Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(1519,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1520.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.g (of order \(2\), degree \(1\), 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32x^{14} + 380x^{12} - 1752x^{10} + 1904x^{8} + 7824x^{6} + 7352x^{4} + 2992x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.3 | ||
Root | \(3.52761 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.1519 |
Dual form | 1520.2.g.f.1519.13 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.59462i | − | 1.49800i | −0.662568 | − | 0.749002i | \(-0.730533\pi\) | ||
0.662568 | − | 0.749002i | \(-0.269467\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73205 | + | 1.41421i | −0.774597 | + | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.38587 | −1.27974 | −0.639869 | − | 0.768484i | \(-0.721011\pi\) | ||||
−0.639869 | + | 0.768484i | \(0.721011\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.73205 | −1.24402 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.75265i | 0.528445i | 0.964462 | + | 0.264223i | \(0.0851153\pi\) | ||||
−0.964462 | + | 0.264223i | \(0.914885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.21196 | 1.72289 | 0.861444 | − | 0.507853i | \(-0.169561\pi\) | ||||
0.861444 | + | 0.507853i | \(0.169561\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.66935 | + | 4.49401i | 0.947421 | + | 1.16035i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.69213i | 1.62308i | 0.584297 | + | 0.811540i | \(0.301370\pi\) | ||||
−0.584297 | + | 0.811540i | \(0.698630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.34307 | − | 4.14682i | −0.308122 | − | 0.951347i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.78504i | 1.91705i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.86450 | 1.22283 | 0.611416 | − | 0.791309i | \(-0.290600\pi\) | ||||
0.611416 | + | 0.791309i | \(0.290600\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.89939i | 0.365538i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.43110i | 1.19422i | 0.802158 | + | 0.597112i | \(0.203685\pi\) | ||||
−0.802158 | + | 0.597112i | \(0.796315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.35549 | −1.14148 | −0.570740 | − | 0.821131i | \(-0.693344\pi\) | ||||
−0.570740 | + | 0.821131i | \(0.693344\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54747 | 0.791613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.86450 | − | 4.78834i | 0.991281 | − | 0.809377i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.66449 | 0.273640 | 0.136820 | − | 0.990596i | \(-0.456312\pi\) | ||||
0.136820 | + | 0.990596i | \(0.456312\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 16.1177i | − | 2.58089i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.78504i | − | 1.37199i | −0.727605 | − | 0.685996i | \(-0.759367\pi\) | ||
0.727605 | − | 0.685996i | \(-0.240633\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.907241 | −0.138353 | −0.0691764 | − | 0.997604i | \(-0.522037\pi\) | ||||
−0.0691764 | + | 0.997604i | \(0.522037\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.46410 | − | 5.27792i | 0.963611 | − | 0.786785i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.1576 | 1.48164 | 0.740819 | − | 0.671704i | \(-0.234437\pi\) | ||||
0.740819 | + | 0.671704i | \(0.234437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.46410 | 0.637729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.3635 | 2.43138 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7594 | 1.47792 | 0.738961 | − | 0.673748i | \(-0.235317\pi\) | ||||
0.738961 | + | 0.673748i | \(0.235317\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.47863 | − | 3.03569i | −0.334218 | − | 0.409332i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.7594 | + | 3.48477i | −1.42512 | + | 0.461569i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.35549 | 0.827415 | 0.413707 | − | 0.910410i | \(-0.364234\pi\) | ||||
0.413707 | + | 0.910410i | \(0.364234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.19615 | −0.281189 | −0.140594 | − | 0.990067i | \(-0.544901\pi\) | ||||
−0.140594 | + | 0.990067i | \(0.544901\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.6362 | 1.59202 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7594 | + | 8.78504i | −1.33454 | + | 1.08965i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.49401i | 0.549031i | 0.961583 | + | 0.274516i | \(0.0885175\pi\) | ||||
−0.961583 | + | 0.274516i | \(0.911483\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 15.2161i | − | 1.83181i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.70295 | −0.202103 | −0.101051 | − | 0.994881i | \(-0.532221\pi\) | ||||
−0.101051 | + | 0.994881i | \(0.532221\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.58630i | − | 0.419745i | −0.977729 | − | 0.209872i | \(-0.932695\pi\) | ||
0.977729 | − | 0.209872i | \(-0.0673049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.7110 | − | 2.59462i | −1.46774 | − | 0.299601i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.93426i | − | 0.676271i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.3803 | 1.84293 | 0.921466 | − | 0.388459i | \(-0.126993\pi\) | ||||
0.921466 | + | 0.388459i | \(0.126993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.26795 | −0.696439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.57139 | −0.172482 | −0.0862411 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862411 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.46410 | − | 11.5911i | −1.02653 | − | 1.25723i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.6862 | 1.78895 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.43110i | − | 0.681695i | −0.940119 | − | 0.340847i | \(-0.889286\pi\) | ||
0.940119 | − | 0.340847i | \(-0.110714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.0329 | −2.20484 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.4901i | 1.70994i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.19077 | + | 5.28312i | 0.840355 | + | 0.542036i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.66449 | −0.169003 | −0.0845017 | − | 0.996423i | \(-0.526930\pi\) | ||||
−0.0845017 | + | 0.996423i | \(0.526930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.54099i | − | 0.657395i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.19615 | 0.815548 | 0.407774 | − | 0.913083i | \(-0.366305\pi\) | ||||
0.407774 | + | 0.913083i | \(0.366305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4820i | 1.32842i | 0.747544 | + | 0.664212i | \(0.231233\pi\) | ||||
−0.747544 | + | 0.664212i | \(0.768767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.4239 | − | 15.2161i | −1.21245 | − | 1.48494i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.68325i | 0.936115i | 0.883698 | + | 0.468058i | \(0.155046\pi\) | ||||
−0.883698 | + | 0.468058i | \(0.844954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2161i | 1.45744i | 0.684811 | + | 0.728721i | \(0.259885\pi\) | ||||
−0.684811 | + | 0.728721i | \(0.740115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.31872i | − | 0.409915i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.88298 | 0.271208 | 0.135604 | − | 0.990763i | \(-0.456703\pi\) | ||||
0.135604 | + | 0.990763i | \(0.456703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.1576 | + | 8.29365i | −0.947201 | + | 0.773387i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −23.1834 | −2.14330 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 22.6587i | − | 2.07712i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.92820 | 0.720746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.7938 | −2.05525 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.19615 | + | 9.89949i | 0.464758 | + | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.7719i | − | 1.48826i | −0.668033 | − | 0.744132i | \(-0.732863\pi\) | ||
0.668033 | − | 0.744132i | \(-0.267137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.35394i | 0.207253i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.0820i | − | 1.14298i | −0.820609 | − | 0.571489i | \(-0.806366\pi\) | ||
0.820609 | − | 0.571489i | \(-0.193634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.54747 | + | 14.0406i | 0.394316 | + | 1.21747i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.68615 | − | 3.28985i | −0.231187 | − | 0.283145i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.277401i | 0.0237000i | 0.999930 | + | 0.0118500i | \(0.00377206\pi\) | ||||
−0.999930 | + | 0.0118500i | \(0.996228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4007i | 1.47591i | 0.674851 | + | 0.737954i | \(0.264208\pi\) | ||||
−0.674851 | + | 0.737954i | \(0.735792\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 26.3551i | − | 2.21950i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.8874i | 0.910452i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.09494 | − | 11.1390i | −0.755294 | − | 0.925042i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 11.5826i | − | 0.955320i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.6603 | −0.955245 | −0.477623 | − | 0.878565i | \(-0.658501\pi\) | ||||
−0.477623 | + | 0.878565i | \(0.658501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3635 | 1.41302 | 0.706512 | − | 0.707701i | \(-0.250268\pi\) | ||||
0.706512 | + | 0.707701i | \(0.250268\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 24.9754i | − | 2.01914i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.0080 | − | 8.98803i | 0.884187 | − | 0.721936i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.79315i | 0.143109i | 0.997437 | + | 0.0715545i | \(0.0227960\pi\) | ||||
−0.997437 | + | 0.0715545i | \(0.977204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 27.9166i | − | 2.21393i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8564 | −1.56490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6362 | 0.989746 | 0.494873 | − | 0.868965i | \(-0.335215\pi\) | ||||
0.494873 | + | 0.868965i | \(0.335215\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.87645 | + | 6.43110i | −0.613181 | + | 0.500660i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1922i | 0.788696i | 0.918961 | + | 0.394348i | \(0.129029\pi\) | ||||
−0.918961 | + | 0.394348i | \(0.870971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.5885 | 1.96834 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.01242 | + | 15.4762i | 0.383309 | + | 1.18349i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6359 | 1.41686 | 0.708430 | − | 0.705781i | \(-0.249404\pi\) | ||||
0.708430 | + | 0.705781i | \(0.249404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.38587 | + | 16.5873i | −0.255948 | + | 1.25388i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 16.4901i | − | 1.23947i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6606 | −1.17053 | −0.585263 | − | 0.810843i | \(-0.699009\pi\) | ||||
−0.585263 | + | 0.810843i | \(0.699009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1390i | 0.827954i | 0.910287 | + | 0.413977i | \(0.135861\pi\) | ||||
−0.910287 | + | 0.413977i | \(0.864139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.69818i | 0.421222i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.88298 | + | 2.35394i | −0.211961 | + | 0.173065i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.7290 | −0.857709 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 6.43110i | − | 0.467793i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.28303i | − | 0.0928369i | −0.998922 | − | 0.0464185i | \(-0.985219\pi\) | ||
0.998922 | − | 0.0464185i | \(-0.0147808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0884 | 1.01411 | 0.507053 | − | 0.861915i | \(-0.330735\pi\) | ||||
0.507053 | + | 0.861915i | \(0.330735\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.7938 | + | 27.9166i | 1.63230 | + | 1.99915i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.79315i | 0.127757i | 0.997958 | + | 0.0638784i | \(0.0203470\pi\) | ||||
−0.997958 | + | 0.0638784i | \(0.979653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.22228i | − | 0.157533i | −0.996893 | − | 0.0787665i | \(-0.974902\pi\) | ||
0.996893 | − | 0.0787665i | \(-0.0250982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6603 | 0.822451 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 21.7748i | − | 1.52829i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4239 | + | 15.2161i | 0.867724 | + | 1.06274i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.8866 | −1.52122 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.26795 | − | 2.35394i | 0.502735 | − | 0.162826i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.68615 | 0.184922 | 0.0924610 | − | 0.995716i | \(-0.470527\pi\) | ||||
0.0924610 | + | 0.995716i | \(0.470527\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.41851i | 0.302751i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.57139 | − | 1.28303i | 0.107168 | − | 0.0875021i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.5189 | 1.46080 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.30509 | −0.628780 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 41.5713i | 2.79639i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.1802i | − | 1.28440i | −0.766536 | − | 0.642201i | \(-0.778021\pi\) | ||
0.766536 | − | 0.642201i | \(-0.221979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.73205 | + | 18.2832i | −0.248803 | + | 1.21888i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0737i | 0.734988i | 0.930026 | + | 0.367494i | \(0.119784\pi\) | ||||
−0.930026 | + | 0.367494i | \(0.880216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.1244 | −0.999446 | −0.499723 | − | 0.866185i | \(-0.666565\pi\) | ||||
−0.499723 | + | 0.866185i | \(0.666565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.3971 | −1.01306 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.76268i | − | 0.574062i | −0.957921 | − | 0.287031i | \(-0.907332\pi\) | ||
0.957921 | − | 0.287031i | \(-0.0926683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.5935 | + | 14.3650i | −1.14767 | + | 0.937071i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 42.5007i | − | 2.76072i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.01062i | − | 0.453479i | −0.973955 | − | 0.226740i | \(-0.927193\pi\) | ||
0.973955 | − | 0.226740i | \(-0.0728066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2161i | 0.980157i | 0.871678 | + | 0.490079i | \(0.163032\pi\) | ||||
−0.871678 | + | 0.490079i | \(0.836968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.9611i | 1.40881i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.73205 | + | 6.31319i | −0.493983 | + | 0.403335i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.34312 | − | 25.7599i | −0.530860 | − | 1.63906i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.07715i | 0.258379i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.35440i | 0.464206i | 0.972691 | + | 0.232103i | \(0.0745606\pi\) | ||||
−0.972691 | + | 0.232103i | \(0.925439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2784i | 0.646200i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −30.0745 | + | 24.5557i | −1.88334 | + | 1.53774i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.5123 | 1.65379 | 0.826897 | − | 0.562353i | \(-0.190104\pi\) | ||||
0.826897 | + | 0.562353i | \(0.190104\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.63574 | −0.350188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 24.0012i | − | 1.48564i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.4507 | −0.891069 | −0.445535 | − | 0.895265i | \(-0.646986\pi\) | ||||
−0.445535 | + | 0.895265i | \(0.646986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.6359 | + | 15.2161i | −1.14479 | + | 0.934720i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.6862 | −1.02118 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.78504i | 0.535633i | 0.963470 | + | 0.267817i | \(0.0863021\pi\) | ||||
−0.963470 | + | 0.267817i | \(0.913698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4007i | 1.05702i | 0.848928 | + | 0.528509i | \(0.177249\pi\) | ||||
−0.848928 | + | 0.528509i | \(0.822751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 54.5723i | 3.30287i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.58622 | + | 1.75265i | 0.517768 | + | 0.105689i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7637i | 1.12740i | 0.825979 | + | 0.563701i | \(0.190623\pi\) | ||||
−0.825979 | + | 0.563701i | \(0.809377\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.7190 | 1.42002 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.35394i | − | 0.140425i | −0.997532 | − | 0.0702123i | \(-0.977632\pi\) | ||
0.997532 | − | 0.0702123i | \(-0.0223677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.52864 | −0.388087 | −0.194044 | − | 0.980993i | \(-0.562160\pi\) | ||||
−0.194044 | + | 0.980993i | \(0.562160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.7077 | − | 21.2519i | 0.811973 | − | 1.25886i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.7450i | 1.75579i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.7846 | −1.63439 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.31872i | 0.253168i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7594 | −0.628573 | −0.314286 | − | 0.949328i | \(-0.601765\pi\) | ||||
−0.314286 | + | 0.949328i | \(0.601765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0080 | + | 8.98803i | −0.640913 | + | 0.523303i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.32898 | −0.193167 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.4300 | 2.10680 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.07180 | 0.177055 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 21.2659i | − | 1.22169i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.80385 | − | 3.10583i | 0.217808 | − | 0.177839i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.8904i | − | 0.906911i | −0.891279 | − | 0.453456i | \(-0.850191\pi\) | ||
0.891279 | − | 0.453456i | \(-0.149809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 34.9808 | 1.98999 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.3506i | 1.43750i | 0.695269 | + | 0.718749i | \(0.255285\pi\) | ||||
−0.695269 | + | 0.718749i | \(0.744715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.00481i | − | 0.452459i | −0.974074 | − | 0.226229i | \(-0.927360\pi\) | ||
0.974074 | − | 0.226229i | \(-0.0726399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.8866 | + | 17.8703i | −1.23317 | + | 1.00688i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.6359 | 1.04670 | 0.523348 | − | 0.852119i | \(-0.324683\pi\) | ||||
0.523348 | + | 0.852119i | \(0.324683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2715 | −0.631082 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.1244 | 1.40230 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.7511 | − | 8.98803i | 1.54411 | − | 0.500107i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.21196 | − | 30.4323i | 0.344578 | − | 1.68808i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.4801 | 2.18325 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.3923 | −1.89611 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.30509 | −0.511454 | −0.255727 | − | 0.966749i | \(-0.582315\pi\) | ||||
−0.255727 | + | 0.966749i | \(0.582315\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.21196 | −0.340413 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.35549 | − | 7.78386i | −0.347238 | − | 0.425278i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.3069 | 0.833820 | 0.416910 | − | 0.908948i | \(-0.363113\pi\) | ||||
0.416910 | + | 0.908948i | \(0.363113\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 7.48024i | − | 0.406271i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.1390i | − | 0.603210i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.58622 | 0.463612 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.5189 | + | 26.3551i | 1.15854 | + | 1.41891i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.86450 | −0.314823 | −0.157411 | − | 0.987533i | \(-0.550315\pi\) | ||||
−0.157411 | + | 0.987533i | \(0.550315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.7990i | 0.629782i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.9449i | − | 1.70026i | −0.526576 | − | 0.850128i | \(-0.676525\pi\) | ||
0.526576 | − | 0.850128i | \(-0.323475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.94960 | − | 2.40833i | 0.156548 | − | 0.127821i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −58.7906 | −3.11153 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.8346i | − | 0.782943i | −0.920190 | − | 0.391471i | \(-0.871966\pi\) | ||
0.920190 | − | 0.391471i | \(-0.128034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3923 | + | 11.1390i | −0.810121 | + | 0.586262i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20.5707i | − | 1.07968i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.07180 | + | 6.21166i | 0.265470 | + | 0.325133i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3652 | −1.27185 | −0.635927 | − | 0.771749i | \(-0.719382\pi\) | ||||
−0.635927 | + | 0.771749i | \(0.719382\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.7862i | 1.70678i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.4300 | −1.89135 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.66449 | −0.0861840 | −0.0430920 | − | 0.999071i | \(-0.513721\pi\) | ||||
−0.0430920 | + | 0.999071i | \(0.513721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.6854 | − | 13.4820i | 1.32639 | − | 0.696209i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.9497i | 2.05751i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.05844 | 0.413934 | 0.206967 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206967 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.5167 | −2.22943 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 9.68325i | − | 0.494791i | −0.968915 | − | 0.247396i | \(-0.920425\pi\) | ||
0.968915 | − | 0.247396i | \(-0.0795747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.39230 | + | 10.2784i | 0.427711 | + | 0.523837i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.38587 | 0.172113 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.4641 | 1.08827 | 0.544137 | − | 0.838997i | \(-0.316857\pi\) | ||||
0.544137 | + | 0.838997i | \(0.316857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.2460i | 1.98475i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.9428 | −1.71219 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.3716 | + | 23.1653i | −1.42753 | + | 1.16557i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.31268i | 0.0658814i | 0.999457 | + | 0.0329407i | \(0.0104872\pi\) | ||||
−0.999457 | + | 0.0329407i | \(0.989513\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 36.4300 | − | 11.7990i | 1.82378 | − | 0.590687i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12.8622i | − | 0.642307i | −0.947027 | − | 0.321154i | \(-0.895929\pi\) | ||
0.947027 | − | 0.321154i | \(-0.104071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.4801 | −1.96664 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.8564 | − | 8.86422i | 0.539459 | − | 0.440467i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.91728i | 0.144604i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.3551i | − | 1.30318i | −0.758573 | − | 0.651588i | \(-0.774103\pi\) | ||
0.758573 | − | 0.651588i | \(-0.225897\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.719751 | 0.0355027 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.5189 | −1.05887 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.72172 | − | 2.22228i | 0.133604 | − | 0.109087i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 45.1482 | 2.21092 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.0926i | − | 0.981588i | −0.871276 | − | 0.490794i | \(-0.836707\pi\) | ||
0.871276 | − | 0.490794i | \(-0.163293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.3551i | − | 1.28447i | −0.766508 | − | 0.642235i | \(-0.778007\pi\) | ||
0.766508 | − | 0.642235i | \(-0.221993\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37.9087 | −1.84318 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.7846 | + | 6.69213i | 1.59029 | + | 0.324616i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.43588 | 0.359848 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.2487 | 1.36386 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7694 | −1.00043 | −0.500214 | − | 0.865902i | \(-0.666745\pi\) | ||||
−0.500214 | + | 0.865902i | \(0.666745\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3069 | −0.735603 | −0.367801 | − | 0.929904i | \(-0.619889\pi\) | ||||
−0.367801 | + | 0.929904i | \(0.619889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28.9014 | + | 23.5979i | −1.38572 | + | 1.13143i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.87645 | − | 24.3190i | −0.376782 | − | 1.16334i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.3964 | −1.83256 | −0.916280 | − | 0.400537i | \(-0.868823\pi\) | ||||
−0.916280 | + | 0.400537i | \(0.868823\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.6603 | −0.793345 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.86450 | 0.278631 | 0.139315 | − | 0.990248i | \(-0.455510\pi\) | ||||
0.139315 | + | 0.990248i | \(0.455510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.09494 | + | 11.1390i | 0.431142 | + | 0.528038i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.2539i | 1.43096i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.35394i | 0.111089i | 0.998456 | + | 0.0555447i | \(0.0176895\pi\) | ||||
−0.998456 | + | 0.0555447i | \(0.982310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.3971 | 0.725023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 45.0518i | − | 2.11672i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.4300 | − | 29.7450i | 1.70787 | − | 1.39447i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.4558i | − | 1.19077i | −0.803439 | − | 0.595387i | \(-0.796999\pi\) | ||
0.803439 | − | 0.595387i | \(-0.203001\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.7110 | −0.593298 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.2487 | 1.12938 | 0.564688 | − | 0.825305i | \(-0.308997\pi\) | ||||
0.564688 | + | 0.825305i | \(0.308997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.49346 | −0.441198 | −0.220599 | − | 0.975365i | \(-0.570801\pi\) | ||||
−0.220599 | + | 0.975365i | \(0.570801\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.3205 | − | 28.5617i | −1.08146 | − | 1.32452i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5935 | −0.814129 | −0.407065 | − | 0.913399i | \(-0.633448\pi\) | ||||
−0.407065 | + | 0.913399i | \(0.633448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 15.2161i | − | 0.702616i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.65254 | 0.214378 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.59008i | − | 0.0731119i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.6583 | + | 2.43287i | −0.993750 | + | 0.111628i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.1547 | −1.83856 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.75265i | − | 0.0800808i | −0.999198 | − | 0.0400404i | \(-0.987251\pi\) | ||
0.999198 | − | 0.0400404i | \(-0.0127487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3397 | 0.471452 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 51.5198i | 2.34423i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.88298 | − | 2.35394i | 0.130909 | − | 0.106887i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.6414i | 1.20724i | 0.797273 | + | 0.603619i | \(0.206275\pi\) | ||||
−0.797273 | + | 0.603619i | \(0.793725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 32.7862i | − | 1.48264i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.9629i | 1.71324i | 0.515945 | + | 0.856622i | \(0.327441\pi\) | ||||
−0.515945 | + | 0.856622i | \(0.672559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.0377 | −1.93832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.25036 | + | 11.3293i | 0.415773 | + | 0.509216i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.76596 | 0.258639 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.4007i | 0.778963i | 0.921034 | + | 0.389481i | \(0.127346\pi\) | ||||
−0.921034 | + | 0.389481i | \(0.872654\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.4449 | 1.18147 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.4507 | −0.644325 | −0.322163 | − | 0.946684i | \(-0.604410\pi\) | ||||
−0.322163 | + | 0.946684i | \(0.604410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.1962 | + | 11.5911i | −0.631720 | + | 0.515798i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 66.3923i | − | 2.94859i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 35.1402i | − | 1.55756i | −0.627297 | − | 0.778780i | \(-0.715839\pi\) | ||
0.627297 | − | 0.778780i | \(-0.284161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1427i | 0.537163i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.87645 | − | 2.55103i | 0.347754 | − | 0.112631i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.0665 | − | 23.3516i | −0.840170 | − | 1.02899i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.8028i | 0.782965i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 48.3530i | − | 2.12246i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.43110i | − | 0.281751i | −0.990027 | − | 0.140876i | \(-0.955008\pi\) | ||
0.990027 | − | 0.140876i | \(-0.0449918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7719i | 0.733383i | 0.930343 | + | 0.366692i | \(0.119510\pi\) | ||||
−0.930343 | + | 0.366692i | \(0.880490\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 43.0377 | + | 8.78504i | 1.87832 | + | 0.383411i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 42.5318i | − | 1.85271i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3923 | 0.495318 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.7190 | −1.02932 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 54.5723i | − | 2.36379i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6942 | − | 16.7719i | −0.592051 | − | 0.725112i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.6333i | 1.75345i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.82403i | 0.337005i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1962 | 0.524354 | 0.262177 | − | 0.965020i | \(-0.415560\pi\) | ||||
0.262177 | + | 0.965020i | \(0.415560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.9014 | 1.24028 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.5189 | − | 26.3551i | −0.921767 | − | 1.12893i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.61250i | 0.154459i | 0.997013 | + | 0.0772297i | \(0.0246075\pi\) | ||||
−0.997013 | + | 0.0772297i | \(0.975393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.19615 | 0.349803 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.6686 | − | 8.63744i | 1.13612 | − | 0.367967i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.4616 | −2.35847 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.10759 | + | 7.48024i | 0.259253 | + | 0.317518i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.7332i | 1.09035i | 0.838321 | + | 0.545176i | \(0.183537\pi\) | ||||
−0.838321 | + | 0.545176i | \(0.816463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.63574 | −0.238367 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.4323i | 1.28485i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.1922i | 0.429550i | 0.976664 | + | 0.214775i | \(0.0689018\pi\) | ||||
−0.976664 | + | 0.214775i | \(0.931098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.99347 | + | 4.07715i | −0.210077 | + | 0.171527i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.2224 | 0.891259 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.7862i | 1.37447i | 0.726435 | + | 0.687235i | \(0.241176\pi\) | ||||
−0.726435 | + | 0.687235i | \(0.758824\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.4721i | 0.982276i | 0.871082 | + | 0.491138i | \(0.163419\pi\) | ||||
−0.871082 | + | 0.491138i | \(0.836581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.32898 | −0.139070 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.86450 | − | 28.7300i | 0.244566 | − | 1.19813i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.4901i | 0.686491i | 0.939246 | + | 0.343246i | \(0.111526\pi\) | ||||
−0.939246 | + | 0.343246i | \(0.888474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 36.5541i | − | 1.51914i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.32051 | 0.220732 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.8576i | 0.781000i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.1547 | − | 32.7862i | 1.66019 | − | 1.35554i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.6156 | 1.38746 | 0.693732 | − | 0.720233i | \(-0.255965\pi\) | ||||
0.693732 | + | 0.720233i | \(0.255965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.53590 | + | 26.3551i | 0.351716 | + | 1.08594i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.65254 | 0.191380 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.5254i | − | 0.719681i | −0.933014 | − | 0.359840i | \(-0.882831\pi\) | ||
0.933014 | − | 0.359840i | \(-0.117169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.0442 | + | 39.2460i | 1.31368 | + | 1.60893i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.76596 | −0.235985 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.70295 | 0.0695806 | 0.0347903 | − | 0.999395i | \(-0.488924\pi\) | ||||
0.0347903 | + | 0.999395i | \(0.488924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.2161i | − | 0.620679i | −0.950626 | − | 0.310340i | \(-0.899557\pi\) | ||
0.950626 | − | 0.310340i | \(-0.100443\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 16.7719i | − | 0.683004i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.7321 | + | 11.2122i | −0.558287 | + | 0.455840i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.6534i | 0.716529i | 0.933620 | + | 0.358265i | \(0.116631\pi\) | ||||
−0.933620 | + | 0.358265i | \(0.883369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −56.4974 | −2.28939 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 63.0986 | 2.55270 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.8401i | 1.56874i | 0.620295 | + | 0.784369i | \(0.287013\pi\) | ||||
−0.620295 | + | 0.784369i | \(0.712987\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.4801 | − | 32.2354i | 1.59199 | − | 1.29985i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.9086i | 0.841748i | 0.907119 | + | 0.420874i | \(0.138277\pi\) | ||||
−0.907119 | + | 0.420874i | \(0.861723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 21.8453i | − | 0.878035i | −0.898478 | − | 0.439018i | \(-0.855327\pi\) | ||
0.898478 | − | 0.439018i | \(-0.144673\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.1390i | 0.446992i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.7748i | 0.872390i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.10759 | − | 18.8576i | −0.243914 | − | 0.753099i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.1390i | 0.444140i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.9166i | − | 1.11134i | −0.831402 | − | 0.555672i | \(-0.812461\pi\) | ||
0.831402 | − | 0.555672i | \(-0.187539\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.96953i | − | 0.277014i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.7190 | + | 29.0498i | 0.941261 | + | 1.15280i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.7308 | 1.09874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.35549 | 0.251419 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.0783i | 1.10903i | 0.832175 | + | 0.554514i | \(0.187096\pi\) | ||||
−0.832175 | + | 0.554514i | \(0.812904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.3652 | −0.960871 | −0.480435 | − | 0.877030i | \(-0.659521\pi\) | ||||
−0.480435 | + | 0.877030i | \(0.659521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.32898 | − | 4.07715i | −0.131078 | − | 0.160538i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.3300 | −1.07445 | −0.537227 | − | 0.843437i | \(-0.680528\pi\) | ||||
−0.537227 | + | 0.843437i | \(0.680528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1390i | 0.437243i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 55.8333i | − | 2.18828i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.85993i | 0.229317i | 0.993405 | + | 0.114658i | \(0.0365773\pi\) | ||||
−0.993405 | + | 0.114658i | \(0.963423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.5007 | + | 22.6587i | 0.722883 | + | 0.885347i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.3843i | 0.522170i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.0241 | 1.28644 | 0.643218 | − | 0.765683i | \(-0.277599\pi\) | ||||
0.643218 | + | 0.765683i | \(0.277599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.07715i | − | 0.158583i | −0.996851 | − | 0.0792914i | \(-0.974734\pi\) | ||
0.996851 | − | 0.0792914i | \(-0.0252658\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 107.862 | 4.18900 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.7329 | − | 17.8879i | −1.07543 | − | 0.693664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.7151i | 1.46034i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −49.7654 | −1.92404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.84910i | − | 0.148593i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3069 | 0.590038 | 0.295019 | − | 0.955491i | \(-0.404674\pi\) | ||||
0.295019 | + | 0.955491i | \(0.404674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.30509 | + | 1.89939i | 0.358153 | + | 0.0731077i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.99347 | 0.191915 | 0.0959573 | − | 0.995385i | \(-0.469409\pi\) | ||||
0.0959573 | + | 0.995385i | \(0.469409\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.63574 | 0.216280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.7321 | 1.10101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 0.186285i | − | 0.00712801i | −0.999994 | − | 0.00356400i | \(-0.998866\pi\) | ||
0.999994 | − | 0.00356400i | \(-0.00113446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.392305 | − | 0.480473i | −0.0149892 | − | 0.0183579i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.2419i | 1.49717i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 66.8372 | 2.54629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.0594i | − | 1.52393i | −0.647618 | − | 0.761965i | \(-0.724235\pi\) | ||
0.647618 | − | 0.761965i | \(-0.275765\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.1469i | 0.841293i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.6083 | − | 30.1389i | −0.933447 | − | 1.14323i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 58.7906 | 2.22685 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.7358 | −0.859948 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.5167 | −1.41698 | −0.708492 | − | 0.705718i | \(-0.750624\pi\) | ||||
−0.708492 | + | 0.705718i | \(0.750624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.23553 | − | 6.90235i | −0.0843147 | − | 0.260327i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 37.2718 | + | 45.6484i | 1.40374 | + | 1.71922i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.7511 | −1.04369 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.3923 | −1.06630 | −0.533148 | − | 0.846022i | \(-0.678991\pi\) | ||||
−0.533148 | + | 0.846022i | \(0.678991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −61.1322 | −2.29264 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.2718 | −1.39584 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.3971 | − | 18.8576i | −0.575820 | − | 0.705233i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.1899 | −0.679314 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 47.0700i | − | 1.75541i | −0.479197 | − | 0.877707i | \(-0.659072\pi\) | ||
0.479197 | − | 0.877707i | \(-0.340928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 45.6484i | − | 1.70004i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.4801 | 1.46828 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.5058 | + | 6.43110i | 1.17010 | + | 0.238845i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0797 | 0.670538 | 0.335269 | − | 0.942122i | \(-0.391173\pi\) | ||||
0.335269 | + | 0.942122i | \(0.391173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.1769 | 1.41396 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.07137i | − | 0.224558i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.37945i | 0.198695i | 0.995053 | + | 0.0993473i | \(0.0316755\pi\) | ||||
−0.995053 | + | 0.0993473i | \(0.968325\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.3803 | + | 20.0617i | 0.604198 | + | 0.739988i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.87645 | −0.290133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.84910i | − | 0.141591i | −0.997491 | − | 0.0707956i | \(-0.977446\pi\) | ||
0.997491 | − | 0.0707956i | \(-0.0225538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −66.8372 | + | 21.6472i | −2.45532 | + | 0.795231i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.41129i | 0.271894i | 0.990716 | + | 0.135947i | \(0.0434077\pi\) | ||||
−0.990716 | + | 0.135947i | \(0.956592\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.1962 | − | 16.4901i | 0.739930 | − | 0.604150i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.86450 | 0.214571 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 32.7862i | − | 1.19798i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.6686 | −0.973152 | −0.486576 | − | 0.873638i | \(-0.661754\pi\) | ||||
−0.486576 | + | 0.873638i | \(0.661754\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.0819 | 0.695382 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.0745 | + | 24.5557i | −1.09452 | + | 0.893675i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 49.4703i | − | 1.79803i | −0.437920 | − | 0.899014i | \(-0.644285\pi\) | ||
0.437920 | − | 0.899014i | \(-0.355715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.6686 | 0.968010 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.4449 | −0.958626 | −0.479313 | − | 0.877644i | \(-0.659114\pi\) | ||||
−0.479313 | + | 0.877644i | \(0.659114\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 51.5198i | − | 1.86514i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 35.3205 | + | 43.2586i | 1.27702 | + | 1.56402i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.4801 | 1.42554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.1962 | 0.872536 | 0.436268 | − | 0.899817i | \(-0.356300\pi\) | ||||
0.436268 | + | 0.899817i | \(0.356300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 68.7894i | − | 2.47739i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.88298 | 0.103694 | 0.0518468 | − | 0.998655i | \(-0.483489\pi\) | ||||
0.0518468 | + | 0.998655i | \(0.483489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.35549 | + | 31.1354i | −0.228296 | + | 1.11842i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.6226i | 0.524583i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.4300 | + | 11.7990i | −1.30524 | + | 0.422742i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.98468i | − | 0.106800i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.2152 | −0.436535 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.53590 | − | 3.10583i | −0.0905101 | − | 0.110852i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 45.4990i | − | 1.62186i | −0.585141 | − | 0.810932i | \(-0.698961\pi\) | ||
0.585141 | − | 0.810932i | \(-0.301039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.4941i | 1.33483i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.76139 | −0.347075 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.6424 | −0.484456 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 39.4801 | + | 48.3530i | 1.40021 | + | 1.71491i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0443 | 1.34760 | 0.673798 | − | 0.738915i | \(-0.264662\pi\) | ||||
0.673798 | + | 0.738915i | \(0.264662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.9760i | 2.40482i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0012i | 0.848040i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.28555 | 0.221812 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 34.3923 | − | 28.0812i | 1.21217 | − | 0.989732i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.7938 | 0.802381 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.53590 | −0.0891574 | −0.0445787 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445787 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7687 | 1.53693 | 0.768464 | − | 0.639894i | \(-0.221022\pi\) | ||||
0.768464 | + | 0.639894i | \(0.221022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.1482 | 1.58342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.8866 | + | 17.8703i | −0.766654 | + | 0.625970i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.21849 | + | 3.76217i | 0.0426296 | + | 0.131622i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 78.4958 | 2.74286 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.679492 | 0.0237144 | 0.0118572 | − | 0.999930i | \(-0.496226\pi\) | ||||
0.0118572 | + | 0.999930i | \(0.496226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.6362 | −0.440471 | −0.220236 | − | 0.975447i | \(-0.570683\pi\) | ||||
−0.220236 | + | 0.975447i | \(0.570683\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.54747 | − | 22.2780i | 0.158323 | − | 0.775619i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.20417i | 0.0418730i | 0.999781 | + | 0.0209365i | \(0.00666478\pi\) | ||||
−0.999781 | + | 0.0209365i | \(0.993335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7.06183i | − | 0.245268i | −0.992452 | − | 0.122634i | \(-0.960866\pi\) | ||
0.992452 | − | 0.122634i | \(-0.0391341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.6847 | 1.68885 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.8744i | 1.03508i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4139 | − | 17.6534i | −0.498815 | − | 0.610921i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 12.0716i | − | 0.417255i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.35549 | 0.219416 | 0.109708 | − | 0.993964i | \(-0.465008\pi\) | ||||
0.109708 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3590 | −0.426172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.10759 | −0.210357 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −44.3205 | + | 36.1875i | −1.52467 | + | 1.24489i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.8438 | −0.922366 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9393i | 0.581357i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.76139 | 0.334616 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.79796i | 0.335476i | 0.985832 | + | 0.167738i | \(0.0536462\pi\) | ||||
−0.985832 | + | 0.167738i | \(0.946354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30.5684 | − | 19.7169i | −1.04542 | − | 0.674302i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.7594 | 0.367535 | 0.183768 | − | 0.982970i | \(-0.441171\pi\) | ||||
0.183768 | + | 0.982970i | \(0.441171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.1427i | − | 0.414305i | −0.978309 | − | 0.207153i | \(-0.933580\pi\) | ||
0.978309 | − | 0.207153i | \(-0.0664196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 77.1769 | 2.63018 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.98507i | 0.135653i | 0.997697 | + | 0.0678267i | \(0.0216065\pi\) | ||||
−0.997697 | + | 0.0678267i | \(0.978393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.2783 | + | 26.3551i | −1.09749 | + | 0.896101i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 72.0905i | 2.44832i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.7091i | 0.973888i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.9166i | 0.945919i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.21196 | 0.210243 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.5935 | − | 33.5184i | −0.594768 | − | 1.13313i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8544 | −0.670435 | −0.335217 | − | 0.942141i | \(-0.608810\pi\) | ||||
−0.335217 | + | 0.942141i | \(0.608810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.9166i | 0.941605i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3013 | 1.15564 | 0.577820 | − | 0.816165i | \(-0.303904\pi\) | ||||
0.577820 | + | 0.816165i | \(0.303904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.9721 | −0.402893 | −0.201446 | − | 0.979500i | \(-0.564564\pi\) | ||||
−0.201446 | + | 0.979500i | \(0.564564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.3205 | + | 28.5617i | 0.783910 | + | 0.960090i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29.4223i | − | 0.987905i | −0.869489 | − | 0.493953i | \(-0.835552\pi\) | ||
0.869489 | − | 0.493953i | \(-0.164448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.7874i | 1.90459i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 10.9855i | − | 0.368030i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6424 | − | 42.1218i | −0.456526 | − | 1.40955i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.1249 | − | 22.1474i | 0.906686 | − | 0.740306i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 94.5220i | − | 3.15600i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 40.8728i | − | 1.36318i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 72.0035i | 2.39879i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 7.97014i | − | 0.265230i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.7529 | − | 19.2933i | −0.523644 | − | 0.641331i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4820i | 0.447664i | 0.974628 | + | 0.223832i | \(0.0718567\pi\) | ||||
−0.974628 | + | 0.223832i | \(0.928143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.5885 | −1.01456 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7694 | −0.688122 | −0.344061 | − | 0.938947i | \(-0.611803\pi\) | ||||
−0.344061 | + | 0.938947i | \(0.611803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.75410i | − | 0.0911473i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.05844 | − | 9.86954i | −0.266404 | − | 0.326277i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.2939i | 1.46271i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.7300i | 0.947717i | 0.880601 | + | 0.473858i | \(0.157139\pi\) | ||||
−0.880601 | + | 0.473858i | \(0.842861\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.2295 | −1.35856 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5787 | −0.348201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.66449 | − | 8.15430i | 0.0547281 | − | 0.268112i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 50.3157i | − | 1.65258i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.2487 | 0.401867 | 0.200934 | − | 0.979605i | \(-0.435602\pi\) | ||||
0.200934 | + | 0.979605i | \(0.435602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.99562 | − | 18.5118i | −0.196498 | − | 0.606701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65.7751 | 2.15338 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.3152 | − | 16.5873i | 0.664378 | − | 0.542463i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 55.8107i | − | 1.82326i | −0.411017 | − | 0.911628i | \(-0.634826\pi\) | ||
0.411017 | − | 0.911628i | \(-0.365174\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.7694 | −0.677785 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 48.0023i | − | 1.56483i | −0.622756 | − | 0.782416i | \(-0.713987\pi\) | ||
0.622756 | − | 0.782416i | \(-0.286013\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 51.5198i | − | 1.67772i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.09494 | + | 11.1390i | 0.295858 | + | 0.362351i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.7805 | 1.71513 | 0.857567 | − | 0.514372i | \(-0.171975\pi\) | ||||
0.857567 | + | 0.514372i | \(0.171975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 22.2780i | − | 0.723173i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 48.3530i | − | 1.56795i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.7594 | −0.348532 | −0.174266 | − | 0.984699i | \(-0.555755\pi\) | ||||
−0.174266 | + | 0.984699i | \(0.555755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.81448 | + | 2.22228i | 0.0587152 | + | 0.0719112i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.2452i | 0.945364i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.939245i | − | 0.0303298i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.39230 | 0.302978 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 36.1384i | − | 1.16454i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.4018 | + | 19.9240i | −0.785523 | + | 0.641377i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.6025 | −1.69158 | −0.845791 | − | 0.533514i | \(-0.820871\pi\) | ||||
−0.845791 | + | 0.533514i | \(0.820871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.3205 | − | 72.0035i | −0.749163 | − | 2.31309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4139 | −0.462565 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 58.9165i | − | 1.88878i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −78.9602 | − | 16.1177i | −2.52875 | − | 0.516179i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.6359 | −0.596215 | −0.298107 | − | 0.954532i | \(-0.596355\pi\) | ||||
−0.298107 | + | 0.954532i | \(0.596355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.2715 | 0.360238 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 56.7874i | − | 1.81308i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0617i | 0.639870i | 0.947440 | + | 0.319935i | \(0.103661\pi\) | ||||
−0.947440 | + | 0.319935i | \(0.896339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.53590 | − | 3.10583i | −0.0808004 | − | 0.0989599i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 89.2349i | 2.84038i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.32051 | −0.169182 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4307 | 0.426641 | 0.213321 | − | 0.976982i | \(-0.431572\pi\) | ||||
0.213321 | + | 0.976982i | \(0.431572\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.1432i | 0.766160i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.14277 | + | 3.84910i | 0.0996326 | + | 0.122025i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.2880i | 0.832551i | 0.909239 | + | 0.416275i | \(0.136665\pi\) | ||||
−0.909239 | + | 0.416275i | \(0.863335\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.16152i | 0.100026i |
(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 | 1520.2.g.f.1519.3 | yes | 16 | |
4.3 | odd | 2 | inner | 1520.2.g.f.1519.16 | yes | 16 | |
5.4 | even | 2 | inner | 1520.2.g.f.1519.14 | yes | 16 | |
19.18 | odd | 2 | inner | 1520.2.g.f.1519.15 | yes | 16 | |
20.19 | odd | 2 | inner | 1520.2.g.f.1519.1 | ✓ | 16 | |
76.75 | even | 2 | inner | 1520.2.g.f.1519.4 | yes | 16 | |
95.94 | odd | 2 | inner | 1520.2.g.f.1519.2 | yes | 16 | |
380.379 | even | 2 | inner | 1520.2.g.f.1519.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1520.2.g.f.1519.1 | ✓ | 16 | 20.19 | odd | 2 | inner | |
1520.2.g.f.1519.2 | yes | 16 | 95.94 | odd | 2 | inner | |
1520.2.g.f.1519.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1520.2.g.f.1519.4 | yes | 16 | 76.75 | even | 2 | inner | |
1520.2.g.f.1519.13 | yes | 16 | 380.379 | even | 2 | inner | |
1520.2.g.f.1519.14 | yes | 16 | 5.4 | even | 2 | inner | |
1520.2.g.f.1519.15 | yes | 16 | 19.18 | odd | 2 | inner | |
1520.2.g.f.1519.16 | yes | 16 | 4.3 | odd | 2 | inner |