0394055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.2462 | −0.875265 | ||||||||
\(647\) | 36.4924 | 1.43467 | 0.717333 | − | 0.696731i | \(-0.245363\pi\) | ||||
0.717333 | + | 0.696731i | \(0.245363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.9848 | −1.60880 | ||||||||
\(650\) | 0.876894 | 0.0343946 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | 33.5464 | 1.31277 | 0.656386 | − | 0.754425i | \(-0.272084\pi\) | ||||
0.656386 | + | 0.754425i | \(0.272084\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.6155 | 1.31347 | ||||||||
\(656\) | 0.561553 | 0.0219250 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.56155 | 0.255796 | ||||||||
\(659\) | 35.6155 | 1.38738 | 0.693692 | − | 0.720272i | \(-0.255983\pi\) | ||||
0.693692 | + | 0.720272i | \(0.255983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.1231 | 1.59950 | 0.799752 | − | 0.600331i | \(-0.204964\pi\) | ||||
0.799752 | + | 0.600331i | \(0.204964\pi\) | |||||||
\(662\) | 8.49242 | 0.330067 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.876894 | 0.0340301 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.43845 | 0.133137 | ||||||||
\(668\) | −2.24621 | −0.0869085 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.2462 | −0.704913 | ||||||||
\(671\) | 28.4924 | 1.09994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3153 | 0.397627 | 0.198814 | − | 0.980037i | \(-0.436291\pi\) | ||||
0.198814 | + | 0.980037i | \(0.436291\pi\) | |||||||
\(674\) | 2.63068 | 0.101330 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6847 | −0.487871 | ||||||||
\(677\) | −27.3693 | −1.05189 | −0.525944 | − | 0.850519i | \(-0.676288\pi\) | ||||
−0.525944 | + | 0.850519i | \(0.676288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5616 | 0.635574 | ||||||||
\(680\) | 18.2462 | 0.699710 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.0000 | −0.612672 | ||||||||
\(683\) | 40.4924 | 1.54940 | 0.774700 | − | 0.632329i | \(-0.217901\pi\) | ||||
0.774700 | + | 0.632329i | \(0.217901\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.6847 | −0.446448 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.68466 | −0.216726 | ||||||||
\(689\) | 1.26137 | 0.0480542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.9460 | −0.492490 | −0.246245 | − | 0.969208i | \(-0.579197\pi\) | ||||
−0.246245 | + | 0.969208i | \(0.579197\pi\) | |||||||
\(692\) | 14.4924 | 0.550919 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.9309 | 0.528809 | ||||||||
\(695\) | 43.0540 | 1.63313 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0.246211 | 0.00931923 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.56155 | −0.0590211 | ||||||||
\(701\) | −17.7538 | −0.670551 | −0.335276 | − | 0.942120i | \(-0.608829\pi\) | ||||
−0.335276 | + | 0.942120i | \(0.608829\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 3.12311 | 0.117706 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.1922 | 0.496496 | ||||||||
\(707\) | −0.246211 | −0.00925973 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3693 | 1.32832 | 0.664161 | − | 0.747589i | \(-0.268789\pi\) | ||||
0.664161 | + | 0.747589i | \(0.268789\pi\) | |||||||
\(710\) | 39.3693 | 1.47750 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.0000 | −0.524672 | ||||||||
\(713\) | 5.12311 | 0.191862 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.49242 | −0.168007 | ||||||||
\(716\) | −16.8078 | −0.628136 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.5616 | 0.394154 | ||||||||
\(719\) | −14.5616 | −0.543054 | −0.271527 | − | 0.962431i | \(-0.587529\pi\) | ||||
−0.271527 | + | 0.962431i | \(0.587529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.93087 | 0.369845 | ||||||||
\(722\) | −9.24621 | −0.344108 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.87689 | −0.255578 | ||||||||
\(725\) | −5.36932 | −0.199411 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2462 | −0.676715 | −0.338357 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338357 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(728\) | −0.561553 | −0.0208125 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.24621 | −0.0831360 | ||||||||
\(731\) | 40.4924 | 1.49767 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.2462 | 1.56040 | 0.780200 | − | 0.625531i | \(-0.215117\pi\) | ||||
0.780200 | + | 0.625531i | \(0.215117\pi\) | |||||||
\(734\) | −22.5616 | −0.832762 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 22.2462 | 0.819450 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.6155 | −0.647998 | −0.323999 | − | 0.946057i | \(-0.605027\pi\) | ||||
−0.323999 | + | 0.946057i | \(0.605027\pi\) | |||||||
\(740\) | −6.56155 | −0.241207 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.24621 | −0.0824610 | ||||||||
\(743\) | −40.9848 | −1.50359 | −0.751794 | − | 0.659398i | \(-0.770811\pi\) | ||||
−0.751794 | + | 0.659398i | \(0.770811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.2462 | 0.961587 | ||||||||
\(746\) | 6.87689 | 0.251781 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.2462 | −0.813402 | ||||||||
\(749\) | 3.12311 | 0.114116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.49242 | −0.309893 | −0.154946 | − | 0.987923i | \(-0.549521\pi\) | ||||
−0.154946 | + | 0.987923i | \(0.549521\pi\) | |||||||
\(752\) | −6.56155 | −0.239275 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.93087 | −0.0703181 | ||||||||
\(755\) | −50.4233 | −1.83509 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.630683 | −0.0229226 | −0.0114613 | − | 0.999934i | \(-0.503648\pi\) | ||||
−0.0114613 | + | 0.999934i | \(0.503648\pi\) | |||||||
\(758\) | −17.0540 | −0.619428 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.00000 | −0.290191 | ||||||||
\(761\) | 52.7386 | 1.91177 | 0.955887 | − | 0.293735i | \(-0.0948982\pi\) | ||||
0.955887 | + | 0.293735i | \(0.0948982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.5616 | −0.527164 | ||||||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.2462 | −0.370211 | ||||||||
\(767\) | −7.36932 | −0.266091 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.82292 | −0.0657361 | −0.0328681 | − | 0.999460i | \(-0.510464\pi\) | ||||
−0.0328681 | + | 0.999460i | \(0.510464\pi\) | |||||||
\(770\) | 8.00000 | 0.288300 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.68466 | −0.348558 | ||||||||
\(773\) | −21.3002 | −0.766114 | −0.383057 | − | 0.923725i | \(-0.625129\pi\) | ||||
−0.383057 | + | 0.923725i | \(0.625129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | −16.5616 | −0.594525 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.63068 | 0.166018 | ||||||||
\(779\) | 1.75379 | 0.0628360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.0000 | −1.71758 | ||||||||
\(782\) | 7.12311 | 0.254722 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 5.75379 | 0.205362 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.1231 | −0.681665 | −0.340833 | − | 0.940124i | \(-0.610709\pi\) | ||||
−0.340833 | + | 0.940124i | \(0.610709\pi\) | |||||||
\(788\) | 3.93087 | 0.140031 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.75379 | 0.204711 | ||||||||
\(791\) | 9.68466 | 0.344347 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.12311 | 0.181927 | ||||||||
\(794\) | −24.2462 | −0.860466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.1771 | 0.856934 | ||||||||
\(797\) | 34.4233 | 1.21934 | 0.609668 | − | 0.792657i | \(-0.291303\pi\) | ||||
0.609668 | + | 0.792657i | \(0.291303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.7386 | 1.65349 | ||||||||
\(800\) | 1.56155 | 0.0552092 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.246211 | 0.00869402 | ||||||||
\(803\) | 2.73863 | 0.0966443 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56155 | −0.0902829 | ||||||||
\(806\) | −2.87689 | −0.101334 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.246211 | 0.00866168 | ||||||||
\(809\) | 33.8617 | 1.19052 | 0.595258 | − | 0.803535i | \(-0.297050\pi\) | ||||
0.595258 | + | 0.803535i | \(0.297050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.3153 | −0.432450 | −0.216225 | − | 0.976344i | \(-0.569374\pi\) | ||||
−0.216225 | + | 0.976344i | \(0.569374\pi\) | |||||||
\(812\) | 3.43845 | 0.120666 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 20.4924 | 0.717818 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.7538 | −0.621126 | ||||||||
\(818\) | −7.61553 | −0.266271 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.43845 | −0.0502328 | ||||||||
\(821\) | −43.4773 | −1.51737 | −0.758684 | − | 0.651459i | \(-0.774157\pi\) | ||||
−0.758684 | + | 0.651459i | \(0.774157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.6847 | 1.24389 | 0.621944 | − | 0.783061i | \(-0.286343\pi\) | ||||
0.621944 | + | 0.783061i | \(0.286343\pi\) | |||||||
\(824\) | −9.93087 | −0.345958 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.1231 | 0.456611 | ||||||||
\(827\) | 0.738634 | 0.0256848 | 0.0128424 | − | 0.999918i | \(-0.495912\pi\) | ||||
0.0128424 | + | 0.999918i | \(0.495912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.7386 | −0.859208 | −0.429604 | − | 0.903017i | \(-0.641347\pi\) | ||||
−0.429604 | + | 0.903017i | \(0.641347\pi\) | |||||||
\(830\) | −2.24621 | −0.0779671 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.561553 | 0.0194683 | ||||||||
\(833\) | −7.12311 | −0.246801 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.75379 | 0.199118 | ||||||||
\(836\) | 9.75379 | 0.337342 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.8617 | 1.16973 | ||||||||
\(839\) | 33.6155 | 1.16054 | 0.580268 | − | 0.814425i | \(-0.302948\pi\) | ||||
0.580268 | + | 0.814425i | \(0.302948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1771 | −0.592313 | ||||||||
\(842\) | −12.1771 | −0.419650 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.4924 | 0.567693 | ||||||||
\(845\) | 32.4924 | 1.11777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.24621 | 0.0428203 | ||||||||
\(848\) | 2.24621 | 0.0771352 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.1231 | −0.381519 | ||||||||
\(851\) | −2.56155 | −0.0878089 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.56155 | −0.156185 | −0.0780923 | − | 0.996946i | \(-0.524883\pi\) | ||||
−0.0780923 | + | 0.996946i | \(0.524883\pi\) | |||||||
\(854\) | −9.12311 | −0.312186 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.12311 | −0.106746 | ||||||||
\(857\) | −13.6847 | −0.467459 | −0.233730 | − | 0.972302i | \(-0.575093\pi\) | ||||
−0.233730 | + | 0.972302i | \(0.575093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1771 | 0.415477 | 0.207738 | − | 0.978184i | \(-0.433390\pi\) | ||||
0.207738 | + | 0.978184i | \(0.433390\pi\) | |||||||
\(860\) | 14.5616 | 0.496545 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.6847 | 0.534222 | ||||||||
\(863\) | 38.7386 | 1.31868 | 0.659339 | − | 0.751846i | \(-0.270836\pi\) | ||||
0.659339 | + | 0.751846i | \(0.270836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.1231 | −1.26222 | ||||||||
\(866\) | 2.31534 | 0.0786785 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.12311 | 0.173890 | ||||||||
\(869\) | −7.01515 | −0.237973 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | 14.5616 | 0.493116 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.12311 | −0.105641 | ||||||||
\(875\) | −8.80776 | −0.297757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8617 | 0.738218 | 0.369109 | − | 0.929386i | \(-0.379663\pi\) | ||||
0.369109 | + | 0.929386i | \(0.379663\pi\) | |||||||
\(878\) | 17.6155 | 0.594495 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.00000 | −0.269680 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.1231 | −0.576238 | −0.288119 | − | 0.957595i | \(-0.593030\pi\) | ||||
−0.288119 | + | 0.957595i | \(0.593030\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.9309 | −1.27431 | ||||||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.31534 | 0.144732 | ||||||||
\(890\) | 35.8617 | 1.20209 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.12311 | −0.171534 | ||||||||
\(893\) | −20.4924 | −0.685753 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43.0540 | 1.43914 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.2462 | −0.542143 | ||||||||
\(899\) | 17.6155 | 0.587511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | 1.75379 | 0.0583948 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.68466 | −0.322107 | ||||||||
\(905\) | 17.6155 | 0.585560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.5464 | −0.582619 | −0.291309 | − | 0.956629i | \(-0.594091\pi\) | ||||
−0.291309 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(908\) | 26.8078 | 0.889647 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.43845 | 0.0476841 | ||||||||
\(911\) | 39.0540 | 1.29392 | 0.646958 | − | 0.762526i | \(-0.276041\pi\) | ||||
0.646958 | + | 0.762526i | \(0.276041\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.73863 | 0.0906355 | ||||||||
\(914\) | −17.3693 | −0.574526 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.2462 | −0.470708 | ||||||||
\(917\) | 13.1231 | 0.433363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.26137 | −0.0416086 | −0.0208043 | − | 0.999784i | \(-0.506623\pi\) | ||||
−0.0208043 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(920\) | 2.56155 | 0.0844519 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.73863 | 0.287792 | ||||||||
\(923\) | −8.63068 | −0.284082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | −9.43845 | −0.310167 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.43845 | −0.112873 | ||||||||
\(929\) | 40.5616 | 1.33078 | 0.665391 | − | 0.746495i | \(-0.268265\pi\) | ||||
0.665391 | + | 0.746495i | \(0.268265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.12311 | 0.102356 | ||||||||
\(932\) | −14.4924 | −0.474715 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.68466 | 0.316892 | ||||||||
\(935\) | 56.9848 | 1.86360 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1771 | 0.593819 | 0.296910 | − | 0.954906i | \(-0.404044\pi\) | ||||
0.296910 | + | 0.954906i | \(0.404044\pi\) | |||||||
\(938\) | −7.12311 | −0.232578 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.8078 | 0.548209 | ||||||||
\(941\) | −39.0540 | −1.27312 | −0.636562 | − | 0.771226i | \(-0.719644\pi\) | ||||
−0.636562 | + | 0.771226i | \(0.719644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.561553 | −0.0182867 | ||||||||
\(944\) | −13.1231 | −0.427121 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.7538 | −0.577225 | ||||||||
\(947\) | 26.0691 | 0.847133 | 0.423566 | − | 0.905865i | \(-0.360778\pi\) | ||||
0.423566 | + | 0.905865i | \(0.360778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.492423 | 0.0159847 | ||||||||
\(950\) | 4.87689 | 0.158227 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.12311 | 0.230861 | ||||||||
\(953\) | −50.0000 | −1.61966 | −0.809829 | − | 0.586665i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586665i | \(0.800440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51.2311 | −1.65780 | ||||||||
\(956\) | 28.4924 | 0.921511 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.61553 | 0.310664 | ||||||||
\(959\) | −4.56155 | −0.147300 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 1.43845 | 0.0463774 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.0540 | 0.549272 | ||||||||
\(965\) | 24.8078 | 0.798590 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.2462 | −0.844021 | −0.422011 | − | 0.906591i | \(-0.638676\pi\) | ||||
−0.422011 | + | 0.906591i | \(0.638676\pi\) | |||||||
\(968\) | −1.24621 | −0.0400547 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 42.4233 | 1.36213 | ||||||||
\(971\) | −39.6155 | −1.27132 | −0.635661 | − | 0.771968i | \(-0.719273\pi\) | ||||
−0.635661 | + | 0.771968i | \(0.719273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.8078 | 0.538832 | ||||||||
\(974\) | −1.43845 | −0.0460908 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.12311 | 0.292023 | ||||||||
\(977\) | 46.8078 | 1.49751 | 0.748757 | − | 0.662845i | \(-0.230651\pi\) | ||||
0.748757 | + | 0.662845i | \(0.230651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.7235 | −1.39741 | ||||||||
\(980\) | −2.56155 | −0.0818258 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.7386 | −0.725619 | ||||||||
\(983\) | 23.8617 | 0.761071 | 0.380536 | − | 0.924766i | \(-0.375740\pi\) | ||||
0.380536 | + | 0.924766i | \(0.375740\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0691 | −0.320829 | ||||||||
\(986\) | 24.4924 | 0.779998 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.75379 | 0.0557955 | ||||||||
\(989\) | 5.68466 | 0.180762 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.2462 | 0.325482 | 0.162741 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162741 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(992\) | −5.12311 | −0.162659 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.3693 | 0.487485 | ||||||||
\(995\) | −61.9309 | −1.96334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.4773 | −1.50362 | −0.751810 | − | 0.659380i | \(-0.770819\pi\) | ||||
−0.751810 | + | 0.659380i | \(0.770819\pi\) | |||||||
\(998\) | 16.6307 | 0.526435 | ||||||||
\(999\) | 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 | 2898.2.a.ba.1.1 | 2 | ||
3.2 | odd | 2 | 966.2.a.l.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 7728.2.a.bm.1.2 | 2 | |||
21.20 | even | 2 | 6762.2.a.bw.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.a.l.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2898.2.a.ba.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6762.2.a.bw.1.1 | 2 | 21.20 | even | 2 | |||
7728.2.a.bm.1.2 | 2 | 12.11 | even | 2 |