Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.2 | ||
Root | \(-0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.g.1889.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 2.44949i | −0.377964 | + | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.19615 | 1.26025 | 0.630126 | − | 0.776493i | \(-0.283003\pi\) | ||||
0.630126 | + | 0.776493i | \(0.283003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.34847i | − | 1.68585i | −0.538028 | − | 0.842927i | \(-0.680830\pi\) | ||
0.538028 | − | 0.842927i | \(-0.319170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.07107i | 1.31306i | 0.754298 | + | 0.656532i | \(0.227977\pi\) | ||||
−0.754298 | + | 0.656532i | \(0.772023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.44949i | 0.439941i | 0.975506 | + | 0.219971i | \(0.0705962\pi\) | ||||
−0.975506 | + | 0.219971i | \(0.929404\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.73205 | − | 4.24264i | 0.292770 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.66025 | 1.35250 | 0.676252 | − | 0.736670i | \(-0.263603\pi\) | ||||
0.676252 | + | 0.736670i | \(0.263603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.66025 | 1.26323 | 0.631614 | − | 0.775283i | \(-0.282393\pi\) | ||||
0.631614 | + | 0.775283i | \(0.282393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3137i | 1.55406i | 0.629465 | + | 0.777029i | \(0.283274\pi\) | ||||
−0.629465 | + | 0.777029i | \(0.716726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.44949i | − | 0.330289i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.66025 | −1.12747 | −0.563735 | − | 0.825956i | \(-0.690636\pi\) | ||||
−0.563735 | + | 0.825956i | \(0.690636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.44949i | 0.313625i | 0.987628 | + | 0.156813i | \(0.0501218\pi\) | ||||
−0.987628 | + | 0.156813i | \(0.949878\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.24264i | 0.526235i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1421i | 1.67836i | 0.543852 | + | 0.839181i | \(0.316965\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | − | 1.41421i | −0.394771 | − | 0.161165i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0000 | 1.46261 | 0.731307 | − | 0.682048i | \(-0.238911\pi\) | ||||
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.73205 | −0.190117 | −0.0950586 | − | 0.995472i | \(-0.530304\pi\) | ||||
−0.0950586 | + | 0.995472i | \(0.530304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 2.44949i | 0.628971 | + | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7279i | 1.30586i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1464i | 1.74096i | 0.492207 | + | 0.870478i | \(0.336190\pi\) | ||||
−0.492207 | + | 0.870478i | \(0.663810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.46410 | −0.344691 | −0.172345 | − | 0.985037i | \(-0.555135\pi\) | ||||
−0.172345 | + | 0.985037i | \(0.555135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.79796i | 0.965422i | 0.875780 | + | 0.482711i | \(0.160348\pi\) | ||||
−0.875780 | + | 0.482711i | \(0.839652\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1421i | 1.36717i | 0.729870 | + | 0.683586i | \(0.239581\pi\) | ||||
−0.729870 | + | 0.683586i | \(0.760419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.07107i | 0.665190i | 0.943070 | + | 0.332595i | \(0.107924\pi\) | ||||
−0.943070 | + | 0.332595i | \(0.892076\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.89898i | 0.456832i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.19615 | + | 12.7279i | −0.476331 | + | 1.16677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | −0.443678 | −0.221839 | − | 0.975083i | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3205 | 1.51330 | 0.756650 | − | 0.653820i | \(-0.226835\pi\) | ||||
0.756650 | + | 0.653820i | \(0.226835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0000 | + | 7.34847i | 1.56080 | + | 0.637193i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.41421i | − | 0.120824i | −0.998174 | − | 0.0604122i | \(-0.980758\pi\) | ||
0.998174 | − | 0.0604122i | \(-0.0192415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.2474i | − | 1.03882i | −0.854527 | − | 0.519408i | \(-0.826153\pi\) | ||
0.854527 | − | 0.519408i | \(-0.173847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 12.2474i | − | 1.01710i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.07107i | 0.579284i | 0.957135 | + | 0.289642i | \(0.0935363\pi\) | ||||
−0.957135 | + | 0.289642i | \(0.906464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.24264i | − | 0.340777i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.1464i | − | 1.36843i | −0.729279 | − | 0.684217i | \(-0.760144\pi\) | ||
0.729279 | − | 0.684217i | \(-0.239856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | + | 2.82843i | 0.546019 | + | 0.222911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | −0.391630 | −0.195815 | − | 0.980641i | \(-0.562735\pi\) | ||||
−0.195815 | + | 0.980641i | \(0.562735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.1244 | 0.938211 | 0.469105 | − | 0.883142i | \(-0.344576\pi\) | ||||
0.469105 | + | 0.883142i | \(0.344576\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 4.89898i | 0.151186 | − | 0.370328i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 7.07107i | − | 0.528516i | −0.964452 | − | 0.264258i | \(-0.914873\pi\) | ||
0.964452 | − | 0.264258i | \(-0.0851271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6969i | 1.09241i | 0.837650 | + | 0.546207i | \(0.183929\pi\) | ||||
−0.837650 | + | 0.546207i | \(0.816071\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.66025 | −0.636715 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.34847i | 0.537373i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.1421i | 1.02329i | 0.859197 | + | 0.511645i | \(0.170964\pi\) | ||||
−0.859197 | + | 0.511645i | \(0.829036\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.41421i | − | 0.100759i | −0.998730 | − | 0.0503793i | \(-0.983957\pi\) | ||
0.998730 | − | 0.0503793i | \(-0.0160430\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.3205 | − | 7.07107i | −1.21566 | − | 0.496292i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0000 | −1.04765 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3923 | 0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.66025 | 0.590624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 2.44949i | −0.407307 | − | 0.166282i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.7279i | − | 0.856173i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.2474i | 0.820150i | 0.912052 | + | 0.410075i | \(0.134497\pi\) | ||||
−0.912052 | + | 0.410075i | \(0.865503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.8564 | 0.919682 | 0.459841 | − | 0.888001i | \(-0.347906\pi\) | ||||
0.459841 | + | 0.888001i | \(0.347906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.89898i | 0.323734i | 0.986813 | + | 0.161867i | \(0.0517515\pi\) | ||||
−0.986813 | + | 0.161867i | \(0.948248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07107i | 0.463241i | 0.972806 | + | 0.231621i | \(0.0744028\pi\) | ||||
−0.972806 | + | 0.231621i | \(0.925597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0000 | −0.978492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3848i | 1.18921i | 0.804017 | + | 0.594606i | \(0.202692\pi\) | ||||
−0.804017 | + | 0.594606i | \(0.797308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.44949i | 0.157786i | 0.996883 | + | 0.0788928i | \(0.0251385\pi\) | ||||
−0.996883 | + | 0.0788928i | \(0.974862\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.66025 | + | 8.48528i | 0.553283 | + | 0.542105i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.0000 | −1.14531 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.19615 | 0.327978 | 0.163989 | − | 0.986462i | \(-0.447564\pi\) | ||||
0.163989 | + | 0.986462i | \(0.447564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.46410 | 0.216085 | 0.108042 | − | 0.994146i | \(-0.465542\pi\) | ||||
0.108042 | + | 0.994146i | \(0.465542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00000 | + | 12.2474i | −0.310685 | + | 0.761019i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.41421i | 0.0872041i | 0.999049 | + | 0.0436021i | \(0.0138834\pi\) | ||||
−0.999049 | + | 0.0436021i | \(0.986117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 19.5959i | − | 1.20377i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.9808 | −1.58408 | −0.792038 | − | 0.610472i | \(-0.790980\pi\) | ||||
−0.792038 | + | 0.610472i | \(0.790980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.6969i | − | 0.892775i | −0.894840 | − | 0.446388i | \(-0.852710\pi\) | ||
0.894840 | − | 0.446388i | \(-0.147290\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.82843i | − | 0.170561i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.1421i | − | 0.843649i | −0.906677 | − | 0.421825i | \(-0.861390\pi\) | ||
0.906677 | − | 0.421825i | \(-0.138610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.2474i | − | 0.728035i | −0.931392 | − | 0.364018i | \(-0.881405\pi\) | ||
0.931392 | − | 0.364018i | \(-0.118595\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.66025 | + | 21.2132i | −0.511199 | + | 1.25218i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0526 | 1.11306 | 0.556531 | − | 0.830827i | \(-0.312132\pi\) | ||||
0.556531 | + | 0.830827i | \(0.312132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0000 | 0.873334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.92820 | −0.400668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | − | 12.2474i | 0.288195 | − | 0.705931i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.24264i | − | 0.242933i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1244 | 0.687509 | 0.343755 | − | 0.939060i | \(-0.388301\pi\) | ||||
0.343755 | + | 0.939060i | \(0.388301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4949i | 1.38453i | 0.721642 | + | 0.692267i | \(0.243388\pi\) | ||||
−0.721642 | + | 0.692267i | \(0.756612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.65685i | − | 0.317721i | −0.987301 | − | 0.158860i | \(-0.949218\pi\) | ||
0.987301 | − | 0.158860i | \(-0.0507819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0000 | −0.559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 38.1838i | − | 2.12460i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.89898i | 0.271746i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.66025 | + | 21.2132i | −0.477455 | + | 1.16952i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0000 | 1.37412 | 0.687062 | − | 0.726599i | \(-0.258900\pi\) | ||||
0.687062 | + | 0.726599i | \(0.258900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.46410 | 0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | −0.381314 | −0.190657 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190657 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.46410 | −0.187592 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.07107i | − | 0.379595i | −0.981823 | − | 0.189797i | \(-0.939217\pi\) | ||
0.981823 | − | 0.189797i | \(-0.0607831\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.5959i | − | 1.04895i | −0.851427 | − | 0.524473i | \(-0.824262\pi\) | ||
0.851427 | − | 0.524473i | \(-0.175738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.66025 | −0.460939 | −0.230469 | − | 0.973080i | \(-0.574026\pi\) | ||||
−0.230469 | + | 0.973080i | \(0.574026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 24.4949i | − | 1.30005i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.3137i | − | 0.597115i | −0.954392 | − | 0.298557i | \(-0.903495\pi\) | ||
0.954392 | − | 0.298557i | \(-0.0965054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.0000 | −1.84211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.89898i | 0.255725i | 0.991792 | + | 0.127862i | \(0.0408116\pi\) | ||||
−0.991792 | + | 0.127862i | \(0.959188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.7128 | − | 11.3137i | −1.43878 | − | 0.587378i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0000 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724071\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.3205 | 0.892052 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.73205 | 0.0885037 | 0.0442518 | − | 0.999020i | \(-0.485910\pi\) | ||||
0.0442518 | + | 0.999020i | \(0.485910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 2.44949i | 0.305788 | + | 0.124838i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.5269i | 1.64918i | 0.565731 | + | 0.824590i | \(0.308594\pi\) | ||||
−0.565731 | + | 0.824590i | \(0.691406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.6969i | − | 0.743256i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.5167 | −1.13294 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.7990i | 0.988714i | 0.869259 | + | 0.494357i | \(0.164597\pi\) | ||||
−0.869259 | + | 0.494357i | \(0.835403\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.07107i | 0.350500i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5959i | 0.968956i | 0.874804 | + | 0.484478i | \(0.160990\pi\) | ||||
−0.874804 | + | 0.484478i | \(0.839010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.66025 | − | 21.2132i | 0.426143 | − | 1.04383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.00000 | 0.147264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.73205 | 0.0846162 | 0.0423081 | − | 0.999105i | \(-0.486529\pi\) | ||||
0.0423081 | + | 0.999105i | \(0.486529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3923 | −0.504101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | − | 2.44949i | −0.290360 | − | 0.118539i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65685i | 0.272481i | 0.990676 | + | 0.136241i | \(0.0435020\pi\) | ||||
−0.990676 | + | 0.136241i | \(0.956498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.7423i | − | 1.76572i | −0.469632 | − | 0.882862i | \(-0.655613\pi\) | ||
0.469632 | − | 0.882862i | \(-0.344387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.5959i | 0.935262i | 0.883924 | + | 0.467631i | \(0.154892\pi\) | ||||
−0.883924 | + | 0.467631i | \(0.845108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 32.5269i | − | 1.54540i | −0.634771 | − | 0.772700i | \(-0.718906\pi\) | ||
0.634771 | − | 0.772700i | \(-0.281094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0416i | 1.13459i | 0.823513 | + | 0.567297i | \(0.192011\pi\) | ||||
−0.823513 | + | 0.567297i | \(0.807989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2474i | 0.576710i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.3923 | − | 4.24264i | −0.487199 | − | 0.198898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0000 | 1.49690 | 0.748448 | − | 0.663193i | \(-0.230799\pi\) | ||||
0.748448 | + | 0.663193i | \(0.230799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1244 | 0.564688 | 0.282344 | − | 0.959313i | \(-0.408888\pi\) | ||||
0.282344 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0000 | −0.511213 | −0.255607 | − | 0.966781i | \(-0.582275\pi\) | ||||
−0.255607 | + | 0.966781i | \(0.582275\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7846 | −0.961797 | −0.480899 | − | 0.876776i | \(-0.659689\pi\) | ||||
−0.480899 | + | 0.876776i | \(0.659689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | − | 4.89898i | 0.0923514 | − | 0.226214i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.07107i | − | 0.325128i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.6969i | 0.674342i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9090 | −1.50365 | −0.751825 | − | 0.659363i | \(-0.770826\pi\) | ||||
−0.751825 | + | 0.659363i | \(0.770826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 12.2474i | − | 0.558436i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 29.6985i | − | 1.34854i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.5563i | − | 0.702048i | −0.936366 | − | 0.351024i | \(-0.885834\pi\) | ||
0.936366 | − | 0.351024i | \(-0.114166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.7423i | 1.65479i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.6410 | − | 14.1421i | −1.55386 | − | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.0000 | −0.761025 | −0.380512 | − | 0.924776i | \(-0.624252\pi\) | ||||
−0.380512 | + | 0.924776i | \(0.624252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.3731 | 1.62179 | 0.810897 | − | 0.585188i | \(-0.198979\pi\) | ||||
0.810897 | + | 0.585188i | \(0.198979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.66025 | 0.383859 | 0.191930 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191930 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 16.9706i | − | 0.747812i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2474i | 0.538642i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.19615 | −0.227648 | −0.113824 | − | 0.993501i | \(-0.536310\pi\) | ||||
−0.113824 | + | 0.993501i | \(0.536310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.7423i | 1.60663i | 0.595554 | + | 0.803315i | \(0.296933\pi\) | ||||
−0.595554 | + | 0.803315i | \(0.703067\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.7279i | 0.554437i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21.2132i | − | 0.918846i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 24.4949i | − | 1.05901i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.92820 | − | 7.07107i | 0.298419 | − | 0.304572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | 0.214967 | 0.107483 | − | 0.994207i | \(-0.465721\pi\) | ||||
0.107483 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1244 | 0.519350 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0000 | 0.555840 | 0.277920 | − | 0.960604i | \(-0.410355\pi\) | ||||
0.277920 | + | 0.960604i | \(0.410355\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.9615 | 2.21364 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.0000 | + | 31.8434i | −0.552816 | + | 1.35412i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.1421i | − | 0.599222i | −0.954062 | − | 0.299611i | \(-0.903143\pi\) | ||
0.954062 | − | 0.299611i | \(-0.0968568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.2474i | 0.518012i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.6410 | −1.45994 | −0.729972 | − | 0.683477i | \(-0.760467\pi\) | ||||
−0.729972 | + | 0.683477i | \(0.760467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.2474i | − | 0.515254i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 39.5980i | − | 1.66003i | −0.557738 | − | 0.830017i | \(-0.688331\pi\) | ||
0.557738 | − | 0.830017i | \(-0.311669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0000 | 0.795125 | 0.397563 | − | 0.917575i | \(-0.369856\pi\) | ||||
0.397563 | + | 0.917575i | \(0.369856\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685i | 0.235907i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 29.3939i | − | 1.22368i | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||
0.790980 | − | 0.611842i | \(-0.209571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.73205 | − | 4.24264i | 0.0718576 | − | 0.176014i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.0000 | −0.662652 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.8564 | 0.571915 | 0.285958 | − | 0.958242i | \(-0.407688\pi\) | ||||
0.285958 | + | 0.958242i | \(0.407688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | 0.741677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5885 | −0.640141 | −0.320071 | − | 0.947394i | \(-0.603707\pi\) | ||||
−0.320071 | + | 0.947394i | \(0.603707\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.00000 | − | 22.0454i | 0.368964 | − | 0.903774i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.3848i | 0.751182i | 0.926786 | + | 0.375591i | \(0.122560\pi\) | ||||
−0.926786 | + | 0.375591i | \(0.877440\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.5403i | 1.89842i | 0.314645 | + | 0.949209i | \(0.398114\pi\) | ||||
−0.314645 | + | 0.949209i | \(0.601886\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.5885 | −0.633761 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 12.2474i | − | 0.497109i | −0.968618 | − | 0.248554i | \(-0.920045\pi\) | ||
0.968618 | − | 0.248554i | \(-0.0799554\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 21.2132i | − | 0.858194i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | −0.161558 | −0.0807792 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807792 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 48.0833i | − | 1.93576i | −0.251414 | − | 0.967880i | \(-0.580896\pi\) | ||
0.251414 | − | 0.967880i | \(-0.419104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.9444i | 1.08299i | 0.840705 | + | 0.541493i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541493i | \(0.817859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.3923 | − | 25.4558i | 0.416359 | − | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.9808 | 1.03592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.0000 | −1.15447 | −0.577236 | − | 0.816577i | \(-0.695869\pi\) | ||||
−0.577236 | + | 0.816577i | \(0.695869\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.66025 | 0.343672 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | + | 12.2474i | −0.475457 | + | 0.485262i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.41421i | − | 0.0558581i | −0.999610 | − | 0.0279290i | \(-0.991109\pi\) | ||
0.999610 | − | 0.0279290i | \(-0.00889125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4949i | 0.965984i | 0.875625 | + | 0.482992i | \(0.160450\pi\) | ||||
−0.875625 | + | 0.482992i | \(0.839550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | −0.817127 | −0.408564 | − | 0.912730i | \(-0.633970\pi\) | ||||
−0.408564 | + | 0.912730i | \(0.633970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.2474i | − | 0.480754i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 18.3848i | − | 0.719452i | −0.933058 | − | 0.359726i | \(-0.882870\pi\) | ||
0.933058 | − | 0.359726i | \(-0.117130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.0000 | −1.17220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11.3137i | − | 0.440720i | −0.975419 | − | 0.220360i | \(-0.929277\pi\) | ||
0.975419 | − | 0.220360i | \(-0.0707231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.1464i | − | 0.666919i | −0.942764 | − | 0.333459i | \(-0.891784\pi\) | ||
0.942764 | − | 0.333459i | \(-0.108216\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −31.1769 | − | 12.7279i | −1.20899 | − | 0.493568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0000 | 0.774403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.46410 | −0.133730 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3205 | 0.665681 | 0.332841 | − | 0.942983i | \(-0.391993\pi\) | ||||
0.332841 | + | 0.942983i | \(0.391993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.0000 | − | 17.1464i | −1.61181 | − | 0.658020i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.0416i | − | 0.919927i | −0.887938 | − | 0.459964i | \(-0.847862\pi\) | ||
0.887938 | − | 0.459964i | \(-0.152138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.44949i | 0.0935902i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.7128 | 1.05577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.9444i | 1.02501i | 0.858683 | + | 0.512506i | \(0.171283\pi\) | ||||
−0.858683 | + | 0.512506i | \(0.828717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.2132i | 0.804663i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.0000 | 1.70450 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.41421i | − | 0.0534141i | −0.999643 | − | 0.0267071i | \(-0.991498\pi\) | ||
0.999643 | − | 0.0267071i | \(-0.00850213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 36.7423i | − | 1.38576i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.46410 | − | 8.48528i | 0.130281 | − | 0.319122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | 0.187779 | 0.0938895 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938895 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.92820 | 0.259463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.5885 | −0.581351 | −0.290676 | − | 0.956822i | \(-0.593880\pi\) | ||||
−0.290676 | + | 0.956822i | \(0.593880\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | − | 9.79796i | −0.893807 | − | 0.364895i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 14.1421i | − | 0.525226i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2474i | 0.454233i | 0.973868 | + | 0.227116i | \(0.0729298\pi\) | ||||
−0.973868 | + | 0.227116i | \(0.927070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.9808 | −0.960933 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.1918i | − | 1.44758i | −0.690018 | − | 0.723792i | \(-0.742398\pi\) | ||
0.690018 | − | 0.723792i | \(-0.257602\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.82843i | − | 0.104186i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0000 | 0.809283 | 0.404642 | − | 0.914475i | \(-0.367396\pi\) | ||||
0.404642 | + | 0.914475i | \(0.367396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.07107i | − | 0.259412i | −0.991552 | − | 0.129706i | \(-0.958597\pi\) | ||
0.991552 | − | 0.129706i | \(-0.0414034\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 12.2474i | − | 0.448712i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.6410 | − | 14.1421i | −1.26576 | − | 0.516742i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0000 | 1.24068 | 0.620339 | − | 0.784334i | \(-0.286995\pi\) | ||||
0.620339 | + | 0.784334i | \(0.286995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.66025 | 0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.1244 | −0.439508 | −0.219754 | − | 0.975555i | \(-0.570525\pi\) | ||||
−0.219754 | + | 0.975555i | \(0.570525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00000 | − | 17.1464i | 0.253417 | − | 0.620742i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.2132i | 0.765964i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.89898i | 0.176662i | 0.996091 | + | 0.0883309i | \(0.0281533\pi\) | ||||
−0.996091 | + | 0.0883309i | \(0.971847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.5885 | −0.560678 | −0.280339 | − | 0.959901i | \(-0.590447\pi\) | ||||
−0.280339 | + | 0.959901i | \(0.590447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.89898i | − | 0.175977i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 63.6396i | − | 2.28013i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0000 | −0.715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.6985i | 1.05998i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.89898i | − | 0.174630i | −0.996181 | − | 0.0873149i | \(-0.972171\pi\) | ||
0.996181 | − | 0.0873149i | \(-0.0278286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.3205 | − | 7.07107i | −0.615846 | − | 0.251418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.1051 | −1.34975 | −0.674876 | − | 0.737931i | \(-0.735803\pi\) | ||||
−0.674876 | + | 0.737931i | \(0.735803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.0000 | 1.59199 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | − | 4.89898i | −0.422944 | − | 0.172666i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.1421i | − | 0.497211i | −0.968605 | − | 0.248606i | \(-0.920028\pi\) | ||
0.968605 | − | 0.248606i | \(-0.0799723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.7423i | − | 1.29020i | −0.764099 | − | 0.645099i | \(-0.776816\pi\) | ||
0.764099 | − | 0.645099i | \(-0.223184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.66025 | 0.303355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.7423i | 1.28545i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.7696i | 1.28327i | 0.767012 | + | 0.641633i | \(0.221743\pi\) | ||||
−0.767012 | + | 0.641633i | \(0.778257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.0000 | 1.91718 | 0.958590 | − | 0.284791i | \(-0.0919241\pi\) | ||||
0.958590 | + | 0.284791i | \(0.0919241\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.8701i | 0.934363i | 0.884161 | + | 0.467182i | \(0.154731\pi\) | ||||
−0.884161 | + | 0.467182i | \(0.845269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.7423i | 1.27611i | 0.769989 | + | 0.638057i | \(0.220262\pi\) | ||||
−0.769989 | + | 0.638057i | \(0.779738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.9808 | − | 25.4558i | −0.900180 | − | 0.881993i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.0000 | −0.726735 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.0526 | 0.657767 | 0.328884 | − | 0.944370i | \(-0.393328\pi\) | ||||
0.328884 | + | 0.944370i | \(0.393328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.1244 | −0.417091 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.00000 | + | 22.0454i | −0.309244 | + | 0.757489i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 14.1421i | − | 0.484786i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 48.9898i | − | 1.67738i | −0.544610 | − | 0.838689i | \(-0.683322\pi\) | ||
0.544610 | − | 0.838689i | \(-0.316678\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5167 | 0.769154 | 0.384577 | − | 0.923093i | \(-0.374347\pi\) | ||||
0.384577 | + | 0.923093i | \(0.374347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.5959i | − | 0.668604i | −0.942466 | − | 0.334302i | \(-0.891499\pi\) | ||
0.942466 | − | 0.334302i | \(-0.108501\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.5980i | 1.34793i | 0.738763 | + | 0.673965i | \(0.235410\pi\) | ||||
−0.738763 | + | 0.673965i | \(0.764590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.3848i | 0.623661i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.89898i | 0.165996i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1244 | + | 29.6985i | −0.409878 | + | 1.00399i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.0000 | −1.45201 | −0.726003 | − | 0.687691i | \(-0.758624\pi\) | ||||
−0.726003 | + | 0.687691i | \(0.758624\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.9615 | 1.75063 | 0.875314 | − | 0.483555i | \(-0.160655\pi\) | ||||
0.875314 | + | 0.483555i | \(0.160655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.00000 | −0.168263 | −0.0841317 | − | 0.996455i | \(-0.526812\pi\) | ||||
−0.0841317 | + | 0.996455i | \(0.526812\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.4449 | −0.988662 | −0.494331 | − | 0.869274i | \(-0.664587\pi\) | ||||
−0.494331 | + | 0.869274i | \(0.664587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.00000 | − | 12.2474i | 0.167695 | − | 0.410766i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 63.6396i | − | 2.12962i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.2474i | 0.409387i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.3205 | −0.577671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.7878i | 1.95850i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 25.4558i | − | 0.846181i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.0000 | −0.763702 | −0.381851 | − | 0.924224i | \(-0.624713\pi\) | ||||
−0.381851 | + | 0.924224i | \(0.624713\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.07107i | − | 0.234275i | −0.993116 | − | 0.117137i | \(-0.962628\pi\) | ||
0.993116 | − | 0.117137i | \(-0.0373718\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.44949i | − | 0.0810663i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3205 | + | 42.4264i | −0.571974 | + | 1.40104i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.00000 | −0.164935 | −0.0824674 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824674 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.6410 | 1.14022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.9090 | 1.07971 | 0.539854 | − | 0.841759i | \(-0.318479\pi\) | ||||
0.539854 | + | 0.841759i | \(0.318479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.0000 | + | 36.7423i | −1.17985 | + | 1.20418i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.7279i | − | 0.416248i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.7423i | − | 1.20032i | −0.799880 | − | 0.600160i | \(-0.795104\pi\) | ||
0.799880 | − | 0.600160i | \(-0.204896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.3013 | −1.41158 | −0.705791 | − | 0.708421i | \(-0.749408\pi\) | ||||
−0.705791 | + | 0.708421i | \(0.749408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 24.4949i | − | 0.797664i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.65685i | 0.183823i | 0.995767 | + | 0.0919115i | \(0.0292977\pi\) | ||||
−0.995767 | + | 0.0919115i | \(0.970702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 56.5685i | − | 1.83243i | −0.400681 | − | 0.916217i | \(-0.631227\pi\) | ||
0.400681 | − | 0.916217i | \(-0.368773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 24.4949i | − | 0.792636i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.46410 | + | 1.41421i | 0.111862 | + | 0.0456673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0000 | 0.806452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.73205 | 0.0557567 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0000 | 0.321578 | 0.160789 | − | 0.986989i | \(-0.448596\pi\) | ||||
0.160789 | + | 0.986989i | \(0.448596\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.19615 | 0.166752 | 0.0833762 | − | 0.996518i | \(-0.473430\pi\) | ||||
0.0833762 | + | 0.996518i | \(0.473430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0000 | + | 12.2474i | 0.961756 | + | 0.392635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.82843i | 0.0904894i | 0.998976 | + | 0.0452447i | \(0.0144068\pi\) | ||||
−0.998976 | + | 0.0452447i | \(0.985593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14.6969i | − | 0.469716i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.9090 | −1.04963 | −0.524816 | − | 0.851215i | \(-0.675866\pi\) | ||||
−0.524816 | + | 0.851215i | \(0.675866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.44949i | 0.0780472i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.1421i | 0.449694i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0000 | −1.30241 | −0.651204 | − | 0.758903i | \(-0.725736\pi\) | ||||
−0.651204 | + | 0.758903i | \(0.725736\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12.2474i | − | 0.387881i | −0.981013 | − | 0.193940i | \(-0.937873\pi\) | ||
0.981013 | − | 0.193940i | \(-0.0621268\pi\) | |||||||
\(998\) | 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 | 3024.2.k.g.1889.2 | 4 | ||
3.2 | odd | 2 | inner | 3024.2.k.g.1889.4 | 4 | ||
4.3 | odd | 2 | 189.2.c.c.188.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 3024.2.k.g.1889.3 | 4 | ||
12.11 | even | 2 | 189.2.c.c.188.4 | yes | 4 | ||
21.20 | even | 2 | inner | 3024.2.k.g.1889.1 | 4 | ||
28.27 | even | 2 | 189.2.c.c.188.2 | yes | 4 | ||
36.7 | odd | 6 | 567.2.o.e.377.2 | 8 | |||
36.11 | even | 6 | 567.2.o.e.377.3 | 8 | |||
36.23 | even | 6 | 567.2.o.e.188.1 | 8 | |||
36.31 | odd | 6 | 567.2.o.e.188.4 | 8 | |||
84.83 | odd | 2 | 189.2.c.c.188.3 | yes | 4 | ||
252.83 | odd | 6 | 567.2.o.e.377.4 | 8 | |||
252.139 | even | 6 | 567.2.o.e.188.3 | 8 | |||
252.167 | odd | 6 | 567.2.o.e.188.2 | 8 | |||
252.223 | even | 6 | 567.2.o.e.377.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.c.c.188.1 | ✓ | 4 | 4.3 | odd | 2 | ||
189.2.c.c.188.2 | yes | 4 | 28.27 | even | 2 | ||
189.2.c.c.188.3 | yes | 4 | 84.83 | odd | 2 | ||
189.2.c.c.188.4 | yes | 4 | 12.11 | even | 2 | ||
567.2.o.e.188.1 | 8 | 36.23 | even | 6 | |||
567.2.o.e.188.2 | 8 | 252.167 | odd | 6 | |||
567.2.o.e.188.3 | 8 | 252.139 | even | 6 | |||
567.2.o.e.188.4 | 8 | 36.31 | odd | 6 | |||
567.2.o.e.377.1 | 8 | 252.223 | even | 6 | |||
567.2.o.e.377.2 | 8 | 36.7 | odd | 6 | |||
567.2.o.e.377.3 | 8 | 36.11 | even | 6 | |||
567.2.o.e.377.4 | 8 | 252.83 | odd | 6 | |||
3024.2.k.g.1889.1 | 4 | 21.20 | even | 2 | inner | ||
3024.2.k.g.1889.2 | 4 | 1.1 | even | 1 | trivial | ||
3024.2.k.g.1889.3 | 4 | 7.6 | odd | 2 | inner | ||
3024.2.k.g.1889.4 | 4 | 3.2 | odd | 2 | inner |