Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(1,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, 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("4900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.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: | \(39.1266969904\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 11x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.04547\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.1 |
$q$-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 | ||||||||
\(3\) | −1.73205 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.27492 | −1.59045 | −0.795224 | − | 0.606316i | \(-0.792647\pi\) | ||||
−0.795224 | + | 0.606316i | \(0.792647\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.62685 | −0.728557 | −0.364278 | − | 0.931290i | \(-0.618684\pi\) | ||||
−0.364278 | + | 0.931290i | \(0.618684\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.418627 | −0.101532 | −0.0507659 | − | 0.998711i | \(-0.516166\pi\) | ||||
−0.0507659 | + | 0.998711i | \(0.516166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.27492 | 0.751318 | 0.375659 | − | 0.926758i | \(-0.377416\pi\) | ||||
0.375659 | + | 0.926758i | \(0.377416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.82300 | 1.63121 | 0.815604 | − | 0.578610i | \(-0.196405\pi\) | ||||
0.815604 | + | 0.578610i | \(0.196405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.27492 | 0.793832 | 0.396916 | − | 0.917855i | \(-0.370080\pi\) | ||||
0.396916 | + | 0.917855i | \(0.370080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27492 | 0.588192 | 0.294096 | − | 0.955776i | \(-0.404981\pi\) | ||||
0.294096 | + | 0.955776i | \(0.404981\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.13642 | 1.59045 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.97368 | 1.63966 | 0.819831 | − | 0.572605i | \(-0.194067\pi\) | ||||
0.819831 | + | 0.572605i | \(0.194067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.54983 | 0.728557 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.72508 | −0.581760 | −0.290880 | − | 0.956760i | \(-0.593948\pi\) | ||||
−0.290880 | + | 0.956760i | \(0.593948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.15068 | 0.327975 | 0.163988 | − | 0.986462i | \(-0.447564\pi\) | ||||
0.163988 | + | 0.986462i | \(0.447564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.50958 | −0.949519 | −0.474760 | − | 0.880115i | \(-0.657465\pi\) | ||||
−0.474760 | + | 0.880115i | \(0.657465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.725083 | 0.101532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.67232 | 0.779153 | 0.389577 | − | 0.920994i | \(-0.372621\pi\) | ||||
0.389577 | + | 0.920994i | \(0.372621\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.67232 | −0.751318 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.27492 | −0.426358 | −0.213179 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213179 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5498 | −1.73488 | −0.867439 | − | 0.497543i | \(-0.834236\pi\) | ||||
−0.867439 | + | 0.497543i | \(0.834236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.52165 | −0.430237 | −0.215119 | − | 0.976588i | \(-0.569014\pi\) | ||||
−0.215119 | + | 0.976588i | \(0.569014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.5498 | −1.63121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.54983 | −0.539966 | −0.269983 | − | 0.962865i | \(-0.587018\pi\) | ||||
−0.269983 | + | 0.962865i | \(0.587018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.50958 | −0.761888 | −0.380944 | − | 0.924598i | \(-0.624401\pi\) | ||||
−0.380944 | + | 0.924598i | \(0.624401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.27492 | 0.818492 | 0.409246 | − | 0.912424i | \(-0.365792\pi\) | ||||
0.409246 | + | 0.912424i | \(0.365792\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.40437 | 0.812736 | 0.406368 | − | 0.913710i | \(-0.366795\pi\) | ||||
0.406368 | + | 0.913710i | \(0.366795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.40437 | −0.793832 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.00000 | −0.741999 | −0.370999 | − | 0.928633i | \(-0.620985\pi\) | ||||
−0.370999 | + | 0.928633i | \(0.620985\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.67232 | −0.588192 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5498 | −1.34826 | −0.674129 | − | 0.738613i | \(-0.735481\pi\) | ||||
−0.674129 | + | 0.738613i | \(0.735481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2871 | −1.11215 | −0.556076 | − | 0.831132i | \(-0.687694\pi\) | ||||
−0.556076 | + | 0.831132i | \(0.687694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.52165 | −0.340450 | −0.170225 | − | 0.985405i | \(-0.554450\pi\) | ||||
−0.170225 | + | 0.985405i | \(0.554450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5498 | −1.10627 | −0.553137 | − | 0.833090i | \(-0.686569\pi\) | ||||
−0.553137 | + | 0.833090i | \(0.686569\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.2749 | −1.63966 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.30136 | −0.404637 | −0.202319 | − | 0.979320i | \(-0.564848\pi\) | ||||
−0.202319 | + | 0.979320i | \(0.564848\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.8248 | 1.52952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.45203 | 0.581760 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6460 | 1.38836 | 0.694179 | − | 0.719802i | \(-0.255768\pi\) | ||||
0.694179 | + | 0.719802i | \(0.255768\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.72508 | −0.327975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7251 | −0.937055 | −0.468527 | − | 0.883449i | \(-0.655215\pi\) | ||||
−0.468527 | + | 0.883449i | \(0.655215\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.3183 | 1.82135 | 0.910674 | − | 0.413126i | \(-0.135563\pi\) | ||||
0.910674 | + | 0.413126i | \(0.135563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0997 | 1.11110 | 0.555550 | − | 0.831483i | \(-0.312508\pi\) | ||||
0.555550 | + | 0.831483i | \(0.312508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2749 | 0.949519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.8564 | 1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.54983 | −0.618507 | −0.309253 | − | 0.950980i | \(-0.600079\pi\) | ||||
−0.309253 | + | 0.950980i | \(0.600079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7251 | −1.03555 | −0.517776 | − | 0.855516i | \(-0.673240\pi\) | ||||
−0.517776 | + | 0.855516i | \(0.673240\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.20822 | 0.176235 | 0.0881176 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881176 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.82475 | −0.779153 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.67232 | −0.444291 | −0.222145 | − | 0.975014i | \(-0.571306\pi\) | ||||
−0.222145 | + | 0.975014i | \(0.571306\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.476171 | 0.0368472 | 0.0184236 | − | 0.999830i | \(-0.494135\pi\) | ||||
0.0184236 | + | 0.999830i | \(0.494135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.09967 | −0.469205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.4811 | −1.55715 | −0.778573 | − | 0.627553i | \(-0.784056\pi\) | ||||
−0.778573 | + | 0.627553i | \(0.784056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.67232 | 0.426358 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.27492 | −0.543753 | −0.271876 | − | 0.962332i | \(-0.587644\pi\) | ||||
−0.271876 | + | 0.962332i | \(0.587644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2749 | −1.80434 | −0.902170 | − | 0.431380i | \(-0.858027\pi\) | ||||
−0.902170 | + | 0.431380i | \(0.858027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.4690 | 1.73488 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.20822 | 0.161481 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.175248 | 0.0126805 | 0.00634026 | − | 0.999980i | \(-0.497982\pi\) | ||||
0.00634026 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.3183 | −1.53453 | −0.767263 | − | 0.641332i | \(-0.778382\pi\) | ||||
−0.767263 | + | 0.641332i | \(0.778382\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.60271 | −0.612918 | −0.306459 | − | 0.951884i | \(-0.599144\pi\) | ||||
−0.306459 | + | 0.951884i | \(0.599144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.2749 | 1.22459 | 0.612293 | − | 0.790631i | \(-0.290247\pi\) | ||||
0.612293 | + | 0.790631i | \(0.290247\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.09967 | 0.430237 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.2749 | −1.19493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.6495 | 1.76578 | 0.882892 | − | 0.469576i | \(-0.155593\pi\) | ||||
0.882892 | + | 0.469576i | \(0.155593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.88054 | 0.539966 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.2749 | 0.761888 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.09967 | 0.0739717 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.71780 | 0.583787 | 0.291893 | − | 0.956451i | \(-0.405715\pi\) | ||||
0.291893 | + | 0.956451i | \(0.405715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5287 | 1.29617 | 0.648084 | − | 0.761569i | \(-0.275571\pi\) | ||||
0.648084 | + | 0.761569i | \(0.275571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.27492 | 0.216413 | 0.108206 | − | 0.994128i | \(-0.465489\pi\) | ||||
0.108206 | + | 0.994128i | \(0.465489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.2750 | −0.935189 | −0.467594 | − | 0.883943i | \(-0.654879\pi\) | ||||
−0.467594 | + | 0.883943i | \(0.654879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6005 | −0.818492 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.549834 | 0.0355658 | 0.0177829 | − | 0.999842i | \(-0.494339\pi\) | ||||
0.0177829 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.82475 | 0.632868 | 0.316434 | − | 0.948615i | \(-0.397514\pi\) | ||||
0.316434 | + | 0.948615i | \(0.397514\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.60271 | −0.547377 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.8248 | −0.812736 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5498 | −1.29709 | −0.648547 | − | 0.761175i | \(-0.724623\pi\) | ||||
−0.648547 | + | 0.761175i | \(0.724623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −41.2657 | −2.59435 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6482 | 0.726594 | 0.363297 | − | 0.931673i | \(-0.381651\pi\) | ||||
0.363297 | + | 0.931673i | \(0.381651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.779710 | −0.0480790 | −0.0240395 | − | 0.999711i | \(-0.507653\pi\) | ||||
−0.0240395 | + | 0.999711i | \(0.507653\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1244 | 0.741999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4502 | −0.881042 | −0.440521 | − | 0.897742i | \(-0.645206\pi\) | ||||
−0.440521 | + | 0.897742i | \(0.645206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.82475 | 0.596811 | 0.298406 | − | 0.954439i | \(-0.403545\pi\) | ||||
0.298406 | + | 0.954439i | \(0.403545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2750 | −0.857704 | −0.428852 | − | 0.903375i | \(-0.641082\pi\) | ||||
−0.428852 | + | 0.903375i | \(0.641082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9260 | −0.649484 | −0.324742 | − | 0.945803i | \(-0.605278\pi\) | ||||
−0.324742 | + | 0.945803i | \(0.605278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8248 | −0.989691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.92820 | −0.404750 | −0.202375 | − | 0.979308i | \(-0.564866\pi\) | ||||
−0.202375 | + | 0.979308i | \(0.564866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.4093 | −1.59045 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.5498 | −1.18843 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.4690 | 1.34826 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.5145 | −1.51326 | −0.756631 | − | 0.653843i | \(-0.773156\pi\) | ||||
−0.756631 | + | 0.653843i | \(0.773156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.5498 | 1.11215 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.82475 | −0.557111 | −0.278555 | − | 0.960420i | \(-0.589856\pi\) | ||||
−0.278555 | + | 0.960420i | \(0.589856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.5002 | 1.89354 | 0.946772 | − | 0.321904i | \(-0.104323\pi\) | ||||
0.946772 | + | 0.321904i | \(0.104323\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.6197 | −1.43894 | −0.719472 | − | 0.694521i | \(-0.755616\pi\) | ||||
−0.719472 | + | 0.694521i | \(0.755616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5498 | −1.26255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.09967 | 0.340450 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.37097 | −0.0762827 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.0049 | 1.10627 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8248 | 0.979737 | 0.489868 | − | 0.871796i | \(-0.337045\pi\) | ||||
0.489868 | + | 0.871796i | \(0.337045\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.30136 | 0.234310 | 0.117155 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117155 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.45017 | 0.404637 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2749 | −0.935489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.1244 | −0.650870 | −0.325435 | − | 0.945564i | \(-0.605511\pi\) | ||||
−0.325435 | + | 0.945564i | \(0.605511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.72508 | −0.199399 | −0.0996996 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0996996 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.6495 | −0.728557 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.18408 | −0.435595 | −0.217797 | − | 0.975994i | \(-0.569887\pi\) | ||||
−0.217797 | + | 0.975994i | \(0.569887\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.3746 | 1.91978 | 0.959889 | − | 0.280382i | \(-0.0904610\pi\) | ||||
0.959889 | + | 0.280382i | \(0.0904610\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.27492 | −0.435522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.1413 | −1.52952 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.03341 | 0.314941 | 0.157471 | − | 0.987524i | \(-0.449666\pi\) | ||||
0.157471 | + | 0.987524i | \(0.449666\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.97368 | −0.516417 | −0.258209 | − | 0.966089i | \(-0.583132\pi\) | ||||
−0.258209 | + | 0.966089i | \(0.583132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.2296 | −0.578352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6495 | −1.11206 | −0.556030 | − | 0.831162i | \(-0.687676\pi\) | ||||
−0.556030 | + | 0.831162i | \(0.687676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.0997 | −1.38836 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.14849 | 0.314173 | 0.157087 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157087 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.3746 | 1.64146 | 0.820728 | − | 0.571319i | \(-0.193568\pi\) | ||||
0.820728 | + | 0.571319i | \(0.193568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.27492 | −0.165620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.5764 | 0.937055 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8109 | −0.542585 | −0.271293 | − | 0.962497i | \(-0.587451\pi\) | ||||
−0.271293 | + | 0.962497i | \(0.587451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | 0.149813 | 0.0749064 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749064 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.60271 | −0.428532 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −52.6103 | −2.60780 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0997 | −0.993865 | −0.496932 | − | 0.867789i | \(-0.665540\pi\) | ||||
−0.496932 | + | 0.867789i | \(0.665540\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.9244 | −1.82135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.6893 | −1.11110 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0997 | −0.639961 | −0.319980 | − | 0.947424i | \(-0.603676\pi\) | ||||
−0.319980 | + | 0.947424i | \(0.603676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27492 | −0.208347 | −0.104173 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.0000 | −1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3746 | −0.885073 | −0.442536 | − | 0.896751i | \(-0.645921\pi\) | ||||
−0.442536 | + | 0.896751i | \(0.645921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1578 | 0.872606 | 0.436303 | − | 0.899800i | \(-0.356288\pi\) | ||||
0.436303 | + | 0.899800i | \(0.356288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.6197 | 1.22556 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8248 | 1.13709 | 0.568547 | − | 0.822651i | \(-0.307506\pi\) | ||||
0.568547 | + | 0.822651i | \(0.307506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1244 | 0.576046 | 0.288023 | − | 0.957624i | \(-0.407002\pi\) | ||||
0.288023 | + | 0.957624i | \(0.407002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.0767 | 0.618507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.17525 | −0.149849 | −0.0749246 | − | 0.997189i | \(-0.523872\pi\) | ||||
−0.0749246 | + | 0.997189i | \(0.523872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.6495 | 0.925259 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.0405 | 1.03555 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.37097 | 0.0641312 | 0.0320656 | − | 0.999486i | \(-0.489791\pi\) | ||||
0.0320656 | + | 0.999486i | \(0.489791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.17525 | −0.101532 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.15068 | −0.0999505 | −0.0499752 | − | 0.998750i | \(-0.515914\pi\) | ||||
−0.0499752 | + | 0.998750i | \(0.515914\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.7035 | −0.726673 | −0.363337 | − | 0.931658i | \(-0.618363\pi\) | ||||
−0.363337 | + | 0.931658i | \(0.618363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.82475 | −0.176235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.3446 | −0.521627 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.82475 | 0.448904 | 0.224452 | − | 0.974485i | \(-0.427941\pi\) | ||||
0.224452 | + | 0.974485i | \(0.427941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1993 | −1.19459 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.93039 | −0.132789 | −0.0663943 | − | 0.997793i | \(-0.521150\pi\) | ||||
−0.0663943 | + | 0.997793i | \(0.521150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.82475 | 0.444291 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.5498 | −1.28844 | −0.644218 | − | 0.764842i | \(-0.722817\pi\) | ||||
−0.644218 | + | 0.764842i | \(0.722817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.78959 | −0.0805993 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.62541 | 0.0727635 | 0.0363818 | − | 0.999338i | \(-0.488417\pi\) | ||||
0.0363818 | + | 0.999338i | \(0.488417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.824752 | −0.0368472 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7682 | −1.41647 | −0.708236 | − | 0.705975i | \(-0.750509\pi\) | ||||
−0.708236 | + | 0.705975i | \(0.750509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.5649 | 0.469205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.4502 | −0.640492 | −0.320246 | − | 0.947334i | \(-0.603766\pi\) | ||||
−0.320246 | + | 0.947334i | \(0.603766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.0170 | 0.751318 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.3375 | 1.51016 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.4743 | 1.55715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.82475 | 0.430430 | 0.215215 | − | 0.976567i | \(-0.430955\pi\) | ||||
0.215215 | + | 0.976567i | \(0.430955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.34683 | −0.321254 | −0.160627 | − | 0.987015i | \(-0.551352\pi\) | ||||
−0.160627 | + | 0.987015i | \(0.551352\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.37097 | −0.0597203 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.1993 | 1.66084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.78523 | 0.423845 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.6005 | 0.543753 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5498 | −0.754526 | −0.377263 | − | 0.926106i | \(-0.623135\pi\) | ||||
−0.377263 | + | 0.926106i | \(0.623135\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 42.0454 | 1.80434 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.5386 | 0.878168 | 0.439084 | − | 0.898446i | \(-0.355303\pi\) | ||||
0.439084 | + | 0.898446i | \(0.355303\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0000 | 0.596420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.97368 | −0.422598 | −0.211299 | − | 0.977421i | \(-0.567769\pi\) | ||||
−0.211299 | + | 0.977421i | \(0.567769\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.64950 | −0.238949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.82475 | −0.161481 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6317 | 0.953814 | 0.476907 | − | 0.878954i | \(-0.341758\pi\) | ||||
0.476907 | + | 0.878954i | \(0.341758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.37459 | 0.351081 | 0.175540 | − | 0.984472i | \(-0.443833\pi\) | ||||
0.175540 | + | 0.984472i | \(0.443833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.27492 | 0.304446 | 0.152223 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152223 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.303539 | −0.0126805 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.88273 | 0.161640 | 0.0808200 | − | 0.996729i | \(-0.474246\pi\) | ||||
0.0808200 | + | 0.996729i | \(0.474246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.9244 | 1.53453 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.9210 | −1.23920 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.8997 | −0.862623 | −0.431311 | − | 0.902203i | \(-0.641949\pi\) | ||||
−0.431311 | + | 0.902203i | \(0.641949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7251 | 0.441919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.9003 | 0.612918 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.3851 | −1.37096 | −0.685482 | − | 0.728090i | \(-0.740408\pi\) | ||||
−0.685482 | + | 0.728090i | \(0.740408\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.9210 | −1.22459 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.27492 | 0.215527 | 0.107764 | − | 0.994177i | \(-0.465631\pi\) | ||||
0.107764 | + | 0.994177i | \(0.465631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.4022 | −0.462801 | −0.231400 | − | 0.972859i | \(-0.574331\pi\) | ||||
−0.231400 | + | 0.972859i | \(0.574331\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0997 | 0.691779 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3616 | 1.14551 | 0.572757 | − | 0.819725i | \(-0.305874\pi\) | ||||
0.572757 | + | 0.819725i | \(0.305874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.2920 | 1.25977 | 0.629884 | − | 0.776689i | \(-0.283102\pi\) | ||||
0.629884 | + | 0.776689i | \(0.283102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.92442 | −0.358703 | −0.179351 | − | 0.983785i | \(-0.557400\pi\) | ||||
−0.179351 | + | 0.983785i | \(0.557400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.6495 | 1.63121 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.9210 | 1.19493 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.17525 | −0.166478 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0997 | 1.31768 | 0.658839 | − | 0.752284i | \(-0.271048\pi\) | ||||
0.658839 | + | 0.752284i | \(0.271048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.4262 | −1.76578 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.09967 | −0.0829319 | −0.0414660 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414660 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.4071 | 1.23857 | 0.619287 | − | 0.785164i | \(-0.287422\pi\) | ||||
0.619287 | + | 0.785164i | \(0.287422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.9331 | −1.05885 | −0.529425 | − | 0.848357i | \(-0.677592\pi\) | ||||
−0.529425 | + | 0.848357i | \(0.677592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2749 | 0.678100 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.3616 | −1.10988 | −0.554938 | − | 0.831892i | \(-0.687258\pi\) | ||||
−0.554938 | + | 0.831892i | \(0.687258\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.5498 | −1.57960 | −0.789799 | − | 0.613366i | \(-0.789815\pi\) | ||||
−0.789799 | + | 0.613366i | \(0.789815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.450166 | −0.0175094 | −0.00875471 | − | 0.999962i | \(-0.502787\pi\) | ||||
−0.00875471 | + | 0.999962i | \(0.502787\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.90468 | −0.0739717 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.4427 | 1.29491 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0997 | −0.583787 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 71.4743 | 2.75923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.2920 | 1.20622 | 0.603109 | − | 0.797659i | \(-0.293928\pi\) | ||||
0.603109 | + | 0.797659i | \(0.293928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.4043 | −1.78346 | −0.891731 | − | 0.452566i | \(-0.850509\pi\) | ||||
−0.891731 | + | 0.452566i | \(0.850509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.8248 | −1.29617 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.1676 | −0.733430 | −0.366715 | − | 0.930333i | \(-0.619518\pi\) | ||||
−0.366715 | + | 0.930333i | \(0.619518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.67232 | −0.216413 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.9003 | −0.567657 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3746 | 1.15550 | 0.577752 | − | 0.816212i | \(-0.303930\pi\) | ||||
0.577752 | + | 0.816212i | \(0.303930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.55942 | 0.0590672 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.7251 | 0.935189 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.82475 | 0.333306 | 0.166653 | − | 0.986016i | \(-0.446704\pi\) | ||||
0.166653 | + | 0.986016i | \(0.446704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.6630 | 1.23191 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4502 | −0.392464 | −0.196232 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196232 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.6197 | 0.959465 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.952341 | −0.0355658 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.3746 | −1.13278 | −0.566390 | − | 0.824137i | \(-0.691661\pi\) | ||||
−0.566390 | + | 0.824137i | \(0.691661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.0170 | −0.632868 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.10302 | −0.115085 | −0.0575423 | − | 0.998343i | \(-0.518326\pi\) | ||||
−0.0575423 | + | 0.998343i | \(0.518326\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.900331 | −0.0332999 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.6865 | −1.39198 | −0.695991 | − | 0.718050i | \(-0.745035\pi\) | ||||
−0.695991 | + | 0.718050i | \(0.745035\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.5764 | 0.684270 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.9244 | −0.769717 | −0.384859 | − | 0.922976i | \(-0.625750\pi\) | ||||
−0.384859 | + | 0.922976i | \(0.625750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.9003 | 0.547377 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.45203 | 0.236702 | 0.118351 | − | 0.992972i | \(-0.462239\pi\) | ||||
0.118351 | + | 0.992972i | \(0.462239\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7251 | −0.537326 | −0.268663 | − | 0.963234i | \(-0.586582\pi\) | ||||
−0.268663 | + | 0.963234i | \(0.586582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.5934 | 1.29709 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.5934 | −1.29366 | −0.646831 | − | 0.762633i | \(-0.723906\pi\) | ||||
−0.646831 | + | 0.762633i | \(0.723906\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 71.4743 | 2.59435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.9244 | 0.831010 | 0.415505 | − | 0.909591i | \(-0.363605\pi\) | ||||
0.415505 | + | 0.909591i | \(0.363605\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.60271 | 0.310626 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1752 | −0.726594 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.3133 | 1.44997 | 0.724985 | − | 0.688765i | \(-0.241847\pi\) | ||||
0.724985 | + | 0.688765i | \(0.241847\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.1993 | −0.437087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.2131 | 0.793832 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73205 | 0.0617409 | 0.0308705 | − | 0.999523i | \(-0.490172\pi\) | ||||
0.0308705 | + | 0.999523i | \(0.490172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.35050 | 0.0480790 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.5934 | 1.26396 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.8229 | 1.65855 | 0.829276 | − | 0.558839i | \(-0.188753\pi\) | ||||
0.829276 | + | 0.558839i | \(0.188753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.72508 | 0.0964065 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.3375 | 1.21174 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.0284 | 0.881042 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.1993 | −0.604697 | −0.302348 | − | 0.953198i | \(-0.597771\pi\) | ||||
−0.302348 | + | 0.953198i | \(0.597771\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.45017 | 0.261611 | 0.130805 | − | 0.991408i | \(-0.458244\pi\) | ||||
0.130805 | + | 0.991408i | \(0.458244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.0170 | −0.596811 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.04329 | 0.246414 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.3746 | −0.711078 | −0.355539 | − | 0.934661i | \(-0.615703\pi\) | ||||
−0.355539 | + | 0.934661i | \(0.615703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.1583 | −1.60898 | −0.804488 | − | 0.593968i | \(-0.797560\pi\) | ||||
−0.804488 | + | 0.593968i | \(0.797560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0547 | 0.523505 | 0.261752 | − | 0.965135i | \(-0.415700\pi\) | ||||
0.261752 | + | 0.965135i | \(0.415700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.9244 | −1.76868 | −0.884339 | − | 0.466845i | \(-0.845391\pi\) | ||||
−0.884339 | + | 0.466845i | \(0.845391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7251 | 0.857704 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.0170 | 0.588192 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.0997 | 1.41892 | 0.709459 | − | 0.704747i | \(-0.248939\pi\) | ||||
0.709459 | + | 0.704747i | \(0.248939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7251 | −0.369830 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.3923 | −0.357930 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.9244 | 0.649484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 78.0241 | 2.67463 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.1342 | −0.449708 | −0.224854 | − | 0.974392i | \(-0.572190\pi\) | ||||
−0.224854 | + | 0.974392i | \(0.572190\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.6865 | −1.28735 | −0.643673 | − | 0.765301i | \(-0.722590\pi\) | ||||
−0.643673 | + | 0.765301i | \(0.722590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.37459 | −0.0810198 | −0.0405099 | − | 0.999179i | \(-0.512898\pi\) | ||||
−0.0405099 | + | 0.999179i | \(0.512898\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.4257 | 0.559138 | 0.279569 | − | 0.960126i | \(-0.409808\pi\) | ||||
0.279569 | + | 0.960126i | \(0.409808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.1413 | 0.989691 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.3746 | −1.30177 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.25083 | 0.313452 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.8777 | 0.772527 | 0.386263 | − | 0.922389i | \(-0.373766\pi\) | ||||
0.386263 | + | 0.922389i | \(0.373766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000 | 0.404750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.0241 | −1.44952 | −0.724759 | − | 0.689002i | \(-0.758049\pi\) | ||||
−0.724759 | + | 0.689002i | \(0.758049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.5407 | −1.86909 | −0.934547 | − | 0.355840i | \(-0.884195\pi\) | ||||
−0.934547 | + | 0.355840i | \(0.884195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.2301 | 1.31722 | 0.658609 | − | 0.752486i | \(-0.271145\pi\) | ||||
0.658609 | + | 0.752486i | \(0.271145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.4743 | 1.59045 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.3183 | −0.713391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35.5934 | 1.18843 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.0000 | 0.466926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.37459 | −0.0791089 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.8569 | 1.38984 | 0.694918 | − | 0.719089i | \(-0.255440\pi\) | ||||
0.694918 | + | 0.719089i | \(0.255440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0997 | −0.831589 | −0.415795 | − | 0.909459i | \(-0.636496\pi\) | ||||
−0.415795 | + | 0.909459i | \(0.636496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.0575 | −1.29261 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.9244 | −1.54789 | −0.773947 | − | 0.633250i | \(-0.781720\pi\) | ||||
−0.773947 | + | 0.633250i | \(0.781720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.9244 | 1.51326 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.9517 | 0.393396 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.0997 | −1.57810 | −0.789049 | − | 0.614330i | \(-0.789427\pi\) | ||||
−0.789049 | + | 0.614330i | \(0.789427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.0170 | 0.557111 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.3638 | −0.795931 | −0.397965 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397965 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −58.0241 | −1.89354 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.27492 | −0.106759 | −0.0533796 | − | 0.998574i | \(-0.516999\pi\) | ||||
−0.0533796 | + | 0.998574i | \(0.516999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.1413 | −0.948972 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.5649 | 0.343314 | 0.171657 | − | 0.985157i | \(-0.445088\pi\) | ||||
0.171657 | + | 0.985157i | \(0.445088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.0997 | 0.555079 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.3746 | 1.43894 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.6893 | −0.734978 | −0.367489 | − | 0.930028i | \(-0.619782\pi\) | ||||
−0.367489 | + | 0.930028i | \(0.619782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 39.0575 | 1.26255 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2749 | −0.654030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.15068 | 0.0691611 | 0.0345806 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345806 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.37459 | 0.0762827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.9244 | −1.18496 | −0.592481 | − | 0.805585i | \(-0.701851\pi\) | ||||
−0.592481 | + | 0.805585i | \(0.701851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.9210 | 0.957259 | 0.478629 | − | 0.878017i | \(-0.341134\pi\) | ||||
0.478629 | + | 0.878017i | \(0.341134\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.9244 | 1.18011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.9281 | −1.46488 | −0.732440 | − | 0.680832i | \(-0.761618\pi\) | ||||
−0.732440 | + | 0.680832i | \(0.761618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.8248 | 0.534996 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.4743 | 1.06334 | 0.531672 | − | 0.846950i | \(-0.321564\pi\) | ||||
0.531672 | + | 0.846950i | \(0.321564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.8734 | −0.979737 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.418627 | −0.0132580 | −0.00662902 | − | 0.999978i | \(-0.502110\pi\) | ||||
−0.00662902 | + | 0.999978i | \(0.502110\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.8248 | 1.63966 |
(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 | 4900.2.a.be.1.1 | 4 | ||
5.2 | odd | 4 | 980.2.e.f.589.3 | 4 | |||
5.3 | odd | 4 | 980.2.e.f.589.1 | 4 | |||
5.4 | even | 2 | inner | 4900.2.a.be.1.3 | 4 | ||
7.2 | even | 3 | 700.2.i.f.501.3 | 8 | |||
7.4 | even | 3 | 700.2.i.f.401.3 | 8 | |||
7.6 | odd | 2 | 4900.2.a.bf.1.3 | 4 | |||
35.2 | odd | 12 | 140.2.q.a.109.2 | yes | 4 | ||
35.3 | even | 12 | 980.2.q.g.569.1 | 4 | |||
35.4 | even | 6 | 700.2.i.f.401.2 | 8 | |||
35.9 | even | 6 | 700.2.i.f.501.2 | 8 | |||
35.12 | even | 12 | 980.2.q.g.949.1 | 4 | |||
35.13 | even | 4 | 980.2.e.c.589.4 | 4 | |||
35.17 | even | 12 | 980.2.q.b.569.2 | 4 | |||
35.18 | odd | 12 | 140.2.q.a.9.2 | ✓ | 4 | ||
35.23 | odd | 12 | 140.2.q.b.109.2 | yes | 4 | ||
35.27 | even | 4 | 980.2.e.c.589.2 | 4 | |||
35.32 | odd | 12 | 140.2.q.b.9.1 | yes | 4 | ||
35.33 | even | 12 | 980.2.q.b.949.1 | 4 | |||
35.34 | odd | 2 | 4900.2.a.bf.1.1 | 4 | |||
105.2 | even | 12 | 1260.2.bm.a.109.1 | 4 | |||
105.23 | even | 12 | 1260.2.bm.b.109.1 | 4 | |||
105.32 | even | 12 | 1260.2.bm.b.289.2 | 4 | |||
105.53 | even | 12 | 1260.2.bm.a.289.1 | 4 | |||
140.23 | even | 12 | 560.2.bw.a.529.2 | 4 | |||
140.67 | even | 12 | 560.2.bw.a.289.1 | 4 | |||
140.107 | even | 12 | 560.2.bw.e.529.2 | 4 | |||
140.123 | even | 12 | 560.2.bw.e.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.q.a.9.2 | ✓ | 4 | 35.18 | odd | 12 | ||
140.2.q.a.109.2 | yes | 4 | 35.2 | odd | 12 | ||
140.2.q.b.9.1 | yes | 4 | 35.32 | odd | 12 | ||
140.2.q.b.109.2 | yes | 4 | 35.23 | odd | 12 | ||
560.2.bw.a.289.1 | 4 | 140.67 | even | 12 | |||
560.2.bw.a.529.2 | 4 | 140.23 | even | 12 | |||
560.2.bw.e.289.2 | 4 | 140.123 | even | 12 | |||
560.2.bw.e.529.2 | 4 | 140.107 | even | 12 | |||
700.2.i.f.401.2 | 8 | 35.4 | even | 6 | |||
700.2.i.f.401.3 | 8 | 7.4 | even | 3 | |||
700.2.i.f.501.2 | 8 | 35.9 | even | 6 | |||
700.2.i.f.501.3 | 8 | 7.2 | even | 3 | |||
980.2.e.c.589.2 | 4 | 35.27 | even | 4 | |||
980.2.e.c.589.4 | 4 | 35.13 | even | 4 | |||
980.2.e.f.589.1 | 4 | 5.3 | odd | 4 | |||
980.2.e.f.589.3 | 4 | 5.2 | odd | 4 | |||
980.2.q.b.569.2 | 4 | 35.17 | even | 12 | |||
980.2.q.b.949.1 | 4 | 35.33 | even | 12 | |||
980.2.q.g.569.1 | 4 | 35.3 | even | 12 | |||
980.2.q.g.949.1 | 4 | 35.12 | even | 12 | |||
1260.2.bm.a.109.1 | 4 | 105.2 | even | 12 | |||
1260.2.bm.a.289.1 | 4 | 105.53 | even | 12 | |||
1260.2.bm.b.109.1 | 4 | 105.23 | even | 12 | |||
1260.2.bm.b.289.2 | 4 | 105.32 | even | 12 | |||
4900.2.a.be.1.1 | 4 | 1.1 | even | 1 | trivial | ||
4900.2.a.be.1.3 | 4 | 5.4 | even | 2 | inner | ||
4900.2.a.bf.1.1 | 4 | 35.34 | odd | 2 | |||
4900.2.a.bf.1.3 | 4 | 7.6 | odd | 2 |