Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(1,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, 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("8100.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.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: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.28356903014400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 37x^{6} + 399x^{4} - 1195x^{2} + 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1620) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.617787\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.93536 | −1.86539 | −0.932696 | − | 0.360663i | \(-0.882550\pi\) | ||||
−0.932696 | + | 0.360663i | \(0.882550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41269 | −0.727455 | −0.363727 | − | 0.931505i | \(-0.618496\pi\) | ||||
−0.363727 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.90917 | −0.806859 | −0.403429 | − | 0.915011i | \(-0.632182\pi\) | ||||
−0.403429 | + | 0.915011i | \(0.632182\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.86869 | −1.66590 | −0.832951 | − | 0.553347i | \(-0.813350\pi\) | ||||
−0.832951 | + | 0.553347i | \(0.813350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.17891 | −0.958707 | −0.479354 | − | 0.877622i | \(-0.659129\pi\) | ||||
−0.479354 | + | 0.877622i | \(0.659129\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.35922 | −0.700446 | −0.350223 | − | 0.936666i | \(-0.613894\pi\) | ||||
−0.350223 | + | 0.936666i | \(0.613894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.19615 | 0.964901 | 0.482451 | − | 0.875923i | \(-0.339747\pi\) | ||||
0.482451 | + | 0.875923i | \(0.339747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.17891 | −1.10976 | −0.554882 | − | 0.831929i | \(-0.687237\pi\) | ||||
−0.554882 | + | 0.831929i | \(0.687237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.84453 | −1.28963 | −0.644817 | − | 0.764337i | \(-0.723066\pi\) | ||||
−0.644817 | + | 0.764337i | \(0.723066\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.87680 | −0.917801 | −0.458901 | − | 0.888488i | \(-0.651757\pi\) | ||||
−0.458901 | + | 0.888488i | \(0.651757\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.93536 | −0.752636 | −0.376318 | − | 0.926491i | \(-0.622810\pi\) | ||||
−0.376318 | + | 0.926491i | \(0.622810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.9075 | 1.73689 | 0.868445 | − | 0.495785i | \(-0.165120\pi\) | ||||
0.868445 | + | 0.495785i | \(0.165120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.3578 | 2.47969 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.54830 | −1.17420 | −0.587100 | − | 0.809515i | \(-0.699730\pi\) | ||||
−0.587100 | + | 0.809515i | \(0.699730\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.05141 | −0.136882 | −0.0684408 | − | 0.997655i | \(-0.521802\pi\) | ||||
−0.0684408 | + | 0.997655i | \(0.521802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.17891 | 1.17524 | 0.587619 | − | 0.809137i | \(-0.300065\pi\) | ||||
0.587619 | + | 0.809137i | \(0.300065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.05239 | −0.495078 | −0.247539 | − | 0.968878i | \(-0.579622\pi\) | ||||
−0.247539 | + | 0.968878i | \(0.579622\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1663 | −1.68123 | −0.840614 | − | 0.541634i | \(-0.817806\pi\) | ||||
−0.840614 | + | 0.541634i | \(0.817806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.02619 | −0.237148 | −0.118574 | − | 0.992945i | \(-0.537832\pi\) | ||||
−0.118574 | + | 0.992945i | \(0.537832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.9075 | 1.35699 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.18908 | 0.569576 | 0.284788 | − | 0.958591i | \(-0.408077\pi\) | ||||
0.284788 | + | 0.958591i | \(0.408077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.09334 | 0.327893 | 0.163947 | − | 0.986469i | \(-0.447578\pi\) | ||||
0.163947 | + | 0.986469i | \(0.447578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.3578 | 1.50511 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.882978 | −0.0896528 | −0.0448264 | − | 0.998995i | \(-0.514273\pi\) | ||||
−0.0448264 | + | 0.998995i | \(0.514273\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.87680 | 0.584763 | 0.292382 | − | 0.956302i | \(-0.405552\pi\) | ||||
0.292382 | + | 0.956302i | \(0.405552\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.87073 | −0.972592 | −0.486296 | − | 0.873794i | \(-0.661652\pi\) | ||||
−0.486296 | + | 0.873794i | \(0.661652\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5871 | 1.27817 | 0.639085 | − | 0.769136i | \(-0.279313\pi\) | ||||
0.639085 | + | 0.769136i | \(0.279313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 33.8995 | 3.10756 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.17891 | −0.470810 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.93536 | −0.437943 | −0.218971 | − | 0.975731i | \(-0.570270\pi\) | ||||
−0.218971 | + | 0.975731i | \(0.570270\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.1663 | −1.23771 | −0.618857 | − | 0.785504i | \(-0.712404\pi\) | ||||
−0.618857 | + | 0.785504i | \(0.712404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.6244 | 1.78837 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.03883 | −0.430496 | −0.215248 | − | 0.976559i | \(-0.569056\pi\) | ||||
−0.215248 | + | 0.976559i | \(0.569056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.82109 | 0.493739 | 0.246869 | − | 0.969049i | \(-0.420598\pi\) | ||||
0.246869 | + | 0.969049i | \(0.420598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.01894 | 0.586953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.1758 | −1.07940 | −0.539700 | − | 0.841857i | \(-0.681462\pi\) | ||||
−0.539700 | + | 0.841857i | \(0.681462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.17891 | −0.502832 | −0.251416 | − | 0.967879i | \(-0.580896\pi\) | ||||
−0.251416 | + | 0.967879i | \(0.580896\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.84453 | 0.626062 | 0.313031 | − | 0.949743i | \(-0.398656\pi\) | ||||
0.313031 | + | 0.949743i | \(0.398656\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5790 | 1.30661 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7537 | 0.842295 | 0.421148 | − | 0.906992i | \(-0.361627\pi\) | ||||
0.421148 | + | 0.906992i | \(0.361627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.54830 | −0.661487 | −0.330744 | − | 0.943721i | \(-0.607300\pi\) | ||||
−0.330744 | + | 0.943721i | \(0.607300\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.53673 | −0.348979 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.7762 | −1.42753 | −0.713765 | − | 0.700386i | \(-0.753011\pi\) | ||||
−0.713765 | + | 0.700386i | \(0.753011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.97961 | −0.596424 | −0.298212 | − | 0.954500i | \(-0.596390\pi\) | ||||
−0.298212 | + | 0.954500i | \(0.596390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.82109 | 0.284020 | 0.142010 | − | 0.989865i | \(-0.454644\pi\) | ||||
0.142010 | + | 0.989865i | \(0.454644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.5720 | 1.21187 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.61832 | 0.478885 | 0.239443 | − | 0.970911i | \(-0.423035\pi\) | ||||
0.239443 | + | 0.970911i | \(0.423035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7676 | 1.56687 | 0.783435 | − | 0.621474i | \(-0.213466\pi\) | ||||
0.783435 | + | 0.621474i | \(0.213466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4170 | 1.09842 | 0.549208 | − | 0.835686i | \(-0.314930\pi\) | ||||
0.549208 | + | 0.835686i | \(0.314930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3578 | 1.44313 | 0.721564 | − | 0.692348i | \(-0.243424\pi\) | ||||
0.721564 | + | 0.692348i | \(0.243424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.6449 | −1.79992 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0824 | 0.697416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1789 | 1.11380 | 0.556901 | − | 0.830579i | \(-0.311990\pi\) | ||||
0.556901 | + | 0.830579i | \(0.311990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.4952 | 2.07015 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.9822 | 1.34415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.5598 | −1.71161 | −0.855805 | − | 0.517298i | \(-0.826938\pi\) | ||||
−0.855805 | + | 0.517298i | \(0.826938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.9265 | −1.25619 | −0.628097 | − | 0.778135i | \(-0.716166\pi\) | ||||
−0.628097 | + | 0.778135i | \(0.716166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.82109 | 0.450750 | 0.225375 | − | 0.974272i | \(-0.427639\pi\) | ||||
0.225375 | + | 0.974272i | \(0.427639\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.150248 | −0.00984309 | −0.00492154 | − | 0.999988i | \(-0.501567\pi\) | ||||
−0.00492154 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.03102 | −0.584168 | −0.292084 | − | 0.956393i | \(-0.594349\pi\) | ||||
−0.292084 | + | 0.956393i | \(0.594349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0000 | 1.22390 | 0.611949 | − | 0.790897i | \(-0.290386\pi\) | ||||
0.611949 | + | 0.790897i | \(0.290386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1572 | 0.773541 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.10477 | 0.509543 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1354 | −1.38077 | −0.690385 | − | 0.723442i | \(-0.742559\pi\) | ||||
−0.690385 | + | 0.723442i | \(0.742559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.7156 | 2.40567 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.71844 | 0.414277 | 0.207138 | − | 0.978312i | \(-0.433585\pi\) | ||||
0.207138 | + | 0.978312i | \(0.433585\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.0646 | −1.83307 | −0.916536 | − | 0.399952i | \(-0.869027\pi\) | ||||
−0.916536 | + | 0.399952i | \(0.869027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3578 | −1.35814 | −0.679070 | − | 0.734073i | \(-0.737617\pi\) | ||||
−0.679070 | + | 0.734073i | \(0.737617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7537 | −0.646128 | −0.323064 | − | 0.946377i | \(-0.604713\pi\) | ||||
−0.323064 | + | 0.946377i | \(0.604713\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4342 | 0.741764 | 0.370882 | − | 0.928680i | \(-0.379055\pi\) | ||||
0.370882 | + | 0.928680i | \(0.379055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.76596 | 0.104975 | 0.0524876 | − | 0.998622i | \(-0.483285\pi\) | ||||
0.0524876 | + | 0.998622i | \(0.483285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.0041 | 1.71206 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.1789 | 1.77523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.6061 | 1.20382 | 0.601910 | − | 0.798564i | \(-0.294407\pi\) | ||||
0.601910 | + | 0.798564i | \(0.294407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.77255 | 0.565161 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.3578 | 1.40396 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.98775 | 0.512958 | 0.256479 | − | 0.966550i | \(-0.417438\pi\) | ||||
0.256479 | + | 0.966550i | \(0.417438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7022 | −0.606865 | −0.303433 | − | 0.952853i | \(-0.598133\pi\) | ||||
−0.303433 | + | 0.952853i | \(0.598133\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.96156 | 0.393490 | 0.196745 | − | 0.980455i | \(-0.436963\pi\) | ||||
0.196745 | + | 0.980455i | \(0.436963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.0430 | −1.91204 | −0.956021 | − | 0.293297i | \(-0.905248\pi\) | ||||
−0.956021 | + | 0.293297i | \(0.905248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.5367 | −0.701922 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.7036 | 1.59711 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −58.7680 | −3.23998 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.5367 | −1.78838 | −0.894190 | − | 0.447688i | \(-0.852248\pi\) | ||||
−0.894190 | + | 0.447688i | \(0.852248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.87073 | 0.537693 | 0.268846 | − | 0.963183i | \(-0.413358\pi\) | ||||
0.268846 | + | 0.963183i | \(0.413358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.9078 | 0.807303 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −51.1196 | −2.76020 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.54830 | −0.458897 | −0.229448 | − | 0.973321i | \(-0.573692\pi\) | ||||
−0.229448 | + | 0.973321i | \(0.573692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.1789 | 1.08015 | 0.540076 | − | 0.841616i | \(-0.318395\pi\) | ||||
0.540076 | + | 0.841616i | \(0.318395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.9852 | 1.17015 | 0.585077 | − | 0.810978i | \(-0.301064\pi\) | ||||
0.585077 | + | 0.810978i | \(0.301064\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.309878 | 0.0163548 | 0.00817738 | − | 0.999967i | \(-0.497397\pi\) | ||||
0.00817738 | + | 0.999967i | \(0.497397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.53673 | −0.0808803 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.87073 | 0.515248 | 0.257624 | − | 0.966245i | \(-0.417060\pi\) | ||||
0.257624 | + | 0.966245i | \(0.417060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.1890 | 2.19034 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.98775 | −0.465368 | −0.232684 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232684 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.1165 | −0.778539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.357817 | −0.0183798 | −0.00918990 | − | 0.999958i | \(-0.502925\pi\) | ||||
−0.00918990 | + | 0.999958i | \(0.502925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.7374 | −0.701947 | −0.350974 | − | 0.936385i | \(-0.614149\pi\) | ||||
−0.350974 | + | 0.936385i | \(0.614149\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6100 | 1.29848 | 0.649239 | − | 0.760584i | \(-0.275087\pi\) | ||||
0.649239 | + | 0.760584i | \(0.275087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.0735 | 1.16687 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0139 | −0.552774 | −0.276387 | − | 0.961046i | \(-0.589137\pi\) | ||||
−0.276387 | + | 0.961046i | \(0.589137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7237 | −1.03489 | −0.517447 | − | 0.855715i | \(-0.673117\pi\) | ||||
−0.517447 | + | 0.855715i | \(0.673117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.9755 | 0.895423 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.9265 | 0.938150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.82109 | 0.337281 | 0.168641 | − | 0.985678i | \(-0.446062\pi\) | ||||
0.168641 | + | 0.985678i | \(0.446062\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.18908 | 0.255338 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5790 | −0.809936 | −0.404968 | − | 0.914331i | \(-0.632717\pi\) | ||||
−0.404968 | + | 0.914331i | \(0.632717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7156 | 1.44825 | 0.724126 | − | 0.689668i | \(-0.242244\pi\) | ||||
0.724126 | + | 0.689668i | \(0.242244\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45.3013 | −2.19228 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.67116 | 0.0804972 | 0.0402486 | − | 0.999190i | \(-0.487185\pi\) | ||||
0.0402486 | + | 0.999190i | \(0.487185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.5737 | 1.75762 | 0.878811 | − | 0.477170i | \(-0.158337\pi\) | ||||
0.878811 | + | 0.477170i | \(0.158337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.0379 | 0.671523 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5367 | 0.884710 | 0.442355 | − | 0.896840i | \(-0.354143\pi\) | ||||
0.442355 | + | 0.896840i | \(0.354143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.6260 | −0.884946 | −0.442473 | − | 0.896782i | \(-0.645899\pi\) | ||||
−0.442473 | + | 0.896782i | \(0.645899\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.1783 | −1.18824 | −0.594120 | − | 0.804377i | \(-0.702500\pi\) | ||||
−0.594120 | + | 0.804377i | \(0.702500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.1789 | 0.667659 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5860 | 1.29042 | 0.645209 | − | 0.764006i | \(-0.276770\pi\) | ||||
0.645209 | + | 0.764006i | \(0.276770\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7022 | 0.498450 | 0.249225 | − | 0.968446i | \(-0.419824\pi\) | ||||
0.249225 | + | 0.968446i | \(0.419824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.6122 | 1.37619 | 0.688097 | − | 0.725618i | \(-0.258446\pi\) | ||||
0.688097 | + | 0.725618i | \(0.258446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.5672 | −0.720366 | −0.360183 | − | 0.932882i | \(-0.617286\pi\) | ||||
−0.360183 | + | 0.932882i | \(0.617286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | 0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.9075 | 0.547508 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.3001 | 1.15599 | 0.577996 | − | 0.816040i | \(-0.303835\pi\) | ||||
0.577996 | + | 0.816040i | \(0.303835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.8211 | 1.04055 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.9755 | −0.814548 | −0.407274 | − | 0.913306i | \(-0.633521\pi\) | ||||
−0.407274 | + | 0.913306i | \(0.633521\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.5707 | 1.60528 | 0.802641 | − | 0.596463i | \(-0.203428\pi\) | ||||
0.802641 | + | 0.596463i | \(0.203428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.6908 | −1.60743 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 69.9158 | 3.13615 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.17891 | 0.187074 | 0.0935368 | − | 0.995616i | \(-0.470183\pi\) | ||||
0.0935368 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.2519 | −1.66098 | −0.830491 | − | 0.557032i | \(-0.811940\pi\) | ||||
−0.830491 | + | 0.557032i | \(0.811940\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.54796 | 0.334557 | 0.167279 | − | 0.985910i | \(-0.446502\pi\) | ||||
0.167279 | + | 0.985910i | \(0.446502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000 | 0.442374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.7292 | −1.26351 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.03102 | 0.395656 | 0.197828 | − | 0.980237i | \(-0.436611\pi\) | ||||
0.197828 | + | 0.980237i | \(0.436611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.58430 | 0.331638 | 0.165819 | − | 0.986156i | \(-0.446973\pi\) | ||||
0.165819 | + | 0.986156i | \(0.446973\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.4410 | 1.84876 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7156 | −0.509375 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0966 | 0.740536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −41.8791 | −1.80386 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.35782 | 0.144364 | 0.0721819 | − | 0.997391i | \(-0.477004\pi\) | ||||
0.0721819 | + | 0.997391i | \(0.477004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7415 | −0.844084 | −0.422042 | − | 0.906576i | \(-0.638686\pi\) | ||||
−0.422042 | + | 0.906576i | \(0.638686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.7142 | −0.925058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.6122 | −1.25924 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.2320 | −1.66231 | −0.831157 | − | 0.556037i | \(-0.812321\pi\) | ||||
−0.831157 | + | 0.556037i | \(0.812321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.3578 | 0.607271 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.9075 | 0.501842 | 0.250921 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250921 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.45462 | −0.186748 | −0.0933738 | − | 0.995631i | \(-0.529765\pi\) | ||||
−0.0933738 | + | 0.995631i | \(0.529765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.1789 | −0.760764 | −0.380382 | − | 0.924830i | \(-0.624207\pi\) | ||||
−0.380382 | + | 0.924830i | \(0.624207\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.84453 | −0.326572 | −0.163286 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163286 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.6100 | −1.06248 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.6244 | 0.854177 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6070 | −0.479073 | −0.239537 | − | 0.970887i | \(-0.576996\pi\) | ||||
−0.239537 | + | 0.970887i | \(0.576996\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.8211 | 1.06394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.03883 | −0.206920 | −0.103460 | − | 0.994634i | \(-0.532991\pi\) | ||||
−0.103460 | + | 0.994634i | \(0.532991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.0106 | −0.695035 | −0.347518 | − | 0.937673i | \(-0.612975\pi\) | ||||
−0.347518 | + | 0.937673i | \(0.612975\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.35782 | −0.136968 | −0.0684841 | − | 0.997652i | \(-0.521816\pi\) | ||||
−0.0684841 | + | 0.997652i | \(0.521816\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.93536 | 0.200320 | 0.100160 | − | 0.994971i | \(-0.468064\pi\) | ||||
0.100160 | + | 0.994971i | \(0.468064\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.6410 | −1.40143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.7170 | −1.52337 | −0.761687 | − | 0.647945i | \(-0.775628\pi\) | ||||
−0.761687 | + | 0.647945i | \(0.775628\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.33933 | −0.214953 | −0.107477 | − | 0.994208i | \(-0.534277\pi\) | ||||
−0.107477 | + | 0.994208i | \(0.534277\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6422 | 0.467939 | 0.233969 | − | 0.972244i | \(-0.424828\pi\) | ||||
0.233969 | + | 0.972244i | \(0.424828\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.2667 | −0.611649 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.8817 | 2.14840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5367 | −0.897173 | −0.448586 | − | 0.893739i | \(-0.648072\pi\) | ||||
−0.448586 | + | 0.893739i | \(0.648072\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −50.4969 | −2.00076 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.3110 | −0.723242 | −0.361621 | − | 0.932325i | \(-0.617777\pi\) | ||||
−0.361621 | + | 0.932325i | \(0.617777\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.6244 | −0.813348 | −0.406674 | − | 0.913573i | \(-0.633312\pi\) | ||||
−0.406674 | + | 0.913573i | \(0.633312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.2709 | −1.74047 | −0.870234 | − | 0.492639i | \(-0.836032\pi\) | ||||
−0.870234 | + | 0.492639i | \(0.836032\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.53673 | 0.0995752 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.300496 | −0.0117593 | −0.00587967 | − | 0.999983i | \(-0.501872\pi\) | ||||
−0.00587967 | + | 0.999983i | \(0.501872\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.4474 | 1.61456 | 0.807282 | − | 0.590166i | \(-0.200938\pi\) | ||||
0.807282 | + | 0.590166i | \(0.200938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.4313 | −1.80597 | −0.902983 | − | 0.429675i | \(-0.858628\pi\) | ||||
−0.902983 | + | 0.429675i | \(0.858628\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.4550 | −0.675861 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.1459 | −0.854933 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5459 | 0.560701 | 0.280351 | − | 0.959898i | \(-0.409549\pi\) | ||||
0.280351 | + | 0.959898i | \(0.409549\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.4937 | −1.32570 | −0.662850 | − | 0.748752i | \(-0.730653\pi\) | ||||
−0.662850 | + | 0.748752i | \(0.730653\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.35782 | 0.167238 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.5714 | −1.70548 | −0.852738 | − | 0.522339i | \(-0.825060\pi\) | ||||
−0.852738 | + | 0.522339i | \(0.825060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.8685 | 0.947413 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7156 | −1.16848 | −0.584239 | − | 0.811582i | \(-0.698607\pi\) | ||||
−0.584239 | + | 0.811582i | \(0.698607\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.3659 | 1.52897 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.3420 | 1.03269 | 0.516347 | − | 0.856379i | \(-0.327291\pi\) | ||||
0.516347 | + | 0.856379i | \(0.327291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.7816 | 1.23638 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.0041 | −1.09081 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5367 | 0.583494 | 0.291747 | − | 0.956496i | \(-0.405763\pi\) | ||||
0.291747 | + | 0.956496i | \(0.405763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7563 | 0.777330 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.3960 | 1.50652 | 0.753259 | − | 0.657724i | \(-0.228481\pi\) | ||||
0.753259 | + | 0.657724i | \(0.228481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.7156 | 1.81426 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.0672 | −1.74563 | −0.872813 | − | 0.488055i | \(-0.837707\pi\) | ||||
−0.872813 | + | 0.488055i | \(0.837707\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.8995 | 1.25382 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7415 | 0.729167 | 0.364584 | − | 0.931171i | \(-0.381211\pi\) | ||||
0.364584 | + | 0.931171i | \(0.381211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.77717 | 0.360147 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.8945 | −0.842189 | −0.421095 | − | 0.907017i | \(-0.638354\pi\) | ||||
−0.421095 | + | 0.907017i | \(0.638354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.7604 | 1.82553 | 0.912767 | − | 0.408481i | \(-0.133941\pi\) | ||||
0.912767 | + | 0.408481i | \(0.133941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.35782 | −0.232000 | −0.116000 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.116000 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.76596 | −0.0641847 | −0.0320924 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320924 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.73205 | 0.0627868 | 0.0313934 | − | 0.999507i | \(-0.490006\pi\) | ||||
0.0313934 | + | 0.999507i | \(0.490006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.5475 | −1.25071 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.05872 | 0.110444 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.7156 | 0.927329 | 0.463665 | − | 0.886011i | \(-0.346534\pi\) | ||||
0.463665 | + | 0.886011i | \(0.346534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.6837 | 1.10362 | 0.551809 | − | 0.833971i | \(-0.313938\pi\) | ||||
0.551809 | + | 0.833971i | \(0.313938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.5586 | 0.879903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.1789 | 1.22302 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.9502 | 1.70924 | 0.854620 | − | 0.519254i | \(-0.173790\pi\) | ||||
0.854620 | + | 0.519254i | \(0.173790\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −67.0574 | −2.38429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.7030 | −0.948252 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.7573 | 0.416464 | 0.208232 | − | 0.978079i | \(-0.433229\pi\) | ||||
0.208232 | + | 0.978079i | \(0.433229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −81.7891 | −2.89349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.88858 | 0.172514 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.19615 | 0.182687 | 0.0913435 | − | 0.995819i | \(-0.470884\pi\) | ||||
0.0913435 | + | 0.995819i | \(0.470884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.89454 | 0.242100 | 0.121050 | − | 0.992646i | \(-0.461374\pi\) | ||||
0.121050 | + | 0.992646i | \(0.461374\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.6244 | 0.721558 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.2105 | −1.82216 | −0.911080 | − | 0.412230i | \(-0.864750\pi\) | ||||
−0.911080 | + | 0.412230i | \(0.864750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.6367 | −0.405629 | −0.202815 | − | 0.979217i | \(-0.565009\pi\) | ||||
−0.202815 | + | 0.979217i | \(0.565009\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.7374 | 0.477696 | 0.238848 | − | 0.971057i | \(-0.423230\pi\) | ||||
0.238848 | + | 0.971057i | \(0.423230\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.17891 | −0.145139 | −0.0725697 | − | 0.997363i | \(-0.523120\pi\) | ||||
−0.0725697 | + | 0.997363i | \(0.523120\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −119.225 | −4.13092 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.8171 | 0.822256 | 0.411128 | − | 0.911578i | \(-0.365135\pi\) | ||||
0.411128 | + | 0.911578i | \(0.365135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00000 | −0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.5598 | 0.878245 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.3515 | 0.903319 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5197 | −0.428665 | −0.214333 | − | 0.976761i | \(-0.568758\pi\) | ||||
−0.214333 | + | 0.976761i | \(0.568758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.3286 | 1.92415 | 0.962075 | − | 0.272786i | \(-0.0879450\pi\) | ||||
0.962075 | + | 0.272786i | \(0.0879450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.5367 | 1.31486 | 0.657428 | − | 0.753517i | \(-0.271644\pi\) | ||||
0.657428 | + | 0.753517i | \(0.271644\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.54830 | 0.290988 | 0.145494 | − | 0.989359i | \(-0.453523\pi\) | ||||
0.145494 | + | 0.989359i | \(0.453523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.4762 | −0.491070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7891 | 0.399458 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.2104 | −1.62795 | −0.813975 | − | 0.580900i | \(-0.802701\pi\) | ||||
−0.813975 | + | 0.580900i | \(0.802701\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.9388 | 0.806520 | 0.403260 | − | 0.915085i | \(-0.367877\pi\) | ||||
0.403260 | + | 0.915085i | \(0.367877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.2366 | 1.69060 | 0.845298 | − | 0.534295i | \(-0.179423\pi\) | ||||
0.845298 | + | 0.534295i | \(0.179423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.6449 | 0.861072 | 0.430536 | − | 0.902574i | \(-0.358325\pi\) | ||||
0.430536 | + | 0.902574i | \(0.358325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.3578 | 0.816935 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −49.7604 | −1.66517 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.1065 | −1.07081 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.7156 | 1.95610 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.2244 | 1.96651 | 0.983256 | − | 0.182227i | \(-0.0583307\pi\) | ||||
0.983256 | + | 0.182227i | \(0.0583307\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5707 | 1.17851 | 0.589254 | − | 0.807948i | \(-0.299422\pi\) | ||||
0.589254 | + | 0.807948i | \(0.299422\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.5197 | −0.414340 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 69.9158 | 2.30882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8211 | −0.653837 | −0.326919 | − | 0.945052i | \(-0.606010\pi\) | ||||
−0.326919 | + | 0.945052i | \(0.606010\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.2121 | 1.35651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.7441 | 0.418121 | 0.209060 | − | 0.977903i | \(-0.432959\pi\) | ||||
0.209060 | + | 0.977903i | \(0.432959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −72.5367 | −2.37730 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.7799 | −0.417501 | −0.208751 | − | 0.977969i | \(-0.566940\pi\) | ||||
−0.208751 | + | 0.977969i | \(0.566940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.8817 | −1.75649 | −0.878246 | − | 0.478209i | \(-0.841286\pi\) | ||||
−0.878246 | + | 0.478209i | \(0.841286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.7415 | 0.642870 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.01894 | 0.228085 | 0.114042 | − | 0.993476i | \(-0.463620\pi\) | ||||
0.114042 | + | 0.993476i | \(0.463620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.89454 | 0.191345 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.7573 | −0.380855 | −0.190428 | − | 0.981701i | \(-0.560987\pi\) | ||||
−0.190428 | + | 0.981701i | \(0.560987\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.8685 | 0.803045 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.17891 | 0.231578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0401 | −0.419343 | −0.209671 | − | 0.977772i | \(-0.567239\pi\) | ||||
−0.209671 | + | 0.977772i | \(0.567239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7142 | 0.696843 | 0.348422 | − | 0.937338i | \(-0.386718\pi\) | ||||
0.348422 | + | 0.937338i | \(0.386718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.7292 | −0.921016 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.1743 | −0.869382 | −0.434691 | − | 0.900580i | \(-0.643142\pi\) | ||||
−0.434691 | + | 0.900580i | \(0.643142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.46327 | −0.238527 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.9454 | 0.827530 | 0.413765 | − | 0.910384i | \(-0.364214\pi\) | ||||
0.413765 | + | 0.910384i | \(0.364214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.5790 | 0.527181 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5367 | −1.03356 | −0.516782 | − | 0.856117i | \(-0.672870\pi\) | ||||
−0.516782 | + | 0.856117i | \(0.672870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.8724 | 0.946069 | 0.473035 | − | 0.881044i | \(-0.343159\pi\) | ||||
0.473035 | + | 0.881044i | \(0.343159\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8100.2.a.be.1.1 | 8 | ||
3.2 | odd | 2 | inner | 8100.2.a.be.1.2 | 8 | ||
5.2 | odd | 4 | 1620.2.d.e.649.1 | ✓ | 8 | ||
5.3 | odd | 4 | 1620.2.d.e.649.2 | yes | 8 | ||
5.4 | even | 2 | inner | 8100.2.a.be.1.7 | 8 | ||
15.2 | even | 4 | 1620.2.d.e.649.8 | yes | 8 | ||
15.8 | even | 4 | 1620.2.d.e.649.7 | yes | 8 | ||
15.14 | odd | 2 | inner | 8100.2.a.be.1.8 | 8 | ||
45.2 | even | 12 | 1620.2.r.h.109.2 | 16 | |||
45.7 | odd | 12 | 1620.2.r.h.109.7 | 16 | |||
45.13 | odd | 12 | 1620.2.r.h.1189.7 | 16 | |||
45.22 | odd | 12 | 1620.2.r.h.1189.5 | 16 | |||
45.23 | even | 12 | 1620.2.r.h.1189.2 | 16 | |||
45.32 | even | 12 | 1620.2.r.h.1189.4 | 16 | |||
45.38 | even | 12 | 1620.2.r.h.109.4 | 16 | |||
45.43 | odd | 12 | 1620.2.r.h.109.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.d.e.649.1 | ✓ | 8 | 5.2 | odd | 4 | ||
1620.2.d.e.649.2 | yes | 8 | 5.3 | odd | 4 | ||
1620.2.d.e.649.7 | yes | 8 | 15.8 | even | 4 | ||
1620.2.d.e.649.8 | yes | 8 | 15.2 | even | 4 | ||
1620.2.r.h.109.2 | 16 | 45.2 | even | 12 | |||
1620.2.r.h.109.4 | 16 | 45.38 | even | 12 | |||
1620.2.r.h.109.5 | 16 | 45.43 | odd | 12 | |||
1620.2.r.h.109.7 | 16 | 45.7 | odd | 12 | |||
1620.2.r.h.1189.2 | 16 | 45.23 | even | 12 | |||
1620.2.r.h.1189.4 | 16 | 45.32 | even | 12 | |||
1620.2.r.h.1189.5 | 16 | 45.22 | odd | 12 | |||
1620.2.r.h.1189.7 | 16 | 45.13 | odd | 12 | |||
8100.2.a.be.1.1 | 8 | 1.1 | even | 1 | trivial | ||
8100.2.a.be.1.2 | 8 | 3.2 | odd | 2 | inner | ||
8100.2.a.be.1.7 | 8 | 5.4 | even | 2 | inner | ||
8100.2.a.be.1.8 | 8 | 15.14 | odd | 2 | inner |