Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3312,2,Mod(1,3312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3312.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3312.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: | \(26.4464531494\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 207) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3312.1 |
$q$-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 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41421 | 1.29045 | 0.645226 | − | 0.763992i | \(-0.276763\pi\) | ||||
0.645226 | + | 0.763992i | \(0.276763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.41421 | 1.79821 | 0.899105 | − | 0.437732i | \(-0.144218\pi\) | ||||
0.899105 | + | 0.437732i | \(0.144218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.24264 | 1.43216 | 0.716080 | − | 0.698018i | \(-0.245935\pi\) | ||||
0.716080 | + | 0.698018i | \(0.245935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528 | 1.57568 | 0.787839 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.48528 | −1.52400 | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.82843 | −0.793789 | −0.396894 | − | 0.917864i | \(-0.629912\pi\) | ||||
−0.396894 | + | 0.917864i | \(0.629912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.65685 | −0.258757 | −0.129379 | − | 0.991595i | \(-0.541298\pi\) | ||||
−0.129379 | + | 0.991595i | \(0.541298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75736 | 0.267995 | 0.133997 | − | 0.990982i | \(-0.457219\pi\) | ||||
0.133997 | + | 0.990982i | \(0.457219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.343146 | 0.0500530 | 0.0250265 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250265 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.07107 | −0.696565 | −0.348282 | − | 0.937390i | \(-0.613235\pi\) | ||||
−0.348282 | + | 0.937390i | \(0.613235\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.65685 | 0.223410 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.65685 | −0.996838 | −0.498419 | − | 0.866936i | \(-0.666086\pi\) | ||||
−0.498419 | + | 0.866936i | \(0.666086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.828427 | −0.106069 | −0.0530346 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530346 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.58579 | −1.04892 | −0.524460 | − | 0.851435i | \(-0.675733\pi\) | ||||
−0.524460 | + | 0.851435i | \(0.675733\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6569 | 1.62077 | 0.810385 | − | 0.585897i | \(-0.199258\pi\) | ||||
0.810385 | + | 0.585897i | \(0.199258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3137 | 1.55825 | 0.779126 | − | 0.626868i | \(-0.215663\pi\) | ||||
0.779126 | + | 0.626868i | \(0.215663\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.65685 | 1.10050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.89949 | −0.888763 | −0.444381 | − | 0.895838i | \(-0.646576\pi\) | ||||
−0.444381 | + | 0.895838i | \(0.646576\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.82843 | −0.749517 | −0.374759 | − | 0.927122i | \(-0.622274\pi\) | ||||
−0.374759 | + | 0.927122i | \(0.622274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.34315 | 0.471080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0711 | 1.38553 | 0.692765 | − | 0.721163i | \(-0.256392\pi\) | ||||
0.692765 | + | 0.721163i | \(0.256392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.65685 | 0.375185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3137 | −1.12576 | −0.562878 | − | 0.826540i | \(-0.690306\pi\) | ||||
−0.562878 | + | 0.826540i | \(0.690306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.41421 | 0.336412 | 0.168206 | − | 0.985752i | \(-0.446203\pi\) | ||||
0.168206 | + | 0.985752i | \(0.446203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.48528 | 0.820303 | 0.410152 | − | 0.912017i | \(-0.365476\pi\) | ||||
0.410152 | + | 0.912017i | \(0.365476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.48528 | −0.238047 | −0.119023 | − | 0.992891i | \(-0.537976\pi\) | ||||
−0.119023 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4142 | 1.45005 | 0.725024 | − | 0.688724i | \(-0.241829\pi\) | ||||
0.725024 | + | 0.688724i | \(0.241829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.585786 | −0.0546249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.3137 | 2.32050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.48528 | 0.398004 | 0.199002 | − | 0.979999i | \(-0.436230\pi\) | ||||
0.199002 | + | 0.979999i | \(0.436230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.3137 | 1.84813 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.585786 | 0.0500471 | 0.0250236 | − | 0.999687i | \(-0.492034\pi\) | ||||
0.0250236 | + | 0.999687i | \(0.492034\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.97056 | 0.412783 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5858 | −1.35876 | −0.679380 | − | 0.733786i | \(-0.737751\pi\) | ||||
−0.679380 | + | 0.733786i | \(0.737751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.65685 | 0.785864 | 0.392932 | − | 0.919568i | \(-0.371461\pi\) | ||||
0.392932 | + | 0.919568i | \(0.371461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.97056 | −0.399245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.51472 | −0.120888 | −0.0604439 | − | 0.998172i | \(-0.519252\pi\) | ||||
−0.0604439 | + | 0.998172i | \(0.519252\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.41421 | −0.269078 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8284 | −1.47476 | −0.737378 | − | 0.675480i | \(-0.763936\pi\) | ||||
−0.737378 | + | 0.675480i | \(0.763936\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.65685 | 0.437741 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8284 | 0.823270 | 0.411635 | − | 0.911349i | \(-0.364958\pi\) | ||||
0.411635 | + | 0.911349i | \(0.364958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.8995 | −1.20189 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.0000 | 1.34538 | 0.672692 | − | 0.739923i | \(-0.265138\pi\) | ||||
0.672692 | + | 0.739923i | \(0.265138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1716 | −0.830376 | −0.415188 | − | 0.909736i | \(-0.636284\pi\) | ||||
−0.415188 | + | 0.909736i | \(0.636284\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | −0.207950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9706 | 1.53352 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.686292 | 0.0496583 | 0.0248292 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248292 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.65685 | −0.119263 | −0.0596315 | − | 0.998220i | \(-0.518993\pi\) | ||||
−0.0596315 | + | 0.998220i | \(0.518993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.17157 | −0.653448 | −0.326724 | − | 0.945120i | \(-0.605945\pi\) | ||||
−0.326724 | + | 0.945120i | \(0.605945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.24264 | 0.158977 | 0.0794883 | − | 0.996836i | \(-0.474671\pi\) | ||||
0.0794883 | + | 0.996836i | \(0.474671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.9706 | 2.03333 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.970563 | −0.0677870 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.6569 | 1.22135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4853 | 0.859522 | 0.429761 | − | 0.902943i | \(-0.358598\pi\) | ||||
0.429761 | + | 0.902943i | \(0.358598\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.02944 | 0.0702070 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.9706 | −1.96665 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9706 | 0.868573 | 0.434287 | − | 0.900775i | \(-0.357001\pi\) | ||||
0.434287 | + | 0.900775i | \(0.357001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.14214 | 0.407668 | 0.203834 | − | 0.979005i | \(-0.434660\pi\) | ||||
0.203834 | + | 0.979005i | \(0.434660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4853 | 0.957214 | 0.478607 | − | 0.878029i | \(-0.341142\pi\) | ||||
0.478607 | + | 0.878029i | \(0.341142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.6569 | 1.41879 | 0.709394 | − | 0.704812i | \(-0.248969\pi\) | ||||
0.709394 | + | 0.704812i | \(0.248969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.201010 | 0.0131125 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3137 | 1.24930 | 0.624650 | − | 0.780905i | \(-0.285242\pi\) | ||||
0.624650 | + | 0.780905i | \(0.285242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.9706 | −1.47966 | −0.739832 | − | 0.672792i | \(-0.765095\pi\) | ||||
−0.739832 | + | 0.672792i | \(0.765095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.72792 | 0.174281 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.4853 | 1.29302 | 0.646510 | − | 0.762906i | \(-0.276228\pi\) | ||||
0.646510 | + | 0.762906i | \(0.276228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | −0.177822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.34315 | 0.395675 | 0.197837 | − | 0.980235i | \(-0.436608\pi\) | ||||
0.197837 | + | 0.980235i | \(0.436608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.4853 | −1.02435 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.3137 | −1.43758 | −0.718792 | − | 0.695225i | \(-0.755305\pi\) | ||||
−0.718792 | + | 0.695225i | \(0.755305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.97056 | −0.182480 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1421 | 1.10615 | 0.553073 | − | 0.833133i | \(-0.313455\pi\) | ||||
0.553073 | + | 0.833133i | \(0.313455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4853 | 0.758427 | 0.379213 | − | 0.925309i | \(-0.376195\pi\) | ||||
0.379213 | + | 0.925309i | \(0.376195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.1716 | −0.794276 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.65685 | 0.460056 | 0.230028 | − | 0.973184i | \(-0.426118\pi\) | ||||
0.230028 | + | 0.973184i | \(0.426118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.58579 | 0.512185 | 0.256093 | − | 0.966652i | \(-0.417565\pi\) | ||||
0.256093 | + | 0.966652i | \(0.417565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2132 | −0.904331 | −0.452166 | − | 0.891934i | \(-0.649348\pi\) | ||||
−0.452166 | + | 0.891934i | \(0.649348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.65685 | −0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.9706 | 2.23356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.41421 | 0.433143 | 0.216571 | − | 0.976267i | \(-0.430513\pi\) | ||||
0.216571 | + | 0.976267i | \(0.430513\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.48528 | −0.261143 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.485281 | −0.0277871 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8284 | −0.618011 | −0.309005 | − | 0.951060i | \(-0.599996\pi\) | ||||
−0.309005 | + | 0.951060i | \(0.599996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.31371 | 0.528132 | 0.264066 | − | 0.964505i | \(-0.414936\pi\) | ||||
0.264066 | + | 0.964505i | \(0.414936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31371 | 0.0742552 | 0.0371276 | − | 0.999311i | \(-0.488179\pi\) | ||||
0.0371276 | + | 0.999311i | \(0.488179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.4558 | −1.42974 | −0.714871 | − | 0.699256i | \(-0.753515\pi\) | ||||
−0.714871 | + | 0.699256i | \(0.753515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 46.2843 | 2.57533 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.17157 | 0.0645909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.82843 | 0.375324 | 0.187662 | − | 0.982234i | \(-0.439909\pi\) | ||||
0.187662 | + | 0.982234i | \(0.439909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.02944 | −0.274788 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.3137 | −1.35891 | −0.679456 | − | 0.733717i | \(-0.737784\pi\) | ||||
−0.679456 | + | 0.733717i | \(0.737784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.9706 | −1.12253 | −0.561264 | − | 0.827637i | \(-0.689685\pi\) | ||||
−0.561264 | + | 0.827637i | \(0.689685\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.85786 | 0.311783 | 0.155891 | − | 0.987774i | \(-0.450175\pi\) | ||||
0.155891 | + | 0.987774i | \(0.450175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.2843 | −1.70390 | −0.851949 | − | 0.523624i | \(-0.824580\pi\) | ||||
−0.851949 | + | 0.523624i | \(0.824580\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9706 | 1.05108 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.79899 | 0.408218 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5563 | −0.707636 | −0.353818 | − | 0.935314i | \(-0.615117\pi\) | ||||
−0.353818 | + | 0.935314i | \(0.615117\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.3137 | −0.898883 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.48528 | 0.335795 | 0.167898 | − | 0.985804i | \(-0.446302\pi\) | ||||
0.167898 | + | 0.985804i | \(0.446302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.585786 | −0.0300898 | −0.0150449 | − | 0.999887i | \(-0.504789\pi\) | ||||
−0.0150449 | + | 0.999887i | \(0.504789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6569 | −1.10661 | −0.553307 | − | 0.832978i | \(-0.686634\pi\) | ||||
−0.553307 | + | 0.832978i | \(0.686634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.65685 | 0.288300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.89949 | −0.197712 | −0.0988561 | − | 0.995102i | \(-0.531518\pi\) | ||||
−0.0988561 | + | 0.995102i | \(0.531518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.41421 | −0.374953 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.62742 | −0.232831 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.0000 | −1.30490 | −0.652451 | − | 0.757831i | \(-0.726259\pi\) | ||||
−0.652451 | + | 0.757831i | \(0.726259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0416 | 1.50021 | 0.750104 | − | 0.661320i | \(-0.230004\pi\) | ||||
0.750104 | + | 0.661320i | \(0.230004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.6569 | −0.676945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3431 | 0.709223 | 0.354611 | − | 0.935014i | \(-0.384613\pi\) | ||||
0.354611 | + | 0.935014i | \(0.384613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.1421 | −1.28637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.4853 | −1.00077 | −0.500386 | − | 0.865803i | \(-0.666808\pi\) | ||||
−0.500386 | + | 0.865803i | \(0.666808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.4558 | −1.92296 | −0.961480 | − | 0.274875i | \(-0.911364\pi\) | ||||
−0.961480 | + | 0.274875i | \(0.911364\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.5269 | −1.67480 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.82843 | −0.136877 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.68629 | −0.418404 | −0.209202 | − | 0.977872i | \(-0.567087\pi\) | ||||
−0.209202 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.65685 | −0.175737 | −0.0878686 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878686 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.24264 | −0.298626 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.0000 | −1.14546 | −0.572729 | − | 0.819745i | \(-0.694115\pi\) | ||||
−0.572729 | + | 0.819745i | \(0.694115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.65685 | 0.362970 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6274 | 0.501539 | 0.250769 | − | 0.968047i | \(-0.419316\pi\) | ||||
0.250769 | + | 0.968047i | \(0.419316\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68629 | −0.220669 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.9706 | 1.63585 | 0.817927 | − | 0.575322i | \(-0.195123\pi\) | ||||
0.817927 | + | 0.575322i | \(0.195123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.17157 | −0.427163 | −0.213581 | − | 0.976925i | \(-0.568513\pi\) | ||||
−0.213581 | + | 0.976925i | \(0.568513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.97056 | −0.416897 | −0.208449 | − | 0.978033i | \(-0.566841\pi\) | ||||
−0.208449 | + | 0.978033i | \(0.566841\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.85786 | −0.271070 | −0.135535 | − | 0.990773i | \(-0.543275\pi\) | ||||
−0.135535 | + | 0.990773i | \(0.543275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.3137 | −1.35358 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.97056 | 0.228547 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.0711 | −1.33387 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.6863 | −0.762416 | −0.381208 | − | 0.924489i | \(-0.624492\pi\) | ||||
−0.381208 | + | 0.924489i | \(0.624492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.85786 | −0.265992 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.97056 | −0.406495 | −0.203247 | − | 0.979127i | \(-0.565150\pi\) | ||||
−0.203247 | + | 0.979127i | \(0.565150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.68629 | −0.301748 | −0.150874 | − | 0.988553i | \(-0.548209\pi\) | ||||
−0.150874 | + | 0.988553i | \(0.548209\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 62.9117 | 2.83340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.6274 | 2.09153 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.4853 | 1.09611 | 0.548056 | − | 0.836442i | \(-0.315368\pi\) | ||||
0.548056 | + | 0.836442i | \(0.315368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6569 | −0.787280 | −0.393640 | − | 0.919265i | \(-0.628784\pi\) | ||||
−0.393640 | + | 0.919265i | \(0.628784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.62742 | −0.294916 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.1421 | −1.69062 | −0.845310 | − | 0.534276i | \(-0.820584\pi\) | ||||
−0.845310 | + | 0.534276i | \(0.820584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.4558 | 2.01085 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | 0.0881305 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.970563 | 0.0426853 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.7279 | 0.820485 | 0.410243 | − | 0.911976i | \(-0.365444\pi\) | ||||
0.410243 | + | 0.911976i | \(0.365444\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.6985 | 1.56099 | 0.780493 | − | 0.625165i | \(-0.214968\pi\) | ||||
0.780493 | + | 0.625165i | \(0.214968\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −62.9117 | −2.74048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.97056 | 0.214896 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1716 | 0.567340 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.97056 | 0.213701 | 0.106851 | − | 0.994275i | \(-0.465923\pi\) | ||||
0.106851 | + | 0.994275i | \(0.465923\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.45584 | −0.0623615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4853 | −0.533832 | −0.266916 | − | 0.963720i | \(-0.586005\pi\) | ||||
−0.266916 | + | 0.963720i | \(0.586005\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.9706 | 2.25662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.9706 | −1.14690 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.2426 | −0.942451 | −0.471225 | − | 0.882013i | \(-0.656188\pi\) | ||||
−0.471225 | + | 0.882013i | \(0.656188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.1716 | −0.892275 | −0.446138 | − | 0.894964i | \(-0.647201\pi\) | ||||
−0.446138 | + | 0.894964i | \(0.647201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.02944 | 0.379871 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.58579 | 0.359935 | 0.179967 | − | 0.983673i | \(-0.442401\pi\) | ||||
0.179967 | + | 0.983673i | \(0.442401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.75736 | −0.0735432 | −0.0367716 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367716 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.65685 | 0.194204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.2843 | −1.34401 | −0.672006 | − | 0.740546i | \(-0.734567\pi\) | ||||
−0.672006 | + | 0.740546i | \(0.734567\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.3137 | −0.967216 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.3431 | −0.594032 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.02944 | −0.290136 | −0.145068 | − | 0.989422i | \(-0.546340\pi\) | ||||
−0.145068 | + | 0.989422i | \(0.546340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.9706 | −2.18261 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.686292 | 0.0281826 | 0.0140913 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140913 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.8284 | 0.607906 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.68629 | −0.191477 | −0.0957383 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957383 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.65685 | 0.0675845 | 0.0337922 | − | 0.999429i | \(-0.489242\pi\) | ||||
0.0337922 | + | 0.999429i | \(0.489242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.75736 | −0.0714468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.3431 | 0.582170 | 0.291085 | − | 0.956697i | \(-0.405984\pi\) | ||||
0.291085 | + | 0.956697i | \(0.405984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.4558 | 1.59361 | 0.796803 | − | 0.604239i | \(-0.206523\pi\) | ||||
0.796803 | + | 0.604239i | \(0.206523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.5563 | −1.35093 | −0.675464 | − | 0.737393i | \(-0.736057\pi\) | ||||
−0.675464 | + | 0.737393i | \(0.736057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.2426 | 0.894007 | 0.447004 | − | 0.894532i | \(-0.352491\pi\) | ||||
0.447004 | + | 0.894532i | \(0.352491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.6274 | 1.78796 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.7990 | −1.42740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.8701 | 0.990061 | 0.495031 | − | 0.868875i | \(-0.335157\pi\) | ||||
0.495031 | + | 0.868875i | \(0.335157\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.62742 | 0.104266 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.92893 | −0.115686 | −0.0578429 | − | 0.998326i | \(-0.518422\pi\) | ||||
−0.0578429 | + | 0.998326i | \(0.518422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.38478 | 0.330663 | 0.165332 | − | 0.986238i | \(-0.447131\pi\) | ||||
0.165332 | + | 0.986238i | \(0.447131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.00000 | −0.235884 | −0.117942 | − | 0.993020i | \(-0.537630\pi\) | ||||
−0.117942 | + | 0.993020i | \(0.537630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.6569 | −0.850106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.6569 | −0.847498 | −0.423749 | − | 0.905780i | \(-0.639286\pi\) | ||||
−0.423749 | + | 0.905780i | \(0.639286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.94113 | −0.388432 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.1421 | −1.32999 | −0.664994 | − | 0.746848i | \(-0.731566\pi\) | ||||
−0.664994 | + | 0.746848i | \(0.731566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.8579 | −0.461217 | −0.230609 | − | 0.973047i | \(-0.574072\pi\) | ||||
−0.230609 | + | 0.973047i | \(0.574072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4853 | 0.484158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.48528 | −0.328551 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.34315 | −0.0904561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.9706 | −1.57930 | −0.789650 | − | 0.613558i | \(-0.789738\pi\) | ||||
−0.789650 | + | 0.613558i | \(0.789738\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.6985 | 1.37200 | 0.686002 | − | 0.727600i | \(-0.259364\pi\) | ||||
0.686002 | + | 0.727600i | \(0.259364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.1421 | −1.31025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3431 | 0.395769 | 0.197885 | − | 0.980225i | \(-0.436593\pi\) | ||||
0.197885 | + | 0.980225i | \(0.436593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.343146 | 0.0131109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.8284 | 0.868434 | 0.434217 | − | 0.900808i | \(-0.357025\pi\) | ||||
0.434217 | + | 0.900808i | \(0.357025\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.34315 | 0.0888806 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2843 | −0.465300 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.89949 | 0.147282 | 0.0736409 | − | 0.997285i | \(-0.476538\pi\) | ||||
0.0736409 | + | 0.997285i | \(0.476538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.1421 | −1.13683 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.6274 | −1.45273 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.7990 | −1.11912 | −0.559562 | − | 0.828788i | \(-0.689031\pi\) | ||||
−0.559562 | + | 0.828788i | \(0.689031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.48528 | 0.317776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.3137 | −1.54074 | −0.770371 | − | 0.637596i | \(-0.779929\pi\) | ||||
−0.770371 | + | 0.637596i | \(0.779929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6569 | 0.434124 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.5147 | −1.46754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.7574 | −1.40034 | −0.700171 | − | 0.713975i | \(-0.746893\pi\) | ||||
−0.700171 | + | 0.713975i | \(0.746893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0294 | 0.481911 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.79899 | −0.361934 | −0.180967 | − | 0.983489i | \(-0.557923\pi\) | ||||
−0.180967 | + | 0.983489i | \(0.557923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.2843 | −0.894523 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.3137 | −1.59332 | −0.796660 | − | 0.604427i | \(-0.793402\pi\) | ||||
−0.796660 | + | 0.604427i | \(0.793402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.02944 | 0.257885 | 0.128943 | − | 0.991652i | \(-0.458842\pi\) | ||||
0.128943 | + | 0.991652i | \(0.458842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.71573 | −0.355957 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.9706 | 1.05856 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3553 | 0.779267 | 0.389634 | − | 0.920970i | \(-0.372602\pi\) | ||||
0.389634 | + | 0.920970i | \(0.372602\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.65685 | 0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1421 | 0.877461 | 0.438730 | − | 0.898619i | \(-0.355428\pi\) | ||||
0.438730 | + | 0.898619i | \(0.355428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7990 | −1.15271 | −0.576356 | − | 0.817199i | \(-0.695526\pi\) | ||||
−0.576356 | + | 0.817199i | \(0.695526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.48528 | −0.307188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.9706 | −1.26107 | −0.630535 | − | 0.776161i | \(-0.717165\pi\) | ||||
−0.630535 | + | 0.776161i | \(0.717165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.38478 | 0.301579 | 0.150790 | − | 0.988566i | \(-0.451818\pi\) | ||||
0.150790 | + | 0.988566i | \(0.451818\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5147 | 1.41941 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.3431 | −0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.6274 | 1.38220 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.887302 | −0.0316692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6985 | 0.987344 | 0.493672 | − | 0.869648i | \(-0.335654\pi\) | ||||
0.493672 | + | 0.869648i | \(0.335654\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 52.6274 | 1.87122 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.0711 | −1.31312 | −0.656562 | − | 0.754272i | \(-0.727990\pi\) | ||||
−0.656562 | + | 0.754272i | \(0.727990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.54416 | 0.0900058 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.6569 | 1.32888 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.00000 | −0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.1127 | −0.671967 | −0.335983 | − | 0.941868i | \(-0.609069\pi\) | ||||
−0.335983 | + | 0.941868i | \(0.609069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −56.7696 | −1.99345 | −0.996724 | − | 0.0808743i | \(-0.974229\pi\) | ||||
−0.996724 | + | 0.0808743i | \(0.974229\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0294 | −0.386344 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9706 | 0.383811 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.3137 | −0.394851 | −0.197426 | − | 0.980318i | \(-0.563258\pi\) | ||||
−0.197426 | + | 0.980318i | \(0.563258\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.5147 | −0.540809 | −0.270405 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270405 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.79899 | −0.271197 | −0.135599 | − | 0.990764i | \(-0.543296\pi\) | ||||
−0.135599 | + | 0.990764i | \(0.543296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.9706 | 1.83974 | 0.919872 | − | 0.392219i | \(-0.128292\pi\) | ||||
0.919872 | + | 0.392219i | \(0.128292\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.5269 | 1.19629 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.31371 | 0.114676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.9706 | 1.82875 | 0.914373 | − | 0.404872i | \(-0.132684\pi\) | ||||
0.914373 | + | 0.404872i | \(0.132684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.61522 | −0.261972 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2426 | −0.351941 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.82843 | 0.165516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.9411 | 1.77843 | 0.889215 | − | 0.457489i | \(-0.151251\pi\) | ||||
0.889215 | + | 0.457489i | \(0.151251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.6569 | 1.01306 | 0.506529 | − | 0.862223i | \(-0.330928\pi\) | ||||
0.506529 | + | 0.862223i | \(0.330928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0294 | −0.512798 | −0.256399 | − | 0.966571i | \(-0.582536\pi\) | ||||
−0.256399 | + | 0.966571i | \(0.582536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.34315 | 0.215673 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.3431 | −0.757939 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.3137 | −0.652923 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.6569 | −1.47419 | −0.737094 | − | 0.675791i | \(-0.763802\pi\) | ||||
−0.737094 | + | 0.675791i | \(0.763802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0711 | −0.440375 | −0.220188 | − | 0.975458i | \(-0.570667\pi\) | ||||
−0.220188 | + | 0.975458i | \(0.570667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5147 | 0.387501 | 0.193751 | − | 0.981051i | \(-0.437935\pi\) | ||||
0.193751 | + | 0.981051i | \(0.437935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.343146 | −0.0115217 | −0.00576085 | − | 0.999983i | \(-0.501834\pi\) | ||||
−0.00576085 | + | 0.999983i | \(0.501834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.3137 | 0.513605 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.14214 | 0.0716838 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.5442 | 0.352452 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.0000 | −2.40133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.5980 | −1.25257 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.54416 | −0.217535 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.6985 | 1.18535 | 0.592674 | − | 0.805442i | \(-0.298072\pi\) | ||||
0.592674 | + | 0.805442i | \(0.298072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.3726 | 0.443053 | 0.221527 | − | 0.975154i | \(-0.428896\pi\) | ||||
0.221527 | + | 0.975154i | \(0.428896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.3137 | −0.639190 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −57.9411 | −1.91338 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.21320 | 0.105994 | 0.0529969 | − | 0.998595i | \(-0.483123\pi\) | ||||
0.0529969 | + | 0.998595i | \(0.483123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4853 | 0.739311 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3137 | 0.764898 | 0.382449 | − | 0.923977i | \(-0.375081\pi\) | ||||
0.382449 | + | 0.923977i | \(0.375081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.0711 | 0.952766 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.2843 | 0.401739 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.6569 | 1.03418 | 0.517092 | − | 0.855930i | \(-0.327014\pi\) | ||||
0.517092 | + | 0.855930i | \(0.327014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3848 | −0.794921 | −0.397460 | − | 0.917619i | \(-0.630108\pi\) | ||||
−0.397460 | + | 0.917619i | \(0.630108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.65685 | 0.0539546 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.68629 | −0.0872927 | −0.0436464 | − | 0.999047i | \(-0.513897\pi\) | ||||
−0.0436464 | + | 0.999047i | \(0.513897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.0122 | −1.00458 | −0.502292 | − | 0.864698i | \(-0.667510\pi\) | ||||
−0.502292 | + | 0.864698i | \(0.667510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.402020 | 0.0130091 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.00000 | 0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.970563 | −0.0312435 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5147 | 0.498920 | 0.249460 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249460 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.11270 | −0.228257 | −0.114129 | − | 0.993466i | \(-0.536408\pi\) | ||||
−0.114129 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6569 | 0.437819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0416 | 0.961117 | 0.480558 | − | 0.876963i | \(-0.340434\pi\) | ||||
0.480558 | + | 0.876963i | \(0.340434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.9706 | 1.18158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.3137 | −0.743592 | −0.371796 | − | 0.928314i | \(-0.621258\pi\) | ||||
−0.371796 | + | 0.928314i | \(0.621258\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.37258 | −0.171185 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.75736 | −0.0558808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4558 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.31371 | 0.0416474 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.02944 | 0.0959432 | 0.0479716 | − | 0.998849i | \(-0.484724\pi\) | ||||
0.0479716 | + | 0.998849i | \(0.484724\pi\) | |||||||
\(998\) | 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 | 3312.2.a.be.1.1 | 2 | ||
3.2 | odd | 2 | 3312.2.a.u.1.2 | 2 | |||
4.3 | odd | 2 | 207.2.a.e.1.2 | yes | 2 | ||
12.11 | even | 2 | 207.2.a.b.1.1 | ✓ | 2 | ||
20.19 | odd | 2 | 5175.2.a.bc.1.1 | 2 | |||
60.59 | even | 2 | 5175.2.a.bo.1.2 | 2 | |||
92.91 | even | 2 | 4761.2.a.z.1.2 | 2 | |||
276.275 | odd | 2 | 4761.2.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
207.2.a.b.1.1 | ✓ | 2 | 12.11 | even | 2 | ||
207.2.a.e.1.2 | yes | 2 | 4.3 | odd | 2 | ||
3312.2.a.u.1.2 | 2 | 3.2 | odd | 2 | |||
3312.2.a.be.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4761.2.a.k.1.1 | 2 | 276.275 | odd | 2 | |||
4761.2.a.z.1.2 | 2 | 92.91 | even | 2 | |||
5175.2.a.bc.1.1 | 2 | 20.19 | odd | 2 | |||
5175.2.a.bo.1.2 | 2 | 60.59 | even | 2 |