Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3648,2,Mod(2431,3648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3648.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3648 = 2^{6} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3648.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: | \(29.1294266574\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.3 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3648.2431 |
Dual form | 3648.2.k.g.2431.4 |
$q$-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 \(\left(\mathbb{Z}/3648\mathbb{Z}\right)^\times\).
\(n\) | \(1217\) | \(1921\) | \(2053\) | \(2623\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.37228 | 1.50813 | 0.754065 | − | 0.656800i | \(-0.228090\pi\) | ||||
0.754065 | + | 0.656800i | \(0.228090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.792287i | − | 0.299456i | −0.988727 | − | 0.149728i | \(-0.952160\pi\) | ||
0.988727 | − | 0.149728i | \(-0.0478399\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.792287i | 0.238884i | 0.992841 | + | 0.119442i | \(0.0381105\pi\) | ||||
−0.992841 | + | 0.119442i | \(0.961890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.04868i | − | 1.40025i | −0.714020 | − | 0.700125i | \(-0.753127\pi\) | ||
0.714020 | − | 0.700125i | \(-0.246873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.37228 | −0.870719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.37228 | 1.30297 | 0.651485 | − | 0.758662i | \(-0.274146\pi\) | ||||
0.651485 | + | 0.758662i | \(0.274146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.792287i | 0.172891i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.51278i | 1.77504i | 0.460772 | + | 0.887518i | \(0.347572\pi\) | ||||
−0.460772 | + | 0.887518i | \(0.652428\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.37228 | 1.27446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.0974i | 1.87503i | 0.347943 | + | 0.937516i | \(0.386880\pi\) | ||||
−0.347943 | + | 0.937516i | \(0.613120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.74456 | 1.57057 | 0.785285 | − | 0.619135i | \(-0.212516\pi\) | ||||
0.785285 | + | 0.619135i | \(0.212516\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.792287i | − | 0.137919i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.67181i | − | 0.451619i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.04868i | − | 0.829997i | −0.909822 | − | 0.414999i | \(-0.863782\pi\) | ||
0.909822 | − | 0.414999i | \(-0.136218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.04868i | 0.808435i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.30506i | − | 1.41901i | −0.704701 | − | 0.709504i | \(-0.748919\pi\) | ||
0.704701 | − | 0.709504i | \(-0.251081\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.37228 | 0.502710 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.25639i | 0.620858i | 0.950597 | + | 0.310429i | \(0.100473\pi\) | ||||
−0.950597 | + | 0.310429i | \(0.899527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.37228 | 0.910326 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.37228 | −0.752270 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.16915i | − | 0.435316i | −0.976025 | − | 0.217658i | \(-0.930158\pi\) | ||
0.976025 | − | 0.217658i | \(-0.0698417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.67181i | 0.360267i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | + | 1.73205i | 0.529813 | + | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.37228 | −0.687850 | −0.343925 | − | 0.938997i | \(-0.611757\pi\) | ||||
−0.343925 | + | 0.938997i | \(0.611757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.792287i | − | 0.0998188i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 17.0256i | − | 2.11176i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.48913 | 1.15928 | 0.579641 | − | 0.814872i | \(-0.303193\pi\) | ||||
0.579641 | + | 0.814872i | \(0.303193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.51278i | − | 1.02482i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.11684 | −0.481840 | −0.240920 | − | 0.970545i | \(-0.577449\pi\) | ||||
−0.240920 | + | 0.970545i | \(0.577449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.37228 | −0.735808 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.627719 | 0.0715352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.74456 | 0.533805 | 0.266903 | − | 0.963724i | \(-0.414000\pi\) | ||||
0.266903 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.1168 | 1.96505 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.0974i | − | 1.08255i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2665i | 1.40625i | 0.711068 | + | 0.703123i | \(0.248212\pi\) | ||||
−0.711068 | + | 0.703123i | \(0.751788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.74456 | −0.906769 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.4891 | − | 5.84096i | −1.38396 | − | 0.599270i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2665i | − | 1.34701i | −0.739183 | − | 0.673504i | \(-0.764788\pi\) | ||
0.739183 | − | 0.673504i | \(-0.235212\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.792287i | 0.0796278i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7446 | 1.46714 | 0.733569 | − | 0.679615i | \(-0.237853\pi\) | ||||
0.733569 | + | 0.679615i | \(0.237853\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7446 | −1.25576 | −0.627880 | − | 0.778311i | \(-0.716077\pi\) | ||||
−0.627880 | + | 0.778311i | \(0.716077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.67181i | 0.260742i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.48913 | −0.917348 | −0.458674 | − | 0.888605i | \(-0.651675\pi\) | ||||
−0.458674 | + | 0.888605i | \(0.651675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.21782i | 0.787125i | 0.919298 | + | 0.393562i | \(0.128757\pi\) | ||||
−0.919298 | + | 0.393562i | \(0.871243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.04868i | 0.479199i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.75906i | − | 0.353622i | −0.984245 | − | 0.176811i | \(-0.943422\pi\) | ||
0.984245 | − | 0.176811i | \(-0.0565782\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.7075i | 2.67699i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.04868i | − | 0.466750i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.25639i | − | 0.390183i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3723 | 0.942935 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.92820i | 0.624695i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.62772 | 0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7446 | 1.13090 | 0.565449 | − | 0.824784i | \(-0.308703\pi\) | ||||
0.565449 | + | 0.824784i | \(0.308703\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.30506i | 0.819265i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.37686i | − | 0.207667i | −0.994595 | − | 0.103834i | \(-0.966889\pi\) | ||
0.994595 | − | 0.103834i | \(-0.0331110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.37228 | + | 3.16915i | −0.118992 | + | 0.274800i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.37228 | −0.290240 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.11684 | −0.351726 | −0.175863 | − | 0.984415i | \(-0.556272\pi\) | ||||
−0.175863 | + | 0.984415i | \(0.556272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.54601i | − | 0.470406i | −0.971946 | − | 0.235203i | \(-0.924424\pi\) | ||
0.971946 | − | 0.235203i | \(-0.0755756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.25639i | − | 0.358453i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.0511i | 2.82779i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.37228 | −0.525577 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.11684 | −0.173419 | −0.0867093 | − | 0.996234i | \(-0.527635\pi\) | ||||
−0.0867093 | + | 0.996234i | \(0.527635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.74456 | −0.711622 | −0.355811 | − | 0.934558i | \(-0.615795\pi\) | ||||
−0.355811 | + | 0.934558i | \(0.615795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.37228 | 0.434323 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.4891 | 2.36862 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.48913 | −0.597697 | −0.298849 | − | 0.954301i | \(-0.596603\pi\) | ||||
−0.298849 | + | 0.954301i | \(0.596603\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.16915i | 0.251330i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.74456 | 0.531546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.8997i | − | 1.55867i | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||
0.626608 | − | 0.779334i | \(-0.284443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 2.67181i | − | 0.208000i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4891 | 1.35335 | 0.676675 | − | 0.736282i | \(-0.263420\pi\) | ||||
0.676675 | + | 0.736282i | \(0.263420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4891 | −0.960702 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | − | 1.73205i | −0.305888 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.1947i | 1.53537i | 0.640825 | + | 0.767687i | \(0.278593\pi\) | ||||
−0.640825 | + | 0.767687i | \(0.721407\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.04868i | − | 0.381644i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.48913 | −0.111302 | −0.0556512 | − | 0.998450i | \(-0.517723\pi\) | ||||
−0.0556512 | + | 0.998450i | \(0.517723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.63858i | − | 0.419113i | −0.977797 | − | 0.209556i | \(-0.932798\pi\) | ||
0.977797 | − | 0.209556i | \(-0.0672019\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.37228 | 0.397130 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 17.0256i | − | 1.25174i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.25639i | 0.311258i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.792287i | 0.0576304i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.66648i | 0.265297i | 0.991163 | + | 0.132649i | \(0.0423482\pi\) | ||||
−0.991163 | + | 0.132649i | \(0.957652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.8564i | − | 0.997406i | −0.866773 | − | 0.498703i | \(-0.833810\pi\) | ||
0.866773 | − | 0.498703i | \(-0.166190\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.0256i | 1.21923i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.25544 | 0.374434 | 0.187217 | − | 0.982319i | \(-0.440053\pi\) | ||||
0.187217 | + | 0.982319i | \(0.440053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.5769i | − | 1.52955i | −0.644300 | − | 0.764773i | \(-0.722851\pi\) | ||
0.644300 | − | 0.764773i | \(-0.277149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.48913 | −0.669311 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 23.3639i | − | 1.63180i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.51278i | 0.591679i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.37228 | − | 3.16915i | 0.0949227 | − | 0.219215i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.00000 | 0.274075 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 31.3793i | − | 2.14005i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.92820i | − | 0.470317i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.11684 | 0.278191 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.1229i | − | 1.82448i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.744563 | 0.0498596 | 0.0249298 | − | 0.999689i | \(-0.492064\pi\) | ||||
0.0249298 | + | 0.999689i | \(0.492064\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.37228 | 0.424819 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.1168 | 1.59369 | 0.796843 | − | 0.604186i | \(-0.206502\pi\) | ||||
0.796843 | + | 0.604186i | \(0.206502\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.627719 | −0.0413009 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.11684 | −0.269703 | −0.134852 | − | 0.990866i | \(-0.543056\pi\) | ||||
−0.134852 | + | 0.990866i | \(0.543056\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.3537i | 0.936335i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.74456 | −0.308192 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 29.7947i | − | 1.92726i | −0.267240 | − | 0.963630i | \(-0.586112\pi\) | ||
0.267240 | − | 0.963630i | \(-0.413888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0256i | 1.09671i | 0.836245 | + | 0.548356i | \(0.184746\pi\) | ||||
−0.836245 | + | 0.548356i | \(0.815254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.4891 | 1.37289 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.74456 | + | 20.1947i | −0.556403 | + | 1.28496i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.46410i | 0.219529i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.13592i | − | 0.387296i | −0.981071 | − | 0.193648i | \(-0.937968\pi\) | ||
0.981071 | − | 0.193648i | \(-0.0620319\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.74456 | −0.424027 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.1168 | −1.13452 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.75906i | 0.234483i | 0.993103 | + | 0.117242i | \(0.0374052\pi\) | ||||
−0.993103 | + | 0.117242i | \(0.962595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0974i | 0.625010i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.1128i | 1.11688i | 0.829544 | + | 0.558441i | \(0.188600\pi\) | ||||
−0.829544 | + | 0.558441i | \(0.811400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.6873i | − | 0.656513i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 13.2665i | − | 0.811897i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.6873i | 0.651614i | 0.945436 | + | 0.325807i | \(0.105636\pi\) | ||||
−0.945436 | + | 0.325807i | \(0.894364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.5615i | − | 0.823800i | −0.911229 | − | 0.411900i | \(-0.864865\pi\) | ||
0.911229 | − | 0.411900i | \(-0.135135\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.04868i | 0.304447i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.62772 | 0.157884 | 0.0789422 | − | 0.996879i | \(-0.474846\pi\) | ||||
0.0789422 | + | 0.996879i | \(0.474846\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.74456 | 0.523523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.0974i | − | 0.602357i | −0.953568 | − | 0.301179i | \(-0.902620\pi\) | ||
0.953568 | − | 0.301179i | \(-0.0973801\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.3253i | 1.62432i | 0.583435 | + | 0.812160i | \(0.301708\pi\) | ||||
−0.583435 | + | 0.812160i | \(0.698292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.4891 | + | 5.84096i | 0.799027 | + | 0.345989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.48913 | −0.324013 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.2665i | 0.777696i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8564i | 0.809500i | 0.914427 | + | 0.404750i | \(0.132641\pi\) | ||||
−0.914427 | + | 0.404750i | \(0.867359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4891 | 0.785367 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.792287i | − | 0.0459732i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 42.9783 | 2.48550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.37228 | −0.424931 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.7446 | −0.847053 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.1168 | −1.03737 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4891 | 0.998157 | 0.499079 | − | 0.866557i | \(-0.333672\pi\) | ||||
0.499079 | + | 0.866557i | \(0.333672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.7446 | 0.725013 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3537i | 0.813926i | 0.913445 | + | 0.406963i | \(0.133412\pi\) | ||||
−0.913445 | + | 0.406963i | \(0.866588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4891 | 1.10159 | 0.550795 | − | 0.834640i | \(-0.314325\pi\) | ||||
0.550795 | + | 0.834640i | \(0.314325\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 2.67181i | − | 0.150540i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.6873i | − | 0.600256i | −0.953899 | − | 0.300128i | \(-0.902971\pi\) | ||
0.953899 | − | 0.300128i | \(-0.0970294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.48913 | 0.529631 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.4891 | − | 9.30506i | −1.19569 | − | 0.517748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 32.1716i | − | 1.78456i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.21782i | − | 0.454447i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.37228 | 0.185920 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.48913 | −0.521569 | −0.260785 | − | 0.965397i | \(-0.583981\pi\) | ||||
−0.260785 | + | 0.965397i | \(0.583981\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.04868i | − | 0.276666i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.0000 | 1.74835 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.7846i | − | 1.13221i | −0.824333 | − | 0.566105i | \(-0.808450\pi\) | ||
0.824333 | − | 0.566105i | \(-0.191550\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.75906i | 0.204164i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.92820i | 0.375183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 10.5947i | − | 0.572059i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 28.7075i | − | 1.54556i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.0641i | − | 0.701319i | −0.936503 | − | 0.350659i | \(-0.885958\pi\) | ||
0.936503 | − | 0.350659i | \(-0.114042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.6060 | 1.37066 | 0.685328 | − | 0.728234i | \(-0.259659\pi\) | ||||
0.685328 | + | 0.728234i | \(0.259659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.04868i | 0.269478i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.4891 | −1.25020 | −0.625100 | − | 0.780545i | \(-0.714942\pi\) | ||||
−0.625100 | + | 0.780545i | \(0.714942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.4891 | −0.715928 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.25639i | 0.225272i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.7638i | 0.726427i | 0.931706 | + | 0.363214i | \(0.118320\pi\) | ||||
−0.931706 | + | 0.363214i | \(0.881680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3723 | −0.544404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8832 | −0.726678 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.8280i | 1.40041i | 0.713943 | + | 0.700204i | \(0.246908\pi\) | ||||
−0.713943 | + | 0.700204i | \(0.753092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.92820i | − | 0.360668i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.51087 | −0.130358 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.87953i | − | 0.0973183i | −0.998815 | − | 0.0486591i | \(-0.984505\pi\) | ||
0.998815 | − | 0.0486591i | \(-0.0154948\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.62772 | −0.238974 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 50.9783 | 2.62551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.9783 | −1.38578 | −0.692890 | − | 0.721043i | \(-0.743663\pi\) | ||||
−0.692890 | + | 0.721043i | \(0.743663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.7446 | −0.652924 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.9783 | 1.58291 | 0.791457 | − | 0.611224i | \(-0.209323\pi\) | ||||
0.791457 | + | 0.611224i | \(0.209323\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.11684 | 0.107884 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 9.30506i | − | 0.473003i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.11684 | −0.310136 | −0.155068 | − | 0.987904i | \(-0.549560\pi\) | ||||
−0.155068 | + | 0.987904i | \(0.549560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.7330i | 2.31282i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.37686i | 0.119897i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8832 | −0.596399 | −0.298199 | − | 0.954504i | \(-0.596386\pi\) | ||||
−0.298199 | + | 0.954504i | \(0.596386\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.37228 | − | 3.16915i | 0.0687000 | − | 0.158656i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.9538i | 1.19619i | 0.801424 | + | 0.598097i | \(0.204076\pi\) | ||||
−0.801424 | + | 0.598097i | \(0.795924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 44.1485i | − | 2.19919i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.37228 | 0.167570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.92820i | 0.342578i | 0.985221 | + | 0.171289i | \(0.0547931\pi\) | ||||
−0.985221 | + | 0.171289i | \(0.945207\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.11684 | 0.203069 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.16915i | − | 0.155944i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.6819i | − | 0.573443i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.54601i | 0.271589i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.294954i | 0.0144094i | 0.999974 | + | 0.00720471i | \(0.00229335\pi\) | ||||
−0.999974 | + | 0.00720471i | \(0.997707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.7615i | 1.59670i | 0.602196 | + | 0.798349i | \(0.294293\pi\) | ||||
−0.602196 | + | 0.798349i | \(0.705707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.25639i | 0.206953i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.2337 | 1.66058 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.25639i | 0.205981i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.5109 | 0.891637 | 0.445819 | − | 0.895123i | \(-0.352913\pi\) | ||||
0.445819 | + | 0.895123i | \(0.352913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 16.4356i | − | 0.789847i | −0.918714 | − | 0.394923i | \(-0.870771\pi\) | ||
0.918714 | − | 0.394923i | \(-0.129229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 34.0511i | − | 1.63263i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.7446 | − | 34.0511i | 0.705328 | − | 1.62889i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.7228 | −1.89587 | −0.947933 | − | 0.318469i | \(-0.896831\pi\) | ||||
−0.947933 | + | 0.318469i | \(0.896831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.37228 | 0.303442 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 19.4024i | − | 0.921837i | −0.887443 | − | 0.460918i | \(-0.847520\pi\) | ||
0.887443 | − | 0.460918i | \(-0.152480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.7384i | 2.12080i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.11684 | 0.100123 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.6155i | 0.831325i | 0.909519 | + | 0.415663i | \(0.136450\pi\) | ||||
−0.909519 | + | 0.415663i | \(0.863550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.48913 | 0.258473 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.74456 | 0.410855 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.4891 | −0.632380 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.11684 | −0.379690 | −0.189845 | − | 0.981814i | \(-0.560799\pi\) | ||||
−0.189845 | + | 0.981814i | \(0.560799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.37228 | −0.250757 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.6277 | −1.51962 | −0.759812 | − | 0.650143i | \(-0.774709\pi\) | ||||
−0.759812 | + | 0.650143i | \(0.774709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.202380i | − | 0.00940538i | −0.999989 | − | 0.00470269i | \(-0.998503\pi\) | ||
0.999989 | − | 0.00470269i | \(-0.00149692\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −29.4891 | −1.36753 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.0843i | 1.43841i | 0.694797 | + | 0.719206i | \(0.255494\pi\) | ||||
−0.694797 | + | 0.719206i | \(0.744506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.51811i | − | 0.347154i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.48913 | 0.345081 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.37228 | 0.338978 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.4891 | − | 11.0371i | −1.16952 | − | 0.506418i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.16915i | − | 0.145105i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 21.7793i | − | 0.995121i | −0.867429 | − | 0.497560i | \(-0.834229\pi\) | ||
0.867429 | − | 0.497560i | \(-0.165771\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.4891 | −1.16220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.74456 | −0.306888 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 44.7384i | − | 2.03146i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.76631 | 0.261297 | 0.130648 | − | 0.991429i | \(-0.458294\pi\) | ||||
0.130648 | + | 0.991429i | \(0.458294\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8997i | 0.899898i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.0796i | − | 0.951307i | −0.879633 | − | 0.475654i | \(-0.842212\pi\) | ||
0.879633 | − | 0.475654i | \(-0.157788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.2458i | 2.44311i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.67181i | 0.120089i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.16915i | 0.142156i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.55134i | 0.203746i | 0.994797 | + | 0.101873i | \(0.0324835\pi\) | ||||
−0.994797 | + | 0.101873i | \(0.967516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.4891 | −0.781356 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0309i | 0.714782i | 0.933955 | + | 0.357391i | \(0.116334\pi\) | ||||
−0.933955 | + | 0.357391i | \(0.883666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.7228 | 2.21264 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.4891 | 0.554662 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.2665i | 0.588027i | 0.955801 | + | 0.294014i | \(0.0949911\pi\) | ||||
−0.955801 | + | 0.294014i | \(0.905009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.26172i | 0.144290i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | + | 1.73205i | 0.176604 | + | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.9783 | −1.89385 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.37228 | −0.148313 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.1947i | − | 0.886449i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.75906i | − | 0.164687i | −0.996604 | − | 0.0823436i | \(-0.973760\pi\) | ||
0.996604 | − | 0.0823436i | \(-0.0262405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.0000 | −1.39926 | −0.699631 | − | 0.714504i | \(-0.746652\pi\) | ||||
−0.699631 | + | 0.714504i | \(0.746652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.04868i | 0.220342i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.9783 | 2.04640 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.4674 | −2.15076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.9783 | −1.51508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.0000 | −1.38348 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.48913 | 0.0642605 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.04868i | 0.217462i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.11684 | 0.176997 | 0.0884985 | − | 0.996076i | \(-0.471793\pi\) | ||||
0.0884985 | + | 0.996076i | \(0.471793\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.63858i | 0.241975i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.7128i | 1.18709i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4891 | 1.26086 | 0.630432 | − | 0.776245i | \(-0.282878\pi\) | ||||
0.630432 | + | 0.776245i | \(0.282878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.37228 | −0.229283 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.4891 | − | 40.3894i | 0.745062 | − | 1.72065i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.75906i | − | 0.159851i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.0256i | 0.722695i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.1386 | −0.471957 | −0.235979 | − | 0.971758i | \(-0.575830\pi\) | ||||
−0.235979 | + | 0.971758i | \(0.575830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.9783 | −1.98697 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 4.25639i | − | 0.179705i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9783 | 0.968418 | 0.484209 | − | 0.874952i | \(-0.339107\pi\) | ||||
0.484209 | + | 0.874952i | \(0.339107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.6766i | − | 0.533308i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.792287i | − | 0.0332729i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27.1229i | − | 1.13705i | −0.822666 | − | 0.568526i | \(-0.807514\pi\) | ||
0.822666 | − | 0.568526i | \(-0.192486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.87419i | 0.120281i | 0.998190 | + | 0.0601406i | \(0.0191549\pi\) | ||||
−0.998190 | + | 0.0601406i | \(0.980845\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.66648i | − | 0.153169i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 54.2458i | 2.26221i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6060 | −1.56556 | −0.782778 | − | 0.622300i | \(-0.786198\pi\) | ||||
−0.782778 | + | 0.622300i | \(0.786198\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.8564i | 0.575853i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.74456 | −0.113864 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.51087 | 0.103990 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 17.0256i | − | 0.703920i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.38219i | 0.0570493i | 0.999593 | + | 0.0285246i | \(0.00908090\pi\) | ||||
−0.999593 | + | 0.0285246i | \(0.990919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.9783 | − | 15.1460i | −1.44125 | − | 0.624081i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.25544 | −0.216180 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.4891 | −0.964583 | −0.482291 | − | 0.876011i | \(-0.660195\pi\) | ||||
−0.482291 | + | 0.876011i | \(0.660195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 14.3537i | − | 0.588446i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.5769i | 0.883084i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.4674 | 1.81689 | 0.908444 | − | 0.418007i | \(-0.137271\pi\) | ||||
0.908444 | + | 0.418007i | \(0.137271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.6048i | − | 0.799696i | −0.916581 | − | 0.399848i | \(-0.869063\pi\) | ||
0.916581 | − | 0.399848i | \(-0.130937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.48913 | 0.386427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.9783 | 1.42207 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.7446 | −1.65377 | −0.826885 | − | 0.562370i | \(-0.809889\pi\) | ||||
−0.826885 | + | 0.562370i | \(0.809889\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | −0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.4891 | 0.869357 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.37228 | −0.216984 | −0.108492 | − | 0.994097i | \(-0.534602\pi\) | ||||
−0.108492 | + | 0.994097i | \(0.534602\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.3639i | 0.942121i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.0951 | −0.768740 | −0.384370 | − | 0.923179i | \(-0.625581\pi\) | ||||
−0.384370 | + | 0.923179i | \(0.625581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3923i | 0.417702i | 0.977947 | + | 0.208851i | \(0.0669724\pi\) | ||||
−0.977947 | + | 0.208851i | \(0.933028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 8.51278i | − | 0.341606i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.5109 | 0.421109 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.37228 | + | 3.16915i | −0.0548036 | + | 0.126564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 27.1229i | − | 1.08146i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.7663i | 1.70250i | 0.524762 | + | 0.851249i | \(0.324154\pi\) | ||||
−0.524762 | + | 0.851249i | \(0.675846\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.00000 | 0.158986 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.9783 | 1.70554 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 32.1716i | − | 1.27468i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.2665i | 0.523995i | 0.965069 | + | 0.261998i | \(0.0843813\pi\) | ||||
−0.965069 | + | 0.261998i | \(0.915619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.792287i | 0.0312447i | 0.999878 | + | 0.0156224i | \(0.00497296\pi\) | ||||
−0.999878 | + | 0.0156224i | \(0.995027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.3793i | 1.23556i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 36.7229i | − | 1.44373i | −0.692035 | − | 0.721864i | \(-0.743286\pi\) | ||
0.692035 | − | 0.721864i | \(-0.256714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.16915i | 0.124400i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.92820i | 0.271538i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.1168 | −0.865499 | −0.432749 | − | 0.901514i | \(-0.642457\pi\) | ||||
−0.432749 | + | 0.901514i | \(0.642457\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.01544i | − | 0.313189i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.11684 | −0.160613 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.48913 | −0.369644 | −0.184822 | − | 0.982772i | \(-0.559171\pi\) | ||||
−0.184822 | + | 0.982772i | \(0.559171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.0280i | 1.79028i | 0.445784 | + | 0.895141i | \(0.352925\pi\) | ||||
−0.445784 | + | 0.895141i | \(0.647075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.1229i | 1.05337i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.62772 | + | 10.6873i | −0.179455 | + | 0.414434i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −85.9565 | −3.32825 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.744563 | −0.0287865 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.25639i | − | 0.164316i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 14.4463i | − | 0.556864i | −0.960456 | − | 0.278432i | \(-0.910185\pi\) | ||
0.960456 | − | 0.278432i | \(-0.0898148\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.37228 | −0.245269 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.3745i | − | 0.821489i | −0.911750 | − | 0.410745i | \(-0.865269\pi\) | ||
0.911750 | − | 0.410745i | \(-0.134731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5109 | −0.403370 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.97825 | −0.267015 | −0.133508 | − | 0.991048i | \(-0.542624\pi\) | ||||
−0.133508 | + | 0.991048i | \(0.542624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8832 | −0.530448 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.1168 | −0.920115 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0000 | −0.609551 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.9152i | 1.06194i | 0.847389 | + | 0.530972i | \(0.178173\pi\) | ||||
−0.847389 | + | 0.530972i | \(0.821827\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.627719 | 0.0238451 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 18.7027i | − | 0.709434i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 37.2203i | − | 1.40982i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.11684 | 0.155713 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.7228 | −1.42477 | −0.712385 | − | 0.701788i | \(-0.752385\pi\) | ||||
−0.712385 | + | 0.701788i | \(0.752385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.74456 | + | 20.1947i | −0.329807 | + | 0.761658i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 14.3537i | − | 0.540593i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 11.6819i | − | 0.439344i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.9565 | −1.65082 | −0.825411 | − | 0.564533i | \(-0.809056\pi\) | ||||
−0.825411 | + | 0.564533i | \(0.809056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.74456 | 0.177935 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 74.4405i | 2.78782i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.4891 | 0.504465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.7947i | 1.11270i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.7638i | 0.513304i | 0.966504 | + | 0.256652i | \(0.0826195\pi\) | ||||
−0.966504 | + | 0.256652i | \(0.917381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0974i | 0.376045i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17.0256i | − | 0.633187i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 64.3432i | 2.38965i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.7460i | − | 0.917780i | −0.888493 | − | 0.458890i | \(-0.848247\pi\) | ||
0.888493 | − | 0.458890i | \(-0.151753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 49.9894i | − | 1.84893i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9783 | 0.774849 | 0.387425 | − | 0.921901i | \(-0.373365\pi\) | ||||
0.387425 | + | 0.921901i | \(0.373365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.4891 | −0.792638 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.51811i | 0.276933i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0125i | 1.39831i | 0.714968 | + | 0.699157i | \(0.246441\pi\) | ||||
−0.714968 | + | 0.699157i | \(0.753559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.74456 | − | 20.1947i | 0.321240 | − | 0.741871i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.9783 | −1.28323 | −0.641614 | − | 0.767028i | \(-0.721735\pi\) | ||||
−0.641614 | + | 0.767028i | \(0.721735\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.13859 | −0.261538 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.46410i | − | 0.126745i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.51811i | 0.274706i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7228 | 0.573734 | 0.286867 | − | 0.957970i | \(-0.407386\pi\) | ||||
0.286867 | + | 0.957970i | \(0.407386\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.13592i | 0.223605i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.4891 | −1.07322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8614 | −0.394765 | −0.197382 | − | 0.980327i | \(-0.563244\pi\) | ||||
−0.197382 | + | 0.980327i | \(0.563244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.74456 | 0.244812 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.86141 | 0.248726 | 0.124363 | − | 0.992237i | \(-0.460311\pi\) | ||||
0.124363 | + | 0.992237i | \(0.460311\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.51087 | 0.235709 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.1168 | 0.655016 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 20.1947i | − | 0.729188i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.13859 | −0.329546 | −0.164773 | − | 0.986332i | \(-0.552689\pi\) | ||||
−0.164773 | + | 0.986332i | \(0.552689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 3.75906i | − | 0.135379i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.7995i | 1.43149i | 0.698363 | + | 0.715744i | \(0.253912\pi\) | ||||
−0.698363 | + | 0.715744i | \(0.746088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.7228 | 2.00162 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | + | 27.7128i | −0.429945 | + | 0.992915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.16915i | − | 0.113401i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10.0974i | − | 0.360850i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.2554 | −0.901405 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.9783 | −0.391332 | −0.195666 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195666 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 18.1128i | − | 0.644833i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.97825 | −0.105894 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.1229i | 0.963163i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.6873i | 0.379038i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0974i | 0.357667i | 0.983879 | + | 0.178833i | \(0.0572323\pi\) | ||||
−0.983879 | + | 0.178833i | \(0.942768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.8665i | 0.808959i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.2665i | 0.468749i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 3.26172i | − | 0.115104i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.7446 | 0.801640 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 10.6873i | − | 0.376209i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.1168 | −1.12917 | −0.564584 | − | 0.825376i | \(-0.690963\pi\) | ||||
−0.564584 | + | 0.825376i | \(0.690963\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4674 | 1.14008 | 0.570042 | − | 0.821616i | \(-0.306927\pi\) | ||||
0.570042 | + | 0.821616i | \(0.306927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5615i | 0.475621i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 67.1076i | − | 2.35067i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1168 | + | 37.2203i | −0.563857 | + | 1.30217i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00000 | −0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6277 | −0.580311 | −0.290156 | − | 0.956979i | \(-0.593707\pi\) | ||||
−0.290156 | + | 0.956979i | \(0.593707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.2333i | 0.565856i | 0.959141 | + | 0.282928i | \(0.0913058\pi\) | ||||
−0.959141 | + | 0.282928i | \(0.908694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.04868i | − | 0.175772i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.48913 | 0.0517820 | 0.0258910 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258910 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.4487i | − | 1.50904i | −0.656279 | − | 0.754519i | \(-0.727870\pi\) | ||
0.656279 | − | 0.754519i | \(-0.272130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.62772 | −0.0911546 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.2337 | 1.18613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.9783 | 2.04103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.74456 | −0.302256 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −72.9565 | −2.51574 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0974i | 0.347771i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42.1168 | −1.44886 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.21782i | − | 0.282368i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 27.3253i | − | 0.937801i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.9783 | 1.47328 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | −0.753266 | −0.376633 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.4891 | − | 5.84096i | −0.461318 | − | 0.199757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.3176i | 1.61634i | 0.588950 | + | 0.808169i | \(0.299541\pi\) | ||||
−0.588950 | + | 0.808169i | \(0.700459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.4589i | 1.78987i | 0.446193 | + | 0.894937i | \(0.352779\pi\) | ||||
−0.446193 | + | 0.894937i | \(0.647221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.48913 | 0.187069 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.4674 | −1.92217 | −0.961086 | − | 0.276250i | \(-0.910908\pi\) | ||||
−0.961086 | + | 0.276250i | \(0.910908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 68.1022i | 2.31554i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.8614 | −0.402834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.75906i | 0.127517i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 47.9075i | − | 1.62328i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.2665i | − | 0.449003i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.66648i | − | 0.123950i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3514i | 1.12620i | 0.826390 | + | 0.563098i | \(0.190391\pi\) | ||||
−0.826390 | + | 0.563098i | \(0.809609\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 13.8564i | − | 0.467365i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.6060 | −1.13221 | −0.566107 | − | 0.824332i | \(-0.691551\pi\) | ||||
−0.566107 | + | 0.824332i | \(0.691551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.13592i | − | 0.206490i | −0.994656 | − | 0.103245i | \(-0.967077\pi\) | ||
0.994656 | − | 0.103245i | \(-0.0329226\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.4891 | −0.453432 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.0000 | 0.940148 | 0.470074 | − | 0.882627i | \(-0.344227\pi\) | ||||
0.470074 | + | 0.882627i | \(0.344227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.0974i | − | 0.338654i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.792287i | 0.0265426i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.37228 | − | 17.0256i | 0.246704 | − | 0.569738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.02175 | −0.167859 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.9783 | −1.43500 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 88.2969i | 2.94487i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 17.0256i | − | 0.567203i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.37228 | 0.245334 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 19.0149i | − | 0.632076i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.4674 | 1.60933 | 0.804666 | − | 0.593727i | \(-0.202344\pi\) | ||||
0.804666 | + | 0.593727i | \(0.202344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.7446 | 0.489046 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4891 | 0.844492 | 0.422246 | − | 0.906481i | \(-0.361242\pi\) | ||||
0.422246 | + | 0.906481i | \(0.361242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.74456 | 0.0908318 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.1168 | 0.598924 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.88316 | −0.0621873 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 51.3716i | − | 1.69459i | −0.531120 | − | 0.847297i | \(-0.678229\pi\) | ||
0.531120 | − | 0.847297i | \(-0.321771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.4891 | −0.576286 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.1947i | 0.664717i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 32.1716i | − | 1.05780i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.7446 | −0.418586 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.4891 | −1.82054 | −0.910270 | − | 0.414016i | \(-0.864126\pi\) | ||||
−0.910270 | + | 0.414016i | \(0.864126\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.4891 | − | 11.0371i | −0.835372 | − | 0.361727i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 14.3537i | − | 0.469920i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.3537i | 0.469417i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.3723 | 0.567528 | 0.283764 | − | 0.958894i | \(-0.408417\pi\) | ||||
0.283764 | + | 0.958894i | \(0.408417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.4891 | −0.636004 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.75906i | − | 0.122542i | −0.998121 | − | 0.0612708i | \(-0.980485\pi\) | ||
0.998121 | − | 0.0612708i | \(-0.0195153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.9783 | 1.92060 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.67181i | 0.0869141i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.9715i | 0.421519i | 0.977538 | + | 0.210759i | \(0.0675936\pi\) | ||||
−0.977538 | + | 0.210759i | \(0.932406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7846i | 0.674697i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.6873i | 0.346558i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 37.8102i | − | 1.22479i | −0.790551 | − | 0.612396i | \(-0.790206\pi\) | ||
0.790551 | − | 0.612396i | \(-0.209794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.3644i | 0.400103i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.00000 | 0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.26172i | 0.105326i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.4674 | 1.46669 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.48913 | −0.305783 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 46.7277i | − | 1.50422i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.1407i | − | 0.519050i | −0.965736 | − | 0.259525i | \(-0.916434\pi\) | ||
0.965736 | − | 0.259525i | \(-0.0835659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.4891 | + | 9.30506i | 0.690330 | + | 0.298922i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.4674 | −1.42703 | −0.713513 | − | 0.700642i | \(-0.752897\pi\) | ||||
−0.713513 | + | 0.700642i | \(0.752897\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.39403 | −0.140866 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.1716i | 1.03032i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.6048i | 0.627213i | 0.949553 | + | 0.313606i | \(0.101537\pi\) | ||||
−0.949553 | + | 0.313606i | \(0.898463\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5109 | −0.335929 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.21782i | 0.262375i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.02175 | −0.160169 | −0.0800845 | − | 0.996788i | \(-0.525519\pi\) | ||||
−0.0800845 | + | 0.996788i | \(0.525519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.7228 | 0.564696 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.37228 | −0.107341 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 79.2119 | 2.51879 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.74456 | 0.277780 | 0.138890 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138890 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.48913 | 0.301128 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 72.7634i | − | 2.30675i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.6060 | 1.69772 | 0.848859 | − | 0.528619i | \(-0.177290\pi\) | ||||
0.848859 | + | 0.528619i | \(0.177290\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.04868i | 0.159733i |
(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 | 3648.2.k.g.2431.3 | 4 | ||
4.3 | odd | 2 | 3648.2.k.h.2431.4 | 4 | |||
8.3 | odd | 2 | 912.2.k.g.607.2 | yes | 4 | ||
8.5 | even | 2 | 912.2.k.h.607.1 | yes | 4 | ||
19.18 | odd | 2 | 3648.2.k.h.2431.3 | 4 | |||
24.5 | odd | 2 | 2736.2.k.o.2431.3 | 4 | |||
24.11 | even | 2 | 2736.2.k.n.2431.4 | 4 | |||
76.75 | even | 2 | inner | 3648.2.k.g.2431.4 | 4 | ||
152.37 | odd | 2 | 912.2.k.g.607.1 | ✓ | 4 | ||
152.75 | even | 2 | 912.2.k.h.607.2 | yes | 4 | ||
456.227 | odd | 2 | 2736.2.k.o.2431.4 | 4 | |||
456.341 | even | 2 | 2736.2.k.n.2431.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.k.g.607.1 | ✓ | 4 | 152.37 | odd | 2 | ||
912.2.k.g.607.2 | yes | 4 | 8.3 | odd | 2 | ||
912.2.k.h.607.1 | yes | 4 | 8.5 | even | 2 | ||
912.2.k.h.607.2 | yes | 4 | 152.75 | even | 2 | ||
2736.2.k.n.2431.3 | 4 | 456.341 | even | 2 | |||
2736.2.k.n.2431.4 | 4 | 24.11 | even | 2 | |||
2736.2.k.o.2431.3 | 4 | 24.5 | odd | 2 | |||
2736.2.k.o.2431.4 | 4 | 456.227 | odd | 2 | |||
3648.2.k.g.2431.3 | 4 | 1.1 | even | 1 | trivial | ||
3648.2.k.g.2431.4 | 4 | 76.75 | even | 2 | inner | ||
3648.2.k.h.2431.3 | 4 | 19.18 | odd | 2 | |||
3648.2.k.h.2431.4 | 4 | 4.3 | odd | 2 |