Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,3,Mod(1135,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.1135");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.g (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(54.9320212950\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1135.1 | ||
Root | \(-0.707107 + 1.87083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.1135 |
Dual form | 2016.3.g.a.1135.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 9.03316i | − 1.80663i | −0.428976 | − | 0.903316i | \(-0.641125\pi\) | ||||
0.428976 | − | 0.903316i | \(-0.358875\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.4853 | 1.13503 | 0.567513 | − | 0.823365i | \(-0.307906\pi\) | ||||
0.567513 | + | 0.823365i | \(0.307906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 9.03316i | − 0.694858i | −0.937706 | − | 0.347429i | \(-0.887055\pi\) | ||||
0.937706 | − | 0.347429i | \(-0.112945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.3431 | −0.726067 | −0.363034 | − | 0.931776i | \(-0.618259\pi\) | ||||
−0.363034 | + | 0.931776i | \(0.618259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.8701 | −1.51948 | −0.759738 | − | 0.650229i | \(-0.774673\pi\) | ||||
−0.759738 | + | 0.650229i | \(0.774673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 24.6418i | − 1.07138i | −0.844414 | − | 0.535690i | \(-0.820051\pi\) | ||||
0.844414 | − | 0.535690i | \(-0.179949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −56.5980 | −2.26392 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 22.4499i | − 0.774136i | −0.922051 | − | 0.387068i | \(-0.873488\pi\) | ||||
0.922051 | − | 0.387068i | \(-0.126512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.7824i | 0.541367i | 0.962668 | + | 0.270684i | \(0.0872497\pi\) | ||||
−0.962668 | + | 0.270684i | \(0.912750\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −23.8995 | −0.682843 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.2506i | 0.439204i | 0.975589 | + | 0.219602i | \(0.0704759\pi\) | ||||
−0.975589 | + | 0.219602i | \(0.929524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.97056 | −0.170014 | −0.0850069 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850069 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.8284 | 0.530894 | 0.265447 | − | 0.964126i | \(-0.414481\pi\) | ||||
0.265447 | + | 0.964126i | \(0.414481\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 6.19938i | − 0.131902i | −0.997823 | − | 0.0659509i | \(-0.978992\pi\) | ||||
0.997823 | − | 0.0659509i | \(-0.0210081\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.01514i | − 0.151229i | −0.997137 | − | 0.0756145i | \(-0.975908\pi\) | ||||
0.997137 | − | 0.0756145i | \(-0.0240918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 112.782i | − 2.05057i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30.4437 | 0.515994 | 0.257997 | − | 0.966146i | \(-0.416938\pi\) | ||||
0.257997 | + | 0.966146i | \(0.416938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 15.2325i | − 0.249714i | −0.992175 | − | 0.124857i | \(-0.960153\pi\) | ||||
0.992175 | − | 0.124857i | \(-0.0398472\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −81.5980 | −1.25535 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 78.6274 | 1.17354 | 0.586772 | − | 0.809752i | \(-0.300399\pi\) | ||||
0.586772 | + | 0.809752i | \(0.300399\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 17.5345i | − 0.246965i | −0.992347 | − | 0.123482i | \(-0.960594\pi\) | ||||
0.992347 | − | 0.123482i | \(-0.0394062\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 46.6863 | 0.639538 | 0.319769 | − | 0.947495i | \(-0.396395\pi\) | ||||
0.319769 | + | 0.947495i | \(0.396395\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 33.0329i | − 0.428999i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 81.0325i | 1.02573i | 0.858470 | + | 0.512864i | \(0.171416\pi\) | ||||
−0.858470 | + | 0.512864i | \(0.828584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 40.3848 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 111.498i | 1.31174i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −111.941 | −1.25777 | −0.628883 | − | 0.777500i | \(-0.716487\pi\) | ||||
−0.628883 | + | 0.777500i | \(0.716487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.8995 | −0.262632 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 260.788i | 2.74514i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −164.108 | −1.69183 | −0.845916 | − | 0.533317i | \(-0.820945\pi\) | ||||
−0.845916 | + | 0.533317i | \(0.820945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 12.1329i | − 0.120127i | −0.998195 | − | 0.0600636i | \(-0.980870\pi\) | ||||
0.998195 | − | 0.0600636i | \(-0.0191304\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 106.582i | 1.03478i | 0.855750 | + | 0.517389i | \(0.173096\pi\) | ||||
−0.855750 | + | 0.517389i | \(0.826904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −63.5980 | −0.594374 | −0.297187 | − | 0.954819i | \(-0.596048\pi\) | ||||
−0.297187 | + | 0.954819i | \(0.596048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 130.848i | − 1.20044i | −0.799835 | − | 0.600220i | \(-0.795080\pi\) | ||||
0.799835 | − | 0.600220i | \(-0.204920\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 138.225 | 1.22323 | 0.611617 | − | 0.791154i | \(-0.290519\pi\) | ||||
0.611617 | + | 0.791154i | \(0.290519\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −222.593 | −1.93559 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.6569i | 0.274428i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.8823 | 0.288283 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 285.430i | 2.28344i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 114.442i | 0.901114i | 0.892748 | + | 0.450557i | \(0.148775\pi\) | ||||
−0.892748 | + | 0.450557i | \(0.851225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −168.350 | −1.28512 | −0.642558 | − | 0.766237i | \(-0.722127\pi\) | ||||
−0.642558 | + | 0.766237i | \(0.722127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 76.3830i | 0.574308i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −34.6863 | −0.253185 | −0.126592 | − | 0.991955i | \(-0.540404\pi\) | ||||
−0.126592 | + | 0.991955i | \(0.540404\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −107.664 | −0.774561 | −0.387281 | − | 0.921962i | \(-0.626586\pi\) | ||||
−0.387281 | + | 0.921962i | \(0.626586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 112.782i | − 0.788682i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −202.794 | −1.39858 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 252.176i | − 1.69246i | −0.532819 | − | 0.846229i | \(-0.678867\pi\) | ||||
0.532819 | − | 0.846229i | \(-0.321133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 234.486i | 1.55289i | 0.630186 | + | 0.776444i | \(0.282979\pi\) | ||||
−0.630186 | + | 0.776444i | \(0.717021\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 151.598 | 0.978051 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.0968i | − 0.0643109i | −0.999483 | − | 0.0321554i | \(-0.989763\pi\) | ||||
0.999483 | − | 0.0321554i | \(-0.0102372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −65.1960 | −0.404944 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −104.534 | −0.641313 | −0.320657 | − | 0.947196i | \(-0.603904\pi\) | ||||
−0.320657 | + | 0.947196i | \(0.603904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 296.765i | 1.77703i | 0.458843 | + | 0.888517i | \(0.348264\pi\) | ||||
−0.458843 | + | 0.888517i | \(0.651736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.4020 | 0.517172 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 40.0301i | 0.231388i | 0.993285 | + | 0.115694i | \(0.0369091\pi\) | ||||
−0.993285 | + | 0.115694i | \(0.963091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 149.744i | 0.855681i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 294.794 | 1.64689 | 0.823447 | − | 0.567394i | \(-0.192048\pi\) | ||||
0.823447 | + | 0.567394i | \(0.192048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 40.4706i | − 0.223595i | −0.993731 | − | 0.111797i | \(-0.964339\pi\) | ||||
0.993731 | − | 0.111797i | \(-0.0356608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 146.794 | 0.793481 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −154.108 | −0.824105 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 156.929i | 0.821619i | 0.911721 | + | 0.410810i | \(0.134754\pi\) | ||||
−0.911721 | + | 0.410810i | \(0.865246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −261.304 | −1.35390 | −0.676952 | − | 0.736027i | \(-0.736700\pi\) | ||||
−0.676952 | + | 0.736027i | \(0.736700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 145.283i | − 0.737475i | −0.929533 | − | 0.368738i | \(-0.879790\pi\) | ||||
0.929533 | − | 0.368738i | \(-0.120210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 390.508i | − 1.96235i | −0.193122 | − | 0.981175i | \(-0.561861\pi\) | ||||
0.193122 | − | 0.981175i | \(-0.438139\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −59.3970 | −0.292596 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 62.9662i | 0.307152i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −360.451 | −1.72464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 164.049 | 0.777482 | 0.388741 | − | 0.921347i | \(-0.372910\pi\) | ||||
0.388741 | + | 0.921347i | \(0.372910\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 206.213i | − 0.959129i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 44.4020 | 0.204618 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 111.498i | 0.504514i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 10.5830i | − 0.0474574i | −0.999718 | − | 0.0237287i | \(-0.992446\pi\) | ||||
0.999718 | − | 0.0237287i | \(-0.00755379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −213.806 | −0.941877 | −0.470939 | − | 0.882166i | \(-0.656085\pi\) | ||||
−0.470939 | + | 0.882166i | \(0.656085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 232.028i | 1.01322i | 0.862174 | + | 0.506612i | \(0.169102\pi\) | ||||
−0.862174 | + | 0.506612i | \(0.830898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 192.863 | 0.827738 | 0.413869 | − | 0.910336i | \(-0.364177\pi\) | ||||
0.413869 | + | 0.910336i | \(0.364177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −56.0000 | −0.238298 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 327.917i | − 1.37204i | −0.727583 | − | 0.686020i | \(-0.759356\pi\) | ||||
0.727583 | − | 0.686020i | \(-0.240644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 71.8721 | 0.298225 | 0.149112 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149112 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 63.2321i | 0.258090i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 260.788i | 1.05582i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −256.919 | −1.02358 | −0.511790 | − | 0.859110i | \(-0.671018\pi\) | ||||
−0.511790 | + | 0.859110i | \(0.671018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 307.659i | − 1.21604i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −319.352 | −1.24262 | −0.621308 | − | 0.783566i | \(-0.713398\pi\) | ||||
−0.621308 | + | 0.783566i | \(0.713398\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 42.9949 | 0.166004 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 377.357i | − 1.43482i | −0.696653 | − | 0.717408i | \(-0.745328\pi\) | ||||
0.696653 | − | 0.717408i | \(-0.254672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −72.4020 | −0.273215 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 28.1631i | − 0.104696i | −0.998629 | − | 0.0523478i | \(-0.983330\pi\) | ||||
0.998629 | − | 0.0523478i | \(-0.0166704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 399.715i | − 1.47496i | −0.675367 | − | 0.737482i | \(-0.736015\pi\) | ||||
0.675367 | − | 0.737482i | \(-0.263985\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −706.642 | −2.56961 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 102.951i | − 0.371663i | −0.982582 | − | 0.185831i | \(-0.940502\pi\) | ||||
0.982582 | − | 0.185831i | \(-0.0594979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 150.235 | 0.534646 | 0.267323 | − | 0.963607i | \(-0.413861\pi\) | ||||
0.267323 | + | 0.963607i | \(0.413861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 178.561 | 0.630959 | 0.315480 | − | 0.948932i | \(-0.397835\pi\) | ||||
0.315480 | + | 0.948932i | \(0.397835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.4424i | 0.0642591i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −136.647 | −0.472826 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 219.189i | 0.748085i | 0.927411 | + | 0.374043i | \(0.122029\pi\) | ||||
−0.927411 | + | 0.374043i | \(0.877971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 275.002i | − 0.932211i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −222.593 | −0.744458 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 60.3983i | − 0.200659i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −137.598 | −0.451141 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −316.669 | −1.03150 | −0.515748 | − | 0.856741i | \(-0.672486\pi\) | ||||
−0.515748 | + | 0.856741i | \(0.672486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 72.2653i | 0.232364i | 0.993228 | + | 0.116182i | \(0.0370656\pi\) | ||||
−0.993228 | + | 0.116182i | \(0.962934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 81.9512 | 0.261825 | 0.130913 | − | 0.991394i | \(-0.458209\pi\) | ||||
0.130913 | + | 0.991394i | \(0.458209\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 109.150i | 0.344322i | 0.985069 | + | 0.172161i | \(0.0550749\pi\) | ||||
−0.985069 | + | 0.172161i | \(0.944925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 280.294i | − 0.878664i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 356.347 | 1.10324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 511.259i | 1.57310i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.4020 | −0.0498542 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −321.740 | −0.972025 | −0.486012 | − | 0.873952i | \(-0.661549\pi\) | ||||
−0.486012 | + | 0.873952i | \(0.661549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 710.254i | − 2.12016i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −164.049 | −0.486792 | −0.243396 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243396 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 209.533i | 0.614466i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −330.309 | −0.951898 | −0.475949 | − | 0.879473i | \(-0.657895\pi\) | ||||
−0.475949 | + | 0.879473i | \(0.657895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 262.402i | 0.751869i | 0.926646 | + | 0.375934i | \(0.122678\pi\) | ||||
−0.926646 | + | 0.375934i | \(0.877322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 578.098 | 1.63767 | 0.818835 | − | 0.574029i | \(-0.194620\pi\) | ||||
0.818835 | + | 0.574029i | \(0.194620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −158.392 | −0.446174 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 365.114i | 1.01703i | 0.861053 | + | 0.508515i | \(0.169805\pi\) | ||||
−0.861053 | + | 0.508515i | \(0.830195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 472.480 | 1.30881 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 421.725i | − 1.15541i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 520.071i | 1.41709i | 0.705666 | + | 0.708544i | \(0.250648\pi\) | ||||
−0.705666 | + | 0.708544i | \(0.749352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.2061 | −0.0571592 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 526.711i | 1.41210i | 0.708164 | + | 0.706048i | \(0.249524\pi\) | ||||
−0.708164 | + | 0.706048i | \(0.750476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −202.794 | −0.537915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −121.976 | −0.321835 | −0.160918 | − | 0.986968i | \(-0.551445\pi\) | ||||
−0.160918 | + | 0.986968i | \(0.551445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 316.427i | 0.826179i | 0.910690 | + | 0.413089i | \(0.135550\pi\) | ||||
−0.910690 | + | 0.413089i | \(0.864450\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −298.392 | −0.775044 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 92.1474i | 0.236883i | 0.992961 | + | 0.118441i | \(0.0377898\pi\) | ||||
−0.992961 | + | 0.118441i | \(0.962210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 304.157i | 0.777895i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 731.980 | 1.85311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 562.267i | − 1.41629i | −0.706068 | − | 0.708144i | \(-0.749533\pi\) | ||||
0.706068 | − | 0.708144i | \(-0.250467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −81.2061 | −0.202509 | −0.101254 | − | 0.994861i | \(-0.532286\pi\) | ||||
−0.101254 | + | 0.994861i | \(0.532286\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 151.598 | 0.376174 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 202.893i | 0.498508i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 450.735 | 1.10204 | 0.551021 | − | 0.834491i | \(-0.314238\pi\) | ||||
0.551021 | + | 0.834491i | \(0.314238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 80.5463i | − 0.195027i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 364.802i | − 0.879041i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 624.988 | 1.49162 | 0.745809 | − | 0.666160i | \(-0.232063\pi\) | ||||
0.745809 | + | 0.666160i | \(0.232063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 566.476i | − 1.34555i | −0.739848 | − | 0.672774i | \(-0.765103\pi\) | ||||
0.739848 | − | 0.672774i | \(-0.234897\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 698.597 | 1.64376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.3015 | −0.0943829 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 289.528i | − 0.671760i | −0.941905 | − | 0.335880i | \(-0.890966\pi\) | ||||
0.941905 | − | 0.335880i | \(-0.109034\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −597.696 | −1.38036 | −0.690180 | − | 0.723638i | \(-0.742468\pi\) | ||||
−0.690180 | + | 0.723638i | \(0.742468\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 711.409i | 1.62794i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 38.3890i | − 0.0874464i | −0.999044 | − | 0.0437232i | \(-0.986078\pi\) | ||||
0.999044 | − | 0.0437232i | \(-0.0139220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 599.058 | 1.35228 | 0.676138 | − | 0.736775i | \(-0.263652\pi\) | ||||
0.676138 | + | 0.736775i | \(0.263652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1011.18i | 2.27232i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 460.039 | 1.02459 | 0.512293 | − | 0.858811i | \(-0.328796\pi\) | ||||
0.512293 | + | 0.858811i | \(0.328796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −87.0294 | −0.192970 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 215.888i | 0.474479i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 266.323 | 0.582764 | 0.291382 | − | 0.956607i | \(-0.405885\pi\) | ||||
0.291382 | + | 0.956607i | \(0.405885\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 763.123i | − 1.65537i | −0.561196 | − | 0.827683i | \(-0.689659\pi\) | ||||
0.561196 | − | 0.827683i | \(-0.310341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 123.988i | 0.267792i | 0.990995 | + | 0.133896i | \(0.0427488\pi\) | ||||
−0.990995 | + | 0.133896i | \(0.957251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −768.718 | −1.64608 | −0.823038 | − | 0.567986i | \(-0.807723\pi\) | ||||
−0.823038 | + | 0.567986i | \(0.807723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 208.029i | − 0.443558i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 285.019 | 0.602578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1633.99 | 3.43997 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 118.981i | 0.248394i | 0.992258 | + | 0.124197i | \(0.0396355\pi\) | ||||
−0.992258 | + | 0.124197i | \(0.960364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 146.794 | 0.305185 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1482.41i | 3.05652i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 282.577i | − 0.580240i | −0.956990 | − | 0.290120i | \(-0.906305\pi\) | ||||
0.956990 | − | 0.290120i | \(-0.0936952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −388.049 | −0.790323 | −0.395162 | − | 0.918612i | \(-0.629311\pi\) | ||||
−0.395162 | + | 0.918612i | \(0.629311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 277.103i | 0.562075i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.3919 | −0.0933439 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.7157 | 0.0555425 | 0.0277713 | − | 0.999614i | \(-0.491159\pi\) | ||||
0.0277713 | + | 0.999614i | \(0.491159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 727.477i | − 1.44628i | −0.690703 | − | 0.723138i | \(-0.742699\pi\) | ||||
0.690703 | − | 0.723138i | \(-0.257301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −109.598 | −0.217026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 634.183i | − 1.24594i | −0.782246 | − | 0.622969i | \(-0.785926\pi\) | ||||
0.782246 | − | 0.622969i | \(-0.214074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 123.520i | − 0.241723i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 962.774 | 1.86946 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 77.4010i | − 0.149712i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −833.127 | −1.59909 | −0.799546 | − | 0.600605i | \(-0.794927\pi\) | ||||
−0.799546 | + | 0.600605i | \(0.794927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −876.434 | −1.67578 | −0.837891 | − | 0.545838i | \(-0.816211\pi\) | ||||
−0.837891 | + | 0.545838i | \(0.816211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 207.147i | − 0.393069i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −78.2162 | −0.147857 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 62.9662i | 0.118135i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 574.491i | 1.07381i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −87.3970 | −0.162147 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 405.915i | − 0.750305i | −0.926963 | − | 0.375152i | \(-0.877590\pi\) | ||||
0.926963 | − | 0.375152i | \(-0.122410\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1181.97 | −2.16875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 606.024 | 1.10791 | 0.553953 | − | 0.832548i | \(-0.313119\pi\) | ||||
0.553953 | + | 0.832548i | \(0.313119\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 648.131i | 1.17628i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 214.392 | 0.387689 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 36.4442i | − 0.0654294i | −0.999465 | − | 0.0327147i | \(-0.989585\pi\) | ||||
0.999465 | − | 0.0327147i | \(-0.0104153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 206.213i | − 0.368896i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −186.389 | −0.331064 | −0.165532 | − | 0.986204i | \(-0.552934\pi\) | ||||
−0.165532 | + | 0.986204i | \(0.552934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1248.61i | − 2.20993i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 670.891 | 1.17907 | 0.589536 | − | 0.807742i | \(-0.299311\pi\) | ||||
0.589536 | + | 0.807742i | \(0.299311\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 677.082 | 1.18578 | 0.592892 | − | 0.805282i | \(-0.297986\pi\) | ||||
0.592892 | + | 0.805282i | \(0.297986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1394.67i | 2.42552i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 927.901 | 1.60815 | 0.804073 | − | 0.594530i | \(-0.202662\pi\) | ||||
0.804073 | + | 0.594530i | \(0.202662\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 106.848i | − 0.183904i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 100.071i | − 0.171649i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −321.120 | −0.547053 | −0.273526 | − | 0.961865i | \(-0.588190\pi\) | ||||
−0.273526 | + | 0.961865i | \(0.588190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 484.508i | − 0.822595i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 219.255 | 0.369738 | 0.184869 | − | 0.982763i | \(-0.440814\pi\) | ||||
0.184869 | + | 0.982763i | \(0.440814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 294.995 | 0.495790 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 154.802i | 0.258434i | 0.991616 | + | 0.129217i | \(0.0412464\pi\) | ||||
−0.991616 | + | 0.129217i | \(0.958754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 205.862 | 0.342533 | 0.171266 | − | 0.985225i | \(-0.445214\pi\) | ||||
0.171266 | + | 0.985225i | \(0.445214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 315.097i | − 0.520821i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 790.663i | − 1.30258i | −0.758831 | − | 0.651288i | \(-0.774229\pi\) | ||||
0.758831 | − | 0.651288i | \(-0.225771\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −56.0000 | −0.0916530 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 741.471i | 1.20958i | 0.796386 | + | 0.604789i | \(0.206743\pi\) | ||||
−0.796386 | + | 0.604789i | \(0.793257\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −171.578 | −0.278084 | −0.139042 | − | 0.990286i | \(-0.544402\pi\) | ||||
−0.139042 | + | 0.990286i | \(0.544402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 540.198 | 0.872695 | 0.436347 | − | 0.899778i | \(-0.356272\pi\) | ||||
0.436347 | + | 0.899778i | \(0.356272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 296.168i | 0.475391i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1163.38 | 1.86141 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 200.583i | − 0.318892i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 269.399i | − 0.426940i | −0.976950 | − | 0.213470i | \(-0.931523\pi\) | ||||
0.976950 | − | 0.213470i | \(-0.0684766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1033.77 | 1.62798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 63.2321i | 0.0992655i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.1867 | −0.0564535 | −0.0282268 | − | 0.999602i | \(-0.508986\pi\) | ||||
−0.0282268 | + | 0.999602i | \(0.508986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −266.297 | −0.414148 | −0.207074 | − | 0.978325i | \(-0.566394\pi\) | ||||
−0.207074 | + | 0.978325i | \(0.566394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1086.24i | − 1.67888i | −0.543452 | − | 0.839440i | \(-0.682883\pi\) | ||||
0.543452 | − | 0.839440i | \(-0.317117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 380.098 | 0.585666 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1195.35i | − 1.83055i | −0.402832 | − | 0.915274i | \(-0.631974\pi\) | ||||
0.402832 | − | 0.915274i | \(-0.368026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1520.74i | 2.32173i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −685.220 | −1.03979 | −0.519894 | − | 0.854231i | \(-0.674029\pi\) | ||||
−0.519894 | + | 0.854231i | \(0.674029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 993.382i | − 1.50285i | −0.659820 | − | 0.751423i | \(-0.729368\pi\) | ||||
0.659820 | − | 0.751423i | \(-0.270632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 689.980 | 1.03756 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −553.206 | −0.829394 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 190.183i | − 0.283432i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 106.569 | 0.158349 | 0.0791743 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791743 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1004.18i | − 1.48329i | −0.670795 | − | 0.741643i | \(-0.734047\pi\) | ||||
0.670795 | − | 0.741643i | \(-0.265953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 434.188i | 0.639452i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −678.225 | −0.993009 | −0.496505 | − | 0.868034i | \(-0.665383\pi\) | ||||
−0.496505 | + | 0.868034i | \(0.665383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 313.327i | 0.457411i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −72.4020 | −0.105083 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 365.175 | 0.528473 | 0.264236 | − | 0.964458i | \(-0.414880\pi\) | ||||
0.264236 | + | 0.964458i | \(0.414880\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 972.546i | 1.39935i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 86.0387 | 0.123441 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 940.292i | − 1.34136i | −0.741748 | − | 0.670679i | \(-0.766003\pi\) | ||||
0.741748 | − | 0.670679i | \(-0.233997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 469.155i | − 0.667361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.1005 | −0.0454038 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1057.46i | − 1.49148i | −0.666239 | − | 0.745738i | \(-0.732097\pi\) | ||||
0.666239 | − | 0.745738i | \(-0.267903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 413.547 | 0.580010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1018.77 | −1.42486 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1034.82i | − 1.43926i | −0.694360 | − | 0.719628i | \(-0.744312\pi\) | ||||
0.694360 | − | 0.719628i | \(-0.255688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 281.990 | 0.391109 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1270.62i | 1.75258i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 495.145i | 0.681080i | 0.940230 | + | 0.340540i | \(0.110610\pi\) | ||||
−0.940230 | + | 0.340540i | \(0.889390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −281.775 | −0.385465 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 567.494i | − 0.774207i | −0.922036 | − | 0.387103i | \(-0.873476\pi\) | ||||
0.922036 | − | 0.387103i | \(-0.126524\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 981.685 | 1.33200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 544.701 | 0.737078 | 0.368539 | − | 0.929612i | \(-0.379858\pi\) | ||||
0.368539 | + | 0.929612i | \(0.379858\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 731.264i | − 0.984205i | −0.870537 | − | 0.492102i | \(-0.836229\pi\) | ||||
0.870537 | − | 0.492102i | \(-0.163771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2277.95 | −3.05765 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 168.264i | 0.224652i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 666.262i | 0.887166i | 0.896233 | + | 0.443583i | \(0.146293\pi\) | ||||
−0.896233 | + | 0.443583i | \(0.853707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2118.15 | 2.80550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 238.623i | 0.315222i | 0.987501 | + | 0.157611i | \(0.0503791\pi\) | ||||
−0.987501 | + | 0.157611i | \(0.949621\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −614.930 | −0.808055 | −0.404028 | − | 0.914747i | \(-0.632390\pi\) | ||||
−0.404028 | + | 0.914747i | \(0.632390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −346.191 | −0.453723 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 275.002i | − 0.358543i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 178.950 | 0.232705 | 0.116353 | − | 0.993208i | \(-0.462880\pi\) | ||||
0.116353 | + | 0.993208i | \(0.462880\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 631.615i | − 0.817095i | −0.912737 | − | 0.408548i | \(-0.866035\pi\) | ||||
0.912737 | − | 0.408548i | \(-0.133965\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 949.849i | − 1.22561i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 201.241 | 0.258332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 218.923i | − 0.280311i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −91.2061 | −0.116186 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −456.655 | −0.580247 | −0.290124 | − | 0.956989i | \(-0.593696\pi\) | ||||
−0.290124 | + | 0.956989i | \(0.593696\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 365.710i | − 0.462339i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −137.598 | −0.173516 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 218.566i | 0.274236i | 0.990555 | + | 0.137118i | \(0.0437839\pi\) | ||||
−0.990555 | + | 0.137118i | \(0.956216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.5199i | 0.0957695i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 582.891 | 0.725892 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 588.926i | 0.731585i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1347.46 | −1.66559 | −0.832794 | − | 0.553584i | \(-0.813260\pi\) | ||||
−0.832794 | + | 0.553584i | \(0.813260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 672.620 | 0.829371 | 0.414686 | − | 0.909965i | \(-0.363892\pi\) | ||||
0.414686 | + | 0.909965i | \(0.363892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 944.273i | 1.15862i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −659.058 | −0.806681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1162.57i | − 1.41604i | −0.706190 | − | 0.708022i | \(-0.749588\pi\) | ||||
0.706190 | − | 0.708022i | \(-0.250412\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1041.65i | − 1.26567i | −0.774286 | − | 0.632835i | \(-0.781891\pi\) | ||||
0.774286 | − | 0.632835i | \(-0.218109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 278.432 | 0.336678 | 0.168339 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1065.74i | 1.28557i | 0.766046 | + | 0.642785i | \(0.222221\pi\) | ||||
−0.766046 | + | 0.642785i | \(0.777779\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 86.4020 | 0.103724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2680.72 | 3.21045 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 305.844i | − 0.364533i | −0.983249 | − | 0.182267i | \(-0.941657\pi\) | ||||
0.983249 | − | 0.182267i | \(-0.0583434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 337.000 | 0.400713 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 789.516i | − 0.934339i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 92.2898i | − 0.108961i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 400.442 | 0.470555 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 164.018i | 0.192283i | 0.995368 | + | 0.0961417i | \(0.0306502\pi\) | ||||
−0.995368 | + | 0.0961417i | \(0.969350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −851.068 | −0.993078 | −0.496539 | − | 0.868014i | \(-0.665396\pi\) | ||||
−0.496539 | + | 0.868014i | \(0.665396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1179.69 | 1.37333 | 0.686666 | − | 0.726973i | \(-0.259073\pi\) | ||||
0.686666 | + | 0.726973i | \(0.259073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 279.048i | − 0.323346i | −0.986844 | − | 0.161673i | \(-0.948311\pi\) | ||||
0.986844 | − | 0.161673i | \(-0.0516890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 361.598 | 0.418032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1011.71i | 1.16423i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 710.254i | − 0.815447i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 755.176 | 0.863058 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 674.159i | 0.768711i | 0.923185 | + | 0.384355i | \(0.125576\pi\) | ||||
−0.923185 | + | 0.384355i | \(0.874424\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1001.29 | 1.13654 | 0.568271 | − | 0.822841i | \(-0.307613\pi\) | ||||
0.568271 | + | 0.822841i | \(0.307613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −882.010 | −0.998879 | −0.499439 | − | 0.866349i | \(-0.666461\pi\) | ||||
−0.499439 | + | 0.866349i | \(0.666461\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 7.08053i | − 0.00798256i | −0.999992 | − | 0.00399128i | \(-0.998730\pi\) | ||||
0.999992 | − | 0.00399128i | \(-0.00127047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 302.784 | 0.340589 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 178.976i | 0.200422i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2662.92i | − 2.97533i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 376.764 | 0.419092 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 98.9320i | 0.109802i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −365.578 | −0.403953 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −450.372 | −0.496551 | −0.248275 | − | 0.968689i | \(-0.579864\pi\) | ||||
−0.248275 | + | 0.968689i | \(0.579864\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 202.426i | − 0.222201i | −0.993809 | − | 0.111101i | \(-0.964562\pi\) | ||||
0.993809 | − | 0.111101i | \(-0.0354376\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 504.215 | 0.552262 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 445.413i | 0.485728i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1593.73i | 1.73420i | 0.498138 | + | 0.867098i | \(0.334017\pi\) | ||||
−0.498138 | + | 0.867098i | \(0.665983\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −158.392 | −0.171606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 919.749i | − 0.994323i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1039.40 | 1.11884 | 0.559419 | − | 0.828885i | \(-0.311024\pi\) | ||||
0.559419 | + | 0.828885i | \(0.311024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 202.090 | 0.217068 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1392.08i | 1.48885i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 881.765 | 0.941051 | 0.470525 | − | 0.882386i | \(-0.344064\pi\) | ||||
0.470525 | + | 0.882386i | \(0.344064\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 953.344i | 1.01312i | 0.862205 | + | 0.506559i | \(0.169083\pi\) | ||||
−0.862205 | + | 0.506559i | \(0.830917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 171.767i | 0.182149i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.8957 | 0.0178413 | 0.00892063 | − | 0.999960i | \(-0.497160\pi\) | ||||
0.00892063 | + | 0.999960i | \(0.497160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 421.725i | − 0.444389i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1526.31 | −1.60159 | −0.800794 | − | 0.598940i | \(-0.795589\pi\) | ||||
−0.800794 | + | 0.598940i | \(0.795589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1417.57 | 1.48436 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 91.7713i | 0.0956948i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 679.352 | 0.706921 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2360.40i | 2.44601i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1410.39i | − 1.45852i | −0.684235 | − | 0.729262i | \(-0.739864\pi\) | ||||
0.684235 | − | 0.729262i | \(-0.260136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −596.497 | −0.614312 | −0.307156 | − | 0.951659i | \(-0.599377\pi\) | ||||
−0.307156 | + | 0.951659i | \(0.599377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 284.852i | 0.292757i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −146.686 | −0.150140 | −0.0750698 | − | 0.997178i | \(-0.523918\pi\) | ||||
−0.0750698 | + | 0.997178i | \(0.523918\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1397.62 | −1.42760 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 169.457i | 0.172388i | 0.996278 | + | 0.0861939i | \(0.0274704\pi\) | ||||
−0.996278 | + | 0.0861939i | \(0.972530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1312.36 | −1.33235 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 562.533i | − 0.568789i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1686.90i | 1.70222i | 0.524988 | + | 0.851109i | \(0.324070\pi\) | ||||
−0.524988 | + | 0.851109i | \(0.675930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3527.52 | −3.54524 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1736.14i | 1.74136i | 0.491849 | + | 0.870680i | \(0.336321\pi\) | ||||
−0.491849 | + | 0.870680i | \(0.663679\pi\) | |||||||
\(998\) | 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 | 2016.3.g.a.1135.1 | 4 | ||
3.2 | odd | 2 | 224.3.g.a.15.4 | 4 | |||
4.3 | odd | 2 | 504.3.g.a.379.3 | 4 | |||
8.3 | odd | 2 | inner | 2016.3.g.a.1135.4 | 4 | ||
8.5 | even | 2 | 504.3.g.a.379.4 | 4 | |||
12.11 | even | 2 | 56.3.g.a.43.2 | yes | 4 | ||
21.20 | even | 2 | 1568.3.g.h.687.1 | 4 | |||
24.5 | odd | 2 | 56.3.g.a.43.1 | ✓ | 4 | ||
24.11 | even | 2 | 224.3.g.a.15.3 | 4 | |||
48.5 | odd | 4 | 1792.3.d.g.1023.5 | 8 | |||
48.11 | even | 4 | 1792.3.d.g.1023.3 | 8 | |||
48.29 | odd | 4 | 1792.3.d.g.1023.4 | 8 | |||
48.35 | even | 4 | 1792.3.d.g.1023.6 | 8 | |||
84.11 | even | 6 | 392.3.k.i.275.2 | 8 | |||
84.23 | even | 6 | 392.3.k.i.67.4 | 8 | |||
84.47 | odd | 6 | 392.3.k.j.67.4 | 8 | |||
84.59 | odd | 6 | 392.3.k.j.275.2 | 8 | |||
84.83 | odd | 2 | 392.3.g.h.99.2 | 4 | |||
168.5 | even | 6 | 392.3.k.j.67.2 | 8 | |||
168.53 | odd | 6 | 392.3.k.i.275.4 | 8 | |||
168.83 | odd | 2 | 1568.3.g.h.687.2 | 4 | |||
168.101 | even | 6 | 392.3.k.j.275.4 | 8 | |||
168.125 | even | 2 | 392.3.g.h.99.1 | 4 | |||
168.149 | odd | 6 | 392.3.k.i.67.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.1 | ✓ | 4 | 24.5 | odd | 2 | ||
56.3.g.a.43.2 | yes | 4 | 12.11 | even | 2 | ||
224.3.g.a.15.3 | 4 | 24.11 | even | 2 | |||
224.3.g.a.15.4 | 4 | 3.2 | odd | 2 | |||
392.3.g.h.99.1 | 4 | 168.125 | even | 2 | |||
392.3.g.h.99.2 | 4 | 84.83 | odd | 2 | |||
392.3.k.i.67.2 | 8 | 168.149 | odd | 6 | |||
392.3.k.i.67.4 | 8 | 84.23 | even | 6 | |||
392.3.k.i.275.2 | 8 | 84.11 | even | 6 | |||
392.3.k.i.275.4 | 8 | 168.53 | odd | 6 | |||
392.3.k.j.67.2 | 8 | 168.5 | even | 6 | |||
392.3.k.j.67.4 | 8 | 84.47 | odd | 6 | |||
392.3.k.j.275.2 | 8 | 84.59 | odd | 6 | |||
392.3.k.j.275.4 | 8 | 168.101 | even | 6 | |||
504.3.g.a.379.3 | 4 | 4.3 | odd | 2 | |||
504.3.g.a.379.4 | 4 | 8.5 | even | 2 | |||
1568.3.g.h.687.1 | 4 | 21.20 | even | 2 | |||
1568.3.g.h.687.2 | 4 | 168.83 | odd | 2 | |||
1792.3.d.g.1023.3 | 8 | 48.11 | even | 4 | |||
1792.3.d.g.1023.4 | 8 | 48.29 | odd | 4 | |||
1792.3.d.g.1023.5 | 8 | 48.5 | odd | 4 | |||
1792.3.d.g.1023.6 | 8 | 48.35 | even | 4 | |||
2016.3.g.a.1135.1 | 4 | 1.1 | even | 1 | trivial | ||
2016.3.g.a.1135.4 | 4 | 8.3 | odd | 2 | inner |